North Carolina State Standards Alignment Grades One

North Carolina State Standards Alignment Grades One through Twelve

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North Carolina 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 1 ..................................................... 1

Grade 2 ..................................................... 5

Grade 3 ....................................................10

Grade 4 ....................................................17

Grade 5 ....................................................27

Grade 6 ....................................................36

Grade 7 ....................................................46

Grade 8 ....................................................53

Algebra 1 ....................................................58

Geometry ....................................................63

Algebra 2 ....................................................73

Precalculus ....................................................78

AP Statistics ....................................................83

AP Calculus ....................................................88

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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 NameNorth Carolina, Math, 2003, Grade 1, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will read, write, and model whole numbers through 99 and compute with whole numbers.

NC 1.01 - Develop number sense for whole numbers through 99.NC 1.01.a - Connect the model, number word, and number using a variety of representations.

Topic 1 - Numbers and Operations

Obj. 1 - Read a whole number to 30

Obj. 3 - Determine the word form of a whole number to 30Obj. 5 - Count objects to 20Obj. 9 - Identify a number to 20 represented by a point on a number lineObj. 19 - Count objects grouped in tens and onesObj. 20 - Model a number to 100 using tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

NC 1.01.b - Use efficient strategies to count the number of objects in a set.


Obj. 5 - Count objects to 20

Obj. 19 - Count objects grouped in tens and ones

NC 1.01.c - Read and write numbers. Topic 1 - Numbers and Operations

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 100

NC 1.01.d - Compare and order sets and numbers.


Obj. 26 - Compare sets of objects using wordsObj. 27 - Compare whole numbers to 100 using wordsObj. 28 - Order whole numbers to 100 in ascending orderObj. 29 - Order whole numbers to 100 in descending order

NC 1.01.e - Build understanding of place value (ones, tens).


Obj. 20 - Model a number to 100 using tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

Obj. 22 - Represent a 2-digit number as tens and ones

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

Accelerated Math Grade 1

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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 1, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description


Obj. 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

NC 1.01.f - Estimate quantities fewer than or equal to 100.NC 1.01.g - Recognize equivalence in sets and numbers 1-99.NC 1.02 - Use groupings of 2's, 5's, and 10's with models and pictures to count collections of objects.

NC 1.03 - Develop fluency with single-digit addition and corresponding differences using strategies such as modeling, composing and decomposing quantities, using doubles, and making tens.


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

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 modelObj. 40 - Apply the relationship between addition and counting onObj. 41 - Apply the relationship between subtraction and counting back

NC 1.04 - Create, model, and solve problems that use addition, subtraction, and fair shares (between two or three).


Obj. 32 - Relate a picture model to a basic addition fact

Obj. 33 - Determine the basic addition fact shown by a picture model


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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. 36 - Relate a picture model to a basic subtraction factObj. 37 - Determine the basic subtraction fact shown by a picture modelObj. 38 - Determine the basic subtraction fact shown by a number-line modelObj. 39 - Relate a number-line model to a basic subtraction factObj. 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. 44 - Add three 1-digit numbers

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

- MeasurementNC 2 - The learner will use non-standard units of measure and tell time.NC 2.01 - For given objects:NC 2.01.a - Select an attribute (length, capacity, mass) to measure (use non-standard units).NC 2.01.b - Develop strategies to estimate size.

Topic 3 - Geometry and Measurement

Obj. 74 - Estimate length in nonstandard units

NC 2.01.c - Compare, using appropriate language, with respect to the attribute selected.


Obj. 70 - Compare objects using the vocabulary of measurement

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

NC 2.02 - Develop an understanding of the concept of time.

NC 2.02.a - Tell time at the hour and half-hour.


Obj. 76 - Tell time to the hour

Obj. 77 - Tell time to the half hour


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NC 2.02.b - Solve problems involving applications of time (clock and calendar).


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

Obj. 79 - Order the months of the yearObj. 80 - Determine the day of the week from a date on a calendar

- GeometryNC 3 - The learner will identify, describe, draw, and build basic geometric figures.NC 3.01 - Identify, build, draw and name parallelograms, squares, trapezoids, and hexagons.NC 3.02 - Identify, build, and name cylinders, cones, and rectangular prisms.NC 3.03 - Compare and contrast geometric figures.NC 3.04 - Solve problems involving spatial visualization. - Data Analysis and ProbabilityNC 4 - The learner will understand and use data and simple probability concepts.NC 4.01 - Collect, organize, describe and display data using line plots and tallies.

Topic 4 - Data Analysis and Statistics

Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)

NC 4.02 - Describe events as certain, impossible, more likely or less likely to occur. - AlgebraNC 5 - The learner will demonstrate an understanding of classification and patterning.NC 5.01 - Sort and classify objects by two attributes.


Obj. 86 - Determine the group in which an object belongsObj. 87 - Determine the rule used to sort objects

NC 5.02 - Use Venn diagrams to illustrate similarities and differences in two sets.NC 5.03 - Create and extend patterns, identify the pattern unit, and translate into other forms.

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

Obj. 67 - Extend a pictorial growth patternObj. 68 - Determine a pattern on a 1 to 100 chartObj. 69 - Complete a pattern on a 1 to 100 chart


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 2, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will read, write, model, and compute with whole numbers through 999.NC 1.01 - Develop number sense for whole numbers through 999.NC 1.01.a - Connect model, number word, and number using a variety of representations.

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 1,000Obj. 14 - Represent a 3-digit number as hundreds, tens, and ones

Obj. 15 - Determine the 3-digit number represented as hundreds, tens, and ones

NC 1.01.b - Read and write numbers. Topic 1 - Number Sense and Operations

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

NC 1.01.c - Compare and order. Topic 1 - Number Sense and Operations

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

NC 1.01.d - Rename.NC 1.01.e - Estimate.NC 1.01.f - Use a variety of models to build understanding of place value (ones, tens, hundreds).


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

NC 1.02 - Use area or region models and set models of fractions to explore part-whole relationships in contexts.

NC 1.02.a - Represent fractions (halves, thirds, fourths) concretely and symbolically.NC 1.02.b - Compare fractions (halves, thirds, fourths) using models.

NC 1.02.c - Make different representations of the same fraction.



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NC 1.02.d - Combine fractions to describe parts of a whole.NC 1.03 - Create, model, and solve problems that involve addition, subtraction, equal grouping, and division into halves, thirds, and fourths (record in fraction form).


Obj. 24 - Determine a number pair that totals 100

Obj. 25 - Determine a number pair that totals 1,000Obj. 41 - WP: Add or subtract numbers without regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

Obj. 46 - Determine the sum of equal groups using picturesObj. 47 - Use a repeated addition sentence to represent the sum of equal groupsObj. 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

Topic 2 - Algebraic Thinking Obj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers

NC 1.04 - Develop fluency with multi-digit addition and subtraction through 999 using multiple strategies.

NC 1.04.a - Strategies for adding and subtracting numbers.


