New Jersey State Standards Alignment Grades Two through Twelvedoc.renlearn.com/KMNet/R004259018GHD329.pdf · 2009. 8. 31. · New Jersey, Math, 2008, Grade 2, Core Curriculum Content

New Jersey State Standards Alignment Grades Two through Twelve

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New Jersey State Standards Alignment

Standards List with Aligned Product Skills

The Standards List with Aligned Product Skills Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product.

Note to Educator .....................................................iii

Grade 2 ..................................................... 1

Grade 3 ....................................................41

Grade 4 ....................................................61

Grade 5 ....................................................87

Grade 6 ..................................................111

Grade 7 ..................................................139

Grade 8 ..................................................158

Grade 12 ..................................................182

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Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) 338-4204. Sincerely, Renaissance Sales and Funding Staff

P.O. Box 8036 Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204 Fax: (715) 424-4242

www.renlearn.com

Agency Tag Set NameNew Jersey, Math, 2008, Grade 2, Core Curriculum Content Standards, State Department of Education

Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.2 A - Number SenseNJ 4.1.2 A.1 - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well).

Topic 1 - Numbers and Operations

Obj. 9 - Identify a number to 20 represented by a point on a number line

NJ 4.1.2 A.1.a - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Whole numbers through hundreds


Obj. 1 - Read a whole number to 30

Obj. 2 - Read a whole number from 31 to 100Obj. 3 - Determine the word form of a whole number to 30Obj. 4 - Determine the word form of a whole number from 31 to 100Obj. 5 - Count objects to 20Obj. 10 - Locate a number to 20 on a number lineObj. 19 - Count objects grouped in tens and ones

NJ 4.1.2 A.1.b - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Ordinals


Obj. 16 - Answer a question involving an ordinal number up to "tenth"

NJ 4.1.2 A.1.c - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Proper fractions (denominators of 2, 3, 4, 8, 10)

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Grade 1

Accelerated Math Grade 2

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Standard Topic Description Objective Description


NJ 4.1.2 A.2 - By the end of Grade 2, students will: Demonstrate an understanding of whole number place value concepts.


Obj. 20 - Model a number to 100 using tens and ones

Obj. 21 - Recognize a number from a model of tens and ones to 100

Obj. 22 - Represent a 2-digit number as tens and onesObj. 23 - Determine the 2-digit number represented as tens and onesObj. 24 - Determine the value of a digit in a 2-digit numberObj. 25 - Recognize equivalent forms of a 2-digit number using tens and ones

NJ 4.1.2 A.3 - By the end of Grade 2, students will: Understand that numbers have a variety of uses.


Obj. 5 - Count objects to 20

Obj. 6 - Count on by ones from a number less than 100Obj. 7 - Count back by ones from a number less than 20Obj. 8 - Count back by ones from a number between 20 and 100Obj. 16 - Answer a question involving an ordinal number up to "tenth"

NJ 4.1.2 A.4 - By the end of Grade 2, students will: Count and perform simple computations with coins.NJ 4.1.2 A.4.a - Amounts up to $1.00 (using cents notation)


Obj. 17 - Determine the value of a collection of like coinsObj. 18 - Determine the value of a collection of mixed coins

NJ 4.1.2 A.5 - By the end of Grade 2, students will: Compare and order whole numbers.


Obj. 27 - Compare whole numbers to 100 using words

Obj. 28 - Order whole numbers to 100 in ascending orderObj. 29 - Order whole numbers to 100 in descending order

NJ 4.1.2 B - Numerical OperationsNJ 4.1.2 B.1 - By the end of Grade 2, students will: Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems.


Obj. 30 - Determine equivalent forms of a number, up to 10


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Obj. 34 - Relate a number-line model to a basic addition factObj. 35 - Determine the basic addition fact shown by a number-line modelObj. 39 - Relate a number-line model to a basic subtraction factObj. 41 - Apply the relationship between subtraction and counting back

NJ 4.1.2 B.1.a - By the end of Grade 2, students will: Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems. Joining, separating, and comparing


Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects

Obj. 32 - Relate a picture model to a basic addition factObj. 36 - Relate a picture model to a basic subtraction factObj. 37 - Determine the basic subtraction fact shown by a picture modelObj. 40 - Apply the relationship between addition and counting on

NJ 4.1.2 B.2 - By the end of Grade 2, students will: Explore the meanings of multiplication and division by modeling and discussing problems.

NJ 4.1.2 B.3 - By the end of Grade 2, students will: Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as "counting on" and "near doubles") and then commit them to memory.


Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects

Obj. 33 - Determine the basic addition fact shown by a picture modelObj. 35 - Determine the basic addition fact shown by a number-line modelObj. 37 - Determine the basic subtraction fact shown by a picture modelObj. 38 - Determine the basic subtraction fact shown by a number-line model


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Obj. 40 - Apply the relationship between addition and counting onObj. 41 - Apply the relationship between subtraction and counting backObj. 42 - Know basic addition facts to 10 plus 10Obj. 43 - Know basic subtraction facts to 20 minus 10Obj. 46 - WP: Use basic addition or subtraction facts to solve problems

Obj. 47 - Complete an addition and subtraction fact family

Topic 2 - Algebraic Thinking Obj. 62 - Determine equivalent addition or subtraction expressions involving 1-digit numbers

NJ 4.1.2 B.4 - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with:NJ 4.1.2 B.4.a - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: Pencil-and-paper


Obj. 44 - Add three 1-digit numbers

Obj. 49 - Add multiples of 10, sums to 90Obj. 50 - Subtract multiples of 10 up to 90Obj. 53 - Add a 2-digit and a 1-digit number without regroupingObj. 54 - Add two 2-digit numbers without regroupingObj. 55 - Subtract a 1-digit number from a 2-digit number without regroupingObj. 56 - Subtract a 2-digit number from a 2-digit number without regroupingObj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

NJ 4.1.2 B.4.b - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: Mental math


Obj. 42 - Know basic addition facts to 10 plus 10


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Obj. 43 - Know basic subtraction facts to 20 minus 10Obj. 46 - WP: Use basic addition or subtraction facts to solve problems

Obj. 49 - Add multiples of 10, sums to 90Obj. 50 - Subtract multiples of 10 up to 90Obj. 51 - Add zero to any number less than 100Obj. 52 - Subtract zero from any number less than 100

NJ 4.1.2 B.4.c - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: CalculatorNJ 4.1.2 B.5 - By the end of Grade 2, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.NJ 4.1.2 B.5.a - By the end of Grade 2, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 2-digit numbers


Obj. 49 - Add multiples of 10, sums to 90

Obj. 53 - Add a 2-digit and a 1-digit number without regroupingObj. 54 - Add two 2-digit numbers without regroupingObj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

NJ 4.1.2 B.5.b - By the end of Grade 2, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Subtraction of 2-digit numbers


Obj. 50 - Subtract multiples of 10 up to 90

Obj. 55 - Subtract a 1-digit number from a 2-digit number without regroupingObj. 56 - Subtract a 2-digit number from a 2-digit number without regrouping


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Obj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

NJ 4.1.2 B.6 - By the end of Grade 2, students will: Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.


Obj. 42 - Know basic addition facts to 10 plus 10

Obj. 43 - Know basic subtraction facts to 20 minus 10Obj. 44 - Add three 1-digit numbers

Obj. 46 - WP: Use basic addition or subtraction facts to solve problems

Obj. 49 - Add multiples of 10, sums to 90Obj. 50 - Subtract multiples of 10 up to 90Obj. 51 - Add zero to any number less than 100Obj. 52 - Subtract zero from any number less than 100Obj. 53 - Add a 2-digit and a 1-digit number without regroupingObj. 54 - Add two 2-digit numbers without regroupingObj. 55 - Subtract a 1-digit number from a 2-digit number without regroupingObj. 56 - Subtract a 2-digit number from a 2-digit number without regroupingObj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

NJ 4.1.2 B.7 - By the end of Grade 2, students will: Check the reasonableness of results of computations.NJ 4.1.2 B.8 - By the end of Grade 2, students will: Understand and use the inverse relationship between addition and subtraction.


Obj. 48 - Apply the inverse relationship between addition facts and subtraction facts


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Topic 2 - Algebraic Thinking Obj. 60 - Determine a missing addend in a basic addition-fact number sentenceObj. 61 - Determine a missing subtrahend in a basic subtraction-fact number sentenceObj. 63 - Determine a missing addend in an addition sentence with three 1-digit numbersObj. 64 - WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence

NJ 4.1.2 C - EstimationNJ 4.1.2 C.1 - By the end of Grade 2, students will: Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

NJ 4.1.2 C.2 - By the end of Grade 2, students will: Determine the reasonableness of an answer by estimating the result of computations (e.g., 15 + 16 is not 211).

NJ 4.1.2 C.3 - By the end of Grade 2, students will: Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.2 A - Geometric PropertiesNJ 4.2.2 A.1 - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes.NJ 4.2.2 A.1.a - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Inside/outside, left/right, above/below, between

Topic 3 - Geometry and Measurement

Obj. 72 - Apply the vocabulary of position or direction


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NJ 4.2.2 A.1.b - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Smaller/larger/same size, wider/narrower, longer/shorter

NJ 4.2.2 A.1.c - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Congruence (i.e., same size and shape)

NJ 4.2.2 A.2 - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes.


Obj. 82 - Determine the common attributes in a set of geometric shapes

NJ 4.2.2 A.2.a - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. Vertex, edge, face, side

NJ 4.2.2 A.2.b - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid

NJ 4.2.2 A.2.c - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. 2D figures - square, rectangle, circle, triangle


Obj. 81 - Identify a circle, a triangle, a square, or a rectangle


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NJ 4.2.2 A.2.d - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape)

NJ 4.2.2 A.3 - By the end of Grade 2, students will: Describe, identify and create instances of line symmetry.


Obj. 85 - Identify a line of symmetry

NJ 4.2.2 A.4 - By the end of Grade 2, students will: Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.

Topic 2 - Algebraic Thinking Obj. 66 - Extend a repeating picture pattern

Obj. 67 - Extend a pictorial growth pattern

NJ 4.2.2 B - Transforming ShapesNJ 4.2.2 B.1 - By the end of Grade 2, students will: Use simple shapes to make designs, patterns, and pictures.

NJ 4.2.2 B.2 - By the end of Grade 2, students will: Combine and subdivide simple shapes to make other shapes.

NJ 4.2.2 C - Coordinate GeometryNJ 4.2.2 C.1 - By the end of Grade 2, students will: Give and follow directions for getting from one point to another on a map or grid.NJ 4.2.2 D - Units of MeasurementNJ 4.2.2 D.1 - By the end of Grade 2, students will: Directly compare and order objects according to measurable attributes.NJ 4.2.2 D.1.a - By the end of Grade 2, students will: Directly compare and order objects according to measurable attributes. Attributes - length, weight, capacity, time, temperature


Obj. 70 - Compare objects using the vocabulary of measurement

Obj. 71 - Compare and order objects by attributes of height or length


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Obj. 78 - Order events by timeObj. 79 - Order the months of the year

NJ 4.2.2 D.2 - By the end of Grade 2, students will: Recognize the need for a uniform unit of measure.NJ 4.2.2 D.3 - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems.NJ 4.2.2 D.3.a - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Length - inch, foot, yard, centimeter, meter


Obj. 73 - Select the appropriate measurement tool for length, weight, temperature, time, or capacity

NJ 4.2.2 D.3.b - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Weight - pound, gram, kilogram



NJ 4.2.2 D.3.c - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Capacity - pint, quart, liter



NJ 4.2.2 D.3.d - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Time - second, minute, hour, day, week, month, year



Obj. 76 - Tell time to the hourObj. 77 - Tell time to the half hourObj. 80 - Determine the day of the week from a date on a calendar


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NJ 4.2.2 D.3.e - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Temperature - degrees Celsius, degrees Fahrenheit



NJ 4.2.2 D.4 - By the end of Grade 2, students will: Estimate measures.


Obj. 74 - Estimate length in nonstandard units

Obj. 75 - Know the approximate time it takes to complete a task

NJ 4.2.2 E - Measuring Geometric ObjectsNJ 4.2.2 E.1 - By the end of Grade 2, students will: Directly measure the perimeter of simple two-dimensional shapes.NJ 4.2.2 E.2 - By the end of Grade 2, students will: Directly measure the area of simple two-dimensional shapes by covering them with squares.NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.2 A - PatternsNJ 4.3.2 A.1 - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns.

NJ 4.3.2 A.1.a - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Using concrete materials (manipulatives), pictures, rhythms, & whole numbers


Obj. 67 - Extend a pictorial growth patternObj. 69 - Complete a pattern on a 1 to 100 chart

NJ 4.3.2 A.1.b - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Descriptions using words and symbols (e.g., "add two" or "+ 2")


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NJ 4.3.2 A.1.c - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Repeating patterns


NJ 4.3.2 A.1.d - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward)


Obj. 13 - Count by 2s to 50 starting from a multiple of 2

Obj. 14 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively

Topic 2 - Algebraic Thinking Obj. 68 - Determine a pattern on a 1 to 100 chartObj. 69 - Complete a pattern on a 1 to 100 chart

NJ 4.3.2 B - Functions and RelationshipsNJ 4.3.2 B.1 - By the end of Grade 2, students will: Use concrete and pictorial models of function machines to explore the basic concept of a function.NJ 4.3.2 C - ModelingNJ 4.3.2 C.1 - By the end of Grade 2, students will: Recognize and describe changes over time (e.g., temperature, height).NJ 4.3.2 C.2 - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction.NJ 4.3.2 C.2.a - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction. Result unknown (e.g., 6 - 2 = __ or n = 3 + 5)NJ 4.3.2 C.2.b - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction. Part unknown (e.g., 3 + [] = 8)


Obj. 48 - Apply the inverse relationship between addition facts and subtraction facts

Topic 2 - Algebraic Thinking Obj. 60 - Determine a missing addend in a basic addition-fact number sentence


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Obj. 61 - Determine a missing subtrahend in a basic subtraction-fact number sentenceObj. 62 - Determine equivalent addition or subtraction expressions involving 1-digit numbersObj. 63 - Determine a missing addend in an addition sentence with three 1-digit numbersObj. 64 - WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence

NJ 4.3.2 D - ProceduresNJ 4.3.2 D.1 - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition:NJ 4.3.2 D.1.a - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Commutative (e.g., 5 + 3 = 3 + 5)NJ 4.3.2 D.1.b - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Zero as the identity element (e.g., 7 + 0 = 7)


Obj. 51 - Add zero to any number less than 100

Obj. 52 - Subtract zero from any number less than 100

NJ 4.3.2 D.1.c - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Associative (e.g., 7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)


Obj. 44 - Add three 1-digit numbers

NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.2 A - Data Analysis


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NJ 4.4.2 A.1 - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity.NJ 4.4.2 A.1.a - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity. Data collected from students' everyday experiences

NJ 4.4.2 A.1.b - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity. Data generated from chance devices, such as spinners and diceNJ 4.4.2 A.2 - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data.NJ 4.4.2 A.2.a - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data. Pictures, tally chart, pictograph, bar graph, Venn diagram

Topic 4 - Data Analysis and Statistics

Obj. 88 - Read a 2-category tally chart

Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)Obj. 90 - Answer a question using information from a 2-category tally chartObj. 91 - Read a picture graphObj. 92 - Use a picture graph to represent groups of objects (1 symbol = 1 object)Obj. 94 - Read a pictograph (1 symbol = 1 object)Obj. 95 - Use a pictograph to represent groups of objects (1 symbol = 1 object)Obj. 97 - Read a bar graphObj. 98 - Use a bar graph to represent groups of objectsObj. 99 - Answer a question using information from a bar graph


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NJ 4.4.2 A.2.b - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data. Smallest to largest, most frequent (mode)


Obj. 90 - Answer a question using information from a 2-category tally chart

Obj. 99 - Answer a question using information from a bar graph

NJ 4.4.2 B - ProbabilityNJ 4.4.2 B.1 - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability.NJ 4.4.2 B.1.a - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability. Certain, impossibleNJ 4.4.2 B.1.b - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability. More likely, less likely, equally likely

NJ 4.4.2 B.2 - By the end of Grade 2, students will: Provide probability of specific outcomes.NJ 4.4.2 B.2.a - By the end of Grade 2, students will: Provide probability of specific outcomes. Probability of getting specific outcome when coin is tossed, when die is rolled, when spinner is spun (e.g., if spinner has five equal sectors, then probability of getting a particular sector is one out of five)

NJ 4.4.2 B.2.b - By the end of Grade 2, students will: Provide probability of specific outcomes. When picking a marble from a bag with three red marbles and four blue marbles, the probability of getting a red marble is three out of seven

NJ 4.4.2 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.2 C.1 - By the end of Grade 2, students will: Sort and classify objects according to attributes.


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NJ 4.4.2 C.1.a - By the end of Grade 2, students will: Sort and classify objects according to attributes. Venn diagramsNJ 4.4.2 C.2 - By the end of Grade 2, students will: Generate all possibilities in simple counting situations (e.g., all outfits involving two shirts and three pants).NJ 4.4.2 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.2 D.1 - By the end of Grade 2, students will: Follow simple sets of directions (e.g., from one location to another, or from a recipe).

NJ 4.4.2 D.2 - By the end of Grade 2, students will: Color simple maps with a small number of colors.NJ 4.4.2 D.3 - By the end of Grade 2, students will: Play simple two-person games (e.g., tic-tac-toe) and informally explore the idea of what the outcome should be.NJ 4.4.2 D.4 - By the end of Grade 2, students will: Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges").NJ 4.4.2 D.4.a - By the end of Grade 2, students will: Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges"). Paths from one vertex to anotherNJ 4.5 - All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

NJ 4.5.2 A - Problem SolvingNJ 4.5.2 A.1 - By the end of Grade 2, students will: Learn mathematics through problem solving, inquiry, and discovery.


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NJ 4.5.2 A.2 - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts.


Obj. 46 - WP: Use basic addition or subtraction facts to solve problems

Obj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

NJ 4.5.2 A.2.a - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5.2 A.2.b - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5.2 A.2.c - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutions

NJ 4.5.2 A.2.d - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several ways

NJ 4.5.2 A.3 - By the end of Grade 2, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5.2 A.4 - By the end of Grade 2, students will: Pose problems of various types and levels of difficulty.

NJ 4.5.2 A.5 - By the end of Grade 2, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5.2 A.6 - By the end of Grade 2, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5.2 B - Communication


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NJ 4.5.2 B.1 - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5.2 B.1.a - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5.2 B.1.b - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5.2 B.2 - By the end of Grade 2, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

NJ 4.5.2 B.3 - By the end of Grade 2, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5.2 B.4 - By the end of Grade 2, students will: Use the language of mathematics to express mathematical ideas precisely.

Topic 2 - Algebraic Thinking Obj. 65 - WP: Determine a basic addition- or subtraction-fact number sentence for a given situation

NJ 4.5.2 C - ConnectionsNJ 4.5.2 C.1 - By the end of Grade 2, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5.2 C.2 - By the end of Grade 2, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5.2 C.3 - By the end of Grade 2, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5.2 C.4 - By the end of Grade 2, students will: Apply mathematics in practical situations and in other disciplines.


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NJ 4.5.2 C.5 - By the end of Grade 2, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5.2 C.6 - By the end of Grade 2, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5.2 D - ReasoningNJ 4.5.2 D.1 - By the end of Grade 2, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5.2 D.2 - By the end of Grade 2, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5.2 D.3 - By the end of Grade 2, students will: Select and use various types of reasoning and methods of proof.NJ 4.5.2 D.4 - By the end of Grade 2, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5.2 D.5 - By the end of Grade 2, students will: Make and investigate mathematical conjectures.

NJ 4.5.2 D.5.a - By the end of Grade 2, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5.2 D.5.b - By the end of Grade 2, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5.2 D.6 - By the end of Grade 2, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.

NJ 4.5.2 E - Representations


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NJ 4.5.2 E.1 - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5.2 E.1.a - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)


Obj. 20 - Model a number to 100 using tens and ones

Obj. 21 - Recognize a number from a model of tens and ones to 100

NJ 4.5.2 E.1.b - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


Obj. 88 - Read a 2-category tally chart

Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)Obj. 90 - Answer a question using information from a 2-category tally chart

NJ 4.5.2 E.1.c - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5.2 E.1.d - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)


Obj. 91 - Read a picture graph

Obj. 92 - Use a picture graph to represent groups of objects (1 symbol = 1 object)Obj. 94 - Read a pictograph (1 symbol = 1 object)Obj. 95 - Use a pictograph to represent groups of objects (1 symbol = 1 object)Obj. 97 - Read a bar graphObj. 98 - Use a bar graph to represent groups of objects


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Obj. 99 - Answer a question using information from a bar graph

NJ 4.5.2 E.2 - By the end of Grade 2, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5.2 E.3 - By the end of Grade 2, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5.2 F - TechnologyNJ 4.5.2 F.1 - By the end of Grade 2, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5.2 F.2 - By the end of Grade 2, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5.2 F.3 - By the end of Grade 2, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5.2 F.4 - By the end of Grade 2, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5.2 F.5 - By the end of Grade 2, students will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5.2 F.6 - By the end of Grade 2, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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NJ 4.1.2 A.1.a - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Whole numbers through hundreds

Topic 1 - Number Sense and Operations

Obj. 1 - Read a whole number to 1,000

Obj. 2 - Determine the word form of a whole number to 1,000

NJ 4.1.2 A.1.b - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Ordinals


Obj. 8 - Answer a question using an ordinal number up to "twentieth"

NJ 4.1.2 A.1.c - By the end of Grade 2, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 2 pertain to these sets of numbers as well). Proper fractions (denominators of 2, 3, 4, 8, 10)NJ 4.1.2 A.2 - By the end of Grade 2, students will: Demonstrate an understanding of whole number place value concepts.


Obj. 9 - Determine the value of a digit in a 3-digit number

Obj. 10 - Determine which digit is in a specified place in a 3-digit whole number



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Obj. 11 - Determine the result of changing a digit in a 3-digit whole numberObj. 12 - Model a number using hundreds, tens, and ones to 1,000Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000Obj. 14 - Represent a 3-digit number as hundreds, tens, and ones

Obj. 15 - Determine the 3-digit number represented as hundreds, tens, and onesObj. 16 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones

NJ 4.1.2 A.3 - By the end of Grade 2, students will: Understand that numbers have a variety of uses.NJ 4.1.2 A.4 - By the end of Grade 2, students will: Count and perform simple computations with coins.NJ 4.1.2 A.4.a - Amounts up to $1.00 (using cents notation)


Obj. 26 - Determine cent amounts that total a dollar

NJ 4.1.2 A.5 - By the end of Grade 2, students will: Compare and order whole numbers.


Obj. 20 - Compare whole numbers to 1,000 using words

Obj. 21 - Compare whole numbers to 1,000 using the symbols <, >, and =

Obj. 22 - Order whole numbers to 1,000 in ascending orderObj. 23 - Order whole numbers to 1,000 in descending order

NJ 4.1.2 B - Numerical OperationsNJ 4.1.2 B.1 - By the end of Grade 2, students will: Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems.

NJ 4.1.2 B.1.a - By the end of Grade 2, students will: Develop the meanings of addition and subtraction by concretely modeling and discussing a large variety of problems. Joining, separating, and comparing


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NJ 4.1.2 B.2 - By the end of Grade 2, students will: Explore the meanings of multiplication and division by modeling and discussing problems.


Obj. 46 - Determine the sum of equal groups using pictures

Obj. 48 - Use a multiplication sentence to represent the sum of equal groupsObj. 50 - Relate a multiplication sentence to an array modelObj. 53 - Recognize the number of equal groups using picturesObj. 54 - Divide objects into equal groups using picturesObj. 55 - Determine the remainder when dividing objects into equal groupsObj. 56 - Determine the number of equal groups of objects excluding the remainderObj. 57 - WP: Divide objects into equal groups by sharing

NJ 4.1.2 B.3 - By the end of Grade 2, students will: Develop proficiency with basic addition and subtraction number facts using a variety of fact strategies (such as "counting on" and "near doubles") and then commit them to memory.NJ 4.1.2 B.4 - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with:NJ 4.1.2 B.4.a - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: Pencil-and-paper


Obj. 24 - Determine a number pair that totals 100

Obj. 29 - Add two 2-digit numbers with regrouping, given a modelObj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100


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Obj. 37 - Subtract money values using cents or dollars with one regroupingObj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

NJ 4.1.2 B.4.b - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: Mental mathNJ 4.1.2 B.4.c - By the end of Grade 2, students will: Construct, use, and explain procedures for performing addition and subtraction calculations with: CalculatorNJ 4.1.2 B.5 - By the end of Grade 2, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.NJ 4.1.2 B.5.a - By the end of Grade 2, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 2-digit numbers



Obj. 29 - Add two 2-digit numbers with regrouping, given a modelObj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping



Obj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regrouping


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Obj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping




Obj. 29 - Add two 2-digit numbers with regrouping, given a modelObj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 37 - Subtract money values using cents or dollars with one regroupingObj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

NJ 4.1.2 B.7 - By the end of Grade 2, students will: Check the reasonableness of results of computations.NJ 4.1.2 B.8 - By the end of Grade 2, students will: Understand and use the inverse relationship between addition and subtraction.


Obj. 43 - Apply the inverse relationship between addition and subtraction with 2- and 3-digit numbers

Topic 2 - Algebraic Thinking Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbersObj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbers

NJ 4.1.2 C - EstimationNJ 4.1.2 C.1 - By the end of Grade 2, students will: Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.


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NJ 4.1.2 C.2 - By the end of Grade 2, students will: Determine the reasonableness of an answer by estimating the result of computations (e.g., 15 + 16 is not 211).


Obj. 44 - Estimate the sum of two 2-digit numbers

Obj. 45 - Estimate the difference of two 2-digit numbers

NJ 4.1.2 C.3 - By the end of Grade 2, students will: Explore a variety of strategies for estimating both quantities (e.g., the number of marbles in a jar) and results of computation.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.2 A - Geometric PropertiesNJ 4.2.2 A.1 - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes.NJ 4.2.2 A.1.a - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Inside/outside, left/right, above/below, between

NJ 4.2.2 A.1.b - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Smaller/larger/same size, wider/narrower, longer/shorter

NJ 4.2.2 A.1.c - By the end of Grade 2, students will: Identify and describe spatial relationships among objects in space and their relative shapes and sizes. Congruence (i.e., same size and shape)


Obj. 84 - Identify figures that are the same size and shape


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NJ 4.2.2 A.2 - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes.

NJ 4.2.2 A.2.a - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. Vertex, edge, face, side

NJ 4.2.2 A.2.b - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid


Obj. 87 - Name a 3-dimensional geometric shape

NJ 4.2.2 A.2.c - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. 2D figures - square, rectangle, circle, triangle

NJ 4.2.2 A.2.d - By the end of Grade 2, students will: Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes. Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape)

NJ 4.2.2 A.3 - By the end of Grade 2, students will: Describe, identify and create instances of line symmetry.


Obj. 88 - Identify symmetry in a 2-dimensional shape


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NJ 4.2.2 A.4 - By the end of Grade 2, students will: Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.

NJ 4.2.2 B - Transforming ShapesNJ 4.2.2 B.1 - By the end of Grade 2, students will: Use simple shapes to make designs, patterns, and pictures.

NJ 4.2.2 B.2 - By the end of Grade 2, students will: Combine and subdivide simple shapes to make other shapes.

NJ 4.2.2 C - Coordinate GeometryNJ 4.2.2 C.1 - By the end of Grade 2, students will: Give and follow directions for getting from one point to another on a map or grid.


Obj. 89 - Follow directions on a simple map

NJ 4.2.2 D - Units of MeasurementNJ 4.2.2 D.1 - By the end of Grade 2, students will: Directly compare and order objects according to measurable attributes.NJ 4.2.2 D.1.a - By the end of Grade 2, students will: Directly compare and order objects according to measurable attributes. Attributes - length, weight, capacity, time, temperature

NJ 4.2.2 D.2 - By the end of Grade 2, students will: Recognize the need for a uniform unit of measure.NJ 4.2.2 D.3 - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems.NJ 4.2.2 D.3.a - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Length - inch, foot, yard, centimeter, meter


Obj. 76 - Measure length in inches

Obj. 77 - Measure length in centimeters


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NJ 4.2.2 D.3.b - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Weight - pound, gram, kilogramNJ 4.2.2 D.3.c - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Capacity - pint, quart, literNJ 4.2.2 D.3.d - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Time - second, minute, hour, day, week, month, year


Obj. 78 - Tell time to the quarter hour

Obj. 79 - Tell time to 5-minute intervals

NJ 4.2.2 D.3.e - By the end of Grade 2, students will: Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems. Temperature - degrees Celsius, degrees Fahrenheit


Obj. 81 - Read a thermometer in degrees Celsius

Obj. 82 - Read a thermometer in degrees Fahrenheit

NJ 4.2.2 D.4 - By the end of Grade 2, students will: Estimate measures.

NJ 4.2.2 E - Measuring Geometric ObjectsNJ 4.2.2 E.1 - By the end of Grade 2, students will: Directly measure the perimeter of simple two-dimensional shapes.NJ 4.2.2 E.2 - By the end of Grade 2, students will: Directly measure the area of simple two-dimensional shapes by covering them with squares.