Obj. 24 - Determine a number pair that totals 100Obj. 25 - Determine a number pair that totals 1,000Obj. 28 - Add two 3-digit numbers without regroupingObj. 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 regrouping


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Obj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 34 - Add 2- and 3- digit numbers with no more than one regrouping

Obj. 35 - Add two 3-digit numbers with one regroupingObj. 36 - Subtract a 3-digit number from a 3-digit number without regroupingObj. 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. 39 - Subtract a 1- or 2-digit number from a 3-digit number with one regroupingObj. 40 - Subtract a 3-digit number from a 3-digit number with one regroupingObj. 41 - WP: Add or subtract numbers without regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

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 numbersObj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers

NC 1.04.b - Estimation of sums and differences in appropriate situations.


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

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

NC 1.04.c - Relationships between operations.


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 numbers


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Obj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbersObj. 67 - Determine equivalent addition expressions involving 2-digit numbersObj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers

NC 1.05 - Create and solve problems using strategies such as modeling, composing and decomposing quantities, using doubles, and making tens and hundreds.

NC 1.06 - Define and recognize odd and even numbers.


Obj. 6 - Identify odd and even numbers between 100 and 1,000

- MeasurementNC 2 - The learner will recognize and use standard units of metric and customary measurement.NC 2.01 - Estimate and measure using appropriate units.NC 2.01.a - Length (meters, centimeters, feet, inches, yards).


Obj. 76 - Measure length in inches

Obj. 77 - Measure length in centimeters

NC 2.01.b - Temperature (Fahrenheit).


Obj. 82 - Read a thermometer in degrees Fahrenheit

NC 2.02 - Tell time at the five-minute intervals.


Obj. 78 - Tell time to the quarter hour

Obj. 79 - Tell time to 5-minute intervals

- GeometryNC 3 - The learner will perform simple transformations.NC 3.01 - Combine simple figures to create a given shape.NC 3.02 - Describe the change in attributes as two- and three-dimensional figures are cut and rearranged.NC 3.03 - Identify and make:NC 3.03.a - Symmetric figures. Topic 3 - Geometry and

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

NC 3.03.b - Congruent figures. Topic 3 - Geometry and Measurement

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

- Data Analysis and ProbabilityNC 4 - The learner will understand and use data and simple probability concepts.


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NC 4.01 - Collect, organize, describe and display data using Venn diagrams (three sets) and pictographs where symbols represent multiple units (2's, 5's, 10's).


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. 95 - Answer a question using information from a pictograph (1 symbol = more than 1 object)

NC 4.02 - Conduct simple probability experiments; describe the results and make predictions. - AlgebraNC 5 - The learner will recognize and represent patterns and simple mathematical relationships.NC 5.01 - Identify, describe, translate, and extend repeating and growing patterns.


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

Topic 2 - Algebraic Thinking Obj. 70 - Determine an addition or subtraction number pattern given a ruleObj. 71 - Determine the rule for an addition or subtraction number patternObj. 72 - Extend a number pattern involving additionObj. 73 - Extend a number pattern involving subtractionObj. 75 - Determine a repeating pattern corresponding to the same pattern expressed using different elements

NC 5.02 - Write addition and subtraction number sentences to represent a problem; use symbols to represent unknown quantities.

Topic 2 - Algebraic Thinking Obj. 69 - WP: Use an open sentence to represent a given situation


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 3, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will model, identify, and compute with whole numbers through 9,999.NC 1.01 - Develop number sense for whole numbers through 9,999.


Obj. 1 - Read a 4- or 5-digit whole numberObj. 2 - Determine the word form of a 4- or 5-digit whole number

NC 1.01.a - Connect model, number word, and number using a variety of representations.


Obj. 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 form

NC 1.01.b - Build understanding of place value (ones through thousands).


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

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

NC 1.01.c - Compare and order. Topic 1 - Number Sense and Operations

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 order

NC 1.02 - Develop fluency with multi-digit addition and subtraction through 9,999 using:NC 1.02.a - Strategies for adding and subtracting numbers.


Obj. 13 - Add 3- and 4-digit numbers with regroupingObj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping

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



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

NC 1.02.b - Estimation of sums and differences in appropriate situations.


Obj. 28 - Estimate a sum or difference of whole numbers to 10,000 by roundingObj. 29 - Estimate a sum or difference of two 3- to 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

NC 1.02.c - Relationships between operations.

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbersObj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbers

NC 1.03 - Develop fluency with multiplication from 1x1 to 12x12 and division up to two-digit by one-digit numbers using:NC 1.03.a - Strategies for multiplying and dividing numbers.


Obj. 35 - Know basic multiplication facts to 10 x 10Obj. 36 - Know basic multiplication facts for 11 and 12Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic facts

NC 1.03.b - Estimation of products and quotients in appropriate situations.NC 1.03.c - Relationships between operations.


Obj. 41 - Complete a multiplication and division fact family

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic facts


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Obj. 59 - Determine the missing dividend or divisor in a number sentence involving basic facts

NC 1.04 - Use basic properties (identity, commutative, associative, order of operations) for addition, subtraction, multiplication, and division.NC 1.05 - Use area or region models and set models of fractions to explore part-whole relationships.NC 1.05.a - Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).


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

NC 1.05.b - Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.


Obj. 48 - Compare fractions using models

Obj. 49 - Order fractions using modelsObj. 51 - Compare fractions with like denominatorsObj. 52 - Compare fractions with like numerators

NC 1.05.c - Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.


Obj. 50 - Identify equivalent fractions using models

NC 1.05.d - Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.NC 1.05.e - Understand and use mixed numbers and their equivalent fraction forms.


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NC 1.06 - Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.


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

Obj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regroupingObj. 28 - Estimate a sum or difference of whole numbers to 10,000 by roundingObj. 29 - Estimate a sum or difference of two 3- to 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 methodObj. 35 - Know basic multiplication facts to 10 x 10Obj. 36 - Know basic multiplication facts for 11 and 12Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

Topic 2 - Algebraic Thinking Obj. 61 - Determine the operation needed to make a number sentence trueObj. 62 - WP: Determine the operation needed for a given situation

Obj. 63 - WP: Determine a multiplication or division sentence for a given situation

- MeasurementNC 2 - The learner will recognize and use standard units of metric and customary measurement.


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NC 2.01 - Solve problems using measurement concepts and procedures involving:NC 2.01.a - Elapsed time. Topic 3 - Geometry and

MeasurementObj. 76 - Calculate elapsed time within an hour, given two clocks, without regroupingObj. 77 - Calculate elapsed time within an hour, given two clocks, with regroupingObj. 78 - WP: Calculate elapsed time within an hour given two clocks

Obj. 79 - WP: Calculate elapsed time within an hourObj. 80 - WP: Determine the end time given the start time and the elapsed time within an hourObj. 81 - WP: Determine the start time given the end time on a clock and the elapsed time within an hour

Obj. 82 - WP: Determine the start time given the end time and the elapsed time within an hourObj. 83 - Determine a date using a calendar

NC 2.01.b - Equivalent measures within the same measurement system.


Obj. 68 - Convert between inches, feet, and yards

Obj. 69 - Convert between centimeters and metersObj. 75 - Convert hours to minutes or minutes to seconds

NC 2.02 - Estimate and measure using appropriate units.NC 2.02.a - Capacity (cups, pints, quarts, gallons, liters).NC 2.02.b - Length (miles, kilometers)NC 2.02.c - Mass (ounces, pounds, grams, kilograms).NC 2.02.d - Temperature (Fahrenheit, Celsius).


Obj. 84 - Read a thermometer in degrees Fahrenheit or Celsius

- GeometryNC 3 - The learner will recognize and use basic geometric properties of two- and three-dimensional figures.