Obj. 83 - Relate area to the number of square units


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NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.2 A - PatternsNJ 4.3.2 A.1 - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns.

Topic 2 - Algebraic Thinking Obj. 72 - Extend a number pattern involving addition

Obj. 73 - Extend a number pattern involving subtraction

NJ 4.3.2 A.1.a - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Using concrete materials (manipulatives), pictures, rhythms, & whole numbers

NJ 4.3.2 A.1.b - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Descriptions using words and symbols (e.g., "add two" or "+ 2")

Topic 2 - Algebraic Thinking Obj. 71 - Determine the rule for an addition or subtraction number pattern

NJ 4.3.2 A.1.c - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Repeating patterns

Topic 2 - Algebraic Thinking Obj. 75 - Determine a repeating pattern corresponding to the same pattern expressed using different elements

NJ 4.3.2 A.1.d - By the end of Grade 2, students will: Recognize, describe, extend, and create patterns. Whole number patterns that grow or shrink as a result of repeatedly adding or subtracting a fixed number (e.g., skip counting forward or backward)


Obj. 3 - Complete a skip pattern starting from a multiple of 2, 5, or 10

Obj. 4 - Complete a skip pattern of 2, 5, or 10 starting from any number

Obj. 5 - Count on by 100s from any number

Topic 2 - Algebraic Thinking Obj. 70 - Determine an addition or subtraction number pattern given a rule

NJ 4.3.2 B - Functions and Relationships


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NJ 4.3.2 B.1 - By the end of Grade 2, students will: Use concrete and pictorial models of function machines to explore the basic concept of a function.NJ 4.3.2 C - ModelingNJ 4.3.2 C.1 - By the end of Grade 2, students will: Recognize and describe changes over time (e.g., temperature, height).NJ 4.3.2 C.2 - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction.NJ 4.3.2 C.2.a - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction. Result unknown (e.g., 6 - 2 = __ or n = 3 + 5)NJ 4.3.2 C.2.b - By the end of Grade 2, students will: Construct and solve simple open sentences involving addition or subtraction. Part unknown (e.g., 3 + [] = 8)

Topic 2 - Algebraic Thinking Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbers

Obj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbers

NJ 4.3.2 D - ProceduresNJ 4.3.2 D.1 - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition:NJ 4.3.2 D.1.a - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Commutative (e.g., 5 + 3 = 3 + 5)NJ 4.3.2 D.1.b - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Zero as the identity element (e.g., 7 + 0 = 7)

NJ 4.3.2 D.1.c - By the end of Grade 2, students will: Understand and apply (but don't name) the following properties of addition: Associative (e.g., 7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)


Obj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.2 A - Data AnalysisNJ 4.4.2 A.1 - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity.NJ 4.4.2 A.1.a - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity. Data collected from students' everyday experiences

NJ 4.4.2 A.1.b - By the end of Grade 2, students will: Collect, generate, record, and organize data in response to questions, claims, or curiosity. Data generated from chance devices, such as spinners and diceNJ 4.4.2 A.2 - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data.NJ 4.4.2 A.2.a - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data. Pictures, tally chart, pictograph, bar graph, Venn diagram


Obj. 90 - Read a multi-category tally chart

Obj. 91 - Use a tally chart to represent dataObj. 92 - Answer a question using information from a tally chartObj. 93 - Read a pictograph (1 symbol = more than 1 object)Obj. 94 - Use a pictograph to represent data (1 symbol = more than 1 object)Obj. 95 - Answer a question using information from a pictograph (1 symbol = more than 1 object)


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Obj. 96 - Read a bar graph with a y-axis scale by 2sObj. 97 - Use a bar graph with a y-axis scale by 2s to represent dataObj. 98 - Answer a question using information from a bar graph with a y-axis scale by 2s

NJ 4.4.2 A.2.b - By the end of Grade 2, students will: Read, interpret, construct, and analyze displays of data. Smallest to largest, most frequent (mode)NJ 4.4.2 B - ProbabilityNJ 4.4.2 B.1 - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability.NJ 4.4.2 B.1.a - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability. Certain, impossibleNJ 4.4.2 B.1.b - By the end of Grade 2, students will: Use chance devices like spinners and dice to explore concepts of probability. More likely, less likely, equally likely

NJ 4.4.2 B.2 - By the end of Grade 2, students will: Provide probability of specific outcomes.NJ 4.4.2 B.2.a - By the end of Grade 2, students will: Provide probability of specific outcomes. Probability of getting specific outcome when coin is tossed, when die is rolled, when spinner is spun (e.g., if spinner has five equal sectors, then probability of getting a particular sector is one out of five)

NJ 4.4.2 B.2.b - By the end of Grade 2, students will: Provide probability of specific outcomes. When picking a marble from a bag with three red marbles and four blue marbles, the probability of getting a red marble is three out of seven

NJ 4.4.2 C - Discrete Mathematics-Systematic Listing and Counting


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NJ 4.4.2 C.1 - By the end of Grade 2, students will: Sort and classify objects according to attributes.NJ 4.4.2 C.1.a - By the end of Grade 2, students will: Sort and classify objects according to attributes. Venn diagramsNJ 4.4.2 C.2 - By the end of Grade 2, students will: Generate all possibilities in simple counting situations (e.g., all outfits involving two shirts and three pants).NJ 4.4.2 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.2 D.1 - By the end of Grade 2, students will: Follow simple sets of directions (e.g., from one location to another, or from a recipe).

NJ 4.4.2 D.2 - By the end of Grade 2, students will: Color simple maps with a small number of colors.NJ 4.4.2 D.3 - By the end of Grade 2, students will: Play simple two-person games (e.g., tic-tac-toe) and informally explore the idea of what the outcome should be.NJ 4.4.2 D.4 - By the end of Grade 2, students will: Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges").NJ 4.4.2 D.4.a - By the end of Grade 2, students will: Explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges"). Paths from one vertex to anotherNJ 4.5 - All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

NJ 4.5.2 A - Problem SolvingNJ 4.5.2 A.1 - By the end of Grade 2, students will: Learn mathematics through problem solving, inquiry, and discovery.


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NJ 4.5.2 A.2 - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts.NJ 4.5.2 A.2.a - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5.2 A.2.b - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5.2 A.2.c - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutions

NJ 4.5.2 A.2.d - By the end of Grade 2, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several ways

NJ 4.5.2 A.3 - By the end of Grade 2, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5.2 A.4 - By the end of Grade 2, students will: Pose problems of various types and levels of difficulty.

NJ 4.5.2 A.5 - By the end of Grade 2, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5.2 A.6 - By the end of Grade 2, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5.2 B - CommunicationNJ 4.5.2 B.1 - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking.


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NJ 4.5.2 B.1.a - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5.2 B.1.b - By the end of Grade 2, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5.2 B.2 - By the end of Grade 2, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

NJ 4.5.2 B.3 - By the end of Grade 2, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5.2 B.4 - By the end of Grade 2, students will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5.2 C - ConnectionsNJ 4.5.2 C.1 - By the end of Grade 2, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5.2 C.2 - By the end of Grade 2, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5.2 C.3 - By the end of Grade 2, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5.2 C.4 - By the end of Grade 2, students will: Apply mathematics in practical situations and in other disciplines.


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NJ 4.5.2 C.5 - By the end of Grade 2, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5.2 C.6 - By the end of Grade 2, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5.2 D - ReasoningNJ 4.5.2 D.1 - By the end of Grade 2, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5.2 D.2 - By the end of Grade 2, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5.2 D.3 - By the end of Grade 2, students will: Select and use various types of reasoning and methods of proof.NJ 4.5.2 D.4 - By the end of Grade 2, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5.2 D.5 - By the end of Grade 2, students will: Make and investigate mathematical conjectures.

NJ 4.5.2 D.5.a - By the end of Grade 2, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5.2 D.5.b - By the end of Grade 2, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5.2 D.6 - By the end of Grade 2, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.

NJ 4.5.2 E - Representations


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NJ 4.5.2 E.1 - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5.2 E.1.a - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)


Obj. 12 - Model a number using hundreds, tens, and ones to 1,000

Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000

NJ 4.5.2 E.1.b - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


Obj. 90 - Read a multi-category tally chart

Obj. 91 - Use a tally chart to represent data

NJ 4.5.2 E.1.c - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5.2 E.1.d - By the end of Grade 2, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)


Obj. 93 - Read a pictograph (1 symbol = more than 1 object)

Obj. 94 - Use a pictograph to represent data (1 symbol = more than 1 object)Obj. 96 - Read a bar graph with a y-axis scale by 2sObj. 97 - Use a bar graph with a y-axis scale by 2s to represent data

NJ 4.5.2 E.2 - By the end of Grade 2, students will: Select, apply, and translate among mathematical representations to solve problems.


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NJ 4.5.2 E.3 - By the end of Grade 2, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5.2 F - TechnologyNJ 4.5.2 F.1 - By the end of Grade 2, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5.2 F.2 - By the end of Grade 2, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5.2 F.3 - By the end of Grade 2, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5.2 F.4 - By the end of Grade 2, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5.2 F.5 - By the end of Grade 2, students will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5.2 F.6 - By the end of Grade 2, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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NJ 4.1.3 A.1.a - By the end of Grade 3, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well). Whole numbers through hundred thousands


Obj. 1 - Read a 4- or 5-digit whole number

Obj. 2 - Determine the word form of a 4- or 5-digit whole number

NJ 4.1.3 A.1.b - By the end of Grade 3, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 3 pertain to these sets of numbers as well). Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line


Obj. 44 - Determine a pictorial model of a fraction of a whole

Obj. 45 - Determine a pictorial model of a fraction of a set of objects

Obj. 46 - Identify a fraction represented by a point on a number lineObj. 47 - Locate a fraction on a number line

NJ 4.1.3 A.2 - By the end of Grade 3, students will: Demonstrate an understanding of whole number place value concepts.


Obj. 3 - Determine the value of a digit in a 4- or 5-digit whole number



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Obj. 4 - Determine which digit is in a specified place in a 4- or 5-digit whole numberObj. 5 - Represent a 4-digit whole number as thousands, hundreds, tens, and onesObj. 6 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Obj. 7 - Represent a 4- or 5-digit whole number in expanded formObj. 8 - Determine the 4- or 5-digit whole number represented in expanded formObj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones

NJ 4.1.3 A.3 - By the end of Grade 3, students will: Identify whether any whole number is odd or even.NJ 4.1.3 A.4 - By the end of Grade 3, students will: Explore the extension of the place value system to decimals through hundredths.

NJ 4.1.3 A.5 - By the end of Grade 3, students will: Understand the various uses of numbers.NJ 4.1.3 A.5.a - By the end of Grade 3, students will: Understand the various uses of numbers. Counting, measuring, labeling (e.g., numbers on baseball uniforms)

NJ 4.1.3 A.6 - By the end of Grade 3, students will: Compare and order numbers.


Obj. 11 - Compare 4- or 5-digit whole numbers using the symbols <, >, and =Obj. 12 - Order 4- or 5-digit whole numbers in ascending or descending orderObj. 48 - Compare fractions using modelsObj. 49 - Order fractions using modelsObj. 51 - Compare fractions with like denominatorsObj. 52 - Compare fractions with like numerators


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Obj. 53 - WP: Compare equal unit fractions of different-sized wholes

NJ 4.1.3 B - Numerical OperationsNJ 4.1.3 B.1 - By the end of Grade 3, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.


Obj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones

NJ 4.1.3 B.1.a - By the end of Grade 3, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Addition and subtraction: joining, separating, comparing


Obj. 10 - Determine the result of changing a digit in a 4- or 5-digit whole number

NJ 4.1.3 B.1.b - By the end of Grade 3, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Multiplication: repeated addition, area/array


Obj. 33 - Use a multiplication sentence to represent an area or an array model

NJ 4.1.3 B.1.c - By the end of Grade 3, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Division: repeated subtraction, sharing


Obj. 34 - Use a division sentence to represent objects divided into equal groups

NJ 4.1.3 B.2 - By the end of Grade 3, students will: Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction").


Obj. 35 - Know basic multiplication facts to 10 x 10

Obj. 36 - Know basic multiplication facts for 11 and 12Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 38 - Know basic division facts for 11 and 12Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10Obj. 41 - Complete a multiplication and division fact family


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NJ 4.1.3 B.3 - By the end of Grade 3, students will: Construct, use, and explain procedures for performing whole number calculations with:

NJ 4.1.3 B.3.a - By the end of Grade 3, students will: Construct, use, and explain procedures for performing whole number calculations with: Pencil-and-paper


Obj. 13 - Add 3- and 4-digit whole numbers with regrouping

Obj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit whole numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regroupingObj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100Obj. 43 - Multiply a 2-digit whole number by a 1-digit number

NJ 4.1.3 B.3.b - By the end of Grade 3, students will: Construct, use, and explain procedures for performing whole number calculations with: Mental math


Obj. 35 - Know basic multiplication facts to 10 x 10

Obj. 36 - Know basic multiplication facts for 11 and 12Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 38 - Know basic division facts for 11 and 12Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

NJ 4.1.3 B.3.c - By the end of Grade 3, students will: Construct, use, and explain procedures for performing whole number calculations with: CalculatorNJ 4.1.3 B.4 - By the end of Grade 3, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.


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NJ 4.1.3 B.4.a - By the end of Grade 3, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 3-digit numbers



Obj. 14 - Add three 2- to 3-digit whole numbers



Obj. 15 - Subtract 3- and 4-digit whole numbers with regrouping

Obj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping

NJ 4.1.3 B.4.c - By the end of Grade 3, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Multiplication of 2-digit numbers by 1-digit numbers


Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100

Obj. 43 - Multiply a 2-digit whole number by a 1-digit number

NJ 4.1.3 B.5 - By the end of Grade 3, students will: Count and perform simple computations with money.NJ 4.1.3 B.5.a - By the end of Grade 3, students will: Count and perform simple computations with money. Cents notation (¢)NJ 4.1.3 B.6 - By the end of Grade 3, students will: Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.



Obj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit whole numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regroupingObj. 35 - Know basic multiplication facts to 10 x 10Obj. 36 - Know basic multiplication facts for 11 and 12


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Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 38 - Know basic division facts for 11 and 12Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100Obj. 43 - Multiply a 2-digit whole number by a 1-digit number

NJ 4.1.3 B.7 - By the end of Grade 3, students will: Check the reasonableness of results of computations.NJ 4.1.3 C - EstimationNJ 4.1.3 C.1 - By the end of Grade 3, students will: Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.

NJ 4.1.3 C.2 - By the end of Grade 3, students will: Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the result of computations.


Obj. 28 - Estimate a sum or difference of whole numbers to 10,000 by rounding

Obj. 29 - Estimate a sum or difference of two 3- or 4-digit whole numbers using front-end estimationObj. 30 - Estimate a sum or difference of 2- to 4-digit whole numbers using any methodObj. 31 - Estimate a sum of three 2- to 4-digit numbers using any method

Obj. 32 - WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method

NJ 4.1.3 C.3 - By the end of Grade 3, students will: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.


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NJ 4.1.3 C.4 - By the end of Grade 3, students will: Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.3 A - Geometric PropertiesNJ 4.2.3 A.1 - By the end of Grade 3, students will: Identify and describe spatial relationships of two or more objects in space.NJ 4.2.3 A.1.a - By the end of Grade 3, students will: Identify and describe spatial relationships of two or more objects in space. Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)

NJ 4.2.3 A.1.b - By the end of Grade 3, students will: Identify and describe spatial relationships of two or more objects in space. Relative shapes and sizesNJ 4.2.3 A.2 - By the end of Grade 3, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.NJ 4.2.3 A.2.a - By the end of Grade 3, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. Vertex, edge, face, side, angle


Obj. 95 - Determine attributes of a triangle or a quadrilateral from a model

Obj. 96 - Relate a model of a triangle or a quadrilateral to a list of attributes

NJ 4.2.3 A.2.b - By the end of Grade 3, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid


Obj. 97 - Identify a picture of a 3-dimensional shape


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Obj. 98 - Name a 3-dimensional shape from a picture

NJ 4.2.3 A.2.c - By the end of Grade 3, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. 2D figures - square, rectangle, circle, triangle, pentagon, hexagon, octagon


Obj. 95 - Determine attributes of a triangle or a quadrilateral from a model

Obj. 96 - Relate a model of a triangle or a quadrilateral to a list of attributes

NJ 4.2.3 A.3 - By the end of Grade 3, students will: Identify and describe relationships among two-dimensional shapes.NJ 4.2.3 A.3.a - By the end of Grade 3, students will: Identify and describe relationships among two-dimensional shapes. Same size, same shape


Obj. 100 - Identify congruent shapes

NJ 4.2.3 A.3.b - By the end of Grade 3, students will: Identify and describe relationships among two-dimensional shapes. Lines of symmetry


Obj. 101 - Identify mirror images

NJ 4.2.3 A.4 - By the end of Grade 3, students will: Understand and apply concepts involving lines, angles, and circles.NJ 4.2.3 A.4.a - By the end of Grade 3, students will: Understand and apply concepts involving lines, angles, and circles. Line, line segment, endpointNJ 4.2.3 A.5 - By the end of Grade 3, students will: Recognize, describe, extend, and create space-filling patterns.NJ 4.2.3 B - Transforming ShapesNJ 4.2.3 B.1 - By the end of Grade 3, students will: Describe and use geometric transformations (slide, flip, turn).NJ 4.2.3 B.2 - By the end of Grade 3, students will: Investigate the occurrence of geometry in nature and art.NJ 4.2.3 C - Coordinate Geometry


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NJ 4.2.3 C.1 - By the end of Grade 3, students will: Locate and name points in the first quadrant on a coordinate grid.


Obj. 103 - Determine a location using map coordinates

Obj. 104 - Determine the map coordinates for a location

NJ 4.2.3 D - Units of MeasurementNJ 4.2.3 D.1 - By the end of Grade 3, students will: Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.NJ 4.2.3 D.2 - By the end of Grade 3, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems.NJ 4.2.3 D.2.a - By the end of Grade 3, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Length - fractions of an inch (1/4, 1/2), mile, decimeter, kilometer


Obj. 67 - Measure length to the nearest half inch or quarter inch

NJ 4.2.3 D.2.b - By the end of Grade 3, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Area - square inch, square centimeterNJ 4.2.3 D.2.c - By the end of Grade 3, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Weight - ounceNJ 4.2.3 D.2.d - By the end of Grade 3, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Capacity - fluid ounce, cup, gallon, milliliter

NJ 4.2.3 D.3 - By the end of Grade 3, students will: Incorporate estimation in measurement activities (e.g., estimate before measuring).

NJ 4.2.3 E - Measuring Geometric Objects


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NJ 4.2.3 E.1 - By the end of Grade 3, students will: Determine the area of simple two-dimensional shapes on a square grid.


Obj. 89 - Determine the area of a shape composed of rectangles given a picture on a grid

Obj. 90 - WP: Determine the area of a rectangular shape given a picture on a grid

NJ 4.2.3 E.2 - By the end of Grade 3, students will: Determine the perimeter of simple shapes by measuring all of the sides.


Obj. 86 - Determine a method for finding the perimeter of a shape given the side lengths

Obj. 87 - WP: Determine the perimeter of a rectangular shape given a grid with a reference unitObj. 88 - WP: Determine the perimeter of a shape given a model showing all side lengths

NJ 4.2.3 E.3 - By the end of Grade 3, students will: Measure and compare the volume of three-dimensional objects using materials such as rice or cubes.NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.3 A - PatternsNJ 4.3.3 A.1 - By the end of Grade 3, students will: Recognize, describe, extend, and create patterns.

NJ 4.3.3 A.1.a - By the end of Grade 3, students will: Recognize, describe, extend, and create patterns. Descriptions using words and number sentences/expressions

Topic 2 - Algebraic Thinking Obj. 63 - WP: Determine a multiplication or division sentence for a given situation

NJ 4.3.3 A.1.b - By the end of Grade 3, students will: Recognize, describe, extend, and create patterns. Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11,... or 800, 400, 200,...)

Topic 2 - Algebraic Thinking Obj. 64 - Extend a number pattern

NJ 4.3.3 B - Functions and Relationships


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NJ 4.3.3 B.1 - By the end of Grade 3, students will: Use concrete and pictorial models to explore the basic concept of a function.NJ 4.3.3 B.1.a - By the end of Grade 3, students will: Use concrete and pictorial models to explore the basic concept of a function. Input/output tables, T-charts

Topic 2 - Algebraic Thinking Obj. 65 - Determine a rule for a table of related number pairs

Obj. 66 - WP: Find the missing number in a table of paired values

NJ 4.3.3 C - ModelingNJ 4.3.3 C.1 - By the end of Grade 3, students will: Recognize and describe change in quantities.NJ 4.3.3 C.1.a - By the end of Grade 3, students will: Recognize and describe change in quantities. Graphs representing change over time (e.g., temperature, height)NJ 4.3.3 C.2 - By the end of Grade 3, students will: Construct and solve simple open sentences involving addition or subtraction (e.g., 3 + 6 = __, n = 15 - 3, 3 +__= 3, 16 - c = 7).

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbers

Obj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbers

NJ 4.3.3 D - ProceduresNJ 4.3.3 D.1 - By the end of Grade 3, students will: Understand and apply the properties of operations and numbers.NJ 4.3.3 D.1.a - By the end of Grade 3, students will: Understand and apply the properties of operations and numbers. Commutative (e.g., 3 x 7 = 7 x 3)NJ 4.3.3 D.1.b - By the end of Grade 3, students will: Understand and apply the properties of operations and numbers. Identity element for multiplication is 1 (e.g., 1 x 8 = 8)

NJ 4.3.3 D.1.c - By the end of Grade 3, students will: Understand and apply the properties of operations and numbers. Any number multiplied by zero is zero


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NJ 4.3.3 D.2 - By the end of Grade 3, students will: Understand and use the concepts of equals, less than, and greater than to describe relations between numbers.


Obj. 11 - Compare 4- or 5-digit whole numbers using the symbols <, >, and =

Obj. 48 - Compare fractions using models

NJ 4.3.3 D.2.a - By the end of Grade 3, students will: Understand and use the concepts of equals, less than, and greater than to describe relations between numbers. Symbols (=, <, >)


Obj. 51 - Compare fractions with like denominators

Obj. 52 - Compare fractions with like numeratorsObj. 53 - WP: Compare equal unit fractions of different-sized wholes

NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.3 A - Data AnalysisNJ 4.4.3 A.1 - By the end of Grade 3, students will: Collect, generate, organize, and display data in response to questions, claims, or curiosity.NJ 4.4.3 A.1.a - By the end of Grade 3, students will: Collect, generate, organize, and display data in response to questions, claims, or curiosity. Data collected from the classroom environmentNJ 4.4.3 A.2 - By the end of Grade 3, students will: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.NJ 4.4.3 A.2.a - By the end of Grade 3, students will: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data. Pictograph, bar graph, table

Topic 4 - Data Analysis, Statistics, and Probability

Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data

Obj. 106 - Answer a question using information from a bar graph with a scale interval of 5 or 10


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Obj. 110 - Use a frequency table to represent dataObj. 111 - Answer a question using information from a frequency table

Obj. 112 - Determine a question that can be answered from a data representation

NJ 4.4.3 B - ProbabilityNJ 4.4.3 B.1 - By the end of Grade 3, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability.

NJ 4.4.3 B.1.a - By the end of Grade 3, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability. Likely, unlikely, certain, impossible


Obj. 113 - Determine if a situation is certain or impossible

NJ 4.4.3 B.1.b - By the end of Grade 3, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability. More likely, less likely, equally likely


Obj. 114 - Determine which event is least likely or most likely to occur

NJ 4.4.3 B.2 - By the end of Grade 3, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color).NJ 4.4.3 B.2.a - By the end of Grade 3, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color). What students think will happen (intuitive)


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NJ 4.4.3 B.2.b - By the end of Grade 3, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color). Collect data and use that data to predict the probability (experimental)

NJ 4.4.3 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.3 C.1 - By the end of Grade 3, students will: Represent and classify data according to attributes, such as shape or color, and relationships.

NJ 4.4.3 C.1.a - By the end of Grade 3, students will: Represent and classify data according to attributes, such as shape or color, and relationships. Venn diagramsNJ 4.4.3 C.1.b - By the end of Grade 3, students will: Represent and classify data according to attributes, such as shape or color, and relationships. Numerical and alphabetical orderNJ 4.4.3 C.2 - By the end of Grade 3, students will: Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation.NJ 4.4.3 C.2.a - By the end of Grade 3, students will: Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation. Organized lists, chartsNJ 4.4.3 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.3 D.1 - By the end of Grade 3, students will: Follow, devise, and describe practical sets of directions (e.g., to add two 2-digit numbers).


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NJ 4.4.3 D.2 - By the end of Grade 3, students will: Explore vertex-edge graphsNJ 4.4.3 D.2.a - By the end of Grade 3, students will: Explore vertex-edge graphs Vertex, edgeNJ 4.4.3 D.2.b - By the end of Grade 3, students will: Explore vertex-edge graphs PathNJ 4.4.3 D.3 - By the end of Grade 3, students will: Find the smallest number of colors needed to color a map.NJ 4.5 - All students will use mathematical processes of problem solving, communications, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the end of Grade 3, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of Grade 3, students will: Solve problems that arise in mathematics and in other contexts.


Obj. 25 - WP: Determine the amount of change from whole dollar amounts

Obj. 26 - WP: Add or subtract money amounts less than $1Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

NJ 4.5 A.2.a - By the end of Grade 3, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5 A.2.b - By the end of Grade 3, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5 A.2.c - By the end of Grade 3, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutions


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NJ 4.5 A.2.d - By the end of Grade 3, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the end of Grade 3, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the end of Grade 3, students will: Pose problems of various types and levels of difficulty.

NJ 4.5 A.5 - By the end of Grade 3, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5 A.6 - By the end of Grade 3, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of Grade 3, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of Grade 3, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.b - By the end of Grade 3, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5 B.2 - By the end of Grade 3, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

NJ 4.5 B.3 - By the end of Grade 3, students will: Analyze and evaluate the mathematical thinking and strategies of others.


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NJ 4.5 B.4 - By the end of Grade 3, students will: Use the language of mathematics to express mathematical ideas precisely.

Topic 2 - Algebraic Thinking Obj. 63 - WP: Determine a multiplication or division sentence for a given situation

NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the end of Grade 3, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the end of Grade 3, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of Grade 3, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of Grade 3, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of Grade 3, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the end of Grade 3, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of Grade 3, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the end of Grade 3, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the end of Grade 3, students will: Select and use various types of reasoning and methods of proof.


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NJ 4.5 D.4 - By the end of Grade 3, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5 D.5 - By the end of Grade 3, students will: Make and investigate mathematical conjectures.

NJ 4.5 D.5.a - By the end of Grade 3, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5 D.5.b - By the end of Grade 3, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5 D.6 - By the end of Grade 3, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.

NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of Grade 3, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.a - By the end of Grade 3, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)

NJ 4.5 E.1.b - By the end of Grade 3, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


Obj. 110 - Use a frequency table to represent data

Obj. 111 - Answer a question using information from a frequency table


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NJ 4.5 E.1.c - By the end of Grade 3, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5 E.1.d - By the end of Grade 3, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)


Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data

Obj. 106 - Answer a question using information from a bar graph with a scale interval of 5 or 10

NJ 4.5 E.2 - By the end of Grade 3, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the end of Grade 3, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of Grade 3, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of Grade 3, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the end of Grade 3, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the end of Grade 3, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5 F.5 - By the end of Grade 3, students will: Use computer software to make and verify conjectures about geometric objects.


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NJ 4.5 F.6 - By the end of Grade 3, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.4 A - Number SenseNJ 4.1.4 A.1 - By the end of grade 4, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well).

NJ 4.1.4 A.1.a - By the end of grade 4, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well). Whole numbers through millions


Obj. 1 - Read a 6-digit whole number

Obj. 2 - Determine the word form of a 6-digit whole numberObj. 3 - Determine the value of a digit in a 6-digit whole number

NJ 4.1.4 A.1.b - By the end of grade 4, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well). Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 16) as part of a whole, as a subset of a set, and as a location on a number line


Obj. 44 - Identify a mixed number represented by a point on a number line

Obj. 45 - Locate a mixed number on a number lineObj. 48 - Identify an improper fraction represented by a point on a number lineObj. 49 - Locate an improper fraction on a number line



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NJ 4.1.4 A.1.c - By the end of grade 4, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 4 pertain to these sets of numbers as well). Decimals through hundredths


Obj. 62 - Read a decimal number through the hundredths place

Obj. 63 - Determine the word form of a decimal number through the hundredths place

NJ 4.1.4 A.2 - By the end of grade 4, students will: Demonstrate an understanding of place value concepts.


Obj. 4 - Determine which digit is in a specified place in a 6-digit whole number

Obj. 5 - Determine the whole number represented in expanded form written in powers of tenObj. 6 - Represent a 6-digit whole number in expanded form using powers of tenObj. 7 - Convert between proper expanded form and improper expanded form up to a 5-digit whole numberObj. 8 - Convert between standard form and improper expanded form up to a 5-digit whole number

NJ 4.1.4 A.3 - By the end of grade 4, students will: Demonstrate a sense of the relative magnitudes of numbers.

NJ 4.1.4 A.4 - By the end of grade 4, students will: Understand the various uses of numbers.NJ 4.1.4 A.4.a - By the end of grade 4, students will: Understand the various uses of numbers. Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)

NJ 4.1.4 A.5 - By the end of grade 4, students will: Use concrete and pictorial models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number.