NC 3.01 - Use appropriate vocabulary to compare, describe, and classify two- and three-dimensional figures.


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


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

NC 3.02 - Use a rectangular coordinate system to solve problems.

NC 3.02.a - Graph and identify points with whole number and/or letter coordinates.


Obj. 103 - Determine a location using map coordinates

Obj. 104 - Determine the map coordinates for a location

NC 3.02.b - Describe the path between given points on the plane.


Obj. 102 - Determine the directions to a position on a map

- Data Analysis and ProbabilityNC 4 - The learner will understand and use data and simple probability concepts.NC 4.01 - Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems.

Topic 4 - Data Analysis, Statistics, and Probability

Obj. 107 - Read a line plot

Obj. 108 - Use a line plot to represent dataObj. 109 - Answer a question using information from a line plotObj. 110 - Use a frequency table to represent dataObj. 111 - Answer a question using information from a frequency table

NC 4.02 - Determine the number of permutations and combinations of up to three items.NC 4.03 - Solve probability problems using permutations and combinations. - AlgebraNC 5 - The learner will recognize, determine, and represent patterns and simple mathematical relationships.NC 5.01 - Describe and extend numeric and geometric patterns.NC 5.02 - Extend and find missing terms of repeating and growing patterns.

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

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

NC 5.03 - Use symbols to represent unknown quantities in number sentences.

Topic 2 - Algebraic Thinking Obj. 61 - Determine the operation needed to make a number sentence true


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NC 5.04 - Find the value of the unknown in a number sentence.

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbersObj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbersObj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 60 - Recognize equivalent multiplication or division expressions involving basic facts


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 4, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will read, write, model, and compute with non-negative rational numbers.NC 1.01 - Develop number sense for rational numbers 0.01 through 99,999.NC 1.01.a - Connect model, number word, and number using a variety of representations.


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

Obj. 63 - Determine the word form of a decimal number through the hundredths placeObj. 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. 66 - Identify a decimal number to tenths represented by a point on a number lineObj. 67 - Locate a decimal number to tenths on a number line

NC 1.01.b - Build understanding of place value (hundredths through ten thousands).NC 1.01.c - Compare and order rational numbers.


Obj. 52 - Compare fractions on a number lineObj. 53 - Order fractions on a number lineObj. 68 - Determine the decimal number equivalent to a fraction with a denominator of 10 or 100Obj. 69 - Determine a fraction equivalent to a decimal, using a denominator of 10 or 100Obj. 70 - Determine the decimal number equivalent to a fraction modelObj. 71 - Determine the fraction equivalent to a decimal number modelObj. 72 - Compare decimal numbers through the hundredths place

Obj. 73 - Order decimal numbers through the hundredths place

NC 1.01.d - Make estimates of rational numbers in appropriate situations.


Obj. 80 - Round a decimal number to a specified place through hundredths



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NC 1.02 - Develop fluency with multiplication and division:NC 1.02.a - Two-digit by two-digit multiplication (larger numbers with calculator).


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

NC 1.02.b - Up to three-digit by two-digit division (larger numbers with calculator).


Obj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainderObj. 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


NC 1.02.c - Strategies for multiplying and dividing numbers.


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


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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

Obj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainderObj. 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. 42 - WP: Solve a 2-step whole number problem using more than 1 operation

NC 1.02.d - Estimation of products and quotients in appropriate situations.


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

Obj. 31 - Estimate a product of whole numbers using any method


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Obj. 32 - WP: Estimate a product of two whole numbers using any method

NC 1.02.e - Relationships between operations.NC 1.03 - Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers.


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

Obj. 44 - Identify a mixed number represented by a point on a number lineObj. 45 - Locate a mixed number on a number lineObj. 46 - WP: Use a mixed number to represent an amount in a sharing situationObj. 47 - Identify an improper fraction represented by a model of a mixed numberObj. 48 - Identify an improper fraction represented by a point on a number lineObj. 49 - Locate an improper fraction on a number lineObj. 50 - Simplify a fractionObj. 51 - Determine a set of equivalent fractions

NC 1.04 - Develop fluency with addition and subtraction of non-negative rational numbers with like denominators, including decimal fractions through hundredths.NC 1.04.a - Develop and analyze strategies for adding and subtracting numbers.


Obj. 54 - Add fractions with like denominators no greater than 10 using modelsObj. 55 - Add fractions with like denominators no greater than 10Obj. 56 - Add fractions with like denominators no greater than 10 and simplify the sumObj. 57 - WP: Add fractions with like denominators no greater than 10 and simplify the sumObj. 58 - Subtract fractions with like denominators no greater than 10 using models


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Obj. 59 - Subtract fractions with like denominators no greater than 10

Obj. 60 - Subtract fractions with like denominators no greater than 10 and simplify the differenceObj. 61 - WP: Subtract fractions with like denominators no greater than 10 and simplify the differenceObj. 74 - Determine decimal number pairs that total 1 or 10Obj. 75 - Add two decimal numbers through hundredthsObj. 76 - Subtract two decimal numbers through hundredthsObj. 77 - WP: Add or subtract money amounts greater than $1Obj. 79 - WP: Add or subtract decimal numbers of the same place through hundredths

NC 1.04.b - Estimate sums and differences.


Obj. 81 - Estimate a decimal number sum or difference by rounding to whole numbers

NC 1.04.c - Judge the reasonableness of solutions.NC 1.05 - Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.


Obj. 10 - Add a 5-digit or greater whole number and a 3-digit or greater whole number

Obj. 11 - Add three multi-digit whole numbersObj. 13 - Subtract a 3-digit or greater whole number from a 5-digit or greater whole numberObj. 14 - WP: Add a 5-digit or greater whole number and a 3-digit or greater whole numberObj. 15 - WP: Add three multi-digit whole numbersObj. 16 - WP: Subtract a 3-digit or greater whole number from a 5-digit or greater whole numberObj. 18 - WP: Estimate the sum or difference of two whole numbers, all values less than 1,000,000Obj. 19 - WP: Solve a 2-step problem involving addition and/or subtraction of multi-digit whole numbers


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Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000Obj. 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. 25 - Multiply a 3-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

Obj. 30 - Estimate a product of whole numbers by roundingObj. 31 - Estimate a product of whole numbers using any methodObj. 32 - WP: Estimate a product of two whole numbers using any methodObj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainderObj. 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




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Obj. 42 - WP: Solve a 2-step whole number problem using more than 1 operationObj. 54 - Add fractions with like denominators no greater than 10 using modelsObj. 55 - Add fractions with like denominators no greater than 10Obj. 56 - Add fractions with like denominators no greater than 10 and simplify the sumObj. 57 - WP: Add fractions with like denominators no greater than 10 and simplify the sumObj. 58 - Subtract fractions with like denominators no greater than 10 using modelsObj. 59 - Subtract fractions with like denominators no greater than 10

Obj. 60 - Subtract fractions with like denominators no greater than 10 and simplify the differenceObj. 61 - WP: Subtract fractions with like denominators no greater than 10 and simplify the differenceObj. 74 - Determine decimal number pairs that total 1 or 10Obj. 75 - Add two decimal numbers through hundredthsObj. 76 - Subtract two decimal numbers through hundredthsObj. 77 - WP: Add or subtract money amounts greater than $1Obj. 79 - WP: Add or subtract decimal numbers of the same place through hundredths

- MeasurementNC 2 - The learner will understand and use perimeter and area.NC 2.01 - Develop strategies to determine the area of rectangles and the perimeter of plane figures.