Obj. 43 - Identify a mixed number represented by a model


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Obj. 47 - Identify an improper fraction represented by a model of a mixed numberObj. 51 - Determine a set of equivalent fractionsObj. 64 - Determine the decimal number from a pictorial model of tenths or hundredthsObj. 65 - Identify a pictorial model of tenths or hundredths of a decimal numberObj. 70 - Determine the decimal number equivalent to a fraction modelObj. 71 - Determine the fraction equivalent to a decimal number model

NJ 4.1.4 A.6 - By the end of grade 4, students will: Compare and order numbers.


Obj. 52 - Compare fractions on a number line

Obj. 53 - Order fractions on a number lineObj. 72 - Compare decimal numbers through the hundredths place

Obj. 73 - Order decimal numbers through the hundredths place

NJ 4.1.4 A.7 - By the end of grade 4, students will: Explore settings that give rise to negative numbers.NJ 4.1.4 A.7.a - By the end of grade 4, students will: Explore settings that give rise to negative numbers. Temperatures below 0°, debts

NJ 4.1.4 A.7.b - By the end of grade 4, students will: Explore settings that give rise to negative numbers. Extension of the number line

NJ 4.1.4 B - Numerical OperationsNJ 4.1.4 B.1 - By the end of grade 4, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems.


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NJ 4.1.4 B.1.a - By the end of grade 4, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Addition and subtraction: joining, separating, comparing


Obj. 9 - Add up to 4-digit whole numbers in expanded form

NJ 4.1.4 B.1.b - By the end of grade 4, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Multiplication: repeated addition, area/arrayNJ 4.1.4 B.1.c - By the end of grade 4, students will: Develop the meanings of the four basic arithmetic operations by modeling and discussing a large variety of problems. Division: repeated subtraction, sharingNJ 4.1.4 B.2 - By the end of grade 4, students will: Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as "skip counting" and "repeated subtraction") and then commit them to memory.

NJ 4.1.4 B.3 - By the end of grade 4, students will: Construct, use, and explain procedures for performing whole number calculations and with:

NJ 4.1.4 B.3.a - By the end of grade 4, students will: Construct, use, and explain procedures for performing whole number calculations and with: Pencil-and-paper


Obj. 23 - Multiply a 3- or 4-digit whole number by a 1-digit whole number

Obj. 24 - Multiply a 2-digit whole number by a 2-digit whole numberObj. 26 - Multiply three 1- and 2-digit whole numbersObj. 27 - WP: Multiply a multi-digit whole number by a 1-digit whole numberObj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number


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Obj. 34 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 35 - Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 36 - Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 37 - Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 39 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 40 - WP: Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotient


NJ 4.1.4 B.3.b - By the end of grade 4, students will: Construct, use, and explain procedures for performing whole number calculations and with: Mental mathNJ 4.1.4 B.3.c - By the end of grade 4, students will: Construct, use, and explain procedures for performing whole number calculations and with: CalculatorNJ 4.1.4 B.4 - By the end of grade 4, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers.NJ 4.1.4 B.4.a - By the end of grade 4, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Addition of 3-digit numbers


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NJ 4.1.4 B.4.b - By the end of grade 4, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Subtraction of 3-digit numbers


Obj. 12 - Subtract a smaller number from a 3- or 4-digit whole number in expanded form

NJ 4.1.4 B.4.c - By the end of grade 4, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Multiplication of 2-digit numbers


Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000



NJ 4.1.4 B.4.d - By the end of grade 4, students will: Use efficient and accurate pencil-and-paper procedures for computation with whole numbers. Division of 3-digit numbers by 1-digit numbers


Obj. 34 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 35 - Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 36 - Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 37 - Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient



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NJ 4.1.4 B.5 - By the end of grade 4, students will: Construct and use procedures for performing decimal addition and subtraction.


Obj. 75 - Add two decimal numbers through hundredths

Obj. 76 - Subtract two decimal numbers through hundredthsObj. 79 - WP: Add or subtract decimal numbers of the same place through hundredths

NJ 4.1.4 B.6 - By the end of grade 4, students will: Count and perform simple computations with money.NJ 4.1.4 B.6.a - By the end of grade 4, students will: Count and perform simple computations with money. Standard dollars and cents notation


Obj. 77 - WP: Add or subtract money amounts greater than $1

Obj. 78 - WP: Solve a money problem involving 2 steps

NJ 4.1.4 B.7 - By the end of grade 4, students will: Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.




Obj. 34 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 35 - Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient


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Obj. 36 - Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 37 - Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient




Obj. 75 - Add two decimal numbers through hundredths

NJ 4.1.4 B.8 - By the end of grade 4, students will: Check the reasonableness of results of computations.NJ 4.1.4 B.9 - By the end of grade 4, students will: Use concrete models to explore addition and subtraction with fractions.


Obj. 54 - Add fractions with like denominators no greater than 10 using models

Obj. 58 - Subtract fractions with like denominators no greater than 10 using models

NJ 4.1.4 B.10 - By the end of grade 4, students will: Understand and use the inverse relationships between addition and subtraction and between multiplication and division.

NJ 4.1.4 C - EstimationNJ 4.1.4 C.1 - By the end of grade 4, students will: Judge without counting whether a set of objects has less than, more than, or the same number of objects as a reference set.


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NJ 4.1.4 C.2 - By the end of grade 4, students will: Construct and use a variety of estimation strategies (e.g., rounding and mental math) for estimating both quantities and the results of computations.


Obj. 30 - Estimate a product of whole numbers by rounding

Obj. 31 - Estimate a product of whole numbers using any methodObj. 32 - WP: Estimate a product of two whole numbers using any methodObj. 81 - Estimate a decimal number sum or difference by rounding to whole numbers

NJ 4.1.4 C.3 - By the end of grade 4, students will: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.NJ 4.1.4 C.4 - By the end of grade 4, students will: Use estimation to determine whether the result of a computation (either by calculator or by hand) is reasonable.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.4 A - Geometric PropertiesNJ 4.2.4 A.1 - By the end of grade 4, students will: Identify and describe spatial relationships of two or more objects in space.NJ 4.2.4 A.1.a - By the end of grade 4, students will: Identify and describe spatial relationships of two or more objects in space. Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)

NJ 4.2.4 A.1.b - By the end of grade 4, students will: Identify and describe spatial relationships of two or more objects in space. Relative shapes and sizes


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NJ 4.2.4 A.1.c - By the end of grade 4, students will: Identify and describe spatial relationships of two or more objects in space. Shadows (projections) of everyday objects

NJ 4.2.4 A.2 - By the end of grade 4, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.NJ 4.2.4 A.2.a - By the end of grade 4, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. Vertex, edge, face, side, angle


Obj. 126 - Classify a quadrilateral

Obj. 127 - Relate a polygon to attributes or characteristics

NJ 4.2.4 A.2.b - By the end of grade 4, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. 3D figures - cube, rectangular prism, sphere, cone, cylinder, and pyramid

NJ 4.2.4 A.2.c - By the end of grade 4, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. 2D figures - square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon


Obj. 127 - Relate a polygon to attributes or characteristics

NJ 4.2.4 A.2.d - By the end of grade 4, students will: Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them. Inclusive relationships - squares are rectangles, cubes are rectangular prisms

NJ 4.2.4 A.3 - By the end of grade 4, students will: Identify and describe relationships among two-dimensional shapes.


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NJ 4.2.4 A.3.a - By the end of grade 4, students will: Identify and describe relationships among two-dimensional shapes. CongruenceNJ 4.2.4 A.3.b - By the end of grade 4, students will: Identify and describe relationships among two-dimensional shapes. Lines of symmetry


Obj. 129 - Determine lines of symmetry

NJ 4.2.4 A.4 - By the end of grade 4, students will: Understand and apply concepts involving lines, angles, and circles.NJ 4.2.4 A.4.a - By the end of grade 4, students will: Understand and apply concepts involving lines, angles, and circles. Point, line, line segment, endpointNJ 4.2.4 A.4.b - By the end of grade 4, students will: Understand and apply concepts involving lines, angles, and circles. Parallel, perpendicularNJ 4.2.4 A.4.c - By the end of grade 4, students will: Understand and apply concepts involving lines, angles, and circles. Angles - acute, right, obtuse


Obj. 121 - Classify an angle given a picture

Obj. 122 - Classify an angle given its measure

NJ 4.2.4 A.4.d - By the end of grade 4, students will: Understand and apply concepts involving lines, angles, and circles. Circles - diameter, radius, centerNJ 4.2.4 A.5 - By the end of grade 4, students will: Recognize, describe, extend, and create space-filling patterns.NJ 4.2.4 B - Transforming ShapesNJ 4.2.4 B.1 - By the end of grade 4, students will: Use simple shapes to cover an area (tessellations).

NJ 4.2.4 B.2 - By the end of grade 4, students will: Describe and use geometric transformations (slide, flip, turn).


Obj. 130 - Determine the result of a flip, a turn, or a slide


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NJ 4.2.4 B.3 - By the end of grade 4, students will: Investigate the occurrence of geometry in nature and art.NJ 4.2.4 C - Coordinate GeometryNJ 4.2.4 C.1 - By the end of grade 4, students will: Locate and name points in the first quadrant on a coordinate grid.NJ 4.2.4 C.2 - By the end of grade 4, students will: Use coordinates to give or follow directions from one point to another on a map or grid.


Obj. 132 - Determine a path or location on a grid using compass directions

Obj. 133 - Identify the location of an ordered pair in the first quadrant using compass directionsObj. 134 - Determine the ordered pair of a point in the first quadrant using compass directions

NJ 4.2.4 D - Units of MeasurementNJ 4.2.4 D.1 - By the end of grade 4, students will: Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.NJ 4.2.4 D.2 - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems.NJ 4.2.4 D.2.a - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Length - fractions of an inch (1/8, 1/4, 1/2), mile, decimeter, kilometer


Obj. 93 - Measure length to the nearest eighth of an inch

Obj. 94 - Measure length to the nearest millimeter

NJ 4.2.4 D.2.b - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Area - square inch, square centimeterNJ 4.2.4 D.2.c - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Volume - cubic inch, cubic centimeter


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NJ 4.2.4 D.2.d - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Weight - ounceNJ 4.2.4 D.2.e - By the end of grade 4, students will: Select and use appropriate standard units of measure and measurement tools to solve real-life problems. Capacity - fluid ounce, cup, gallon, milliliter

NJ 4.2.4 D.3 - By the end of grade 4, students will: Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long).NJ 4.2.4 D.4 - By the end of grade 4, students will: Incorporate estimation in measurement activities (e.g., estimate before measuring).

NJ 4.2.4 D.5 - By the end of grade 4, students will: Solve problems involving elapsed time.


Obj. 101 - Calculate elapsed time exceeding an hour without regrouping

Obj. 102 - Calculate elapsed time exceeding an hour with regroupingObj. 103 - WP: Calculate elapsed time exceeding an hour without regrouping hoursObj. 104 - WP: Calculate elapsed time exceeding an hour with regrouping hoursObj. 105 - WP: Determine the end time given the start time and the elapsed time exceeding an hourObj. 106 - WP: Determine the start time given the end time and the elapsed time exceeding an hour

Obj. 107 - Read a timetable to answer questionsObj. 108 - WP: Add time intervals involving hours and minutesObj. 109 - Solve an elapsed-time problem using a calendar



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NJ 4.2.4 E.1 - By the end of grade 4, students will: Determine the area of simple two-dimensional shapes on a square grid.


Obj. 114 - Determine the area of a polygon on a grid

Obj. 119 - Estimate the area of an irregular polygon on a grid

NJ 4.2.4 E.2 - By the end of grade 4, students will: Distinguish between perimeter and area and use each appropriately in problem-solving situations.NJ 4.2.4 E.3 - By the end of grade 4, students will: Measure and compare the volume of three-dimensional objects using materials such as rice or cubes.


Obj. 120 - Determine the volume of a rectangular prism given a diagram showing unit cubes

NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.4 A - PatternsNJ 4.3.4 A.1 - By the end of grade 4, students will: Recognize, describe, extend, and create patterns.

NJ 4.3.4 A.1.a - By the end of grade 4, students will: Recognize, describe, extend, and create patterns. Descriptions using words, number sentences/expressions, graphs, tables, variables (e.g., shape, blank, or letter)

NJ 4.3.4 A.1.b - By the end of grade 4, students will: Recognize, describe, extend, and create patterns. Sequences that stop or that continue infinitelyNJ 4.3.4 A.1.c - By the end of grade 4, students will: Recognize, describe, extend, and create patterns. Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11,... or 800, 400, 200,...)


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NJ 4.3.4 A.1.d - By the end of grade 4, students will: Recognize, describe, extend, and create patterns. Sequences can often be extended in more than one way (e.g., the next term after 1, 2, 4,... could be 8, or 7, or ...)NJ 4.3.4 B - Functions and RelationshipsNJ 4.3.4 B.1 - By the end of grade 4, students will: Use concrete and pictorial models to explore the basic concept of a function.NJ 4.3.4 B.1.a - By the end of grade 4, students will: Use concrete and pictorial models to explore the basic concept of a function. Input/output tables, T-charts

Topic 2 - Algebra Obj. 90 - Generate a table of paired numbers based on a rule

Obj. 91 - Determine a rule that relates two variablesObj. 92 - Extend a number pattern in a table of related pairs

NJ 4.3.4 B.1.b - By the end of grade 4, students will: Use concrete and pictorial models to explore the basic concept of a function. Combining two function machines

NJ 4.3.4 B.1.c - By the end of grade 4, students will: Use concrete and pictorial models to explore the basic concept of a function. Reversing a function machine

NJ 4.3.4 C - ModelingNJ 4.3.4 C.1 - By the end of grade 4, students will: Recognize and describe change in quantities.NJ 4.3.4 C.1.a - By the end of grade 4, students will: Recognize and describe change in quantities. Graphs representing change over time (e.g., temperature, height)


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NJ 4.3.4 C.1.b - By the end of grade 4, students will: Recognize and describe change in quantities. How change in one physical quantity can produce a corresponding change in another (e.g., pitch of a sound depends on the rate of vibration)

NJ 4.3.4 C.2 - By the end of grade 4, students will: Construct and solve simple open sentences involving any one operation (e.g., 3 x 6 = __, n = 15 ÷ 3, 3 x __ = 0, 16 - c = 7).

NJ 4.3.4 D - ProceduresNJ 4.3.4 D.1 - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers.NJ 4.3.4 D.1.a - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers. Commutative (e.g., 3 x 7 = 7 x 3)NJ 4.3.4 D.1.b - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers. Identity element for multiplication is 1 (e.g., 1 x 8 = 8)NJ 4.3.4 D.1.c - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers. Associative (e.g., 2 x 4 x 25 can be found by first multiplying either 2 x 4 or 4 x 25)

NJ 4.3.4 D.1.d - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers. Division by zero is undefinedNJ 4.3.4 D.1.e - By the end of grade 4, students will: Understand, name, and apply the properties of operations and numbers. Any number multiplied by zero is zero.


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NJ 4.3.4 D.2 - By the end of grade 4, students will: Understand and use the concepts of equals, less than, and greater than in simple number sentences.NJ 4.3.4 D.2.a - Symbols (=, <, >) Topic 1 - Number Sense and

OperationsObj. 52 - Compare fractions on a number lineObj. 72 - Compare decimal numbers through the hundredths place

NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.4 A - Data AnalysisNJ 4.4.4 A.1 - By the end of grade 4, students will: Collect, generate, organize, and display data in response to questions, claims, or curiosity.NJ 4.4.4 A.1.a - By the end of grade 4, students will: Collect, generate, organize, and display data in response to questions, claims, or curiosity. Data collected from the school environmentNJ 4.4.4 A.2 - By the end of grade 4, students will: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data.NJ 4.4.4 A.2.a - By the end of grade 4, students will: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data. Pictograph, bar graph, line plot, line graph, table


Obj. 135 - Read a line graph

Obj. 136 - Use a line graph to represent dataObj. 137 - Answer a question using information from a line graphObj. 139 - Read a double-bar graph

Obj. 140 - Use a double-bar graph to represent data


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Obj. 141 - Answer a question using information from a double-bar graph

Obj. 142 - Answer a question using information from a table

NJ 4.4.4 A.2.b - By the end of grade 4, students will: Read, interpret, construct, analyze, generate questions about, and draw inferences from displays of data. Average (mean), most frequent (mode), middle term (median)

NJ 4.4.4 B - ProbabilityNJ 4.4.4 B.1 - By the end of grade 4, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability.

NJ 4.4.4 B.1.a - By the end of grade 4, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability. Likely, unlikely, certain, impossible, improbable, fair, unfair

NJ 4.4.4 B.1.b - By the end of grade 4, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability. More likely, less likely, equally likely

NJ 4.4.4 B.1.c - By the end of grade 4, students will: Use everyday events and chance devices, such as dice, coins, and unevenly divided spinners, to explore concepts of probability. Probability of tossing "heads" does not depend on outcomes of previous tosses

NJ 4.4.4 B.2 - By the end of grade 4, students will: Determine probabilities of simple events based on equally likely outcomes and express them as fractions.


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NJ 4.4.4 B.3 - By the end of grade 4, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color).NJ 4.4.4 B.3.a - By the end of grade 4, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color). What students think will happen (intuitive)

NJ 4.4.4 B.3.b - By the end of grade 4, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color). Collect data and use that data to predict the probability (experimental)

NJ 4.4.4 B.3.c - By the end of grade 4, students will: Predict probabilities in a variety of situations (e.g., given the number of items of each color in a bag, what is the probability that an item picked will have a particular color). Analyze all possible outcomes to find the probability (theoretical)

NJ 4.4.4 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.4 C.1 - By the end of grade 4, students will: Represent and classify data according to attributes, such as shape or color, and relationships.

NJ 4.4.4 C.1.a - By the end of grade 4, students will: Represent and classify data according to attributes, such as shape or color, and relationships. Venn diagrams


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NJ 4.4.4 C.1.b - By the end of grade 4, students will: Represent and classify data according to attributes, such as shape or color, and relationships. Numerical and alphabetical orderNJ 4.4.4 C.2 - By the end of grade 4, students will: Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation.NJ 4.4.4 C.2.a - By the end of grade 4, students will: Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation. Organized lists, charts, tree diagramsNJ 4.4.4 C.2.b - By the end of grade 4, students will: Represent all possibilities for a simple counting situation in an organized way and draw conclusions from this representation. Dividing into categories (e.g., to find the total number of rectangles in a grid, find the number of rectangles of each size and add the results)NJ 4.4.4 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.4 D.1 - By the end of grade 4, students will: Follow, devise, and describe practical sets of directions (e.g., to add two 2-digit numbers).

NJ 4.4.4 D.2 - By the end of grade 4, students will: Play two-person games and devise strategies for winning the games (e.g., "make 5" where players alternately add 1 or 2 and the person who reaches 5, or another designated number, is the winner).

NJ 4.4.4 D.3 - By the end of grade 4, students will: Explore vertex-edge graphs and tree diagrams.


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NJ 4.4.4 D.3.a - By the end of grade 4, students will: Explore vertex-edge graphs and tree diagrams. Vertex, edge, neighboring/adjacent, number of neighbors

NJ 4.4.4 D.3.b - By the end of grade 4, students will: Explore vertex-edge graphs and tree diagrams. Path, circuit (i.e., path that ends at its starting point)NJ 4.4.4 D.4 - By the end of grade 4, students will: Find the smallest number of colors needed to color a map or a graph.NJ 4.5 - All students will use mathematical processes of problem solving, communications, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the end of grade 4, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of grade 4, students will: Solve problems that arise in mathematics and in other contexts.


Obj. 27 - WP: Multiply a multi-digit whole number by a 1-digit whole number

Obj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number

Obj. 32 - WP: Estimate a product of two whole numbers using any methodObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient




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Obj. 77 - WP: Add or subtract money amounts greater than $1Obj. 78 - WP: Solve a money problem involving 2 stepsObj. 79 - WP: Add or subtract decimal numbers of the same place through hundredths


Obj. 103 - WP: Calculate elapsed time exceeding an hour without regrouping hoursObj. 104 - WP: Calculate elapsed time exceeding an hour with regrouping hoursObj. 105 - WP: Determine the end time given the start time and the elapsed time exceeding an hourObj. 106 - WP: Determine the start time given the end time and the elapsed time exceeding an hour

Obj. 107 - Read a timetable to answer questions

NJ 4.5 A.2.a - By the end of grade 4, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5 A.2.b - By the end of grade 4, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5 A.2.c - By the end of grade 4, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutionsNJ 4.5 A.2.d - By the end of grade 4, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several ways


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NJ 4.5 A.3 - By the end of grade 4, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the end of grade 4, students will: Pose problems of various types and levels of difficulty.

NJ 4.5 A.5 - By the end of grade 4, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5 A.6 - By the end of grade 4, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of grade 4, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of grade 4, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.b - By the end of grade 4, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5 B.2 - By the end of grade 4, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.NJ 4.5 B.3 - By the end of grade 4, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the end of grade 4, students will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5 C - Connections


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NJ 4.5 C.1 - By the end of grade 4, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).NJ 4.5 C.2 - By the end of grade 4, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of grade 4, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of grade 4, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of grade 4, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the end of grade 4, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of grade 4, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the end of grade 4, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the end of grade 4, students will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the end of grade 4, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.


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NJ 4.5 D.5 - By the end of grade 4, students will: Make and investigate mathematical conjectures.NJ 4.5 D.5.a - By the end of grade 4, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5 D.5.b - By the end of grade 4, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5 D.6 - By the end of grade 4, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of grade 4, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.a - By the end of grade 4, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)

NJ 4.5 E.1.b - By the end of grade 4, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


Obj. 142 - Answer a question using information from a table

NJ 4.5 E.1.c - By the end of grade 4, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5 E.1.d - By the end of grade 4, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)


Obj. 135 - Read a line graph

Obj. 136 - Use a line graph to represent data


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Obj. 137 - Answer a question using information from a line graphObj. 139 - Read a double-bar graph

Obj. 140 - Use a double-bar graph to represent dataObj. 141 - Answer a question using information from a double-bar graph

NJ 4.5 E.2 - By the end of grade 4, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the end of grade 4, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of grade 4, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of grade 4, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the end of grade 4, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the end of grade 4, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5 F.5 - By the end of grade 4, students will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5 F.6 - By the end of grade 4, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.5 A - Number SenseNJ 4.1.5 A.1 - By the end of grade 5, the student will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well).

NJ 4.1.5 A.1.a - By the end of grade 5, the student will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well). All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers


Obj. 30 - Relate a sharing situation to a fraction

NJ 4.1.5 A.1.b - By the end of grade 5, the student will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 5 pertain to these sets of numbers as well). All decimals

NJ 4.1.5 A.2 - By the end of grade 5, the student will: Recognize the decimal nature of United States currency and compute with money.


Obj. 88 - Multiply a money amount by a 2- or 3-digit whole number

Obj. 89 - WP: Multiply a money amount by a 2-digit whole number

NJ 4.1.5 A.3 - By the end of grade 5, the student will: Demonstrate a sense of the relative magnitudes of numbers.


Obj. 33 - Compare fractions with unlike denominators

Obj. 34 - Order fractions with unlike denominators in ascending or descending orderObj. 72 - Compare decimal numbers to thousandths represented in expanded form



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Obj. 73 - Compare decimal numbers of differing places to thousandths

Obj. 74 - Order decimal numbers of differing places to thousandths in ascending or descending order

NJ 4.1.5 A.4 - By the end of grade 5, the student will: Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.


Obj. 31 - Determine equivalent fractions not in simplest form

Obj. 32 - Determine the simplest form of a fractionObj. 47 - Convert a mixed number to an improper fractionObj. 48 - Convert an improper fraction to a mixed numberObj. 70 - Determine a decimal number represented in expanded formObj. 71 - Represent a decimal number in expanded formObj. 90 - Convert a decimal number through thousandths to a simplified fractionObj. 91 - Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation

NJ 4.1.5 A.5 - By the end of grade 5, the student will: Develop and apply number theory concepts in problem solving situations.NJ 4.1.5 A.5.a - By the end of grade 5, the student will: Develop and apply number theory concepts in problem solving situations. Primes, factors, multiples


Obj. 1 - Determine if a number to 50 is prime or composite

Obj. 2 - Determine a complete list of whole number factor pairs for a number to 50Obj. 3 - Determine all the factors of a whole number to 50Obj. 4 - Determine the prime factorization of a number to 50Obj. 7 - Determine the multiple(s) of a number

NJ 4.1.5 A.6 - By the end of grade 5, the student will: Compare and order numbers.


Obj. 33 - Compare fractions with unlike denominators


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Obj. 34 - Order fractions with unlike denominators in ascending or descending orderObj. 72 - Compare decimal numbers to thousandths represented in expanded formObj. 73 - Compare decimal numbers of differing places to thousandths

Obj. 74 - Order decimal numbers of differing places to thousandths in ascending or descending order

NJ 4.1.5 B - Numerical OperationsNJ 4.1.5 B.1 - By the end of grade 5, the student will: Recognize the appropriate use of each arithmetic operation in problem situations.NJ 4.1.5 B.2 - By the end of grade 5, the student will: Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with:NJ 4.1.5 B.2.a - By the end of grade 5, the student will: Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with: Pencil-and-paper


Obj. 35 - Add fractions with like denominators greater than 10 and simplify the sum

Obj. 36 - Add fractions with unlike denominators using a model and do not simplify the sumObj. 37 - Add fractions with unlike denominators and do not simplify the sumObj. 38 - Add fractions with unlike denominators that have factors in common and simplify the sumObj. 39 - Add fractions with unlike denominators that have no factors in commonObj. 40 - Subtract fractions with like denominators greater than 10 and simplify the differenceObj. 41 - Subtract fractions with unlike denominators using a model and do not simplify the differenceObj. 42 - Subtract fractions with unlike denominators and do not simplify the difference


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Obj. 43 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceObj. 44 - Subtract fractions with unlike denominators that have no factors in commonObj. 45 - WP: Add or subtract fractions with like denominators and simplify the sum or differenceObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 49 - Add mixed numbers with like denominators and simplify the sumObj. 50 - Add mixed numbers with unlike denominators and simplify the sumObj. 51 - Subtract mixed numbers with like denominators and simplify the differenceObj. 52 - Subtract mixed numbers with unlike denominators and simplify the differenceObj. 53 - WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference

Obj. 54 - WP: Add or subtract mixed numbers with unlike denominators that have no factors in common

Obj. 75 - Add two decimal numbers of differing places to thousandths

Obj. 76 - Add three or more decimal numbersObj. 77 - Add decimal numbers and whole numbersObj. 78 - Subtract two decimal numbers of differing places to thousandthsObj. 79 - Subtract a decimal number from a whole number or a whole number from a decimal number

Obj. 80 - WP: Add or subtract decimal numbers through thousandths


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Obj. 81 - WP: Add or subtract a decimal number through thousandths and a whole number

NJ 4.1.5 B.2.b - By the end of grade 5, the student will: Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with: Mental mathNJ 4.1.5 B.2.c - By the end of grade 5, the student will: Construct, use, and explain procedures for performing addition and subtraction with fractions and decimals with: CalculatorNJ 4.1.5 B.3 - By the end of grade 5, the student will: Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.


Obj. 14 - Divide a multi-digit whole number by a 1-digit number, with no remainder and at least one zero in the quotient

Obj. 15 - Divide a multi-digit whole number by a 1-digit number, with a remainder and at least one zero in the quotientObj. 16 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed numberObj. 17 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimalObj. 18 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotientObj. 19 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotientObj. 20 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotientObj. 21 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientObj. 22 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number


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Obj. 23 - WP: Divide a whole number, with no remainderObj. 24 - WP: Divide a whole number and interpret the remainder

NJ 4.1.5 B.4 - By the end of grade 5, the student will: Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.


Obj. 12 - WP: Multiply a 3- or 4-digit whole number by a 3-digit whole number

Obj. 15 - Divide a multi-digit whole number by a 1-digit number, with a remainder and at least one zero in the quotientObj. 16 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed numberObj. 17 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimalObj. 18 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotientObj. 19 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotientObj. 20 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotientObj. 21 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientObj. 22 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed numberObj. 23 - WP: Divide a whole number, with no remainderObj. 24 - WP: Divide a whole number and interpret the remainderObj. 25 - WP: Solve a 2-step problem involving whole numbersObj. 29 - WP: Estimate a quotient using any method


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Obj. 35 - Add fractions with like denominators greater than 10 and simplify the sumObj. 36 - Add fractions with unlike denominators using a model and do not simplify the sumObj. 37 - Add fractions with unlike denominators and do not simplify the sumObj. 38 - Add fractions with unlike denominators that have factors in common and simplify the sumObj. 39 - Add fractions with unlike denominators that have no factors in commonObj. 40 - Subtract fractions with like denominators greater than 10 and simplify the differenceObj. 41 - Subtract fractions with unlike denominators using a model and do not simplify the differenceObj. 42 - Subtract fractions with unlike denominators and do not simplify the differenceObj. 43 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceObj. 44 - Subtract fractions with unlike denominators that have no factors in commonObj. 45 - WP: Add or subtract fractions with like denominators and simplify the sum or differenceObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 49 - Add mixed numbers with like denominators and simplify the sumObj. 50 - Add mixed numbers with unlike denominators and simplify the sumObj. 51 - Subtract mixed numbers with like denominators and simplify the differenceObj. 52 - Subtract mixed numbers with unlike denominators and simplify the difference


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Obj. 53 - WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference


Obj. 75 - Add two decimal numbers of differing places to thousandths

Obj. 76 - Add three or more decimal numbersObj. 77 - Add decimal numbers and whole numbersObj. 78 - Subtract two decimal numbers of differing places to thousandthsObj. 79 - Subtract a decimal number from a whole number or a whole number from a decimal number

Obj. 80 - WP: Add or subtract decimal numbers through thousandthsObj. 81 - WP: Add or subtract a decimal number through thousandths and a whole numberObj. 85 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any methodObj. 89 - WP: Multiply a money amount by a 2-digit whole number

NJ 4.1.5 B.5 - By the end of grade 5, the student will: Check the reasonableness of results of computations.NJ 4.1.5 B.6 - By the end of grade 5, the student will: Understand and use the various relationships among operations and properties of operations.NJ 4.1.5 C - EstimationNJ 4.1.5 C.1 - By the end of grade 5, the student will: Use a variety of estimation strategies for both number and computation.