Obj. 110 - Determine the perimeter of a rectangle given a picture showing length and widthObj. 111 - WP: Determine the perimeter of a rectangle given a picture showing length and widthObj. 112 - WP: Determine the perimeter of a square or rectangle


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Obj. 115 - Determine the area of a rectangle given a picture showing the length and widthObj. 116 - Determine the area of a rectangle given the length and width

Obj. 117 - WP: Determine the area of a rectangle

NC 2.02 - Solve problems involving perimeter of plane figures and areas of rectangles.


Obj. 110 - Determine the perimeter of a rectangle given a picture showing length and widthObj. 111 - WP: Determine the perimeter of a rectangle given a picture showing length and widthObj. 112 - WP: Determine the perimeter of a square or rectangleObj. 113 - Determine the missing side length of a rectangle given a side length and the perimeterObj. 115 - Determine the area of a rectangle given a picture showing the length and widthObj. 116 - Determine the area of a rectangle given the length and width

Obj. 117 - WP: Determine the area of a rectangleObj. 118 - Determine the missing side length of a rectangle given a side length and the area

- GeometryNC 3 - The learner will recognize and use geometric properties and relationships.NC 3.01 - Use the coordinate system to describe the location and relative position of points and draw figures in the first quadrant.


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

NC 3.02 - Describe the relative position of lines using concepts of parallelism and perpendicularity.NC 3.03 - Identify, predict, and describe the results of transformations of plane figures.NC 3.03.a - Reflections. Topic 3 - Geometry and

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


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NC 3.03.b - Translations. Topic 3 - Geometry and Measurement

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

NC 3.03.c - Rotations. Topic 3 - Geometry and Measurement

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

- Data Analysis and ProbabilityNC 4 - The learner will understand and use graphs, probability, and data analysis.NC 4.01 - Collect, organize, analyze, and display data (including line graphs and bar graphs) to solve problems.


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. 138 - Answer a question using information from a circle graph

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

NC 4.02 - Describe the distribution of data using median, range and mode.

NC 4.03 - Solve problems by comparing two sets of related data.NC 4.04 - Design experiments and list all possible outcomes and probabilities for an event.


Obj. 143 - List possible outcomes of a simple event

- AlgebraNC 5 - The learner will demonstrate an understanding of mathematical relationships.NC 5.01 - Identify, describe, and generalize relationships in which:NC 5.01.a - Quantities change proportionally.

Topic 2 - Algebra Obj. 91 - Determine a rule that relates two variables

NC 5.01.b - Change in one quantity relates to change in a second quantity.

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

NC 5.02 - Translate among symbolic, numeric, verbal, and pictorial representations of number relationships.

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

Obj. 91 - Determine a rule that relates two variables

NC 5.03 - Verify mathematical relationships using:


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NC 5.03.a - Models, words, and numbers.NC 5.03.b - Order of operations and the identity, commutative, associative, and distributive properties.


Obj. 21 - Apply the distributive property to the multiplication of a 2-digit number by a 1- or 2-digit number

Obj. 22 - Apply the distributive property to multiply a multi-digit number by a 1-digit number


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 5, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will understand and compute with non-negative rational numbers.NC 1.01 - Develop number sense for rational numbers 0.001 through 999,999.NC 1.01.a - Connect model, number word, and number using a variety of representations.


Obj. 70 - Determine a decimal number represented in expanded formObj. 71 - Represent a decimal number in expanded form

NC 1.01.b - Build understanding of place value (thousandths through hundred thousands).


Obj. 69 - Determine the value of a digit in a decimal number to thousandths

NC 1.01.c - Compare and order rational numbers.


Obj. 33 - Compare fractions with unlike denominatorsObj. 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

NC 1.01.d - Make estimates of rational numbers in appropriate situations.


Obj. 26 - Know the effects of rounding

Obj. 55 - Round a fraction to a benchmark number of 0, 1/2, or 1Obj. 82 - Round a decimal number to a specified decimal place to thousandths

NC 1.02 - Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).NC 1.02.a - Develop and analyze strategies for adding and subtracting numbers.


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 sum



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Obj. 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 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


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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 number

NC 1.02.b - Estimate sums and differences.


Obj. 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. 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

NC 1.02.c - Judge the reasonableness of solutions.NC 1.03 - Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.


Obj. 11 - Multiply a 3- or 4-digit whole number by a 3-digit whole number

Obj. 12 - WP: Multiply a 3- or 4-digit whole number by a 3-digit whole numberObj. 13 - Divide a multi-digit whole number by multiples of 100 or 1,000


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Obj. 14 - Divide a multi-digit whole number by a 1-digit number with no remainder and at least one zero in the quotientObj. 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. 27 - Estimate a quotient using compatible numbersObj. 28 - Estimate a quotient using any methodObj. 29 - WP: Estimate a quotient using any methodObj. 35 - Add fractions with like denominators greater than 10 and simplify the sum


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


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

Obj. 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. 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. 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

- MeasurementNC 2 - The learner will recognize and use standard units of metric and customary measurement.


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NC 2.01 - Estimate the measure of an object in one system given the measure of that object in another system.NC 2.02 - Identify, estimate, and measure the angles of plane figures using appropriate tools.


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

- GeometryNC 3 - The learner will understand and use properties and relationships of plane figures.NC 3.01 - Identify, define, describe, and accurately represent triangles, quadrilaterals, and other polygons.NC 3.02 - Make and test conjectures about polygons involving:

NC 3.02.a - Sum of the measures of interior angles.NC 3.02.b - Lengths of sides and diagonals.NC 3.02.c - Parallelism and perpendicularity of sides and diagonals.NC 3.03 - Classify plane figures according to types of symmetry (line, rotational).


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

NC 3.04 - Solve problems involving the properties of triangles, quadrilaterals, and other polygons.NC 3.04.a - Sum of the measures of interior angles.NC 3.04.b - Lengths of sides and diagonals.NC 3.04.c - Parallelism and perpendicularity of sides and diagonals. - Data Analysis and ProbabilityNC 4 - The learner will understand and use graphs and data analysis.NC 4.01 - Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems.


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


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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 problemObj. 158 - Answer a question using information from a Venn diagram

NC 4.02 - Compare and contrast different representations of the same data; discuss the effectiveness of each representation.

NC 4.03 - Solve problems with data from a single set or multiple sets of data using median, range, and mode.


Obj. 159 - Determine the mode from a graph

Obj. 160 - Determine the range from a graphObj. 162 - Determine the median of an odd number of data valuesObj. 163 - Determine the mode of a set of whole number dataObj. 164 - Determine the range of a set of whole number data

- AlgebraNC 5 - The learner will demonstrate an understanding of patterns, relationships, and elementary algebraic representation.NC 5.01 - Describe, extend, and generalize numeric and geometric patterns using tables, graphs, words, and symbols.

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 numbersObj. 111 - Use a first quadrant graph to represent the values from a table generated in context


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NC 5.02 - Use algebraic expressions, patterns, and one-step equations and inequalities to solve problems.