Obj. 26 - Know the effects of rounding

Obj. 27 - Estimate a quotient using compatible numbers


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Obj. 28 - Estimate a quotient using any methodObj. 29 - WP: Estimate a quotient using any methodObj. 56 - Estimate a fraction sum using benchmark numbers 0, 1/2, and 1Obj. 57 - Estimate a fraction difference using benchmark numbers 0, 1/2, and 1Obj. 58 - WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1Obj. 82 - Round a decimal number to a specified decimal place to thousandthsObj. 83 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 84 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 85 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any method

NJ 4.1.5 C.2 - By the end of grade 5, the student will: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.NJ 4.1.5 C.3 - By the end of grade 5, the student will: Determine the reasonableness of an answer by estimating the result of operations.NJ 4.1.5 C.4 - By the end of grade 5, the student will: Determine whether a given estimate is an overestimate or an underestimate.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.5 A - Geometric Properties


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NJ 4.2.5 A.1 - By the end of grade 5, the student will: Understand and apply concepts involving lines and angles.NJ 4.2.5 A.1.a - By the end of grade 5, the student will: Understand and apply concepts involving lines and angles. Notation for line, ray, angle, line segmentNJ 4.2.5 A.1.b - By the end of grade 5, the student will: Understand and apply concepts involving lines and angles. Properties of parallel, perpendicular, and intersecting lines

NJ 4.2.5 A.1.c - By the end of grade 5, the student will: Understand and apply concepts involving lines and angles. Sum of the measures of the interior angles of a triangle is 180°

NJ 4.2.5 A.2 - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons.

NJ 4.2.5 A.2.a - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons. Triangles by angles and sides


Obj. 141 - Classify a triangle by its sides and angles

NJ 4.2.5 A.2.b - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombiNJ 4.2.5 A.2.c - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons. Polygons by number of sides.

NJ 4.2.5 A.2.d - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons. Equilateral, equiangular, regular


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NJ 4.2.5 A.2.e - By the end of grade 5, the student will: Identify, describe, compare, and classify polygons. All points equidistant from a given point form a circleNJ 4.2.5 A.3 - By the end of grade 5, the student will: Identify similar figures.NJ 4.2.5 A.4 - By the end of grade 5, the student will: Understand and apply the concepts of congruence and symmetry (line and rotational).NJ 4.2.5 B - Transforming ShapesNJ 4.2.5 B.1 - By the end of grade 5, the student will: Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.


Obj. 145 - Identify a figure that has reflectional or rotational symmetry

Obj. 146 - Determine the result of a reflection, a rotation, or a translation on a gridObj. 147 - Determine the transformation that generates the image of a figure on a grid

NJ 4.2.5 B.2 - By the end of grade 5, the student will: Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

NJ 4.2.5 C - Coordinate GeometryNJ 4.2.5 C.1 - By the end of grade 5, the student will: Create geometric shapes with specified properties in the first quadrant on a coordinate grid.NJ 4.2.5 D - Units of MeasurementNJ 4.2.5 D.1 - By the end of grade 5, the student will: Select and use appropriate units to measure angles and area.NJ 4.2.5 D.2 - By the end of grade 5, the student will: Convert measurement units within a system (e.g., 3 feet = ___ inches).


Obj. 113 - Convert between customary units of length using fractional amounts

Obj. 114 - Convert between customary units of capacity using fractional amountsObj. 115 - Convert between customary units of weight using fractional amounts


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Obj. 116 - Convert between metric units of capacity using decimal amountsObj. 117 - Convert between metric units of mass using decimal amounts

Obj. 118 - Convert between millimeters or centimeters and meters, or meters and kilometers using decimal amounts

NJ 4.2.5 D.3 - By the end of grade 5, the student will: Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).NJ 4.2.5 D.4 - By the end of grade 5, the student will: Use measurements and estimates to describe and compare phenomena.NJ 4.2.5 E - Measuring Geometric ObjectsNJ 4.2.5 E.1 - By the end of grade 5, the student will: Use a protractor to measure angles.


Obj. 124 - Measure an angle to the nearest 5 degrees

NJ 4.2.5 E.2 - By the end of grade 5, the student will: Develop and apply strategies and formulas for finding perimeter and area.NJ 4.2.5 E.2.a - By the end of grade 5, the student will: Develop and apply strategies and formulas for finding perimeter and area. Square


Obj. 130 - WP: Determine the area of a square or rectangle

Obj. 131 - WP: Determine a missing dimension given the area and another dimension

NJ 4.2.5 E.2.b - By the end of grade 5, the student will: Develop and apply strategies and formulas for finding perimeter and area. Rectangle


Obj. 130 - WP: Determine the area of a square or rectangle

Obj. 131 - WP: Determine a missing dimension given the area and another dimension

NJ 4.2.5 E.3 - By the end of grade 5, the student will: Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa.


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NJ 4.2.5 E.4 - By the end of grade 5, the student will: Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.5 A - PatternsNJ 4.3.5 A.1 - By the end of grade 5, the student will: Recognize, describe, extend, and create patterns involving whole numbers.

Topic 2 - Algebra Obj. 105 - WP: Extend a pattern to solve a problem

NJ 4.3.5 A.1.a - By the end of grade 5, the student will: Recognize, describe, extend, and create patterns involving whole numbers. Descriptions using tables, verbal rules, simple equations, and graphs

Topic 2 - Algebra Obj. 106 - Generate a table of paired numbers based on a variable expression with one operation

Obj. 107 - Generate a table of paired numbers based on a variable expression with two operations

Obj. 108 - Determine the variable expression with one operation for a table of paired numbersObj. 109 - WP: Generate a table of paired numbers based on a variable expression with one operation

Obj. 110 - WP: Determine the variable expression with one operation for a table of paired numbers

NJ 4.3.5 B - Functions & RelationshipsNJ 4.3.5 B.1 - By the end of grade 5, the student will: Describe arithmetic operations as functions, including combining operations and reversing them.NJ 4.3.5 B.2 - By the end of grade 5, the student will: Graph points satisfying a function from T-charts, from verbal rules, and from simple equations.


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NJ 4.3.5 C - ModelingNJ 4.3.5 C.1 - By the end of grade 5, the student will: Use number sentences to model situations.NJ 4.3.5 C.1.a - By the end of grade 5, the student will: Use number sentences to model situations. Using variables to represent unknown quantities

Topic 2 - Algebra Obj. 98 - Use a variable expression with one operation to represent a verbal expression

Obj. 100 - WP: Use a variable expression with one operation to represent a situation

NJ 4.3.5 C.1.b - By the end of grade 5, the student will: Use number sentences to model situations. Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations


Obj. 99 - Use a verbal expression to represent a variable expression with one operationObj. 100 - WP: Use a variable expression with one operation to represent a situationObj. 106 - Generate a table of paired numbers based on a variable expression with one operation

Obj. 107 - Generate a table of paired numbers based on a variable expression with two operations

Obj. 108 - Determine the variable expression with one operation for a table of paired numbersObj. 109 - WP: Generate a table of paired numbers based on a variable expression with one operation

Obj. 110 - WP: Determine the variable expression with one operation for a table of paired numbersObj. 111 - Use a first quadrant graph to represent the values from a table generated in context


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NJ 4.3.5 C.2 - By the end of grade 5, the student will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.NJ 4.3.5 C.2.a - By the end of grade 5, the student will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. Changes over timeNJ 4.3.5 C.2.b - By the end of grade 5, the student will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

NJ 4.3.5 D - ProceduresNJ 4.3.5 D.1 - By the end of grade 5, the student will: Solve simple linear equations with manipulatives and informallyNJ 4.3.5 D.1.a - By the end of grade 5, the student will: Solve simple linear equations with manipulatives and informally Whole-number coefficients only, answers also whole numbers

NJ 4.3.5 D.1.b - By the end of grade 5, the student will: Solve simple linear equations with manipulatives and informally Variables on one side of equationNJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.5 A - Data AnalysisNJ 4.4.5 A.1 - By the end of grade 5, the student will: Collect, generate, organize, and display data.


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NJ 4.4.5 A.1.a - By the end of grade 5, the student will: Collect, generate, organize, and display data. Data generated from surveysNJ 4.4.5 A.2 - By the end of grade 5, the student will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

NJ 4.4.5 A.2.a - By the end of grade 5, the student will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. Bar graph, line graph, circle graph, table


Obj. 152 - Answer a question using information from a line graph that does not start at zero or has a broken vertical scale

Obj. 153 - WP: Extend a line graph to solve a problemObj. 154 - Read a double- or stacked-bar graphObj. 155 - Use a double- or stacked-bar graph to represent data

Obj. 156 - Answer a question using information from a double- or stacked-bar graphObj. 157 - Use information from a table or a chart to solve a problem

NJ 4.4.5 A.2.b - By the end of grade 5, the student will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. Range, median, and mean


Obj. 160 - Determine the range from a graph

Obj. 161 - Determine the mean of a set of whole number data, whole number resultsObj. 162 - Determine the median of an odd number of data valuesObj. 164 - Determine the range of a set of whole number data

NJ 4.4.5 A.3 - By the end of grade 5, the student will: Respond to questions about data and generate their own questions and hypotheses.

NJ 4.4.5 B - ProbabilityNJ 4.4.5 B.1 - By the end of grade 5, the student will: Determine probabilities of events.


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NJ 4.4.5 B.1.a - By the end of grade 5, the student will: Determine probabilities of events. Event, probability of an event


Obj. 167 - Determine the probability of a single event given the total number of possible outcomes

NJ 4.4.5 B.1.b - By the end of grade 5, the student will: Determine probabilities of events. Probability of certain event is 1 and of impossible event is 0NJ 4.4.5 B.2 - By the end of grade 5, the student will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).

NJ 4.4.5 B.2.a - By the end of grade 5, the student will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked

NJ 4.4.5 B.2.b - By the end of grade 5, the student will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Given data obtained experimentally, what is the likely distribution of items in the bag

NJ 4.4.5 B.3 - By the end of grade 5, the student will: Model situations involving probability using simulations (with spinners, dice) and theoretical models.NJ 4.4.5 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.5 C.1 - By the end of grade 5, the student will: Solve counting problems and justify that all possibilities have been enumerated without duplication.


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NJ 4.4.5 C.1.a - By the end of grade 5, the student will: Solve counting problems and justify that all possibilities have been enumerated without duplication. Organized lists, charts, tree diagrams, tables


Obj. 165 - Determine all possible outcomes of a compound event using a list

Obj. 166 - Determine all possible outcomes of a compound event using a tree diagram

NJ 4.4.5 C.2 - By the end of grade 5, the student will: Explore the multiplication principle of counting in simple situations by representing all possibilities in an organized way (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).

NJ 4.4.5 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.5 D.1 - By the end of grade 5, the student will: Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.

NJ 4.5 - All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the end of grade 5, the student will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of grade 5, the student will: Solve problems that arise in mathematics and in other contexts.


Obj. 12 - WP: Multiply a 3- or 4-digit whole number by a 3-digit whole number

Obj. 23 - WP: Divide a whole number, with no remainderObj. 24 - WP: Divide a whole number and interpret the remainder


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Obj. 25 - WP: Solve a 2-step problem involving whole numbersObj. 29 - WP: Estimate a quotient using any methodObj. 45 - WP: Add or subtract fractions with like denominators and simplify the sum or differenceObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 53 - WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference


Obj. 58 - WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1Obj. 80 - WP: Add or subtract decimal numbers through thousandthsObj. 81 - WP: Add or subtract a decimal number through thousandths and a whole numberObj. 85 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any methodObj. 89 - WP: Multiply a money amount by a 2-digit whole number

NJ 4.5 A.2.a - By the end of grade 5, the student will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5 A.2.b - By the end of grade 5, the student will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5 A.2.c - By the end of grade 5, the student will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutions


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NJ 4.5 A.2.d - By the end of grade 5, the student will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the end of grade 5, the student will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.


Obj. 57 - Estimate a fraction difference using benchmark numbers 0, 1/2, and 1

Obj. 58 - WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1

NJ 4.5 A.4 - By the end of grade 5, the student will: Pose problems of various types and levels of difficulty.

NJ 4.5 A.5 - By the end of grade 5, the student will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5 A.6 - By the end of grade 5, the student will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of grade 5, the student will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of grade 5, the student will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.b - By the end of grade 5, the student will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5 B.2 - By the end of grade 5, the student will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.


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NJ 4.5 B.3 - By the end of grade 5, the student will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the end of grade 5, the student will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the end of grade 5, the student will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the end of grade 5, the student will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of grade 5, the student will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of grade 5, the student will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of grade 5, the student will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the end of grade 5, the student will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of grade 5, the student will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the end of grade 5, the student will: Use reasoning to support their mathematical conclusions and problem solutions.


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NJ 4.5 D.3 - By the end of grade 5, the student will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the end of grade 5, the student will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5 D.5 - By the end of grade 5, the student will: Make and investigate mathematical conjectures.

NJ 4.5 D.5.a - By the end of grade 5, the student will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5 D.5.b - By the end of grade 5, the student will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5 D.6 - By the end of grade 5, the student will: Evaluate examples of mathematical reasoning and determine whether they are valid.

NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of grade 5, the student will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.a - By the end of grade 5, the student will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)

NJ 4.5 E.1.b - By the end of grade 5, the student will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


Obj. 157 - Use information from a table or a chart to solve a problem


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NJ 4.5 E.1.c - By the end of grade 5, the student will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)


Obj. 100 - WP: Use a variable expression with one operation to represent a situationObj. 108 - Determine the variable expression with one operation for a table of paired numbersObj. 110 - WP: Determine the variable expression with one operation for a table of paired numbers

NJ 4.5 E.1.d - By the end of grade 5, the student will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)


Obj. 152 - Answer a question using information from a line graph that does not start at zero or has a broken vertical scale

Obj. 153 - WP: Extend a line graph to solve a problemObj. 154 - Read a double- or stacked-bar graphObj. 155 - Use a double- or stacked-bar graph to represent data

Obj. 156 - Answer a question using information from a double- or stacked-bar graph

NJ 4.5 E.2 - By the end of grade 5, the student will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the end of grade 5, the student will: Use representations to model and interpret physical, social, and mathematical phenomena.NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of grade 5, the student will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of grade 5, the student will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.


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NJ 4.5 F.3 - By the end of grade 5, the student will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the end of grade 5, the student will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5 F.5 - By the end of grade 5, the student will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5 F.6 - By the end of grade 5, the student will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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NJ 4.1.6 A.1.a - By the end of Grade 6, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well). All integers

NJ 4.1.6 A.1.b - By the end of Grade 6, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well). All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

NJ 4.1.6 A.1.c - By the end of Grade 6, students will: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well). All decimals

NJ 4.1.6 A.2 - By the end of Grade 6, students will: Recognize the decimal nature of United States currency and compute with money.NJ 4.1.6 A.3 - By the end of Grade 6, students will: Demonstrate a sense of the relative magnitudes of numbers.



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NJ 4.1.6 A.4 - By the end of Grade 6, students will: Explore the use of ratios and proportions in a variety of situations.


Obj. 81 - WP: Determine a ratio using whole numbers less than 50

Obj. 82 - Determine if ratios, using whole numbers less than 50, are equivalentObj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50Obj. 84 - WP: Determine a part given a ratio and another part where the whole is less than 50Obj. 85 - WP: Determine the whole given a ratio and a part where the whole is less than 50

Topic 2 - Algebra Obj. 102 - Solve a proportionNJ 4.1.6 A.5 - By the end of Grade 6, students will: Understand and use whole-number percents between 1 and 100 in a variety of situations.


Obj. 71 - Determine the approximate percent of a region shaded

NJ 4.1.6 A.6 - By the end of Grade 6, students will: Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.


Obj. 68 - Convert a mixed number to a decimal number

Obj. 69 - Convert a decimal number to a mixed numberObj. 70 - Convert a fraction to a repeating decimal number

NJ 4.1.6 A.7 - By the end of Grade 6, students will: Develop and apply number theory concepts in problem solving situations.NJ 4.1.6 A.7.a - By the end of Grade 6, students will: Develop and apply number theory concepts in problem solving situations. Primes, factors, multiples


Obj. 1 - Determine the prime factorization of a number between 50 and 200

NJ 4.1.6 A.7.b - By the end of Grade 6, students will: Develop and apply number theory concepts in problem solving situations. Common multiples, common factors


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NJ 4.1.6 A.7.c - By the end of Grade 6, students will: Develop and apply number theory concepts in problem solving situations. Least common multiple, greatest common factor


Obj. 2 - Determine the greatest common factor of three numbers to 100

Obj. 3 - Determine the least common multiple of three numbersObj. 4 - WP: Determine the least common multiple of two or more numbers

NJ 4.1.6 A.8 - By the end of Grade 6, students will: Compare and order numbers.


Obj. 76 - Compare numbers in decimal and fractional forms

Obj. 77 - Order numbers in decimal and fractional formsObj. 90 - Compare two negative integers or a negative integer and a positive integerObj. 91 - Order negative integers or a mix of positive and negative integers

NJ 4.1.6 B - Numerical OperationsNJ 4.1.6 B.1 - By the end of Grade 6, students will: Recognize the appropriate use of each arithmetic operation in problem situations.NJ 4.1.6 B.2 - By the end of Grade 6, students will: Construct, use, and explain procedures for performing calculations with fractions and decimals with:NJ 4.1.6 B.2.a - By the end of Grade 6, students will: Construct, use, and explain procedures for performing calculations with fractions and decimals with: Pencil-and-paper


Obj. 13 - Add fractions with unlike denominators and simplify the sum

Obj. 14 - Subtract fractions with unlike denominators and simplify the differenceObj. 15 - Subtract a fraction from a whole numberObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 17 - Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum


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Obj. 18 - Subtract a mixed number from a whole numberObj. 19 - Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the differenceObj. 20 - Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer

Obj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference

Obj. 22 - Multiply a fraction by a fractionObj. 23 - Multiply a mixed number by a whole numberObj. 24 - Multiply a mixed number by a fractionObj. 25 - Multiply a mixed number by a mixed numberObj. 28 - Divide a fraction by a whole number resulting in a fractional quotientObj. 29 - Divide a fraction by a fractionObj. 30 - Divide a whole number by a fraction resulting in a fractional quotientObj. 31 - Divide a mixed number by a fractionObj. 32 - Divide a mixed number by a mixed numberObj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 40 - Add three decimal numbers

Obj. 41 - Add and subtract three decimal numbersObj. 42 - WP: Add and subtract three decimal numbers


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Obj. 43 - Multiply a decimal number through thousandths by a whole numberObj. 44 - WP: Multiply a decimal number through thousandths by a whole numberObj. 45 - WP: Multiply a money expression by a decimal numberObj. 46 - Multiply a decimal number greater than one, in tenths, by a decimal number in tenthsObj. 47 - Multiply decimal numbers to thousandths using basic facts

Obj. 48 - Multiply decimal numbers less than one in hundredths or thousandthsObj. 49 - Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digitObj. 50 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Obj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 53 - Divide a decimal number by 10, 100, or 1,000Obj. 54 - Relate division by a whole number power of ten to multiplication by the related decimal fraction power of tenObj. 55 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal placesObj. 56 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberObj. 57 - Divide a whole number or a decimal number by 0.1, 0.01, or 0.001Obj. 60 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole number


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Obj. 61 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Obj. 62 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed

Obj. 63 - Divide a decimal number by a decimal number through thousandths, rounded quotient if neededObj. 64 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if needed

NJ 4.1.6 B.2.b - By the end of Grade 6, students will: Construct, use, and explain procedures for performing calculations with fractions and decimals with: Mental math


Obj. 53 - Divide a decimal number by 10, 100, or 1,000

Obj. 54 - Relate division by a whole number power of ten to multiplication by the related decimal fraction power of tenObj. 57 - Divide a whole number or a decimal number by 0.1, 0.01, or 0.001

NJ 4.1.6 B.2.c - By the end of Grade 6, students will: Construct, use, and explain procedures for performing calculations with fractions and decimals with: Calculator

NJ 4.1.6 B.3 - By the end of Grade 6, students will: Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.


Obj. 9 - Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths



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Obj. 11 - WP: Divide a whole number by a 1- or 2-digit whole number resulting in a decimal quotient






Obj. 13 - Add fractions with unlike denominators and simplify the sumObj. 14 - Subtract fractions with unlike denominators and simplify the differenceObj. 15 - Subtract a fraction from a whole numberObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 17 - Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sumObj. 18 - Subtract a mixed number from a whole numberObj. 19 - Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the differenceObj. 20 - Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer

Obj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference


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Obj. 22 - Multiply a fraction by a fractionObj. 23 - Multiply a mixed number by a whole numberObj. 24 - Multiply a mixed number by a fractionObj. 25 - Multiply a mixed number by a mixed numberObj. 28 - Divide a fraction by a whole number resulting in a fractional quotientObj. 29 - Divide a fraction by a fractionObj. 30 - Divide a whole number by a fraction resulting in a fractional quotientObj. 31 - Divide a mixed number by a fractionObj. 32 - Divide a mixed number by a mixed numberObj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 40 - Add three decimal numbers

Obj. 41 - Add and subtract three decimal numbersObj. 42 - WP: Add and subtract three decimal numbersObj. 43 - Multiply a decimal number through thousandths by a whole numberObj. 44 - WP: Multiply a decimal number through thousandths by a whole numberObj. 45 - WP: Multiply a money expression by a decimal numberObj. 46 - Multiply a decimal number greater than one, in tenths, by a decimal number in tenthsObj. 47 - Multiply decimal numbers to thousandths using basic facts

Obj. 48 - Multiply decimal numbers less than one in hundredths or thousandths


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Obj. 49 - Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digitObj. 50 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Obj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 53 - Divide a decimal number by 10, 100, or 1,000Obj. 55 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal placesObj. 56 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberObj. 57 - Divide a whole number or a decimal number by 0.1, 0.01, or 0.001Obj. 60 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberObj. 61 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Obj. 62 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed

Obj. 63 - Divide a decimal number by a decimal number through thousandths, rounded quotient if neededObj. 64 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededObj. 67 - WP: Solve a 2-step problem involving decimals


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NJ 4.1.6 B.5 - By the end of Grade 6, students will: Find squares and cubes of whole numbers.


Obj. 7 - Determine the square of a whole number to 15

Obj. 8 - Determine the cube of a whole number to 15

NJ 4.1.6 B.6 - By the end of Grade 6, students will: Check the reasonableness of results of computations.NJ 4.1.6 B.7 - By the end of Grade 6, students will: Understand and use the various relationships among operations and properties of operations.

Topic 2 - Algebra Obj. 92 - Determine which property of addition or multiplication justifies a step in the simplification of an expression

NJ 4.1.6 B.8 - By the end of Grade 6, students will: Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses.


Obj. 88 - Evaluate a numerical expression of four or more operations, with parentheses, using order of operations

NJ 4.1.6 C - EstimationNJ 4.1.6 C.1 - By the end of Grade 6, students will: Use a variety of strategies for estimating both quantities and the results of computations.


Obj. 52 - WP: Estimate the product of two decimals

Obj. 66 - WP: Estimate the quotient of two decimals

NJ 4.1.6 C.2 - By the end of Grade 6, students will: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.NJ 4.1.6 C.3 - By the end of Grade 6, students will: Determine the reasonableness of an answer by estimating the result of operations.NJ 4.1.6 C.4 - By the end of Grade 6, students will: Determine whether a given estimate is an overestimate or an underestimate.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.6 A - Geometric Properties


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NJ 4.2.6 A.1 - By the end of Grade 6, students will: Understand and apply concepts involving lines and angles.

NJ 4.2.6 A.1.a - By the end of Grade 6, students will: Understand and apply concepts involving lines and angles. Notation for line, ray, angle, line segmentNJ 4.2.6 A.1.b - By the end of Grade 6, students will: Understand and apply concepts involving lines and angles. Properties of parallel, perpendicular, and intersecting lines


Obj. 130 - Identify parallel, perpendicular, or intersecting lines

NJ 4.2.6 A.1.c - By the end of Grade 6, students will: Understand and apply concepts involving lines and angles. Sum of the measures of the interior angles of a triangle is 180°

NJ 4.2.6 A.2 - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles.NJ 4.2.6 A.2.a - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles. Triangles by angles and sides


Obj. 132 - Know the properties of a triangle or a quadrilateral

NJ 4.2.6 A.2.b - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi


Obj. 132 - Know the properties of a triangle or a quadrilateral

NJ 4.2.6 A.2.c - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles. Polygons by number of sides.

NJ 4.2.6 A.2.d - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles. Equilateral, equiangular, regular


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NJ 4.2.6 A.2.e - By the end of Grade 6, students will: Identify, describe, compare, and classify polygons and circles. All points equidistant from a given point form a circle

NJ 4.2.6 A.3 - By the end of Grade 6, students will: Identify similar figures.

NJ 4.2.6 A.4 - By the end of Grade 6, students will: Understand and apply the concepts of congruence and symmetry (line and rotational).


Obj. 133 - Identify congruent shapes shown on a grid or within pattern block arrangements, with different orientationsObj. 135 - Use symmetry to determine a length or an angle measure

NJ 4.2.6 A.5 - By the end of Grade 6, students will: Compare properties of cylinders, prisms, cones, pyramids, and spheres.NJ 4.2.6 A.6 - By the end of Grade 6, students will: Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.NJ 4.2.6 A.7 - By the end of Grade 6, students will: Identify a three-dimensional shape with given projections (top, front and side views).NJ 4.2.6 A.8 - By the end of Grade 6, students will: Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).NJ 4.2.6 B - Transforming ShapesNJ 4.2.6 B.1 - By the end of Grade 6, students will: Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.


Obj. 136 - Determine the result of a reflection, a rotation, or a translation on the Cartesian plane

Obj. 137 - Determine the transformation that generates the image of a figure in the Cartesian plane


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NJ 4.2.6 B.2 - By the end of Grade 6, students will: Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

NJ 4.2.6 C - Coordinate GeometryNJ 4.2.6 C.1 - By the end of Grade 6, students will: Create geometric shapes with specified properties in the first quadrant on a coordinate grid.NJ 4.2.6 D - Units of MeasurementNJ 4.2.6 D.1 - By the end of Grade 6, students will: Select and use appropriate units to measure angles, area, surface area, and volume.

NJ 4.2.6 D.2 - By the end of Grade 6, students will: Use a scale to find a distance on a map or a length on a scale drawing.NJ 4.2.6 D.3 - By the end of Grade 6, students will: Convert measurement units within a system (e.g., 3 feet = ___ inches).


Obj. 117 - Convert between Fahrenheit and Celsius temperature given a formula

NJ 4.2.6 D.4 - By the end of Grade 6, students will: Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).NJ 4.2.6 D.5 - By the end of Grade 6, students will: Use measurements and estimates to describe and compare phenomena.NJ 4.2.6 E - Measuring Geometric ObjectsNJ 4.2.6 E.1 - By the end of Grade 6, students will: Use a protractor to measure angles.


Obj. 119 - Measure an angle, between two rays or in a shape, to the nearest degree

NJ 4.2.6 E.2 - By the end of Grade 6, students will: Develop and apply strategies and formulas for finding perimeter and area.NJ 4.2.6 E.2.a - By the end of Grade 6, students will: Develop and apply strategies and formulas for finding perimeter and area. Triangle, square, rectangle, parallelogram, and trapezoid


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NJ 4.2.6 E.2.b - By the end of Grade 6, students will: Develop and apply strategies and formulas for finding perimeter and area. Circumference and area of a circle


Obj. 124 - Determine the circumference of a circle using 22/7 for pi

Obj. 125 - Determine the circumference of a circle using 3.14 for piObj. 126 - WP: Determine the circumference of a circle

NJ 4.2.6 E.3 - By the end of Grade 6, students will: Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders.NJ 4.2.6 E.4 - By the end of Grade 6, students will: Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa.NJ 4.2.6 E.5 - By the end of Grade 6, students will: Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.6 A - PatternsNJ 4.3.6 A.1 - By the end of Grade 6, students will: Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.NJ 4.3.6 A.1.a - By the end of Grade 6, students will: Recognize, describe, extend, and create patterns involving whole numbers and rational numbers. Descriptions using tables, verbal rules, simple equations, and graphs


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NJ 4.3.6 A.1.b - By the end of Grade 6, students will: Recognize, describe, extend, and create patterns involving whole numbers and rational numbers. Formal iterative formulas (e.g., NEXT = NOW * 3)

NJ 4.3.6 A.1.c - By the end of Grade 6, students will: Recognize, describe, extend, and create patterns involving whole numbers and rational numbers. Recursive patterns, including Pascal's Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8,... (where NEXT = NOW + PREVIOUS)

NJ 4.3.6 B - Functions and RelationshipsNJ 4.3.6 B.1 - By the end of Grade 6, students will: Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).