Topic 2 - Algebra Obj. 100 - WP: Use a variable expression with one operation to represent a situation

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

NC 5.03 - Identify, describe, and analyze situations with constant or varying rates of change.


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 6, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will understand and compute with rational numbers.

NC 1.01 - Develop number sense for negative rational numbers.NC 1.01.a - Connect the model, number word, and number using a variety of representations, including the number line.


Obj. 89 - Identify or locate an integer on a number line

NC 1.01.b - Compare and order. Topic 1 - Number Sense and Operations

Obj. 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

NC 1.01.c - Make estimates in appropriate situations.NC 1.02 - Develop meaning for percents.NC 1.02.a - Connect the model, number word, and number using a variety of representations.NC 1.02.b - Make estimates in appropriate situations.


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

NC 1.03 - Compare and order rational numbers.


Obj. 68 - Convert a mixed number to a decimal numberObj. 69 - Convert a decimal number to a mixed numberObj. 70 - Convert a fraction to a repeating decimal numberObj. 72 - Convert a decimal number to a percentageObj. 73 - Convert a percentage to a decimal numberObj. 74 - Convert a fraction to a percentageObj. 75 - Convert a percentage to a fractionObj. 76 - Compare numbers in decimal and fractional formsObj. 77 - Order numbers in decimal and fractional forms

NC 1.04 - Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.


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

Obj. 14 - Subtract fractions with unlike denominators and simplify the difference



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Obj. 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

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 fraction


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Obj. 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 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. 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 neededObj. 67 - WP: Solve a 2-step problem involving decimals

NC 1.04.a - Analyze computational strategies.NC 1.04.b - Describe the effect of operations on size.NC 1.04.c - Estimate the results of computations.


Obj. 52 - WP: Estimate the product of two decimalsObj. 66 - WP: Estimate the quotient of two decimals

NC 1.04.d - Judge the reasonableness of solutions.NC 1.05 - Develop fluency in the use of factors, multiples, exponential notation, and prime factorization.


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

Obj. 2 - Determine the greatest common factor of three numbers to 100Obj. 3 - Determine the least common multiple of three numbersObj. 4 - WP: Determine the least common multiple of two or more numbers

NC 1.06 - Use exponential, scientific, and calculator notation to write very large and very small numbers.


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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 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

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 quotient


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Obj. 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 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. 52 - WP: Estimate the product of two decimalsObj. 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 places


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Obj. 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. 66 - WP: Estimate the quotient of two decimalsObj. 67 - WP: Solve a 2-step problem involving decimals

- MeasurementNC 2 - The learner will select and use appropriate tools to measure two- and three-dimensional figures.NC 2.01 - Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.


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

NC 2.02 - Solve problems involving perimeter/circumference and area of plane figures.


Obj. 120 - Determine the perimeter of a complex shape

Obj. 121 - Determine the area of a complex shape


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Obj. 122 - WP: Determine the perimeter or the area of a complex shapeObj. 124 - Determine the circumference of a circle using 22/7 for piObj. 125 - Determine the circumference of a circle using 3.14 for piObj. 126 - WP: Determine the circumference of a circle

- GeometryNC 3 - The learner will understand and use properties and relationships of geometric figures in the coordinate plane.NC 3.01 - Identify and describe the intersection of figures in a plane.NC 3.02 - Identify the radius, diameter, chord, center, and circumference of a circle; determine the relationships among them.


Obj. 123 - Answer a question about the parts and relationships in a circle

NC 3.03 - Transform figures in the coordinate plane and describe the transformation.


Obj. 136 - Determine the result of a reflection, a rotation, or a translation on the Cartesian planeObj. 137 - Determine the transformation that generates the image of a figure in the Cartesian plane

NC 3.04 - Solve problems involving geometric figures in the coordinate plane. - Data Analysis and ProbabilityNC 4 - The learner will understand and determine probabilities.NC 4.01 - Develop fluency with counting strategies to determine the sample space for an event. Include lists, tree diagrams, frequency distribution tables, permutations, combinations, and the Fundamental Counting Principle.


Obj. 157 - Determine the number of possible combinations of a set of objects

NC 4.02 - Use a sample space to determine the probability of an event.

NC 4.03 - Conduct experiments involving simple and compound events.


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NC 4.04 - Determine and compare experimental and theoretical probabilities for simple and compound events.


Obj. 151 - Determine an experimental probability given a list of results

Obj. 152 - Determine the probability of a single eventObj. 154 - Make a prediction based on an experimental probability

Obj. 155 - Make a prediction based on a theoretical probability

NC 4.05 - Determine and compare experimental and theoretical probabilities for independent and dependent events.


Obj. 156 - Compare predictions from experimental and theoretical probability

NC 4.06 - Design and conduct experiments or surveys to solve problems; report and analyze results.

- AlgebraNC 5 - The learner will demonstrate an understanding of simple algebraic expressions.NC 5.01 - Simplify algebraic expressions and verify the results using the basic properties of rational numbers.NC 5.01.a - Identity.NC 5.01.b - Commutative.NC 5.01.c - Associative.NC 5.01.d - Distributive.NC 5.01.e - Order of operations.NC 5.02 - Use and evaluate algebraic expressions.

Topic 2 - Algebra Obj. 95 - WP: Use a variable expression with two operations to represent a situationObj. 98 - Evaluate a 1-variable expression, with two or three operations, using whole number substitutionObj. 99 - Evaluate a 2-variable expression, with two or three operations, using whole number substitutionObj. 100 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbersObj. 103 - WP: Generate a table of paired numbers based on a variable expression with two operations

NC 5.03 - Solve simple (one- and two-step) equations or inequalities.

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


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NC 5.04 - Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.


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

Obj. 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


Obj. 134 - Determine a length given a scale


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 7, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will understand and compute with rational numbers.

NC 1.01 - Develop and use ratios, proportions, and percents to solve problems.


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. 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. 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

Obj. 52 - WP: Determine a unit rate

Obj. 53 - WP: Use a unit rate to solve a problem

Topic 2 - Algebra Obj. 70 - Solve a proportion involving decimalsObj. 71 - WP: Solve a proportionObj. 72 - WP: Use direct variation to solve a problem


Obj. 106 - Determine the scale for a drawing or map questionObj. 107 - WP: Solve a problem involving a map or scale drawing


Obj. 136 - Use a proportion to make an estimate, related to a population, based on a sample

NC 1.02 - Develop fluency in addition, subtraction, multiplication, and division of rational numbers.


Obj. 30 - WP: Answer a question involving a fraction and a decimal

Obj. 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 integersObj. 43 - WP: Multiply or divide integers

NC 1.02.a - Analyze computational strategies.


Obj. 35 - Add integers using a number lineObj. 36 - Add integers using a model


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Obj. 38 - Subtract integers using a number line

NC 1.02.b - Describe the effect of operations on size.NC 1.02.c - Estimate the results of computations.


Obj. 54 - Estimate the product of a fraction and a whole numberObj. 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

NC 1.02.d - Judge the reasonableness of solutions.NC 1.03 - Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.


Obj. 30 - WP: Answer a question involving a fraction and a decimal

Obj. 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 integersObj. 43 - WP: Multiply or divide integersObj. 54 - Estimate the product of a fraction and a whole numberObj. 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

- MeasurementNC 2 - The learner will understand and use measurement involving two- and three-dimensional figures.NC 2.01 - Draw objects to scale and use scale drawings to solve problems.