NJ 4.3.6 C - ModelingNJ 4.3.6 C.1 - By the end of Grade 6, students will: Use patterns, relations, and linear functions to model situations.NJ 4.3.6 C.1.a - By the end of Grade 6, students will: Use patterns, relations, and linear functions to model situations. Using variables to represent unknown quantities

NJ 4.3.6 C.1.b - By the end of Grade 6, students will: Use patterns, relations, and linear functions to model situations. Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

Topic 2 - Algebra Obj. 93 - Use a variable expression with two operations to represent a verbal expression

Obj. 94 - Use a verbal expression to represent a variable expression with two operationsObj. 95 - WP: Use a variable expression with two operations to represent a situation


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Obj. 96 - WP: Use a 2-variable equation to represent a situation involving a direct proportionObj. 97 - WP: Use a 2-variable linear equation to represent a situation

Obj. 103 - WP: Generate a table of paired numbers based on a variable expression with two operations

Obj. 104 - Use a 2-variable equation to construct an input-output table

Obj. 105 - Use a 2-variable equation to represent a relationship expressed in a tableObj. 106 - Use a first quadrant graph to represent the values in an input-output tableObj. 107 - Use a graph to determine the entries in an input-output table

NJ 4.3.6 C.2 - By the end of Grade 6, students will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.NJ 4.3.6 C.2.a - By the end of Grade 6, students will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. Changes over timeNJ 4.3.6 C.2.b - By the end of Grade 6, students will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. Relations between quantities

NJ 4.3.6 C.2.c - By the end of Grade 6, students will: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events. Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

NJ 4.3.6 D - Procedures


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NJ 4.3.6 D.1 - By the end of Grade 6, students will: Solve simple linear equations with manipulatives and informally.NJ 4.3.6 D.1.a - By the end of Grade 6, students will: Solve simple linear equations with manipulatives and informally. Whole-number coefficients only, answers also whole numbers

Topic 2 - Algebra Obj. 101 - Solve a 1-step equation involving whole numbers

NJ 4.3.6 D.1.b - By the end of Grade 6, students will: Solve simple linear equations with manipulatives and informally. Variables on one or both sides of equation

NJ 4.3.6 D.2 - By the end of Grade 6, students will: Understand and apply the properties of operations and numbers.

Topic 2 - Algebra Obj. 92 - Determine which property of addition or multiplication justifies a step in the simplification of an expression

NJ 4.3.6 D.2.a - By the end of Grade 6, students will: Understand and apply the properties of operations and numbers. Distributive property

NJ 4.3.6 D.2.b - By the end of Grade 6, students will: Understand and apply the properties of operations and numbers. The product of a number and its reciprocal is 1

NJ 4.3.6 D.3 - By the end of Grade 6, students will: Evaluate numerical expressions.


Obj. 88 - Evaluate a numerical expression of four or more operations, with parentheses, using order of operations

NJ 4.3.6 D.4 - By the end of Grade 6, students will: Extend understanding and use of inequality.

NJ 4.3.6 D.4.a - By the end of Grade 6, students will: Extend understanding and use of inequality. Symbols (greater than or equal to, not equal to, less than or equal to)


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.6 A - Data AnalysisNJ 4.4.6 A.1 - By the end of Grade 6, students will: Collect, generate, organize, and display data.NJ 4.4.6 A.1.a - By the end of Grade 6, students will: Collect, generate, organize, and display data. Data generated from surveysNJ 4.4.6 A.2 - By the end of Grade 6, students will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

NJ 4.4.6 A.2.a - By the end of Grade 6, students will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. Bar graph, line graph, circle graph, table, histogram


Obj. 140 - Read a double-line graph

Obj. 141 - Answer a question using information from a double-line graph

Obj. 145 - Use a frequency table to represent 2 related data setsObj. 146 - Answer a question using information from a frequency table representing 2 related data sets

NJ 4.4.6 A.2.b - By the end of Grade 6, students will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. Range, median, and mean


Obj. 147 - Determine the mean of a set of whole number data

Obj. 148 - Determine the median of a set of whole number data


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NJ 4.4.6 A.2.c - By the end of Grade 6, students will: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data. Calculators and computers used to record and process information

NJ 4.4.6 A.3 - By the end of Grade 6, students will: Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.

NJ 4.4.6 B - ProbabilityNJ 4.4.6 B.1 - By the end of Grade 6, students will: Determine probabilities of events.NJ 4.4.6 B.1.a - By the end of Grade 6, students will: Determine probabilities of events. Event, complementary event, probability of an event


Obj. 152 - Determine the probability of a single event

Obj. 153 - Determine the probability of the complement of a single event

NJ 4.4.6 B.1.b - By the end of Grade 6, students will: Determine probabilities of events. Multiplication rule for probabilitiesNJ 4.4.6 B.1.c - By the end of Grade 6, students will: Determine probabilities of events. Probability of certain event is 1 and of impossible event is 0NJ 4.4.6 B.1.d - By the end of Grade 6, students will: Determine probabilities of events. Probabilities of event and complementary event add up to 1NJ 4.4.6 B.2 - By the end of Grade 6, students will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).


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NJ 4.4.6 B.2.a - By the end of Grade 6, students will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked

NJ 4.4.6 B.2.b - By the end of Grade 6, students will: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Given data obtained experimentally, what is the likely distribution of items in the bag

NJ 4.4.6 B.3 - By the end of Grade 6, students will: Explore compound events.NJ 4.4.6 B.4 - By the end of Grade 6, students will: Model situations involving probability using simulations (with spinners, dice) and theoretical models.NJ 4.4.6 B.5 - By the end of Grade 6, students will: Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.NJ 4.4.6 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.6 C.1 - By the end of Grade 6, students will: Solve counting problems and justify that all possibilities have been enumerated without duplication.NJ 4.4.6 C.1.a - By the end of Grade 6, students will: Solve counting problems and justify that all possibilities have been enumerated without duplication. Organized lists, charts, tree diagrams, tables


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NJ 4.4.6 C.1.b - By the end of Grade 6, students will: Solve counting problems and justify that all possibilities have been enumerated without duplication. Venn diagrams

NJ 4.4.6 C.2 - By the end of Grade 6, students will: Apply the multiplication principle of counting.NJ 4.4.6 C.2.a - By the end of Grade 6, students will: Apply the multiplication principle of counting. Simple situations (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).


Obj. 157 - Determine the number of possible combinations of a set of objects

NJ 4.4.6 C.2.b - By the end of Grade 6, students will: Apply the multiplication principle of counting. Number of ways a specified number of items can be arranged in order (concept of permutation)NJ 4.4.6 C.2.c - By the end of Grade 6, students will: Apply the multiplication principle of counting. Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)

NJ 4.4.6 C.3 - By the end of Grade 6, students will: List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person's hand once).


Obj. 157 - Determine the number of possible combinations of a set of objects



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NJ 4.4.6 D.1 - By the end of Grade 6, students will: Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.

NJ 4.4.6 D.2 - By the end of Grade 6, students will: Analyze vertex-edge graphs and tree diagrams.NJ 4.4.6 D.2.a - By the end of Grade 6, students will: Analyze vertex-edge graphs and tree diagrams. Can a picture or a vertex-edge graph be drawn with a single line? (degree of vertex)NJ 4.4.6 D.2.b - By the end of Grade 6, students will: Analyze vertex-edge graphs and tree diagrams. Can you get from any vertex to any other vertex? (connectedness)

NJ 4.4.6 D.3 - By the end of Grade 6, students will: Use vertex-edge graphs to find solutions to practical problems.NJ 4.4.6 D.3.a - By the end of Grade 6, students will: Use vertex-edge graphs to find solutions to practical problems. Delivery route that stops at specified sites but involves least travelNJ 4.4.6 D.3.b - By the end of Grade 6, students will: Use vertex-edge graphs to find solutions to practical problems. Shortest route from one site on a map to anotherNJ 4.5 - All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

NJ 4.5 A - Problem Solving


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NJ 4.5 A.1 - By the end of Grade 6, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of Grade 6, students will: Solve problems that arise in mathematics and in other contexts.



Obj. 12 - WP: Solve a multi-step problem involving whole numbersObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference

Obj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 42 - WP: Add and subtract three decimal numbersObj. 44 - WP: Multiply a decimal number through thousandths by a whole numberObj. 45 - WP: Multiply a money expression by a decimal numberObj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 56 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberObj. 64 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededObj. 67 - WP: Solve a 2-step problem involving decimals


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NJ 4.5 A.2.a - By the end of Grade 6, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems


NJ 4.5 A.2.c - By the end of Grade 6, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutionsNJ 4.5 A.2.d - By the end of Grade 6, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the end of Grade 6, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the end of Grade 6, students will: Pose problems of various types and levels of difficulty.


NJ 4.5 A.6 - By the end of Grade 6, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of Grade 6, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of Grade 6, students will: Use communication to organize and clarify their mathematical thinking. Reading and writing


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NJ 4.5 B.1.b - By the end of Grade 6, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning


NJ 4.5 B.3 - By the end of Grade 6, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the end of Grade 6, students will: Use the language of mathematics to express mathematical ideas precisely.

Topic 2 - Algebra Obj. 93 - Use a variable expression with two operations to represent a verbal expression

Obj. 105 - Use a 2-variable equation to represent a relationship expressed in a table

NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the end of Grade 6, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the end of Grade 6, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of Grade 6, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of Grade 6, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of Grade 6, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).


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NJ 4.5 C.6 - By the end of Grade 6, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of Grade 6, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the end of Grade 6, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the end of Grade 6, students will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the end of Grade 6, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5 D.5 - By the end of Grade 6, students will: Make and investigate mathematical conjectures.


NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of Grade 6, students will: Create and use representations to organize, record, and communicate mathematical ideas.


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NJ 4.5 E.1.a - By the end of Grade 6, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)



Obj. 145 - Use a frequency table to represent 2 related data sets



Obj. 141 - Answer a question using information from a double-line graph


NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of Grade 6, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of Grade 6, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the end of Grade 6, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.


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NJ 4.5 F.4 - By the end of Grade 6, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).




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Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.7 A - Number SenseNJ 4.1.7 A.1 - By the end of Grade 7, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well):

NJ 4.1.7 A.1.a - By the end of Grade 7, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well): Rational numbersNJ 4.1.7 A.1.b - By the end of Grade 7, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well): Percents

NJ 4.1.7 A.1.c - By the end of Grade 7, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 7 pertain to these sets of numbers as well): Whole numbers with exponents

NJ 4.1.7 A.2 - By the end of Grade 7, students will: Demonstrate a sense of the relative magnitudes of numbers.

NJ 4.1.7 A.3 - By the end of Grade 7, students will: Understand and use ratios, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.


Obj. 18 - Determine a percent of a whole number using less than 100%



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Obj. 19 - Determine a percent of a whole number using more than 100%

Obj. 20 - Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 21 - Determine a whole number given a part and a percentage less than 100%Obj. 22 - WP: Determine a percent of a whole number using less than 100%Obj. 23 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 24 - WP: Determine a whole number given a part and a percentageObj. 25 - WP: Determine the percent of decrease applied to a number

Obj. 26 - WP: Determine the percent of increase applied to a number

Obj. 27 - WP: Determine the result of applying a percent of decrease to a valueObj. 28 - WP: Determine the result of applying a percent of increase to a valueObj. 29 - WP: Answer a question involving a fraction and a percentObj. 44 - WP: Determine the ratio of two whole numbers, at least one of which is larger than 50Obj. 45 - Determine ratios equivalent to a given ratio of two whole numbers, at least one of which is larger than 50Obj. 46 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Obj. 47 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50


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Obj. 48 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50Obj. 49 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50Obj. 50 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Obj. 51 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50

Topic 2 - Algebra Obj. 70 - Solve a proportion involving decimalsObj. 71 - WP: Solve a proportionObj. 72 - WP: Use direct variation to solve a problem

NJ 4.1.7 A.4 - By the end of Grade 7, students will: Compare and order numbers of all named types.


Obj. 59 - Compare rational numbers (positive and negative)

Obj. 60 - Order rational numbers (positive and negative)

NJ 4.1.7 A.5 - By the end of Grade 7, students will: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.


Obj. 12 - Convert a decimal number to a percentage greater than 100%

Obj. 13 - Convert a percentage to a decimal number greater than 1Obj. 14 - Convert a decimal number in thousandths to a percentage

Obj. 15 - Convert a percentage to a decimal number in thousandthsObj. 16 - Convert a mixed number to a percentageObj. 17 - Convert a percentage to a mixed number

NJ 4.1.7 A.6 - By the end of Grade 7, students will: Understand that all fractions can be represented as repeating or terminating decimals.NJ 4.1.7 B - Numerical OperationsNJ 4.1.7 B.1 - By the end of Grade 7, students will: Use and explain procedures for performing calculations with integers and all number types named above with:


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NJ 4.1.7 B.1.a - By the end of Grade 7, students will: Use and explain procedures for performing calculations with integers and all number types named above with: Pencil-and-paper


Obj. 18 - Determine a percent of a whole number using less than 100%

Obj. 19 - Determine a percent of a whole number using more than 100%

Obj. 20 - Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 21 - Determine a whole number given a part and a percentage less than 100%Obj. 22 - WP: Determine a percent of a whole number using less than 100%Obj. 23 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 24 - WP: Determine a whole number given a part and a percentageObj. 25 - WP: Determine the percent of decrease applied to a number

Obj. 26 - WP: Determine the percent of increase applied to a number

Obj. 27 - WP: Determine the result of applying a percent of decrease to a valueObj. 28 - WP: Determine the result of applying a percent of increase to a valueObj. 30 - WP: Answer a question involving a fraction and a decimalObj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbersObj. 37 - Add integersObj. 39 - Subtract integersObj. 40 - WP: Add and subtract using integersObj. 41 - Multiply integersObj. 42 - Divide integers


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NJ 4.1.7 B.1.b - By the end of Grade 7, students will: Use and explain procedures for performing calculations with integers and all number types named above with: Mental math


Obj. 37 - Add integers

Obj. 39 - Subtract integersObj. 41 - Multiply integersObj. 42 - Divide integers

NJ 4.1.7 B.1.c - By the end of Grade 7, students will: Use and explain procedures for performing calculations with integers and all number types named above with: CalculatorNJ 4.1.7 B.2 - By the end of Grade 7, students will: Use exponentiation to find whole number powers of numbers.


Obj. 1 - Determine the exponential notation that represents a repeated multiplication

Obj. 2 - Determine the repeated multiplication that is represented by a number raised to a powerObj. 5 - Evaluate a whole number power of a whole numberObj. 6 - Determine an exponential form of a whole number

NJ 4.1.7 B.3 - By the end of Grade 7, students will: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.


Obj. 11 - Evaluate a numerical expression, with parentheses and exponents, using order of operations

NJ 4.1.7 C - EstimationNJ 4.1.7 C.1 - By the end of Grade 7, students will: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.


Obj. 54 - Estimate the product of a fraction and a whole number

Obj. 55 - Estimate the quotient of a whole number divided by a fraction

Obj. 56 - WP: Estimate the result of dividing or multiplying a whole number by a fraction

NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.7 A - Geometric Properties


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NJ 4.2.7 A.1 - By the end of Grade 7, students will: Understand and apply properties of polygons.NJ 4.2.7 A.1.a - By the end of Grade 7, students will: Understand and apply properties of polygons. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombiNJ 4.2.7 A.1.b - By the end of Grade 7, students will: Understand and apply properties of polygons. Regular polygonsNJ 4.2.7 A.2 - By the end of Grade 7, students will: Understand and apply the concept of similarity.NJ 4.2.7 A.2.a - By the end of Grade 7, students will: Understand and apply the concept of similarity. Using proportions to find missing measures


Obj. 104 - Determine a missing dimension given two similar shapes

Obj. 105 - WP: Solve a problem involving similar shapes

NJ 4.2.7 A.2.b - By the end of Grade 7, students will: Understand and apply the concept of similarity. Scale drawings


Obj. 106 - Determine the scale for a drawing or map question

Obj. 107 - WP: Solve a problem involving a map or scale drawing

NJ 4.2.7 A.2.c - By the end of Grade 7, students will: Understand and apply the concept of similarity. Models of 3D objectsNJ 4.2.7 A.3 - By the end of Grade 7, students will: Use logic and reasoning to make and support conjectures about geometric objects.

NJ 4.2.7 B - Transforming ShapesNJ 4.2.7 B.1 - By the end of Grade 7, students will: Understand and apply transformations.NJ 4.2.7 B.1.a - By the end of Grade 7, students will: Understand and apply transformations. Finding the image, given the pre-image, and vice-versa


Obj. 121 - Determine the coordinates of a translated, a rotated, or a reflected shape on the Cartesian plane


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NJ 4.2.7 B.1.b - By the end of Grade 7, students will: Understand and apply transformations. Sequence of transformations needed to map one figure onto another

NJ 4.2.7 B.1.c - By the end of Grade 7, students will: Understand and apply transformations. Reflections, rotations, and translations result in images congruent to the pre-image

NJ 4.2.7 B.1.d - By the end of Grade 7, students will: Understand and apply transformations. Dilations (stretching/shrinking) result in images similar to the pre-image

NJ 4.2.7 C - Coordinate GeometryNJ 4.2.7 C.1 - By the end of Grade 7, students will: Use coordinates in four quadrants to represent geometric concepts.


Obj. 117 - Determine the location of a simple shape on the Cartesian plane given the coordinates of its verticesObj. 118 - Determine the coordinates of a missing point determined by geometric information

Obj. 119 - Determine a side length of a shape on the Cartesian plane

NJ 4.2.7 C.2 - By the end of Grade 7, students will: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).

NJ 4.2.7 D - Units of MeasurementNJ 4.2.7 D.1 - By the end of Grade 7, students will: Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").NJ 4.2.7 D.2 - By the end of Grade 7, students will: Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.NJ 4.2.7 D.3 - By the end of Grade 7, students will: Recognize that all measurements of continuous quantities are approximations.


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NJ 4.2.7 E - Measuring Geometric ObjectsNJ 4.2.7 E.1 - By the end of Grade 7, students will: Develop and apply strategies for finding perimeter and area.NJ 4.2.7 E.1.a - By the end of Grade 7, students will: Develop and apply strategies for finding perimeter and area. Geometric figures made by combining triangles, rectangles and circles or parts of circles

NJ 4.2.7 E.1.b - By the end of Grade 7, students will: Develop and apply strategies for finding perimeter and area. Estimation of area using grids of various sizes


Obj. 87 - Estimate the area of an irregular shape or a circle on a grid

NJ 4.2.7 E.2 - By the end of Grade 7, students will: Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).


Obj. 96 - WP: Solve a problem involving the volume of a geometric solid

NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.7 A - PatternsNJ 4.3.7 A.1 - By the end of Grade 7, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.NJ 4.3.7 A.1.a - By the end of Grade 7, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions


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NJ 4.3.7 A.1.b - By the end of Grade 7, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Finite and infinite sequencesNJ 4.3.7 A.1.c - By the end of Grade 7, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Generating sequences by using calculators to repeatedly apply a formula

NJ 4.3.7 B - Functions and RelationshipsNJ 4.3.7 B.1 - By the end of Grade 7, students will: Graph functions, and understand and describe their general behavior.NJ 4.3.7 B.1.a - By the end of Grade 7, students will: Graph functions, and understand and describe their general behavior. Equations involving two variablesNJ 4.3.7 C - ModelingNJ 4.3.7 C.1 - By the end of Grade 7, students will: Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

NJ 4.3.7 C.2 - By the end of Grade 7, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations.

NJ 4.3.7 C.2.a - By the end of Grade 7, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations. Using manipulatives, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

Topic 2 - Algebra Obj. 68 - Use a variable expression with two operations to represent a table of paired numbers

Obj. 69 - WP: Use a 2-variable expression to represent a situationObj. 75 - WP: Use a 1-variable 1-step equation to represent a situation


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Obj. 80 - WP: Use a 1-variable linear inequality to represent a situation

Obj. 81 - Use a table to represent a linear functionObj. 82 - Use a graph to represent the ordered pairs in a function table

NJ 4.3.7 C.2.b - By the end of Grade 7, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations. Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

NJ 4.3.7 D - ProceduresNJ 4.3.7 D.1 - By the end of Grade 7, students will: Use graphing techniques on a number line.NJ 4.3.7 D.1.a - By the end of Grade 7, students will: Use graphing techniques on a number line. Absolute value


Obj. 33 - Evaluate the absolute value of an integer

NJ 4.3.7 D.1.b - By the end of Grade 7, students will: Use graphing techniques on a number line. Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is "left 3, right 6")NJ 4.3.7 D.2 - By the end of Grade 7, students will: Solve simple linear equations informally and graphically.

Topic 2 - Algebra Obj. 73 - Solve a 1-step linear equation involving integers

Obj. 83 - Determine the graph of a 1-operation linear function

NJ 4.3.7 D.2.a - By the end of Grade 7, students will: Solve simple linear equations informally and graphically. Multi-step, integer coefficients only (although answers may not be integers)


NJ 4.3.7 D.2.b - By the end of Grade 7, students will: Solve simple linear equations informally and graphically. Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology



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NJ 4.3.7 D.3 - By the end of Grade 7, students will: Create, evaluate, and simplify algebraic expressions involving variables.NJ 4.3.7 D.3.a - By the end of Grade 7, students will: Create, evaluate, and simplify algebraic expressions involving variables. Order of operations, including appropriate use of parenthesesNJ 4.3.7 D.3.b - By the end of Grade 7, students will: Create, evaluate, and simplify algebraic expressions involving variables. Substitution of a number for a variable

Topic 2 - Algebra Obj. 61 - Evaluate a rational expression involving variables with two or more terms in the numerator or denominator

Obj. 62 - Evaluate a 1-variable expression, with two or three operations, using integer substitution

Obj. 63 - Evaluate a 2-variable expression, with two or three operations, using integer substitution

Obj. 64 - Evaluate an algebraic expression involving whole number exponentsObj. 65 - WP: Evaluate a variable expressionObj. 66 - WP: Evaluate a variable expression involving exponents

NJ 4.3.7 D.4 - By the end of Grade 7, students will: Understand and apply the properties of operations, numbers, equations, and inequalities.

NJ 4.3.7 D.4.a - By the end of Grade 7, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Additive inverse


Obj. 34 - Determine the opposite of an integer

NJ 4.3.7 D.4.b - By the end of Grade 7, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Multiplicative inverse


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.7 A - Data AnalysisNJ 4.4.7 A.1 - By the end of Grade 7, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).


Obj. 132 - Determine the mean of a set of data

Obj. 133 - Determine the mode(s) of a set of dataObj. 134 - Determine the median of a set of dataObj. 135 - WP: Use the mean of a data set to solve a problem

NJ 4.4.7 A.1.a - By the end of Grade 7, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Type of display most appropriate for given dataNJ 4.4.7 A.1.b - By the end of Grade 7, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Box-and-whisker plot, upper quartile, lower quartileNJ 4.4.7 A.1.c - By the end of Grade 7, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Scatter plotNJ 4.4.7 A.1.d - By the end of Grade 7, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Calculators and computer used to record and process information


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NJ 4.4.7 A.2 - By the end of Grade 7, students will: Make inferences and formulate and evaluate arguments based on displays and analysis of data.NJ 4.4.7 B - ProbabilityNJ 4.4.7 B.1 - By the end of Grade 7, students will: Interpret probabilities as ratios, percents, and decimals.

NJ 4.4.7 B.2 - By the end of Grade 7, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.

NJ 4.4.7 B.2.a - By the end of Grade 7, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models. Frequency, relative frequency

NJ 4.4.7 B.3 - By the end of Grade 7, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.7 B.4 - By the end of Grade 7, students will: Play and analyze probability-based games, and discuss the concepts of fairness and expected value.NJ 4.4.7 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.7 C.1 - By the end of Grade 7, students will: Apply the multiplication principle of counting.NJ 4.4.7 C.1.a - By the end of Grade 7, students will: Apply the multiplication principle of counting. Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)


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NJ 4.4.7 C.2 - By the end of Grade 7, students will: Explore counting problems involving Venn diagrams with three attributes (e.g., there are 15, 20, and 25 students respectively in the chess club, the debating team, and the engineering society; how many different students belong to the three clubs if there are 6 students in chess and debating, 7 students in chess and engineering, 8 students in debating and engineering, and 2 students in all three?).

NJ 4.4.7 C.3 - By the end of Grade 7, students will: Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts.NJ 4.4.7 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.7 D.1 - By the end of Grade 7, students will: Use vertex-edge graphs to represent and find solutions to practical problems.NJ 4.4.7 D.1.a - By the end of Grade 7, students will: Use vertex-edge graphs to represent and find solutions to practical problems. Finding the shortest network connecting specified sitesNJ 4.4.7 D.1.b - By the end of Grade 7, students will: Use vertex-edge graphs to represent and find solutions to practical problems. Finding the shortest route on a map from one site to anotherNJ 4.4.7 D.1.c - By the end of Grade 7, students will: Use vertex-edge graphs to represent and find solutions to practical problems. Finding the shortest circuit on a map that makes a tour of specified sites


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NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the end of Grade 7, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of Grade 7, students will: Solve problems that arise in mathematics and in other contexts.


Obj. 43 - WP: Multiply or divide integers

Obj. 46 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Obj. 48 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50Obj. 50 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Topic 2 - Algebra Obj. 71 - WP: Solve a proportionNJ 4.5 A.2.a - By the end of Grade 7, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems


NJ 4.5 A.2.c - By the end of Grade 7, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutionsNJ 4.5 A.2.d - By the end of Grade 7, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several ways


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NJ 4.5 A.3 - By the end of Grade 7, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the end of Grade 7, students will: Pose problems of various types and levels of difficulty.


NJ 4.5 A.6 - By the end of Grade 7, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of Grade 7, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of Grade 7, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.b - By the end of Grade 7, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning


NJ 4.5 B.3 - By the end of Grade 7, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the end of Grade 7, students will: Use the language of mathematics to express mathematical ideas precisely.

Topic 2 - Algebra Obj. 80 - WP: Use a 1-variable linear inequality to represent a situation

NJ 4.5 C - Connections


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NJ 4.5 C.1 - By the end of Grade 7, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the end of Grade 7, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of Grade 7, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of Grade 7, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of Grade 7, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the end of Grade 7, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of Grade 7, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the end of Grade 7, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the end of Grade 7, students will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the end of Grade 7, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.


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NJ 4.5 D.5 - By the end of Grade 7, students will: Make and investigate mathematical conjectures.


NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of Grade 7, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.a - By the end of Grade 7, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)




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NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of Grade 7, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of Grade 7, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the end of Grade 7, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the end of Grade 7, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).




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Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.8 A - Number SenseNJ 4.1.8 A.1 - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well):

NJ 4.1.8 A.1.a - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Rational numbersNJ 4.1.8 A.1.b - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Percents

NJ 4.1.8 A.1.c - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Exponents

NJ 4.1.8 A.1.d - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Roots



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NJ 4.1.8 A.1.e - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Absolute valuesNJ 4.1.8 A.1.f - By the end of grade 8, students will: Extend understanding of the number system by constructing meanings for the following (unless otherwise noted, all indicators for grade 8 pertain to these sets of numbers as well): Numbers represented in scientific notation


Obj. 4 - Convert a number less than 1 to scientific notation

Obj. 5 - Convert a number less than 1 from scientific notation to standard form

NJ 4.1.8 A.2 - By the end of grade 8, students will: Demonstrate a sense of the relative magnitudes of numbers.


Obj. 19 - Compare rational numbers and/or irrational numbers in various forms

Obj. 20 - Order rational numbers and irrational numbers

NJ 4.1.8 A.3 - By the end of grade 8, students will: Understand and use ratios, rates, proportions, and percents (including percents greater than 100 and less than 1) in a variety of situations.


Obj. 21 - Determine a percent of a number given a percent that is not a whole percent

Obj. 22 - Determine the percent one number is of another numberObj. 24 - WP: Determine a given percent of a numberObj. 25 - WP: Determine the percent one number is of another number

Obj. 26 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Obj. 29 - WP: Find the result of two consecutive percentage changes applied to a given numberObj. 30 - WP: Estimate a given percent of a number

NJ 4.1.8 A.4 - By the end of grade 8, students will: Compare and order numbers of all named types.


Obj. 19 - Compare rational numbers and/or irrational numbers in various forms


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Obj. 20 - Order rational numbers and irrational numbers

NJ 4.1.8 A.5 - By the end of grade 8, students will: Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number.NJ 4.1.8 A.6 - By the end of grade 8, students will: Recognize that repeating decimals correspond to fractions and determine their fractional equivalents.NJ 4.1.8 A.6.a - By the end of grade 8, students will: Recognize that repeating decimals correspond to fractions and determine their fractional equivalents. 5/7 = 0. 714285714285... = 0.714285 repeating


Obj. 17 - Convert a repeating decimal to a fraction or a mixed number

NJ 4.1.8 A.7 - By the end of grade 8, students will: Construct meanings for common irrational numbers, such as pi and the square root of 2.