Obj. 107 - WP: Solve a problem involving a map or scale drawing

NC 2.02 - Solve problems involving volume and surface area of cylinders, prisms, and composite shapes.


Obj. 93 - Determine the volume of a rectangular or a triangular prism


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Obj. 94 - Determine the volume of a cylinderObj. 95 - WP: Determine the volume of a cylinderObj. 96 - WP: Solve a problem involving the volume of a geometric solidObj. 97 - Determine the surface area of a 3-dimensional shape given a net

Obj. 98 - Determine the surface area of a triangular prismObj. 99 - Determine the surface area of a cylinderObj. 100 - WP: Determine the surface area of a geometric solid

- GeometryNC 3 - The learner will understand and use properties and relationships in geometry.NC 3.01 - Using three-dimensional figures:NC 3.01.a - Identify, describe, and draw from various views (top, side, front, corner).


Obj. 124 - Relate a 3-dimensional shape to its top and side views

NC 3.01.b - Build from various views.

NC 3.01.c - Describe cross-sectional views.NC 3.02 - Identify, define, and describe similar and congruent polygons with respect to angle measures, length of sides, and proportionality of sides.


Obj. 101 - Identify corresponding parts of congruent shapes

Obj. 102 - Identify congruent shapes given side and angle measures

NC 3.03 - Use scaling and proportional reasoning to solve problems related to similar and congruent polygons.


Obj. 103 - Determine a missing dimension given two congruent shapes

Obj. 104 - Determine a missing dimension given two similar shapes

Obj. 105 - WP: Solve a problem involving similar shapes

- Data Analysis and ProbabilityNC 4 - The learner will understand and use graphs and data analysis.


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NC 4.01 - Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.


Obj. 125 - Answer a question using information from a circle graph using percentage calculations

Obj. 126 - Use a circle graph to represent percentage dataObj. 127 - Use a histogram to represent dataObj. 128 - Answer a question using information from a histogramObj. 129 - Read a double stem-and-leaf plotObj. 130 - Answer a question using information from a double stem-and-leaf plotObj. 131 - Answer a question using information from a Venn diagram containing summarized data

NC 4.02 - Calculate, use, and interpret the mean, median, mode, range, frequency distribution, and inter-quartile range for a set of data.


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

NC 4.03 - Describe how the mean, median, mode, range, frequency distribution, and inter-quartile range of a set of data affect its graph.NC 4.04 - Identify outliers and determine their effect on the mean, median, mode, and range of a set of data.NC 4.05 - Solve problems involving two or more sets of data using appropriate statistical measures. - AlgebraNC 5 - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.

NC 5.01 - Identify, analyze, and create linear relations, sequences, and functions using symbols, graphs, tables, diagrams, and written descriptions.

Topic 2 - Algebra Obj. 68 - Use a variable expression with two operations to represent a table of paired numbers


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Obj. 76 - Determine the graph of an inequality on a number lineObj. 79 - Determine the graph of the solution set of a 1-step linear inequalityObj. 81 - Use a table to represent a linear functionObj. 82 - Use a graph to represent the ordered pairs in a function tableObj. 83 - Determine the graph of a 1-operation linear function

NC 5.02 - Translate among different representations of algebraic expressions, equations and inequalities.

Topic 2 - Algebra Obj. 68 - Use a variable expression with two operations to represent a table of paired numbers

Obj. 76 - Determine the graph of an inequality on a number lineObj. 79 - Determine the graph of the solution set of a 1-step linear inequality

NC 5.03 - Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.

Topic 2 - Algebra Obj. 61 - Evaluate a rational expression involving variables with two or more terms in the numerator or denominatorObj. 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 exponentsObj. 69 - WP: Use a 2-variable expression to represent a situationObj. 73 - Solve a 1-step linear equation involving integersObj. 74 - Solve a 2-step linear equation involving integersObj. 75 - WP: Use a 1-variable 1-step equation to represent a situation

Obj. 77 - Determine some solutions to a 1-variable linear inequality


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Obj. 78 - Solve a 1-step linear inequalityObj. 80 - WP: Use a 1-variable linear inequality to represent a situation

NC 5.04 - Develop fluency in the use of formulas to solve problems.


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Agency Tag Set NameNorth Carolina, Math, 2003, Grade 8, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description - Number and OperationsNC 1 - The learner will understand and compute with real numbers.NC 1.01 - Develop number sense for the real numbers.NC 1.01.a - Define and use irrational numbers.


Obj. 15 - Approximate the location of a square root on a number lineObj. 18 - Identify rational or irrational numbers

NC 1.01.b - Compare and order. Topic 1 - Number Sense and Operations

Obj. 19 - Compare rational numbers and/or irrational numbers in various formsObj. 20 - Order rational numbers and irrational numbers

NC 1.01.c - Use estimates of irrational numbers in appropriate situations.


Obj. 16 - Determine the square root of a whole number to the nearest tenth



Obj. 6 - Add or subtract signed fractions or mixed numbers

Obj. 7 - Multiply or divide signed fractions or mixed numbersObj. 8 - Add or subtract signed decimalsObj. 9 - Multiply or divide signed decimalsObj. 21 - Determine a percent of a number given a percent that is not a whole percentObj. 22 - Determine the percent one number is of another numberObj. 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. 27 - Solve a problem involving simple interestObj. 28 - Solve a problem involving annually compounded interest



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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

- MeasurementNC 2 - The learner will understand and use measurement concepts.NC 2.01 - Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

NC 2.02 - Apply and use concepts of indirect measurement.


Obj. 67 - Determine a measure of length, weight or mass, or capacity or volume using proportional relationships

- GeometryNC 3 - The learner will understand and use properties and relationships in geometry.NC 3.01 - Represent problem situations with geometric models.NC 3.02 - Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.


Obj. 70 - WP: Solve a problem involving scale

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

NC 3.03 - Identify, predict, and describe dilations in the coordinate plane. - Data Analysis and ProbabilityNC 4 - The learner will understand and use graphs and data analysis.NC 4.01 - Collect, organize, analyze, and display data (including scatterplots) to solve problems.


Obj. 76 - Use a circle graph to organize data


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Obj. 77 - Use a scatter plot to organize dataObj. 78 - Determine if a scatter plot shows a positive relationship, a negative relationship, or no relationship between the variablesObj. 80 - Answer a question using information from a scatter plotObj. 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 plotsObj. 89 - Compare the medians, the modes, or the ranges of the data in a double stem-and-leaf plotObj. 90 - Determine the median of the data in a frequency table or a bar graphObj. 91 - Determine the mean of the data in a frequency table or a bar graph

NC 4.02 - Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.


Obj. 79 - Approximate a trend line for a scatter plot

Obj. 80 - Answer a question using information from a scatter plot

NC 4.03 - Identify misuses of statistical and numerical data. - AlgebraNC 5 - The learner will understand and use linear relations and functions.NC 5.01 - Develop an understanding of function.NC 5.01.a - Translate among verbal, tabular, graphic, and algebraic representations of functions.

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operationsObj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situationObj. 42 - Determine the graph of a line for a given table of values


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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 functionObj. 50 - WP: Determine a linear graph that can represent a situation

NC 5.01.b - Identify relations and functions as linear or nonlinear.NC 5.01.c - Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.