NJ 4.1.8 B - Numerical OperationsNJ 4.1.8 B.1 - By the end of grade 8, students will: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with:

NJ 4.1.8 B.1.a - By the end of grade 8, students will: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: Pencil-and-paper


Obj. 2 - Evaluate a zero or negative power of an integer

Obj. 3 - Evaluate a numerical expression involving integer exponents and/or integer basesObj. 6 - Add or subtract signed fractions or mixed numbersObj. 7 - Multiply or divide signed fractions or mixed numbersObj. 8 - Add or subtract signed decimals


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Obj. 9 - Multiply or divide signed decimals

NJ 4.1.8 B.1.b - By the end of grade 8, students will: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: Mental mathNJ 4.1.8 B.1.c - By the end of grade 8, students will: Use and explain procedures for performing calculations involving addition, subtraction, multiplication, division, and exponentiation with integers and all number types named above with: CalculatorNJ 4.1.8 B.2 - By the end of grade 8, students will: Use exponentiation to find whole number powers of numbers.


Obj. 1 - Evaluate an integer raised to a whole number power

NJ 4.1.8 B.3 - By the end of grade 8, students will: Find square and cube roots of numbers and understand the inverse nature of powers and roots.


Obj. 12 - Determine the square root of a perfect-square fraction or decimal

Obj. 13 - Determine both square roots of a perfect square

NJ 4.1.8 B.4 - By the end of grade 8, students will: Solve problems involving proportions and percents.


Obj. 23 - Determine a number given a part and a decimal percentage or a percentage more than 100%

Obj. 24 - WP: Determine a given percent of a numberObj. 25 - WP: Determine the percent one number is of another number

Obj. 26 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Obj. 29 - WP: Find the result of two consecutive percentage changes applied to a given numberObj. 30 - WP: Estimate a given percent of a number


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NJ 4.1.8 B.5 - By the end of grade 8, students will: Understand and apply the standard algebraic order of operations, including appropriate use of parentheses.


Obj. 10 - Evaluate a numerical expression involving nested parentheses

NJ 4.1.8 C - EstimationNJ 4.1.8 C.1 - By the end of grade 8, students will: Estimate square and cube roots of numbers.


Obj. 14 - Determine the two closest integers to a given square root

Obj. 15 - Approximate the location of a square root on a number lineObj. 16 - Determine the square root of a whole number to the nearest tenth

NJ 4.1.8 C.2 - By the end of grade 8, students will: Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation.NJ 4.1.8 C.3 - By the end of grade 8, students will: Recognize the limitations of estimation and assess the amount of error resulting from estimation.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.8 A - Geometric PropertiesNJ 4.2.8 A.1 - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes.NJ 4.2.8 A.1.a - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes. Complementary and supplementary angles

NJ 4.2.8 A.1.b - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes. Vertical anglesNJ 4.2.8 A.1.c - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes. Bisectors and perpendicular bisectors


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NJ 4.2.8 A.1.d - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes. Parallel, perpendicular, and intersecting planesNJ 4.2.8 A.1.e - By the end of grade 8, students will: Understand and apply concepts involving lines, angles, and planes. Intersection of plane with cube, cylinder, cone, and sphereNJ 4.2.8 A.2 - By the end of grade 8, students will: Understand and apply the Pythagorean theorem.


Obj. 71 - Determine the length of the hypotenuse of a right triangle using the Pythagorean theoremObj. 72 - Determine the length of a leg of a right triangle using the Pythagorean theoremObj. 73 - WP: Use the Pythagorean theorem to find a length or a distance

Obj. 74 - Determine a distance on the Cartesian plane using the Pythagorean theoremObj. 75 - Determine if a triangle is a right triangle by using the Pythagorean theorem

NJ 4.2.8 A.3 - By the end of grade 8, students will: Understand and apply properties of polygons.NJ 4.2.8 A.3.a - By the end of grade 8, students will: Understand and apply properties of polygons. Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombiNJ 4.2.8 A.3.b - By the end of grade 8, students will: Understand and apply properties of polygons. Regular polygonsNJ 4.2.8 A.3.c - By the end of grade 8, students will: Understand and apply properties of polygons. Sum of measures of interior angles of a polygonNJ 4.2.8 A.3.d - By the end of grade 8, students will: Understand and apply properties of polygons. Which polygons can be used alone to generate a tessellation and why


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NJ 4.2.8 A.4 - By the end of grade 8, students will: Understand and apply the concept of similarity.NJ 4.2.8 A.4.a - By the end of grade 8, students will: Understand and apply the concept of similarity. Using proportions to find missing measures

NJ 4.2.8 A.4.b - By the end of grade 8, students will: Understand and apply the concept of similarity. Scale drawingsNJ 4.2.8 A.4.c - By the end of grade 8, students will: Understand and apply the concept of similarity. Models of 3D objectsNJ 4.2.8 A.5 - By the end of grade 8, students will: Use logic and reasoning to make and support conjectures about geometric objects.

NJ 4.2.8 A.6 - By the end of grade 8, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).NJ 4.2.8 A.6.a - By the end of grade 8, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Congruent angles or line segmentsNJ 4.2.8 A.6.b - By the end of grade 8, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Midpoint of a line segmentNJ 4.2.8 A.7 - By the end of grade 8, students will: Create two-dimensional representations (e.g., nets or projective views) for the surfaces of three-dimensional objects.

NJ 4.2.8 B - Transforming ShapesNJ 4.2.8 B.1 - By the end of grade 8, students will: Understand and apply transformations.


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NJ 4.2.8 B.1.a - By the end of grade 8, students will: Understand and apply transformations. Finding the image, given the pre-image, and vice-versaNJ 4.2.8 B.1.b - By the end of grade 8, students will: Understand and apply transformations. Sequence of transformations needed to map one figure onto another

NJ 4.2.8 B.1.c - By the end of grade 8, students will: Understand and apply transformations. Reflections, rotations, and translations result in images congruent to the pre-image

NJ 4.2.8 B.1.d - By the end of grade 8, students will: Understand and apply transformations. Dilations (stretching/shrinking) result in images similar to the pre-image

NJ 4.2.8 B.2 - By the end of grade 8, students will: Use iterative procedures to generate geometric patterns.NJ 4.2.8 B.2.a - By the end of grade 8, students will: Use iterative procedures to generate geometric patterns. Fractals (e.g., the Koch Snowflake)NJ 4.2.8 B.2.b - By the end of grade 8, students will: Use iterative procedures to generate geometric patterns. Self-similarityNJ 4.2.8 B.2.c - By the end of grade 8, students will: Use iterative procedures to generate geometric patterns. Construction of initial stages

NJ 4.2.8 B.2.d - By the end of grade 8, students will: Use iterative procedures to generate geometric patterns. Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski's Triangle)NJ 4.2.8 C - Coordinate Geometry


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NJ 4.2.8 C.1 - By the end of grade 8, students will: Use coordinates in four quadrants to represent geometric concepts.NJ 4.2.8 C.2 - By the end of grade 8, students will: Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).

NJ 4.2.8 D - Units of MeasurementNJ 4.2.8 D.1 - By the end of grade 8, students will: Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").


Obj. 56 - WP: Solve a problem involving mixed units

NJ 4.2.8 D.2 - By the end of grade 8, students will: Use approximate equivalents between standard and metric systems to estimate measurements (e.g., 5 kilometers is about 3 miles).NJ 4.2.8 D.3 - By the end of grade 8, students will: Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements.NJ 4.2.8 D.4 - By the end of grade 8, students will: Select and use appropriate units and tools to measure quantities to the degree of precision needed in a particular problem-solving situation.NJ 4.2.8 D.5 - By the end of grade 8, students will: Recognize that all measurements of continuous quantities are approximations.NJ 4.2.8 D.6 - By the end of grade 8, students will: Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).



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NJ 4.2.8 E.1 - By the end of grade 8, students will: Develop and apply strategies for finding perimeter and area.NJ 4.2.8 E.1.a - By the end of grade 8, students will: Develop and apply strategies for finding perimeter and area. Geometric figures made by combining triangles, rectangles and circles or parts of circles

NJ 4.2.8 E.1.b - By the end of grade 8, students will: Develop and apply strategies for finding perimeter and area. Estimation of area using grids of various sizesNJ 4.2.8 E.1.c - By the end of grade 8, students will: Develop and apply strategies for finding perimeter and area. Impact of a dilation on the perimeter and area of a 2-dimensional figureNJ 4.2.8 E.2 - By the end of grade 8, students will: Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height).NJ 4.2.8 E.3 - By the end of grade 8, students will: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure.


Obj. 64 - Solve a problem involving the surface area or the volume of a pyramid or a cone

NJ 4.2.8 E.3.a - By the end of grade 8, students will: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure. Volume - prism, cone, pyramid


Obj. 60 - Determine the volume of a pyramid or a cone

Obj. 61 - WP: Determine the volume of a pyramid or a cone

NJ 4.2.8 E.3.b - By the end of grade 8, students will: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure. Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base)


Obj. 62 - Determine the surface area of a pyramid or a cone


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Obj. 63 - WP: Determine the surface area of a pyramid or a cone

NJ 4.2.8 E.3.c - By the end of grade 8, students will: Develop and apply strategies and formulas for finding the surface area and volume of a three-dimensional figure. Impact of a dilation on the surface area and volume of a three-dimensional figure

NJ 4.2.8 E.4 - By the end of grade 8, students will: Use formulas to find the volume and surface area of a sphere.

NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.8 A - PatternsNJ 4.3.8 A.1 - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.NJ 4.3.8 A.1.a - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions

Topic 2 - Algebra Obj. 42 - Determine the graph of a line for a given table of values

Obj. 43 - Determine the table of values that represents a linear equation with rational coefficients in two variablesObj. 44 - Determine a linear equation in two variables that represents a table of valuesObj. 45 - Determine the graph of a 2-operation linear function

NJ 4.3.8 A.1.b - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Finite and infinite sequences


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NJ 4.3.8 A.1.c - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)

NJ 4.3.8 A.1.d - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)NJ 4.3.8 A.1.e - By the end of grade 8, students will: Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers. Generating sequences by using calculators to repeatedly apply a formula

NJ 4.3.8 B - Functions and RelationshipsNJ 4.3.8 B.1 - By the end of grade 8, students will: Graph functions, and understand and describe their general behavior.NJ 4.3.8 B.1.a - By the end of grade 8, students will: Graph functions, and understand and describe their general behavior. Equations involving two variables

Topic 2 - Algebra Obj. 42 - Determine the graph of a line for a given table of values

Obj. 45 - Determine the graph of a 2-operation linear function

NJ 4.3.8 B.1.b - By the end of grade 8, students will: Graph functions, and understand and describe their general behavior. Rates of change (informal notion of slope)

NJ 4.3.8 B.2 - By the end of grade 8, students will: Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.


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NJ 4.3.8 C - ModelingNJ 4.3.8 C.1 - By the end of grade 8, students will: Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

NJ 4.3.8 C.2 - By the end of grade 8, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations.

NJ 4.3.8 C.2.a - By the end of grade 8, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations. Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities

Topic 2 - Algebra Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situation

Obj. 50 - WP: Determine a linear graph that can represent a situation

NJ 4.3.8 C.2.b - By the end of grade 8, students will: Use patterns, relations, symbolic algebra, and linear functions to model situations. Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

NJ 4.3.8 D - ProceduresNJ 4.3.8 D.1 - By the end of grade 8, students will: Use graphing techniques on a number line.NJ 4.3.8 D.1.a - By the end of grade 8, students will: Use graphing techniques on a number line. Absolute valueNJ 4.3.8 D.1.b - By the end of grade 8, students will: Use graphing techniques on a number line. Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is "left 3, right 6")


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NJ 4.3.8 D.2 - By the end of grade 8, students will: Solve simple linear equations informally, graphically, and using formal algebraic methods.

NJ 4.3.8 D.2.a - By the end of grade 8, students will: Solve simple linear equations informally, graphically, and using formal algebraic methods. Multi-step, integer coefficients only (although answers may not be integers)NJ 4.3.8 D.2.b - By the end of grade 8, students will: Solve simple linear equations informally, graphically, and using formal algebraic methods. Simple literal equations (e.g., A = lw)

NJ 4.3.8 D.2.c - By the end of grade 8, students will: Solve simple linear equations informally, graphically, and using formal algebraic methods. Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

Topic 2 - Algebra Obj. 37 - Solve a 1-step equation involving rational numbers

Obj. 38 - Solve a 2-step equation involving rational numbers

NJ 4.3.8 D.3 - By the end of grade 8, students will: Solve simple linear inequalities.

Topic 2 - Algebra Obj. 52 - Solve a 2-step linear inequality in one variable

NJ 4.3.8 D.4 - By the end of grade 8, students will: Create, evaluate, and simplify algebraic expressions involving variables.

Topic 2 - Algebra Obj. 32 - Evaluate an algebraic expression involving negative integer exponents

Obj. 33 - Simplify an algebraic expression by combining like terms

Obj. 35 - Multiply two monomial algebraic expressions

NJ 4.3.8 D.4.a - By the end of grade 8, students will: Create, evaluate, and simplify algebraic expressions involving variables. Order of operations, including appropriate use of parenthesesNJ 4.3.8 D.4.b - By the end of grade 8, students will: Create, evaluate, and simplify algebraic expressions involving variables. Distributive property

Topic 2 - Algebra Obj. 36 - Use the distributive property to simplify an algebraic expression


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NJ 4.3.8 D.4.c - By the end of grade 8, students will: Create, evaluate, and simplify algebraic expressions involving variables. Substitution of a number for a variable

Topic 2 - Algebra Obj. 31 - Evaluate a 2-variable expression with two or three operations substituting fractions or decimals

NJ 4.3.8 D.4.d - By the end of grade 8, students will: Create, evaluate, and simplify algebraic expressions involving variables. Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situationObj. 53 - WP: Use a 2-step linear inequality in one variable to represent a situation

NJ 4.3.8 D.5 - By the end of grade 8, students will: Understand and apply the properties of operations, numbers, equations, and inequalities.

NJ 4.3.8 D.5.a - By the end of grade 8, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Additive inverseNJ 4.3.8 D.5.b - By the end of grade 8, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Multiplicative inverse

NJ 4.3.8 D.5.c - By the end of grade 8, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Addition and multiplication properties of equalityNJ 4.3.8 D.5.d - By the end of grade 8, students will: Understand and apply the properties of operations, numbers, equations, and inequalities. Addition and multiplication properties of inequalities


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.8 A - Data AnalysisNJ 4.4.8 A.1 - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode).

NJ 4.4.8 A.1.a - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Type of display most appropriate for given dataNJ 4.4.8 A.1.b - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Box-and-whisker plot, upper quartile, lower quartile


Obj. 82 - Read a box-and-whisker plot

Obj. 83 - Use a box-and-whisker plot to organize dataObj. 84 - Answer a question using information from a box-and-whisker plotObj. 85 - Answer a question using information from two box-and-whisker plots

NJ 4.4.8 A.1.c - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Scatter plot


Obj. 77 - Use a scatter plot to organize data

Obj. 80 - Answer a question using information from a scatter plot


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NJ 4.4.8 A.1.d - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Calculators and computer used to record and process information

NJ 4.4.8 A.1.e - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Finding the median and mean (weighted average) using frequency data.


Obj. 90 - Determine the median of the data in a frequency table or a bar graph

Obj. 91 - Determine the mean of the data in a frequency table or a bar graph

NJ 4.4.8 A.1.f - By the end of grade 8, students will: Select and use appropriate representations for sets of data, and measures of central tendency (mean, median, and mode). Effect of additional data on measures of central tendency


Obj. 88 - Analyze the effect that changing elements in a data set has on the mean, the median, or the range

NJ 4.4.8 A.2 - By the end of grade 8, students will: Make inferences and formulate and evaluate arguments based on displays and analysis of data sets.NJ 4.4.8 A.3 - By the end of grade 8, students will: Estimate lines of best fit and use them to interpolate within the range of the data.


Obj. 79 - Approximate a trend line for a scatter plot

NJ 4.4.8 A.4 - By the end of grade 8, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.8 B - ProbabilityNJ 4.4.8 B.1 - By the end of grade 8, students will: Interpret probabilities as ratios, percents, and decimals.

NJ 4.4.8 B.2 - By the end of grade 8, students will: Determine probabilities of compound events.


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NJ 4.4.8 B.3 - By the end of grade 8, students will: Explore the probabilities of conditional events (e.g., if there are seven marbles in a bag, three red and four green, what is the probability that two marbles picked from the bag, without replacement, are both red).

NJ 4.4.8 B.4 - By the end of grade 8, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models.

NJ 4.4.8 B.4.a - By the end of grade 8, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models. Frequency, relative frequency

NJ 4.4.8 B.5 - By the end of grade 8, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.8 B.6 - By the end of grade 8, students will: Play and analyze probability-based games, and discuss the concepts of fairness and expected value.NJ 4.4.8 C - Discrete Mathematics-Systematic Listing and CountingNJ 4.4.8 C.1 - By the end of grade 8, students will: Apply the multiplication principle of counting.NJ 4.4.8 C.1.a - By the end of grade 8, students will: Apply the multiplication principle of counting. Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates of 3 class officers from a 23 student class)


Obj. 94 - Determine the number of permutations possible in a given situation

NJ 4.4.8 C.1.b - By the end of grade 8, students will: Apply the multiplication principle of counting. Factorial notation


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NJ 4.4.8 C.1.c - By the end of grade 8, students will: Apply the multiplication principle of counting. Concept of combinations (e.g., number of possible delegations of 3 out of 23 students)


Obj. 95 - Determine the number of combinations possible in a given situation

NJ 4.4.8 C.2 - By the end of grade 8, students will: Explore counting problems involving Venn diagrams with three attributes (e.g., there are 15, 20, and 25 students respectively in the chess club, the debating team, and the engineering society; how many different students belong to the three clubs if there are 6 students in chess and debating, 7 students in chess and engineering, 8 students in debating and engineering, and 2 students in all three?).

NJ 4.4.8 C.3 - By the end of grade 8, students will: Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts.NJ 4.4.8 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.8 D.1 - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems.NJ 4.4.8 D.1.a - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Finding the shortest network connecting specified sitesNJ 4.4.8 D.1.b - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Finding a minimal route that includes every street (e.g., for trash pick-up)


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NJ 4.4.8 D.1.c - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Finding the shortest route on a map from one site to anotherNJ 4.4.8 D.1.d - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Finding the shortest circuit on a map that makes a tour of specified sites

NJ 4.4.8 D.1.e - By the end of grade 8, students will: Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems. Limitations of computers (e.g., the number of routes for a delivery truck visiting n sites is n!, so finding the shortest circuit by examining all circuits would overwhelm the capacity of any computer, now or in the future, even if n is less than 100)


NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the end of grade 8, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the end of grade 8, students will: Solve problems that arise in mathematics and in other contexts.NJ 4.5 A.2.a - By the end of grade 8, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems


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NJ 4.5 A.2.b - By the end of grade 8, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5 A.2.c - By the end of grade 8, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutionsNJ 4.5 A.2.d - By the end of grade 8, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the end of grade 8, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the end of grade 8, students will: Pose problems of various types and levels of difficulty.

NJ 4.5 A.5 - By the end of grade 8, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5 A.6 - By the end of grade 8, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the end of grade 8, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.a - By the end of grade 8, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.b - By the end of grade 8, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning


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NJ 4.5 B.2 - By the end of grade 8, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.NJ 4.5 B.3 - By the end of grade 8, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the end of grade 8, students will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the end of grade 8, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).NJ 4.5 C.2 - By the end of grade 8, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the end of grade 8, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the end of grade 8, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the end of grade 8, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the end of grade 8, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the end of grade 8, students will: Recognize that mathematical facts, procedures, and claims must be justified.


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NJ 4.5 D.2 - By the end of grade 8, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the end of grade 8, students will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the end of grade 8, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.NJ 4.5 D.5 - By the end of grade 8, students will: Make and investigate mathematical conjectures.NJ 4.5 D.5.a - By the end of grade 8, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5 D.5.b - By the end of grade 8, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5 D.6 - By the end of grade 8, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the end of grade 8, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.a - By the end of grade 8, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)

NJ 4.5 E.1.b - By the end of grade 8, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)


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NJ 4.5 E.1.c - By the end of grade 8, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5 E.1.d - By the end of grade 8, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)NJ 4.5 E.2 - By the end of grade 8, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the end of grade 8, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the end of grade 8, students will: Use technology to gather, analyze, and communicate mathematical information.NJ 4.5 F.2 - By the end of grade 8, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the end of grade 8, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the end of grade 8, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5 F.5 - By the end of grade 8, students will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5 F.6 - By the end of grade 8, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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Standard Topic Description Objective DescriptionNJ 4.1 - All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.NJ 4.1.12 A - Number SenseNJ 4.1.12 A.1 - By the End of Grade 12, students will: Extend understanding of the number system to all real numbers.NJ 4.1.12 A.2 - By the End of Grade 12, students will: Compare and order rational and irrational numbers.

NJ 4.1.12 A.3 - By the End of Grade 12, students will: Develop conjectures and informal proofs of properties of number systems and sets of numbers.NJ 4.1.12 B - Numerical Operations

NJ 4.1.12 B.1 - By the End of Grade 12, students will: Extend understanding and use of operations to real numbers and algebraic procedures.


Obj. 1 - Evaluate a numerical expression involving multiple forms of rational numbers

Obj. 2 - Simplify a complex fraction

Obj. 3 - Evaluate a multi-step numerical expression involving absolute valueObj. 5 - Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers

NJ 4.1.12 B.2 - By the End of Grade 12, students will: Develop, apply, and explain methods for solving problems involving rational and negative exponents.


Obj. 5 - Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers

NJ 4.1.12 B.3 - By the End of Grade 12, students will: Perform operations on matrices.NJ 4.1.12 B.3.1 - By the End of Grade 12, students will: Perform operations on matrices. Addition and subtractionNJ 4.1.12 B.3.2 - By the End of Grade 12, students will: Perform operations on matrices. Scalar multiplication

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Algebra 1


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NJ 4.1.12 B.4 - By the End of Grade 12, students will: Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.


Obj. 4 - Evaluate a fraction raised to an integer power

Obj. 5 - Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers

Topic 5 - Properties of Powers Obj. 58 - Apply the product of powers property to a monomial numerical expressionObj. 59 - Apply the product of powers property to a monomial algebraic expressionObj. 60 - Apply the power of a power property to a monomial numerical expressionObj. 61 - Apply the power of a power property to a monomial algebraic expressionObj. 62 - Apply the power of a product property to a monomial algebraic expressionObj. 63 - Apply the quotient of powers property to monomial numerical expressionsObj. 64 - Apply the quotient of powers property to monomial algebraic expressionsObj. 65 - Apply the power of a quotient property to monomial algebraic expressionsObj. 67 - Apply properties of exponents to monomial algebraic expressions

NJ 4.1.12 C - EstimationNJ 4.1.12 C.1 - By the End of Grade 12, students will: Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.


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NJ 4.2.12 A - Geometric Properties

NJ 4.2.12 A.1 - By the End of Grade 12, students will: Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use Pythagorean Theorem to decide whether an object can fit through a doorway).NJ 4.2.12 A.2 - By the End of Grade 12, students will: Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets or projective views).

NJ 4.2.12 A.3 - By the End of Grade 12, students will: Apply the properties of geometric shapes.NJ 4.2.12 A.3.1 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Parallel lines - transversal, alternate interior angles, corresponding angles

NJ 4.2.12 A.3.2 - By the End of Grade 12, students will: Apply the properties of geometric shapes. TrianglesNJ 4.2.12 A.3.2.a - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Conditions for congruence

NJ 4.2.12 A.3.2.b - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Segment joining midpoints of two sides is parallel to and half the length of the third sideNJ 4.2.12 A.3.2.c - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Triangle InequalityNJ 4.2.12 A.3.2.d - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Special right triangles


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NJ 4.2.12 A.3.3 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Minimal conditions for a shape to be a special quadrilateralNJ 4.2.12 A.3.4 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Circles - arcs, central and inscribed angles, chords, tangentsNJ 4.2.12 A.3.5 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Self-similarityNJ 4.2.12 A.4 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems.

NJ 4.2.12 A.4.1 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Verification or refutation of proposed proofsNJ 4.2.12 A.4.2 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Simple proofs involving congruent trianglesNJ 4.2.12 A.4.3 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Counterexamples to incorrect conjecturesNJ 4.2.12 A.5 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).NJ 4.2.12 A.5.1 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular bisector of a line segment


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NJ 4.2.12 A.5.2 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Bisector of an angle

NJ 4.2.12 A.5.3 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular or parallel linesNJ 4.2.12 B - Transforming ShapesNJ 4.2.12 B.1 - By the End of Grade 12, students will: Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic representation, and, conversely, determine whether and how one representation can be transformed to another by a transformation or a sequence of transformations.NJ 4.2.12 B.2 - By the End of Grade 12, students will: Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.NJ 4.2.12 B.3 - By the End of Grade 12, students will: Determine whether two or more given shapes can be used to generate a tessellation.

NJ 4.2.12 B.4 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns.

NJ 4.2.12 B.4.1 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Fractals (e.g., Sierpinski's Triangle)


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NJ 4.2.12 B.4.2 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Patterns in areas and perimeters of self-similar figuresNJ 4.2.12 B.4.3 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Outcome of extending iterative process indefinitelyNJ 4.2.12 C - Coordinate Geometry

NJ 4.2.12 C.1 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments.

NJ 4.2.12 C.1.1 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Distance between two pointsNJ 4.2.12 C.1.2 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Midpoint and slope of a line segment

Topic 3 - Linear Equations and Inequalities

Obj. 26 - Determine the slope of a line given two points on the line

NJ 4.2.12 C.1.3 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Finding the intersection of two linesNJ 4.2.12 C.1.4 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines with the same slope are parallelNJ 4.2.12 C.1.5 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines that are perpendicular have slopes whose product is -1


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NJ 4.2.12 C.2 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors.NJ 4.2.12 C.2.1 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectorsNJ 4.2.12 C.3 - By the End of Grade 12, students will: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.NJ 4.2.12 D - Units of Measurement

NJ 4.2.12 D.1 - By the End of Grade 12, students will: Understand and use the concept of significant digits.

NJ 4.2.12 D.2 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation.

NJ 4.2.12 D.2.1 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Degree of accuracy of a given measurement toolNJ 4.2.12 D.2.2 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Finding the interval in which a computed measure (e.g., area or volume) lies, given the degree of precision of linear measurements

NJ 4.2.12 E - Measuring Geometric ObjectsNJ 4.2.12 E.1 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems.


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NJ 4.2.12 E.1.1 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems. Similar trianglesNJ 4.2.12 E.1.2 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems. Pythagorean theorem

NJ 4.2.12 E.1.3 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems. Right triangle trigonometry (sine, cosine, tangent)

NJ 4.2.12 E.2 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures.

NJ 4.2.12 E.2.1 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures. Approximation of area using grids of different sizesNJ 4.2.12 E.2.2 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures. Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given conditions using graphing calculators, dynamic geometric software, and/or spreadsheets

NJ 4.2.12 E.2.3 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures. Estimation of area, perimeter, volume, and surface area


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NJ 4.3 - All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.NJ 4.3.12 A - PatternsNJ 4.3.12 A.1 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series.

NJ 4.3.12 A.1.1 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series. Explicit formulas for nth terms

NJ 4.3.12 A.1.2 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series. Sums of finite arithmetic series

NJ 4.3.12 A.1.3 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series. Sums of finite and infinite geometric seriesNJ 4.3.12 A.2 - By the End of Grade 12, students will: Develop an informal notion of limit.NJ 4.3.12 A.3 - By the End of Grade 12, students will: Use inductive reasoning to form generalizations.

NJ 4.3.12 B - Functions and RelationshipsNJ 4.3.12 B.1 - By the End of Grade 12, students will: Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.

Topic 2 - Relations and Functions

Obj. 8 - Determine if a relation is a function


Obj. 30 - Determine the graph of a linear equation given in slope-intercept, point-slope, or standard form


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Obj. 32 - Determine an equation that represents a graphed lineObj. 37 - Determine the graph of a 2-variable absolute value equationObj. 40 - Determine the graph of a 2-variable linear inequalityObj. 41 - Determine a 2-variable linear inequality represented by a graphObj. 44 - Determine the graph of a 1-variable absolute value inequality

Topic 8 - Quadratic Equations and Functions

Obj. 86 - Determine the graph of a given quadratic function

Topic 9 - Exponential Equations and Functions

Obj. 95 - Determine the graph of an exponential function

NJ 4.3.12 B.2 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques.