Topic 2 - Algebra Obj. 46 - Determine the slope of a line given its graph or a graph of a line with a given slopeObj. 47 - Determine the x- or y-intercept of a line given its graphObj. 48 - WP: Interpret the meaning of the slope of a graphed line

Obj. 49 - WP: Interpret the meaning of the y-intercept of a graphed line

NC 5.01.d - Interpret and compare properties of linear functions from tables, graphs, or equations.

Topic 2 - Algebra Obj. 48 - WP: Interpret the meaning of the slope of a graphed line

NC 5.02 - Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.

NC 5.03 - Solve problems using linear equations and inequalities; justify symbolically and graphically.

Topic 2 - Algebra Obj. 37 - Solve a 1-step equation involving rational numbers

Obj. 38 - Solve a 2-step equation involving rational numbersObj. 41 - WP: Solve a problem involving a 1-variable, 2-step equationObj. 52 - Solve a 2-step linear inequality in one variableObj. 53 - WP: Use a 2-step linear inequality in one variable to represent a situationObj. 54 - WP: Solve a problem involving a 2-step linear inequality in one variable


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Obj. 55 - Determine the graph of the solutions to a 2-step linear inequality in one variable

NC 5.04 - Solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.

Topic 2 - Algebra Obj. 37 - Solve a 1-step equation involving rational numbers

Obj. 38 - Solve a 2-step equation involving rational numbersObj. 41 - WP: Solve a problem involving a 1-variable, 2-step equation


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Agency Tag Set NameNorth Carolina, Math, 2003, Algebra 1, Standard Course of Study, State Department of Education

Standard Topic Description Objective DescriptionNC 1 - The learner will perform operations with numbers and expressions to solve problems.


Obj. 1 - Evaluate a numerical expression involving multiple forms of rational numbersObj. 2 - Simplify a complex fraction

Obj. 4 - Evaluate a fraction raised to an integer powerObj. 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 expression

Topic 10 - Radical Expressions Obj. 99 - Multiply monomial numerical expressions involving radicalsObj. 100 - Divide monomial numerical expressions involving radicalsObj. 101 - Add and/or subtract numerical radical expressionsObj. 102 - Multiply a binomial numerical radical expression by a numerical radical expression

NC 1.01 - Write equivalent forms of algebraic expressions to solve problems.NC 1.01.a - Apply the laws of exponents.

Topic 5 - Properties of Powers Obj. 59 - Apply the product of powers property to a monomial algebraic 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. 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

NC 1.01.b - Operate with polynomials.

Topic 6 - Polynomial Expressions Obj. 69 - Simplify a polynomial expression by combining like terms

Obj. 70 - Add polynomial expressions

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

Accelerated Math Grades 9 - 12

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Standard Topic Description Objective Description


Obj. 71 - Subtract polynomial expressionsObj. 72 - Multiply a polynomial by a monomialObj. 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

Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial expression by a monomialObj. 118 - Divide a polynomial expression by a binomial

NC 1.01.c - Factor polynomials. Topic 7 - Factor Algebraic Expressions

Obj. 79 - Factor the GCF from a polynomial expressionObj. 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

NC 1.02 - Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.NC 1.03 - Model and solve problems using direct variation.

Topic 3 - Linear Equations and Inequalities

Obj. 18 - WP: Determine an equation representing a direct variation or an inverse variation

NC 2 - The learner will describe geometric figures in the coordinate plane algebraically.NC 2.01 - Find the lengths and midpoints of segments to solve problems.


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NC 2.02 - Use the parallelism or perpendicularity of lines and segments to solve problems.


Obj. 35 - Determine if two lines are perpendicular or parallel given the equations of the linesObj. 36 - Determine an equation for a line that goes through a given point and is parallel or perpendicular to a given line

NC 3 - The learner will collect, organize, and interpret data with matrices and linear models to solve problems.NC 3.01 - Use matrices to display and interpret data.NC 3.02 - Operate (addition, subtraction, scalar multiplication) with matrices to solve problems.NC 3.03 - Create linear models for sets of data to solve problems.NC 3.03.a - Interpret constants and coefficients in the context of the data.

NC 3.03.b - Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.NC 4 - The learner will use relations and functions to solve problems.

NC 4.01 - Use linear functions or inequalities to model and solve problems; justify results.


Obj. 16 - WP: Determine a linear equation that can be used to solve a percent problem

NC 4.01.a - Solve using tables, graphs, and algebraic properties.


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 sidesObj. 20 - Solve a 1-variable absolute value equationObj. 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. 38 - Solve a 2-variable linear inequality for the dependent variable


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Obj. 40 - Determine the graph of a 2-variable linear inequalityObj. 42 - Determine the graph of the solutions to a problem that can be described by a 2-variable linear inequalityObj. 43 - Solve a 1-variable absolute value inequality

NC 4.01.b - Interpret constants and coefficients in the context of the problem.NC 4.02 - Graph, factor, and evaluate quadratic functions to solve problems.

Topic 8 - Quadratic Equations and Functions

Obj. 86 - Determine the graph of a given quadratic function

Obj. 87 - WP: Answer a question using the graph of a quadratic functionObj. 88 - Solve a quadratic equation by graphing the associated quadratic functionObj. 91 - Solve a quadratic equation by factoring

NC 4.03 - Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.

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. 49 - Solve a system of linear equations in two variables using any methodObj. 50 - WP: Determine a system of linear equations that represents a given situationObj. 51 - WP: Solve a mixture problem that can be represented by a system of linear equationsObj. 52 - WP: Solve a motion problem that can be represented by a system of linear equationsObj. 53 - Solve a number problem that can be represented by a linear system of equations


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Obj. 55 - Determine the graph of the solution set of a system of linear inequalities in two variablesObj. 56 - WP: Determine a system of linear inequalities that represents a given situationObj. 57 - WP: Determine possible solutions to a problem that can be represented by a system of linear inequalities

NC 4.04 - Graph and evaluate exponential functions to solve problems.

Topic 9 - Exponential Equations and Functions

Obj. 95 - Determine the graph of an exponential function

Obj. 96 - WP: Evaluate an exponential growth or an exponential decay functionObj. 97 - Solve a problem involving exponential growth or exponential decay


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Agency Tag Set NameNorth Carolina, Math, 2003, Geometry, Standard Course of Study, State Department of Education

Standard Topic Description Objective DescriptionNC 1 - The learner will perform operations with real numbers to solve problems.NC 1.01 - Use the trigonometric ratios to model and solve problems involving right triangles.