NJ 4.3.12 B.2.1 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Slope of a line


Obj. 27 - Determine the slope of a line given an equation of the line

NJ 4.3.12 B.2.2 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Domain and range


Obj. 9 - Determine the domain or range of a function

Obj. 10 - WP: Determine a reasonable domain or range for a function in a given situation

NJ 4.3.12 B.2.3 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Intercepts


Obj. 28 - Determine the x- or y-intercept of a line given an equation

NJ 4.3.12 B.2.4 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Continuity


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NJ 4.3.12 B.2.5 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Maximum/minimum

NJ 4.3.12 B.2.6 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Estimating roots of equationsNJ 4.3.12 B.2.7 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of equations

Topic 4 - Systems of Linear Equations and Inequalities

Obj. 45 - Solve a system of linear equations in two variables by graphing

Obj. 46 - Solve a system of linear equations in two variables by substitutionObj. 47 - Solve a system of linear equations in two variables by eliminationObj. 48 - Determine the number of solutions to a system of linear equationsObj. 49 - Solve a system of linear equations in two variables using any methodObj. 54 - Determine if a given ordered pair is a solution to a system of linear inequalities

NJ 4.3.12 B.2.8 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of linear inequalities using graphing techniquesNJ 4.3.12 B.2.9 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Rates of change


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NJ 4.3.12 B.3 - By the End of Grade 12, students will: Understand and perform transformations on commonly-used functions.

NJ 4.3.12 B.3.1 - By the End of Grade 12, students will: Understand and perform transformations on commonly-used functions. Translations, reflections, dilations

NJ 4.3.12 B.3.2 - By the End of Grade 12, students will: Understand and perform transformations on commonly-used functions. Effects on linear and quadratic graphs of parameter changes in equations

NJ 4.3.12 B.3.3 - By the End of Grade 12, students will: Understand and perform transformations on commonly-used functions. Using graphing calculators or computers for more complex functions

NJ 4.3.12 B.4 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions.

NJ 4.3.12 B.4.1 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Linear vs. non-linear


Obj. 12 - Determine if a function is linear or nonlinear

Obj. 13 - Determine whether a graph or a table represents a linear or nonlinear function

NJ 4.3.12 B.4.2 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Symmetry


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NJ 4.3.12 B.4.3 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Increasing/decreasing on an interval

NJ 4.3.12 C - ModelingNJ 4.3.12 C.1 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities.NJ 4.3.12 C.1.1 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of mailing a first-class letter over the past 200 years)


Obj. 16 - WP: Determine a linear equation that can be used to solve a percent problem


Obj. 94 - WP: Use a given quadratic equation to solve a problem

NJ 4.3.12 C.1.2 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Direct and inverse variation


Obj. 18 - WP: Determine an equation representing a direct variation or an inverse variation

Obj. 19 - WP: Solve a direct- or inverse-variation problem

NJ 4.3.12 C.1.3 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Absolute value


Obj. 20 - Solve a 1-variable absolute value equation

NJ 4.3.12 C.1.4 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Expressions, equations and inequalities


Obj. 16 - WP: Determine a linear equation that can be used to solve a percent problem


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NJ 4.3.12 C.1.5 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Same function can model variety of phenomenaNJ 4.3.12 C.1.6 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Growth/decay and change in the natural world

Topic 9 - Exponential Equations and Functions

Obj. 96 - WP: Evaluate an exponential growth or an exponential decay function

Obj. 97 - Solve a problem involving exponential growth or exponential decay

NJ 4.3.12 C.1.7 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Applications in mathematics, biology, and economics (including compound interest)NJ 4.3.12 C.2 - By the End of Grade 12, students will: Analyze and describe how a change in an independent variable leads to change in a dependent one.NJ 4.3.12 C.3 - By the End of Grade 12, students will: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).NJ 4.3.12 D - ProceduresNJ 4.3.12 D.1 - By the End of Grade 12, students will: Evaluate and simplify expressions.NJ 4.3.12 D.1.1 - By the End of Grade 12, students will: Evaluate and simplify expressions. Add and subtract polynomials

Topic 6 - Polynomial Expressions Obj. 70 - Add polynomial expressions

Obj. 71 - Subtract polynomial expressions

NJ 4.3.12 D.1.2 - By the End of Grade 12, students will: Evaluate and simplify expressions. Multiply a polynomial by a monomial or binomial

Topic 6 - Polynomial Expressions Obj. 72 - Multiply a polynomial by a monomial


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Obj. 73 - Multiply two binomials of the form (x +/- a)(x +/- b)Obj. 74 - Multiply two binomials of the form (ax +/- b)(cx +/- d)Obj. 75 - Multiply two binomials of the form (ax +/- by)(cx +/- dy)Obj. 76 - Square a binomialObj. 77 - Multiply two nonlinear binomialsObj. 78 - Multiply a trinomial by a binomial

NJ 4.3.12 D.1.3 - By the End of Grade 12, students will: Evaluate and simplify expressions. Divide a polynomial by a monomial

Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial expression by a monomial

NJ 4.3.12 D.1.4 - By the End of Grade 12, students will: Evaluate and simplify expressions. Perform simple operations with rational expressions

Topic 12 - Rational Expressions Obj. 115 - Multiply rational expressions

Obj. 116 - Divide rational expressions

Obj. 120 - Add or subtract two rational expressions with like denominatorsObj. 121 - Add or subtract two rational expressions with unlike monomial denominatorsObj. 122 - Add or subtract two rational expressions with unlike polynomial denominators

NJ 4.3.12 D.1.5 - By the End of Grade 12, students will: Evaluate and simplify expressions. Evaluate polynomial and rational expressions

NJ 4.3.12 D.2 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities.NJ 4.3.12 D.2.1 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Linear equations and inequalities - algebraically


Obj. 14 - Solve a 1-variable linear equation that requires simplification and has the variable on one side

Obj. 15 - Solve a 1-variable linear equation with the variable on both sides


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Obj. 21 - Solve a 1-variable linear inequality with the variable on one sideObj. 22 - Solve a 1-variable linear inequality with the variable on both sidesObj. 23 - Solve a 1-variable compound inequalityObj. 43 - Solve a 1-variable absolute value inequality

NJ 4.3.12 D.2.2 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Quadratic equations - factoring (including trinomials when the coefficient of x2 is 1) and using the quadratic formula

Topic 7 - Factor Algebraic Expressions

Obj. 79 - Factor the GCF from a polynomial expression

Obj. 80 - Factor trinomials that result in factors of the form (x +/- a)(x +/- b)

Obj. 81 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)Obj. 82 - Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy)Obj. 83 - Factor the difference of two squaresObj. 84 - Factor a perfect-square trinomialObj. 85 - Factor a polynomial that has a GCF and two linear binomial factors


Obj. 91 - Solve a quadratic equation by factoringObj. 92 - Solve a quadratic equation using the quadratic formula

NJ 4.3.12 D.2.3 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Literal equationsNJ 4.3.12 D.2.4 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. All types of equations and inequalities using graphing, computer, and graphing calculator techniques


Obj. 88 - Solve a quadratic equation by graphing the associated quadratic function


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NJ 4.3.12 D.3 - By the End of Grade 12, students will: Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.12 A - Data AnalysisNJ 4.4.12 A.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.12 A.1.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)NJ 4.4.12 A.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts.

NJ 4.4.12 A.2.1 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts. Accuracy and reasonableness of conclusions drawn

NJ 4.4.12 A.2.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts. Correlation vs. causationNJ 4.4.12 A.2.3 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts. Bias in conclusions drawn (e.g., influence of how data is displayed)


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NJ 4.4.12 A.2.4 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts. Statistical claims based on sampling

NJ 4.4.12 A.3 - By the End of Grade 12, students will: Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.NJ 4.4.12 A.4 - By the End of Grade 12, students will: Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of the data.NJ 4.4.12 A.5 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions.

NJ 4.4.12 A.5.1 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions. Measures of dispersion: variance, standard deviation, outliers

NJ 4.4.12 A.5.2 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions. Correlation coefficientNJ 4.4.12 A.5.3 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions. Normal distribution (e.g., approximately 95% of the sample lies between two standard deviations on either side of the mean)

NJ 4.4.12 A.6 - By the End of Grade 12, students will: Distinguish between randomized experiments and observational studies.

NJ 4.4.12 B - Probability


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NJ 4.4.12 B.1 - By the End of Grade 12, students will: Calculate the expected value of a probability-based game, given the probabilities and payoffs of the various outcomes, and determine whether the game is fair.

NJ 4.4.12 B.2 - By the End of Grade 12, students will: Use concepts and formulas of area to calculate geometric probabilities.NJ 4.4.12 B.3 - By the End of Grade 12, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.NJ 4.4.12 B.4 - By the End of Grade 12, students will: Determine probabilities in complex situations.NJ 4.4.12 B.4.1 - By the End of Grade 12, students will: Determine probabilities in complex situations. Conditional eventsNJ 4.4.12 B.4.2 - By the End of Grade 12, students will: Determine probabilities in complex situations. Complementary eventsNJ 4.4.12 B.4.3 - By the End of Grade 12, students will: Determine probabilities in complex situations. Dependent and independent eventsNJ 4.4.12 B.5 - By the End of Grade 12, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 B.6 - By the End of Grade 12, students will: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).



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NJ 4.4.12 C.1 - By the End of Grade 12, students will: Calculate combinations with replacement (e.g., the number of possible ways of tossing a coin 5 times and getting 3 heads) and without replacement (e.g., number of possible delegations of 3 out of 23 students).

NJ 4.4.12 C.2 - By the End of Grade 12, students will: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.NJ 4.4.12 C.3 - By the End of Grade 12, students will: Justify solutions to counting problems.NJ 4.4.12 C.4 - By the End of Grade 12, students will: Recognize and explain relationships involving combinations and Pascal's Triangle, and apply those methods to situations involving probability.NJ 4.4.12 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.12 D.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.NJ 4.4.12 D.1.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every edge in a graphNJ 4.4.12 D.1.2 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every vertex in a graph


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NJ 4.4.12 D.1.3 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring

NJ 4.4.12 D.1.4 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Applications to science (e.g., who-eats-whom graphs, genetic trees, molecular structures)

NJ 4.4.12 D.2 - By the End of Grade 12, students will: Explore strategies for making fair decisions.

NJ 4.4.12 D.2.1 - By the End of Grade 12, students will: Explore strategies for making fair decisions. Combining individual preferences into a group decision (e.g., determining winner of an election or selection process)NJ 4.4.12 D.2.2 - By the End of Grade 12, students will: Explore strategies for making fair decisions. Determining how many Student Council representatives each class (9th, 10th, 11th, and 12th grade) gets when the classes have unequal sizes (apportionment)


NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the End of Grade 12, students will: Learn mathematics through problem solving, inquiry, and discovery.


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NJ 4.5 A.2 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts.NJ 4.5 A.2.1 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems

NJ 4.5 A.2.2 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Non-routine problems

NJ 4.5 A.2.3 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutionsNJ 4.5 A.2.4 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the End of Grade 12, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the End of Grade 12, students will: Pose problems of various types and levels of difficulty.

NJ 4.5 A.5 - By the End of Grade 12, students will: Monitor their progress and reflect on the process of their problem solving activity.

NJ 4.5 A.6 - By the End of Grade 12, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking.


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NJ 4.5 B.1.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.2 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning

NJ 4.5 B.2 - By the End of Grade 12, students will: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

NJ 4.5 B.3 - By the End of Grade 12, students will: Analyze and evaluate the mathematical thinking and strategies of others.NJ 4.5 B.4 - By the End of Grade 12, students will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the End of Grade 12, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the End of Grade 12, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the End of Grade 12, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the End of Grade 12, students will: Apply mathematics in practical situations and in other disciplines.


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NJ 4.5 C.5 - By the End of Grade 12, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the End of Grade 12, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the End of Grade 12, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the End of Grade 12, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the End of Grade 12, students will: Select and use various types of reasoning and methods of proof.NJ 4.5 D.4 - By the End of Grade 12, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.

NJ 4.5 D.5 - By the End of Grade 12, students will: Make and investigate mathematical conjectures.

NJ 4.5 D.5.1 - By the End of Grade 12, students will: Make and investigate mathematical conjectures. Counterexamples as a means of disproving conjecturesNJ 4.5 D.5.2 - By the End of Grade 12, students will: Make and investigate mathematical conjectures. Verifying conjectures using informal reasoning or proofs.NJ 4.5 D.6 - By the End of Grade 12, students will: Evaluate examples of mathematical reasoning and determine whether they are valid.

NJ 4.5 E - Representations


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NJ 4.5 E.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)

NJ 4.5 E.1.2 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Pictorial representations (e.g., diagrams, charts, or tables)

NJ 4.5 E.1.3 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5 E.1.4 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)NJ 4.5 E.2 - By the End of Grade 12, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the End of Grade 12, students will: Use representations to model and interpret physical, social, and mathematical phenomena.

NJ 4.5 F - TechnologyNJ 4.5 F.1 - By the End of Grade 12, students will: Use technology to gather, analyze, and communicate mathematical information.

NJ 4.5 F.2 - By the End of Grade 12, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.


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NJ 4.5 F.3 - By the End of Grade 12, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the End of Grade 12, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

NJ 4.5 F.5 - By the End of Grade 12, students will: Use computer software to make and verify conjectures about geometric objects.

NJ 4.5 F.6 - By the End of Grade 12, students will: Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).


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NJ 4.1.12 B.1 - By the End of Grade 12, students will: Extend understanding and use of operations to real numbers and algebraic procedures.NJ 4.1.12 B.2 - By the End of Grade 12, students will: Develop, apply, and explain methods for solving problems involving rational and negative exponents.NJ 4.1.12 B.3 - By the End of Grade 12, students will: Perform operations on matrices.NJ 4.1.12 B.3.1 - By the End of Grade 12, students will: Perform operations on matrices. Addition and subtractionNJ 4.1.12 B.3.2 - By the End of Grade 12, students will: Perform operations on matrices. Scalar multiplicationNJ 4.1.12 B.4 - By the End of Grade 12, students will: Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.

NJ 4.1.12 C - Estimation

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Geometry


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NJ 4.1.12 C.1 - By the End of Grade 12, students will: Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.12 A - Geometric Properties

NJ 4.2.12 A.1 - By the End of Grade 12, students will: Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use Pythagorean Theorem to decide whether an object can fit through a doorway).

Topic 3 - Relationships Within Triangles

Obj. 21 - WP: Determine a length or an angle measure using triangle relationships

Topic 5 - Quadrilaterals and Other Polygons

Obj. 32 - WP: Solve a problem using the properties of angles and/or sides of polygons

Topic 6 - Similarity Obj. 43 - WP: Determine a length using similarity

Topic 7 - Right Triangles and Trigonometry

Obj. 47 - WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangleObj. 48 - WP: Solve a problem involving a complex figure using the Pythagorean theoremObj. 52 - WP: Determine a length in a right triangle using a sine, cosine, or tangent ratio

Topic 9 - Area Obj. 83 - WP: Determine a length or an area involving a sector of a circle

Topic 10 - Surface Area and Volume

Obj. 102 - WP: Solve a problem involving the volume of a complex solid figureObj. 106 - WP: Solve a problem involving two solid figures that have the same surface area or volume


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NJ 4.2.12 A.2 - By the End of Grade 12, students will: Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets or projective views).


Topic 2 - Parallel and Perpendicular lines

Obj. 10 - Determine the measure of an angle formed by parallel lines and one or more transversals

Obj. 11 - Identify parallel lines using angle relationshipsObj. 12 - Determine the measure of an angle in a figure involving parallel and/or perpendicular lines


Topic 4 - Congruent Triangles Obj. 23 - Identify a triangle congruence postulate that justifies a congruence statement

Obj. 24 - Identify congruent triangles using triangle congruence postulates or theorems

NJ 4.2.12 A.3.2.b - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Segment joining midpoints of two sides is parallel to and half the length of the third side

Topic 6 - Similarity Obj. 39 - Determine a length in a triangle using a midsegment

NJ 4.2.12 A.3.2.c - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Triangle Inequality


Obj. 19 - Solve a problem using inequalities in a triangle

NJ 4.2.12 A.3.2.d - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Special right triangles


Obj. 45 - Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

Obj. 46 - Solve a problem using multiple non-trigonometric right-triangle relationships


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Obj. 47 - WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

NJ 4.2.12 A.3.3 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Minimal conditions for a shape to be a special quadrilateralNJ 4.2.12 A.3.4 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Circles - arcs, central and inscribed angles, chords, tangents

Topic 8 - Circles Obj. 54 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angle

Obj. 55 - Solve a problem involving the length of an arcObj. 56 - Determine the length of a line segment, the measure of an angle, or the measure of an arc using a tangent to a circleObj. 57 - Determine a length using a line segment tangent to a circle and the radius that intersects the tangent

Obj. 58 - Determine a length using two intersecting tangents to a circle

Obj. 59 - Determine a length or an arc measure using the properties of congruent chordsObj. 60 - Determine a length using a perpendicular bisector of a chordObj. 61 - Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arcObj. 62 - Determine the measure of an arc or an angle using properties of an inscribed triangle or quadrilateral

Obj. 63 - Determine the measure of an arc or an angle formed by intersecting chords or a chord that intersects a tangent to a circle

NJ 4.2.12 A.3.5 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Self-similarity


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NJ 4.2.12 A.4 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems.

NJ 4.2.12 A.4.1 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Verification or refutation of proposed proofsNJ 4.2.12 A.4.2 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Simple proofs involving congruent triangles

Topic 4 - Congruent Triangles Obj. 23 - Identify a triangle congruence postulate that justifies a congruence statement

NJ 4.2.12 A.4.3 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Counterexamples to incorrect conjecturesNJ 4.2.12 A.5 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).NJ 4.2.12 A.5.1 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular bisector of a line segment


NJ 4.2.12 A.5.3 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular or parallel lines


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NJ 4.2.12 B - Transforming ShapesNJ 4.2.12 B.1 - By the End of Grade 12, students will: Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic representation, and, conversely, determine whether and how one representation can be transformed to another by a transformation or a sequence of transformations.

Topic 11 - Transformations in the coordinate plane

Obj. 107 - Relate the coordinates of a preimage or an image to a translation described using mapping notation

Obj. 108 - Determine the coordinates of a preimage or an image given a reflection across a horizontal line, a vertical line, the line y = x, or the line y = -xObj. 109 - Relate the coordinates of a preimage or an image to a dilation centered at the originObj. 110 - Determine the angle of rotational symmetry of a figureObj. 111 - Determine the coordinates of the image of a figure after two transformations of the same type

Obj. 112 - Determine the coordinates of the image of a figure after two transformations of different types

NJ 4.2.12 B.2 - By the End of Grade 12, students will: Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.NJ 4.2.12 B.3 - By the End of Grade 12, students will: Determine whether two or more given shapes can be used to generate a tessellation.



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NJ 4.2.12 B.4.1 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Fractals (e.g., Sierpinski's Triangle)NJ 4.2.12 B.4.2 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Patterns in areas and perimeters of self-similar figuresNJ 4.2.12 B.4.3 - By the End of Grade 12, students will: Generate and analyze iterative geometric patterns. Outcome of extending iterative process indefinitelyNJ 4.2.12 C - Coordinate Geometry


NJ 4.2.12 C.1.1 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Distance between two points

Topic 1 - Basic Concepts of Geometry

Obj. 4 - Determine the distance between two points

Obj. 5 - Solve a problem involving the distance formula

NJ 4.2.12 C.1.2 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Midpoint and slope of a line segment

Topic 1 - Basic Concepts of Geometry

Obj. 6 - Determine the midpoint of a line segment given the coordinates of the endpoints

Obj. 8 - Solve a problem involving the midpoint formula

NJ 4.2.12 C.1.3 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Finding the intersection of two linesNJ 4.2.12 C.1.4 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines with the same slope are parallel


Obj. 13 - Determine if lines through points with given coordinates are parallel or perpendicular


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NJ 4.2.12 C.1.5 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines that are perpendicular have slopes whose product is -1


Obj. 13 - Determine if lines through points with given coordinates are parallel or perpendicular

NJ 4.2.12 C.2 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors.NJ 4.2.12 C.2.1 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectorsNJ 4.2.12 C.3 - By the End of Grade 12, students will: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.

Topic 8 - Circles Obj. 68 - Determine the radius, center, or diameter of a circle given an equation

Obj. 69 - Determine the area or circumference of a circle given an equation of the circle

NJ 4.2.12 D - Units of Measurement



NJ 4.2.12 D.2.1 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Degree of accuracy of a given measurement tool


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NJ 4.2.12 D.2.2 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Finding the interval in which a computed measure (e.g., area or volume) lies, given the degree of precision of linear measurements


NJ 4.2.12 E.1.1 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems. Similar triangles

Topic 6 - Similarity Obj. 35 - Determine the length of a side or the measure of an angle in similar triangles

NJ 4.2.12 E.1.2 - By the End of Grade 12, students will: Use techniques of indirect measurement to represent and solve problems. Pythagorean theorem


Obj. 18 - Solve for the length of a side of a triangle using the Pythagorean theorem


Obj. 44 - Determine a length in a complex figure using the Pythagorean theorem



Obj. 50 - Determine a length using a sine, cosine, or tangent ratio in a right triangle

Obj. 51 - Determine the measure of an angle using a sine, cosine, or tangent ratio in a right triangleObj. 52 - WP: Determine a length in a right triangle using a sine, cosine, or tangent ratioObj. 53 - WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio

Topic 9 - Area Obj. 76 - Approximate the area of a right triangle using trigonometry


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NJ 4.3.12 A.1.3 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series. Sums of finite and infinite geometric seriesNJ 4.3.12 A.2 - By the End of Grade 12, students will: Develop an informal notion of limit.NJ 4.3.12 A.3 - By the End of Grade 12, students will: Use inductive reasoning to form generalizations.


Topic 8 - Circles Obj. 67 - Determine an equation of a circle





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NJ 4.3.12 B.2.3 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. InterceptsNJ 4.3.12 B.2.4 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. ContinuityNJ 4.3.12 B.2.5 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Maximum/minimum

NJ 4.3.12 B.2.6 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Estimating roots of equationsNJ 4.3.12 B.2.7 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of equationsNJ 4.3.12 B.2.8 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of linear inequalities using graphing techniquesNJ 4.3.12 B.2.9 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Rates of change


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NJ 4.3.12 B.4.1 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Linear vs. non-linearNJ 4.3.12 B.4.2 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Symmetry


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NJ 4.3.12 C.1.2 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Direct and inverse variationNJ 4.3.12 C.1.3 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Absolute valueNJ 4.3.12 C.1.4 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Expressions, equations and inequalitiesNJ 4.3.12 C.1.5 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Same function can model variety of phenomena


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NJ 4.3.12 C.1.6 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Growth/decay and change in the natural worldNJ 4.3.12 C.1.7 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Applications in mathematics, biology, and economics (including compound interest)NJ 4.3.12 C.2 - By the End of Grade 12, students will: Analyze and describe how a change in an independent variable leads to change in a dependent one.NJ 4.3.12 C.3 - By the End of Grade 12, students will: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).NJ 4.3.12 D - ProceduresNJ 4.3.12 D.1 - By the End of Grade 12, students will: Evaluate and simplify expressions.NJ 4.3.12 D.1.1 - By the End of Grade 12, students will: Evaluate and simplify expressions. Add and subtract polynomialsNJ 4.3.12 D.1.2 - By the End of Grade 12, students will: Evaluate and simplify expressions. Multiply a polynomial by a monomial or binomial

NJ 4.3.12 D.1.3 - By the End of Grade 12, students will: Evaluate and simplify expressions. Divide a polynomial by a monomialNJ 4.3.12 D.1.4 - By the End of Grade 12, students will: Evaluate and simplify expressions. Perform simple operations with rational expressions


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NJ 4.3.12 D.2 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities.NJ 4.3.12 D.2.1 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Linear equations and inequalities - algebraicallyNJ 4.3.12 D.2.2 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Quadratic equations - factoring (including trinomials when the coefficient of x2 is 1) and using the quadratic formula

NJ 4.3.12 D.2.3 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Literal equationsNJ 4.3.12 D.2.4 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. All types of equations and inequalities using graphing, computer, and graphing calculator techniquesNJ 4.3.12 D.3 - By the End of Grade 12, students will: Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.12 A - Data Analysis


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NJ 4.4.12 A.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.12 A.1.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)NJ 4.4.12 A.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts.




NJ 4.4.12 A.3 - By the End of Grade 12, students will: Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.NJ 4.4.12 A.4 - By the End of Grade 12, students will: Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of the data.


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NJ 4.4.12 A.5 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions.




NJ 4.4.12 B - ProbabilityNJ 4.4.12 B.1 - By the End of Grade 12, students will: Calculate the expected value of a probability-based game, given the probabilities and payoffs of the various outcomes, and determine whether the game is fair.

NJ 4.4.12 B.2 - By the End of Grade 12, students will: Use concepts and formulas of area to calculate geometric probabilities.

Topic 9 - Area Obj. 86 - Determine a probability using an area model

NJ 4.4.12 B.3 - By the End of Grade 12, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.


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NJ 4.4.12 B.4 - By the End of Grade 12, students will: Determine probabilities in complex situations.NJ 4.4.12 B.4.1 - By the End of Grade 12, students will: Determine probabilities in complex situations. Conditional eventsNJ 4.4.12 B.4.2 - By the End of Grade 12, students will: Determine probabilities in complex situations. Complementary eventsNJ 4.4.12 B.4.3 - By the End of Grade 12, students will: Determine probabilities in complex situations. Dependent and independent eventsNJ 4.4.12 B.5 - By the End of Grade 12, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 B.6 - By the End of Grade 12, students will: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).



NJ 4.4.12 C.2 - By the End of Grade 12, students will: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.NJ 4.4.12 C.3 - By the End of Grade 12, students will: Justify solutions to counting problems.


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NJ 4.4.12 C.4 - By the End of Grade 12, students will: Recognize and explain relationships involving combinations and Pascal's Triangle, and apply those methods to situations involving probability.NJ 4.4.12 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.12 D.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.NJ 4.4.12 D.1.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every edge in a graphNJ 4.4.12 D.1.2 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every vertex in a graphNJ 4.4.12 D.1.3 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring




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NJ 4.5 A - Problem SolvingNJ 4.5 A.1 - By the End of Grade 12, students will: Learn mathematics through problem solving, inquiry, and discovery.NJ 4.5 A.2 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts.NJ 4.5 A.2.1 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Open-ended problems


NJ 4.5 A.2.3 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Problems with multiple solutions


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NJ 4.5 A.2.4 - By the End of Grade 12, students will: Solve problems that arise in mathematics and in other contexts. Problems that can be solved in several waysNJ 4.5 A.3 - By the End of Grade 12, students will: Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.NJ 4.5 A.4 - By the End of Grade 12, students will: Pose problems of various types and levels of difficulty.


NJ 4.5 A.6 - By the End of Grade 12, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.2 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning


NJ 4.5 B.3 - By the End of Grade 12, students will: Analyze and evaluate the mathematical thinking and strategies of others.


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NJ 4.5 B.4 - By the End of Grade 12, students will: Use the language of mathematics to express mathematical ideas precisely.NJ 4.5 C - ConnectionsNJ 4.5 C.1 - By the End of Grade 12, students will: Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).

NJ 4.5 C.2 - By the End of Grade 12, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the End of Grade 12, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the End of Grade 12, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the End of Grade 12, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the End of Grade 12, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the End of Grade 12, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the End of Grade 12, students will: Use reasoning to support their mathematical conclusions and problem solutions.

NJ 4.5 D.3 - By the End of Grade 12, students will: Select and use various types of reasoning and methods of proof.


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NJ 4.5 D.4 - By the End of Grade 12, students will: Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.



NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)


NJ 4.5 E.1.3 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)


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NJ 4.5 E.1.4 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)NJ 4.5 E.2 - By the End of Grade 12, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the End of Grade 12, students will: Use representations to model and interpret physical, social, and mathematical phenomena.


NJ 4.5 F.2 - By the End of Grade 12, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.NJ 4.5 F.3 - By the End of Grade 12, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the End of Grade 12, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).




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Topic 1 - The Real Numbers Obj. 5 - Order rational numbers


NJ 4.1.12 B.1 - By the End of Grade 12, students will: Extend understanding and use of operations to real numbers and algebraic procedures.

Topic 1 - The Real Numbers Obj. 6 - Operations with rational numbers

Obj. 7 - Order of operationsNJ 4.1.12 B.2 - By the End of Grade 12, students will: Develop, apply, and explain methods for solving problems involving rational and negative exponents.

Topic 6 - Roots, Radicals, and Complex Numbers

Obj. 70 - Simplify expressions with fractional exponents

Obj. 73 - Simplify expressions with rational exponents

NJ 4.1.12 B.3 - By the End of Grade 12, students will: Perform operations on matrices.NJ 4.1.12 B.3.1 - By the End of Grade 12, students will: Perform operations on matrices. Addition and subtraction

Topic 5 - Matrices and Determinants

Obj. 59 - Matrices, sums and differences (3 x 3)

NJ 4.1.12 B.3.2 - By the End of Grade 12, students will: Perform operations on matrices. Scalar multiplication

Topic 5 - Matrices and Determinants

Obj. 58 - Matrices, multiply by a constant (2 x 2)



Obj. 70 - Simplify expressions with fractional exponents

Standards List with Aligned Product SkillsProduct NameAccelerated Math Algebra 2


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Obj. 73 - Simplify expressions with rational exponents

NJ 4.1.12 C - EstimationNJ 4.1.12 C.1 - By the End of Grade 12, students will: Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.NJ 4.2 - All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.NJ 4.2.12 A - Geometric Properties





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NJ 4.2.12 A.3.2.b - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Segment joining midpoints of two sides is parallel to and half the length of the third sideNJ 4.2.12 A.3.2.c - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Triangle InequalityNJ 4.2.12 A.3.2.d - By the End of Grade 12, students will: Apply the properties of geometric shapes. Triangles Special right trianglesNJ 4.2.12 A.3.3 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Minimal conditions for a shape to be a special quadrilateralNJ 4.2.12 A.3.4 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Circles - arcs, central and inscribed angles, chords, tangentsNJ 4.2.12 A.3.5 - By the End of Grade 12, students will: Apply the properties of geometric shapes. Self-similarityNJ 4.2.12 A.4 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems.

NJ 4.2.12 A.4.1 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Verification or refutation of proposed proofsNJ 4.2.12 A.4.2 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Simple proofs involving congruent trianglesNJ 4.2.12 A.4.3 - By the End of Grade 12, students will: Use reasoning and some form of proof to verify or refute conjectures and theorems. Counterexamples to incorrect conjectures


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NJ 4.2.12 A.5 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).NJ 4.2.12 A.5.1 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular bisector of a line segment


NJ 4.2.12 A.5.3 - By the End of Grade 12, students will: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology). Perpendicular or parallel linesNJ 4.2.12 B - Transforming ShapesNJ 4.2.12 B.1 - By the End of Grade 12, students will: Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic representation, and, conversely, determine whether and how one representation can be transformed to another by a transformation or a sequence of transformations.NJ 4.2.12 B.2 - By the End of Grade 12, students will: Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.


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NJ 4.2.12 B.3 - By the End of Grade 12, students will: Determine whether two or more given shapes can be used to generate a tessellation.





Topic 11 - Conics and Second-Degree Equations

Obj. 157 - Find distances between 2 points


Topic 3 - Relations, Functions, and Graphs

Obj. 39 - Find slopes from 2 points

NJ 4.2.12 C.1.3 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Finding the intersection of two lines


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NJ 4.2.12 C.1.4 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines with the same slope are parallel


Obj. 42 - Identify parallel and perpendicular lines

NJ 4.2.12 C.1.5 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines that are perpendicular have slopes whose product is -1


Obj. 42 - Identify parallel and perpendicular lines

NJ 4.2.12 C.2 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors.NJ 4.2.12 C.2.1 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectorsNJ 4.2.12 C.3 - By the End of Grade 12, students will: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.

Topic 11 - Conics and Second-Degree Equations

Obj. 160 - Circles, write equations given centers and radii






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Topic 7 - Quadratic Obj. 100 - WP: Pythagorean Theorem


Topic 15 - Trigonometry Obj. 223 - Find the sine, cosine, or tangent

Obj. 234 - Find a side given side and angleObj. 235 - Find unknown sides of right trianglesObj. 236 - WP: Trigonometry


Topic 7 - Quadratic Obj. 102 - WP: Area and perimeter


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Topic 12 - Sequences and Series Obj. 189 - Find general terms of geo seq given first 4 terms


Topic 12 - Sequences and Series Obj. 185 - Find sums of arithmetic series


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NJ 4.3.12 A.1.3 - By the End of Grade 12, students will: Use models and algebraic formulas to represent and analyze sequences and series. Sums of finite and infinite geometric series

Topic 12 - Sequences and Series Obj. 191 - Find sums of finite geometric series

Obj. 192 - Find sums of infinite geometric series

NJ 4.3.12 A.2 - By the End of Grade 12, students will: Develop an informal notion of limit.NJ 4.3.12 A.3 - By the End of Grade 12, students will: Use inductive reasoning to form generalizations.



Obj. 19 - Graph inequalities (number line)

Obj. 20 - Graph inequalities, 1-variable (coordinate plane)Obj. 21 - Graph linear inequalities in 2-variables


Obj. 34 - Graph linear equations, ax + by = cObj. 35 - Graph linear equations, y = ax + b

Topic 7 - Quadratic Obj. 96 - Graph quadratic functions




Obj. 39 - Find slopes from 2 points


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Obj. 26 - Domain and range, relations

Obj. 27 - Domain and range, functionsObj. 28 - Domain and range, determine from graphs

NJ 4.3.12 B.2.3 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. InterceptsNJ 4.3.12 B.2.4 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. ContinuityNJ 4.3.12 B.2.5 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Maximum/minimum


Topic 4 - Systems of Equations and Inequalities

Obj. 44 - Verify ordered pairs are solutions to systems

Obj. 47 - Determine number of solutions for systemsObj. 48 - Graph systems of equations

Obj. 49 - Verify ordered triples are solutions to systems


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NJ 4.3.12 B.2.8 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of linear inequalities using graphing techniques

Topic 4 - Systems of Equations and Inequalities

Obj. 56 - Solve systems of linear inequalities by graphing

Obj. 57 - Solve linear programming problems

NJ 4.3.12 B.2.9 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Rates of change







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Obj. 40 - WP: Linear equations

Topic 7 - Quadratic Obj. 97 - WP: Graph quadratic functions


Topic 7 - Quadratic Obj. 98 - Solve variation problems

Obj. 99 - WP: Variation problems


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NJ 4.3.12 C.1.3 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Absolute value


Obj. 25 - WP: Absolute value and inequalities

NJ 4.3.12 C.1.4 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Expressions, equations and inequalities


Obj. 12 - WP: Solve linear equations

Obj. 18 - WP: Solve linear inequalitiesObj. 25 - WP: Absolute value and inequalities


Obj. 40 - WP: Linear equations


Topic 9 - Exponents and Logarithms

Obj. 139 - WP: Growth and decay problems

NJ 4.3.12 C.1.7 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Applications in mathematics, biology, and economics (including compound interest)NJ 4.3.12 C.2 - By the End of Grade 12, students will: Analyze and describe how a change in an independent variable leads to change in a dependent one.NJ 4.3.12 C.3 - By the End of Grade 12, students will: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).


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NJ 4.3.12 D - ProceduresNJ 4.3.12 D.1 - By the End of Grade 12, students will: Evaluate and simplify expressions.

Topic 10 - Rational Expressions and Equations

Obj. 145 - Simplify rational expressions

Obj. 146 - Simplify rational expressions by factoring

NJ 4.3.12 D.1.1 - By the End of Grade 12, students will: Evaluate and simplify expressions. Add and subtract polynomials

Topic 8 - Polynomials Obj. 110 - Add polynomials

Obj. 111 - Subtract polynomialsObj. 112 - Add and subtract polynomials

NJ 4.3.12 D.1.2 - By the End of Grade 12, students will: Evaluate and simplify expressions. Multiply a polynomial by a monomial or binomial

Topic 8 - Polynomials Obj. 113 - Square a binomial, ax + by

Obj. 114 - Multiply 2 binomialsObj. 115 - Multiply monomials by polynomialsObj. 116 - Multiply binomials by trinomialsObj. 118 - Simplify polynomial expr using multiplication


Topic 8 - Polynomials Obj. 119 - Divide polynomials by monomials


Topic 10 - Rational Expressions and Equations

Obj. 148 - Multiply and simplify rational expressions

Obj. 149 - Divide and simplify rational expressionsObj. 150 - Add rational expressions

Obj. 151 - Subtract rational expressionsObj. 152 - Add and subtract rational expressionsObj. 153 - WP: Rational expressions


Topic 8 - Polynomials Obj. 109 - Evaluate polynomials for given values


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Obj. 11 - Solve linear equations

Obj. 12 - WP: Solve linear equations

Obj. 13 - Solve linear inequalitiesObj. 18 - WP: Solve linear inequalities


Topic 7 - Quadratic Obj. 89 - Factor quadratics, real roots

Obj. 91 - Quadratic formula, 2 real rootsObj. 92 - Quadratic formula, complex rootsObj. 101 - WP: Number problems using quadratic equationsObj. 102 - WP: Area and perimeterObj. 103 - WP: Other problems using quadratic equations

NJ 4.3.12 D.2.3 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Literal equations


Obj. 77 - Solve formulas for specified variables

NJ 4.3.12 D.2.4 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. All types of equations and inequalities using graphing, computer, and graphing calculator techniquesNJ 4.3.12 D.3 - By the End of Grade 12, students will: Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.12 A - Data AnalysisNJ 4.4.12 A.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.12 A.1.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)NJ 4.4.12 A.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts.





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NJ 4.4.12 B.2 - By the End of Grade 12, students will: Use concepts and formulas of area to calculate geometric probabilities.NJ 4.4.12 B.3 - By the End of Grade 12, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.NJ 4.4.12 B.4 - By the End of Grade 12, students will: Determine probabilities in complex situations.NJ 4.4.12 B.4.1 - By the End of Grade 12, students will: Determine probabilities in complex situations. Conditional events

Topic 13 - Probability Obj. 205 - Conditional probability

NJ 4.4.12 B.4.2 - By the End of Grade 12, students will: Determine probabilities in complex situations. Complementary eventsNJ 4.4.12 B.4.3 - By the End of Grade 12, students will: Determine probabilities in complex situations. Dependent and independent events

Topic 13 - Probability Obj. 204 - Probability of independent events

Obj. 206 - Probability of dependent events

NJ 4.4.12 B.5 - By the End of Grade 12, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 B.6 - By the End of Grade 12, students will: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).



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Topic 13 - Probability Obj. 200 - Combinations

NJ 4.4.12 C.2 - By the End of Grade 12, students will: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.

Topic 13 - Probability Obj. 196 - Fundamental Counting Principle

NJ 4.4.12 C.3 - By the End of Grade 12, students will: Justify solutions to counting problems.NJ 4.4.12 C.4 - By the End of Grade 12, students will: Recognize and explain relationships involving combinations and Pascal's Triangle, and apply those methods to situations involving probability.

Topic 13 - Probability Obj. 203 - Probability using Pascal's triangle


NJ 4.4.12 D.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.NJ 4.4.12 D.1.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every edge in a graphNJ 4.4.12 D.1.2 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every vertex in a graph


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NJ 4.4.12 D.1.3 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring







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NJ 4.5 A.6 - By the End of Grade 12, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking.


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NJ 4.5 B.1.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.2 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning



NJ 4.5 C.2 - By the End of Grade 12, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the End of Grade 12, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the End of Grade 12, students will: Apply mathematics in practical situations and in other disciplines.


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NJ 4.5 C.5 - By the End of Grade 12, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the End of Grade 12, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the End of Grade 12, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the End of Grade 12, students will: Use reasoning to support their mathematical conclusions and problem solutions.




NJ 4.5 E - Representations


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NJ 4.5 E.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)




NJ 4.5 F.2 - By the End of Grade 12, students will: Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.


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NJ 4.5 F.3 - By the End of Grade 12, students will: Use graphing calculators and computer software to investigate properties of functions and their graphs.NJ 4.5 F.4 - By the End of Grade 12, students will: Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).




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NJ 4.1.12 B.1 - By the End of Grade 12, students will: Extend understanding and use of operations to real numbers and algebraic procedures.NJ 4.1.12 B.2 - By the End of Grade 12, students will: Develop, apply, and explain methods for solving problems involving rational and negative exponents.NJ 4.1.12 B.3 - By the End of Grade 12, students will: Perform operations on matrices.NJ 4.1.12 B.3.1 - By the End of Grade 12, students will: Perform operations on matrices. Addition and subtractionNJ 4.1.12 B.3.2 - By the End of Grade 12, students will: Perform operations on matrices. Scalar multiplication


Obj. 108 - Matrices, multiply by a constant (2 x 2)



Standards List with Aligned Product SkillsProduct NameAccelerated Math Pre-Calculus


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Topic 11 - Vectors Obj. 158 - Find the distance between 2 points in space


Topic 1 - Review of Fundamental Concepts of Algebra

Obj. 1 - Apply the distance & midpoint formulas

NJ 4.2.12 C.1.3 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Finding the intersection of two lines


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NJ 4.2.12 C.1.4 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines with the same slope are parallelNJ 4.2.12 C.1.5 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines that are perpendicular have slopes whose product is -1NJ 4.2.12 C.2 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors.NJ 4.2.12 C.2.1 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectorsNJ 4.2.12 C.3 - By the End of Grade 12, students will: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.

Topic 7 - Conic Sections Obj. 94 - Circles, determine centers & radii from eqns

Obj. 95 - Circles, write eqns from given information






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Topic 4 - Trigonometric Functions

Obj. 65 - Find trig values given another trig value

Topic 5 - Applications in Trigonometry

Obj. 73 - WP: Right triangles


NJ 4.2.12 E.2.1 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures. Approximation of area using grids of different sizes


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NJ 4.2.12 E.2.2 - By the End of Grade 12, students will: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures. Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given conditions using graphing calculators, dynamic geometric software, and/or spreadsheets




Topic 9 - Sequences and Series Obj. 123 - Find terms of arith seq (1st-term & common diff)

Obj. 124 - Find specified term of arithmetic sequenceObj. 125 - Find terms of arith seq (formula for nth term)Obj. 126 - WP: Arithmetic sequences

Obj. 130 - Find terms of geo seq (1st term & common ratio)Obj. 131 - Find terms of geo seq given first termsObj. 132 - WP: Geometric sequences


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Topic 9 - Sequences and Series Obj. 127 - Find sums of arithmetic series


Topic 9 - Sequences and Series Obj. 133 - Find sums of finite geometric series

Obj. 134 - Find sums of infinite geometric seriesObj. 135 - Evaluate geometric series in sigma notationObj. 136 - WP: Geometric series




Obj. 2 - Graph lines

Obj. 23 - Graph rational functionsTopic 2 - Polynomials Obj. 36 - Graph quadratic functions

Obj. 46 - Graph nth-degree polynomials

Topic 3 - Exponential and Logarithmic Functions

Obj. 55 - Graph exponential functions

Topic 4 - Trigonometric Functions

Obj. 66 - Graph sin & cos using amp, period, & phase shiftObj. 67 - Graph tan & cot functions



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Obj. 16 - Domains & range, functions

NJ 4.3.12 B.2.3 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. InterceptsNJ 4.3.12 B.2.4 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Continuity

Topic 12 - Introduction to Calculus

Obj. 169 - Find intervals where functions are continuous



Obj. 120 - Max & min functions w/ constraints



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NJ 4.3.12 B.2.8 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of linear inequalities using graphing techniquesNJ 4.3.12 B.2.9 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Rates of change




Obj. 22 - Use rigid & nonrigid transformations to graph func





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Topic 2 - Polynomials Obj. 37 - WP: Quadratic functions


Obj. 57 - WP: Exponential functions



Obj. 25 - Solve direct & indirect variation problems


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NJ 4.3.12 C.1.3 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Absolute valueNJ 4.3.12 C.1.4 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Expressions, equations and inequalities


Obj. 5 - WP: Linear Equations

Obj. 15 - WP: Quadratic equationsObj. 34 - WP: Rational equations

Topic 2 - Polynomials Obj. 37 - WP: Quadratic functionsTopic 3 - Exponential and Logarithmic Functions

Obj. 57 - WP: Exponential functions



Obj. 61 - WP: Radioactive decay

NJ 4.3.12 C.1.7 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Applications in mathematics, biology, and economics (including compound interest)


Obj. 60 - WP: Compound interest

NJ 4.3.12 C.2 - By the End of Grade 12, students will: Analyze and describe how a change in an independent variable leads to change in a dependent one.NJ 4.3.12 C.3 - By the End of Grade 12, students will: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).NJ 4.3.12 D - Procedures


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NJ 4.3.12 D.1 - By the End of Grade 12, students will: Evaluate and simplify expressions.NJ 4.3.12 D.1.1 - By the End of Grade 12, students will: Evaluate and simplify expressions. Add and subtract polynomialsNJ 4.3.12 D.1.2 - By the End of Grade 12, students will: Evaluate and simplify expressions. Multiply a polynomial by a monomial or binomial

NJ 4.3.12 D.1.3 - By the End of Grade 12, students will: Evaluate and simplify expressions. Divide a polynomial by a monomialNJ 4.3.12 D.1.4 - By the End of Grade 12, students will: Evaluate and simplify expressions. Perform simple operations with rational expressions


Obj. 32 - Simplify, multiply, & divide rational expressions




Obj. 4 - Solve linear equations

Obj. 5 - WP: Linear EquationsObj. 7 - Solve linear inequalities with 1-variable



Obj. 12 - Solve quad eqns, factor (real roots)

Obj. 13 - Solve quad eqns, quadratic formulaObj. 15 - WP: Quadratic equations


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NJ 4.3.12 D.2.3 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Literal equationsNJ 4.3.12 D.2.4 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. All types of equations and inequalities using graphing, computer, and graphing calculator techniquesNJ 4.3.12 D.3 - By the End of Grade 12, students will: Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.12 A - Data AnalysisNJ 4.4.12 A.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.12 A.1.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)NJ 4.4.12 A.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts.



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NJ 4.4.12 A.5.2 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions. Correlation coefficient


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NJ 4.4.12 A.5.3 - By the End of Grade 12, students will: Analyze data using technology, and use statistical terminology to describe conclusions. Normal distribution (e.g., approximately 95% of the sample lies between two standard deviations on either side of the mean)



Topic 10 - Probability Obj. 150 - Find expected value

NJ 4.4.12 B.2 - By the End of Grade 12, students will: Use concepts and formulas of area to calculate geometric probabilities.NJ 4.4.12 B.3 - By the End of Grade 12, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.NJ 4.4.12 B.4 - By the End of Grade 12, students will: Determine probabilities in complex situations.NJ 4.4.12 B.4.1 - By the End of Grade 12, students will: Determine probabilities in complex situations. Conditional events

Topic 10 - Probability Obj. 146 - Conditional probability

NJ 4.4.12 B.4.2 - By the End of Grade 12, students will: Determine probabilities in complex situations. Complementary eventsNJ 4.4.12 B.4.3 - By the End of Grade 12, students will: Determine probabilities in complex situations. Dependent and independent events

Topic 10 - Probability Obj. 145 - Probability of independent events

Obj. 147 - Probability of dependent events


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NJ 4.4.12 B.5 - By the End of Grade 12, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 B.6 - By the End of Grade 12, students will: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).



Topic 10 - Probability Obj. 143 - WP: Combinations

NJ 4.4.12 C.2 - By the End of Grade 12, students will: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.

Topic 10 - Probability Obj. 137 - Fundamental Counting Principle

NJ 4.4.12 C.3 - By the End of Grade 12, students will: Justify solutions to counting problems.NJ 4.4.12 C.4 - By the End of Grade 12, students will: Recognize and explain relationships involving combinations and Pascal's Triangle, and apply those methods to situations involving probability.NJ 4.4.12 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.12 D.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.


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NJ 4.4.12 D.1.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every edge in a graphNJ 4.4.12 D.1.2 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every vertex in a graphNJ 4.4.12 D.1.3 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring





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Obj. 15 - WP: Quadratic equationsObj. 25 - Solve direct & indirect variation problemsObj. 34 - WP: Rational equations



Obj. 61 - WP: Radioactive decayTopic 5 - Applications in Trigonometry


Topic 9 - Sequences and Series Obj. 126 - WP: Arithmetic sequences

Obj. 132 - WP: Geometric sequencesObj. 136 - WP: Geometric series





Obj. 15 - WP: Quadratic equationsObj. 25 - Solve direct & indirect variation problemsObj. 34 - WP: Rational equations



Obj. 61 - WP: Radioactive decayTopic 5 - Applications in Trigonometry



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Topic 9 - Sequences and Series Obj. 136 - WP: Geometric series



NJ 4.5 A.6 - By the End of Grade 12, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Reading and writingNJ 4.5 B.1.2 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning


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NJ 4.5 C.2 - By the End of Grade 12, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the End of Grade 12, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the End of Grade 12, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the End of Grade 12, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).NJ 4.5 C.6 - By the End of Grade 12, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - Reasoning


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NJ 4.5 D.1 - By the End of Grade 12, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the End of Grade 12, students will: Use reasoning to support their mathematical conclusions and problem solutions.




NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas.NJ 4.5 E.1.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)


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NJ 4.1.12 B.1 - By the End of Grade 12, students will: Extend understanding and use of operations to real numbers and algebraic procedures.NJ 4.1.12 B.2 - By the End of Grade 12, students will: Develop, apply, and explain methods for solving problems involving rational and negative exponents.NJ 4.1.12 B.3 - By the End of Grade 12, students will: Perform operations on matrices.NJ 4.1.12 B.3.1 - By the End of Grade 12, students will: Perform operations on matrices. Addition and subtractionNJ 4.1.12 B.3.2 - By the End of Grade 12, students will: Perform operations on matrices. Scalar multiplicationNJ 4.1.12 B.4 - By the End of Grade 12, students will: Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.


Standards List with Aligned Product SkillsProduct NameAccelerated Math Calculus


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Topic 1 - Prerequisites Obj. 5 - Apply the distance & midpoint formulas

Topic 12 - Vectors and the Geometry of Space

Obj. 209 - Find distance between two points in space


Topic 1 - Prerequisites Obj. 5 - Apply the distance & midpoint formulas

Topic 12 - Vectors and the Geometry of Space

Obj. 210 - Apply midpoint formula for segments in spaces


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NJ 4.2.12 C.1.3 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Finding the intersection of two linesNJ 4.2.12 C.1.4 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines with the same slope are parallelNJ 4.2.12 C.1.5 - By the End of Grade 12, students will: Use coordinate geometry to represent and verify properties of lines and line segments. Lines that are perpendicular have slopes whose product is -1NJ 4.2.12 C.2 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors.NJ 4.2.12 C.2.1 - By the End of Grade 12, students will: Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectorsNJ 4.2.12 C.3 - By the End of Grade 12, students will: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.

Topic 1 - Prerequisites Obj. 6 - Write equations of circles





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NJ 4.2.12 D.2.1 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Degree of accuracy of a given measurement toolNJ 4.2.12 D.2.2 - By the End of Grade 12, students will: Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a situation. Finding the interval in which a computed measure (e.g., area or volume) lies, given the degree of precision of linear measurements






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Topic 5 - Integration Obj. 71 - Sigma notation, find formulas for sums of n terms

Topic 9 - Infinite Series Obj. 150 - List terms of sequencesObj. 152 - Find the nth term of sequences


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Topic 5 - Integration Obj. 68 - Find sums in sigma notation


Topic 9 - Infinite Series Obj. 156 - Find sums of convergent infinite series



Topic 1 - Prerequisites Obj. 10 - Graph lines

Obj. 24 - Graph trig functionsTopic 6 - Transcendental Functions

Obj. 93 - Determine if functions are one-to-oneObj. 101 - Graph exponential functionsObj. 108 - Graph exponential functions w/ various bases




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Topic 1 - Prerequisites Obj. 15 - Domain & range, functions

NJ 4.3.12 B.2.3 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Intercepts

Topic 1 - Prerequisites Obj. 7 - Find intercepts of relations on graphs

NJ 4.3.12 B.2.4 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Continuity

Topic 2 - Limits and Continuity Obj. 33 - Find intervals where functions are continuous


NJ 4.3.12 B.2.6 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Estimating roots of equationsNJ 4.3.12 B.2.7 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of equationsNJ 4.3.12 B.2.8 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Solutions of systems of linear inequalities using graphing techniques


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NJ 4.3.12 B.2.9 - By the End of Grade 12, students will: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques. Rates of change



Topic 1 - Prerequisites Obj. 18 - Graph functions using transformations




NJ 4.3.12 B.4.1 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Linear vs. non-linear


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NJ 4.3.12 B.4.2 - By the End of Grade 12, students will: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions. Symmetry

Topic 1 - Prerequisites Obj. 8 - Identify symmetry with respect to axes & origin


Topic 4 - Applications of Differentiation

Obj. 49 - Find intervals of increase & decrease


Topic 6 - Transcendental Functions

Obj. 112 - Applied problems: Exponential functions

NJ 4.3.12 C.1.2 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Direct and inverse variationNJ 4.3.12 C.1.3 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Absolute valueNJ 4.3.12 C.1.4 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Expressions, equations and inequalities


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Obj. 114 - Find exponential functions containing given pts

Obj. 115 - Applied problems: Exponential growth & decay

NJ 4.3.12 C.1.7 - By the End of Grade 12, students will: Use functions to model real-world phenomena and solve problems that involve varying quantities. Applications in mathematics, biology, and economics (including compound interest)NJ 4.3.12 C.2 - By the End of Grade 12, students will: Analyze and describe how a change in an independent variable leads to change in a dependent one.NJ 4.3.12 C.3 - By the End of Grade 12, students will: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).NJ 4.3.12 D - ProceduresNJ 4.3.12 D.1 - By the End of Grade 12, students will: Evaluate and simplify expressions.NJ 4.3.12 D.1.1 - By the End of Grade 12, students will: Evaluate and simplify expressions. Add and subtract polynomialsNJ 4.3.12 D.1.2 - By the End of Grade 12, students will: Evaluate and simplify expressions. Multiply a polynomial by a monomial or binomial



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Topic 1 - Prerequisites Obj. 1 - Solve 1-step inequalities


NJ 4.3.12 D.2.3 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. Literal equationsNJ 4.3.12 D.2.4 - By the End of Grade 12, students will: Select and use appropriate methods to solve equations and inequalities. All types of equations and inequalities using graphing, computer, and graphing calculator techniquesNJ 4.3.12 D.3 - By the End of Grade 12, students will: Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.


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NJ 4.4 - All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.NJ 4.4.12 A - Data AnalysisNJ 4.4.12 A.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups.NJ 4.4.12 A.1.1 - By the End of Grade 12, students will: Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)NJ 4.4.12 A.2 - By the End of Grade 12, students will: Evaluate the use of data in real-world contexts.





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NJ 4.4.12 B.2 - By the End of Grade 12, students will: Use concepts and formulas of area to calculate geometric probabilities.NJ 4.4.12 B.3 - By the End of Grade 12, students will: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.NJ 4.4.12 B.4 - By the End of Grade 12, students will: Determine probabilities in complex situations.NJ 4.4.12 B.4.1 - By the End of Grade 12, students will: Determine probabilities in complex situations. Conditional eventsNJ 4.4.12 B.4.2 - By the End of Grade 12, students will: Determine probabilities in complex situations. Complementary eventsNJ 4.4.12 B.4.3 - By the End of Grade 12, students will: Determine probabilities in complex situations. Dependent and independent eventsNJ 4.4.12 B.5 - By the End of Grade 12, students will: Estimate probabilities and make predictions based on experimental and theoretical probabilities.NJ 4.4.12 B.6 - By the End of Grade 12, students will: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).




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NJ 4.4.12 C.2 - By the End of Grade 12, students will: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.NJ 4.4.12 C.3 - By the End of Grade 12, students will: Justify solutions to counting problems.NJ 4.4.12 C.4 - By the End of Grade 12, students will: Recognize and explain relationships involving combinations and Pascal's Triangle, and apply those methods to situations involving probability.NJ 4.4.12 D - Discrete Mathematics-Vertex-Edge Graphs and Algorithms

NJ 4.4.12 D.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.NJ 4.4.12 D.1.1 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every edge in a graphNJ 4.4.12 D.1.2 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Circuits that include every vertex in a graphNJ 4.4.12 D.1.3 - By the End of Grade 12, students will: Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems. Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring


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NJ 4.5 A.6 - By the End of Grade 12, students will: Distinguish relevant from irrelevant information, and identify missing information.NJ 4.5 B - CommunicationNJ 4.5 B.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking.NJ 4.5 B.1.1 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Reading and writing


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NJ 4.5 B.1.2 - By the End of Grade 12, students will: Use communication to organize and clarify their mathematical thinking. Discussion, listening, and questioning



NJ 4.5 C.2 - By the End of Grade 12, students will: Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).NJ 4.5 C.3 - By the End of Grade 12, students will: Recognize that mathematics is used in a variety of contexts outside of mathematics.NJ 4.5 C.4 - By the End of Grade 12, students will: Apply mathematics in practical situations and in other disciplines.NJ 4.5 C.5 - By the End of Grade 12, students will: Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).


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NJ 4.5 C.6 - By the End of Grade 12, students will: Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.NJ 4.5 D - ReasoningNJ 4.5 D.1 - By the End of Grade 12, students will: Recognize that mathematical facts, procedures, and claims must be justified.NJ 4.5 D.2 - By the End of Grade 12, students will: Use reasoning to support their mathematical conclusions and problem solutions.




NJ 4.5 E - RepresentationsNJ 4.5 E.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas.


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NJ 4.5 E.1.1 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Concrete representations (e.g., base-ten blocks or algebra tiles)


NJ 4.5 E.1.3 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Symbolic representations (e.g., a formula)NJ 4.5 E.1.4 - By the End of Grade 12, students will: Create and use representations to organize, record, and communicate mathematical ideas. Graphical representations (e.g., a line graph)

Topic 1 - Prerequisites Obj. 10 - Graph lines

Obj. 18 - Graph functions using transformationsObj. 24 - Graph trig functions


Obj. 101 - Graph exponential functionsObj. 108 - Graph exponential functions w/ various bases

NJ 4.5 E.2 - By the End of Grade 12, students will: Select, apply, and translate among mathematical representations to solve problems.NJ 4.5 E.3 - By the End of Grade 12, students will: Use representations to model and interpret physical, social, and mathematical phenomena.


Obj. 114 - Find exponential functions containing given pts



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Documents

New Jersey State Standards Alignment Grades Two through Twelvedoc.renlearn.com/KMNet/R004259018GHD329.pdf · 2009. 8. 31. · New Jersey, Math, 2008, Grade 2, Core Curriculum Content