Topic 7 - Right Triangles and Trigonometry

Obj. 45 - Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

Obj. 47 - WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangleObj. 49 - Determine a sine, cosine, or tangent ratio in a right triangle

Obj. 50 - Determine a length using a sine, cosine, or tangent ratio in a right triangleObj. 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

NC 1.02 - Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

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. 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

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Geometry


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Obj. 64 - Determine the measure of an arc or an angle formed by two tangents, two secants, or a tangent and a secant that intersect outside a circle

Topic 9 - Area Obj. 70 - Determine the area of a quadrilateralObj. 71 - Determine a length given the area of a quadrilateralObj. 72 - WP: Solve a problem involving the area of a quadrilateralObj. 73 - Determine the area of a triangle using Heron's formulaObj. 74 - Determine the area of a regular polygonObj. 75 - Determine a length given the area of a regular polygonObj. 76 - Approximate the area of a right triangle using trigonometryObj. 77 - Approximate the area of a regular polygon using trigonometry

Obj. 78 - Determine the area of a region formed by circles within a circle, a polygon within a circle, or a circle within a polygonObj. 79 - WP: Solve a problem involving the area of a complex shape formed by circles and polygonsObj. 80 - Determine the area of a sector of a circleObj. 81 - Determine the area of a segment of a circleObj. 82 - Determine the length of the radius or the diameter of a circle given the area of a sectorObj. 83 - WP: Determine a length or an area involving a sector of a circle

Obj. 84 - Determine the measure of an arc or an angle given the area of a sector of a circleObj. 85 - Solve a problem involving regular polygons and/or circles that have the same area or perimeterObj. 86 - Determine a probability using an area model


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Topic 10 - Surface Area and Volume

Obj. 87 - Determine a length given the surface area of a right cylinder or a right prism that has a rectangle or a right triangle as a base

Obj. 88 - Solve a problem involving the surface area of a cone or a pyramid that has a rectangle or right triangle as a baseObj. 89 - Determine a length given the surface area of a right prism or a right pyramid that has a regular polygon as its baseObj. 90 - Determine the volume of an oblique prism or an oblique cylinder

Obj. 91 - Determine the volume of a right pyramid or a right coneObj. 92 - Solve a problem involving the volume of a right pyramid or a right coneObj. 93 - Determine the volume of an oblique pyramid or an oblique cone

Obj. 94 - Determine the surface area of a sphereObj. 95 - Determine the radius, diameter, or circumference of a sphere given its surface areaObj. 96 - WP: Solve a problem involving the surface area of a sphere

Obj. 97 - Determine the surface area of a complex solid figureObj. 98 - Solve a problem involving the surface area of a complex solid figureObj. 99 - Determine the volume of a sphere or hemisphereObj. 100 - WP: Determine the volume of a sphere or hemisphereObj. 101 - Determine the volume of a complex solid figureObj. 102 - WP: Solve a problem involving the volume of a complex solid figureObj. 103 - Solve a problem involving the surface areas of similar solid figures


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Obj. 104 - Solve a problem involving the volumes of similar solid figures

Obj. 105 - Solve a problem involving two solid figures that have the same surface area or volumeObj. 106 - WP: Solve a problem involving two solid figures that have the same surface area or volume

NC 1.03 - Use length, area, and volume to model and solve problems involving probability.

Topic 9 - Area Obj. 86 - Determine a probability using an area model

NC 2 - The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

NC 2.01 - Use logic and deductive reasoning to draw conclusions and solve problems.

Topic 4 - Congruent Triangles Obj. 23 - Identify a triangle congruence postulate that justifies a congruence statementObj. 24 - Identify congruent triangles using triangle congruence postulates or theorems

Topic 6 - Similarity Obj. 37 - Identify a triangle similarity postulate that justifies a similarity statementObj. 38 - Identify similar triangles using triangle similarity postulates or theorems

NC 2.02 - Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

Topic 1 - Basic Concepts of Geometry

Obj. 2 - Determine a length or an angle measure using the segment addition postulate or the angle addition postulateObj. 3 - Solve a problem involving a bisected angle or a bisected segment

Obj. 4 - Determine the distance between two pointsObj. 5 - Solve a problem involving the distance formulaObj. 6 - Determine the midpoint of a line segment given the coordinates of the endpointsObj. 7 - Determine the area of a right triangle or a rectangle given the coordinates of the vertices of the figureObj. 8 - Solve a problem involving the midpoint formula

Topic 2 - Parallel and Perpendicular lines

Obj. 10 - Determine the measure of an angle formed by parallel lines and one or more transversals


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Obj. 11 - Identify parallel lines using angle relationshipsObj. 12 - Determine the measure of an angle in a figure involving parallel and/or perpendicular linesObj. 13 - Determine if lines through points with given coordinates are parallel or perpendicularObj. 14 - Determine the coordinates of a point through which a line must pass in order to be parallel or perpendicular to a given line

NC 2.03 - Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:NC 2.03.a - Triangles. Topic 3 - Relationships Within

TrianglesObj. 15 - Determine the measure of an angle using the sum of the interior angles in a triangleObj. 16 - Determine the measure of an angle using angle relationships and the sum of the interior angles in a triangleObj. 17 - Determine a length in a triangle using a medianObj. 18 - Solve for the length of a side of a triangle using the Pythagorean theoremObj. 19 - Solve a problem using inequalities in a triangleObj. 20 - Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationshipsObj. 21 - WP: Determine a length or an angle measure using triangle relationships

Topic 4 - Congruent Triangles Obj. 22 - Determine the length of a side or the measure of an angle in congruent trianglesObj. 23 - Identify a triangle congruence postulate that justifies a congruence statementObj. 24 - Identify congruent triangles using triangle congruence postulates or theoremsObj. 25 - Solve a problem involving a point on the bisector of an angle


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Topic 6 - Similarity Obj. 35 - Determine the length of a side or the measure of an angle in similar trianglesObj. 36 - Determine a length given the perimeters of similar triangles or the lengths of corresponding interior line segmentsObj. 37 - Identify a triangle similarity postulate that justifies a similarity statementObj. 38 - Identify similar triangles using triangle similarity postulates or theoremsObj. 39 - Determine a length in a triangle using a midsegmentObj. 40 - Determine a length using parallel lines and proportional partsObj. 41 - Determine a length in a triangle given the bisector of an angle and other lengthsObj. 42 - Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangleObj. 43 - WP: Determine a length using similarity

Topic 7 - Right Triangles and Trigonometry

Obj. 44 - Determine a length in a complex figure using the Pythagorean theoremObj. 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 relationshipsObj. 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. 49 - Determine a sine, cosine, or tangent ratio in a right triangle

Obj. 50 - Determine a length using a sine, cosine, or tangent ratio in a right triangle


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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. 73 - Determine the area of a triangle using Heron's formulaObj. 76 - Approximate the area of a right triangle using trigonometry

NC 2.03.b - Quadrilaterals. Topic 5 - Quadrilaterals and Other Polygons

Obj. 27 - Determine a length or an angle measure using general properties of parallelogramsObj. 28 - Determine a length or an angle measure using properties of squares, rectangles, or rhombiObj. 29 - Determine a length or an angle measure using properties of kitesObj. 30 - Determine a length or an angle measure using properties of trapezoidsObj. 32 - WP: Solve a problem using the properties of angles and/or sides of polygons

Topic 9 - Area Obj. 70 - Determine the area of a quadrilateralObj. 71 - Determine a length given the area of a quadrilateralObj. 72 - WP: Solve a problem involving the area of a quadrilateral

NC 2.03.c - Other polygons. Topic 5 - Quadrilaterals and Other Polygons

Obj. 26 - Determine the measure of an angle or the sum of the angles in a polygonObj. 31 - Determine a length or an angle measure in a complex figure using properties of polygons

Topic 9 - Area Obj. 74 - Determine the area of a regular polygonObj. 75 - Determine a length given the area of a regular polygonObj. 77 - Approximate the area of a regular polygon using trigonometry


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NC 2.03.d - Circles. Topic 8 - Circles Obj. 54 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angleObj. 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. 63 - Determine the measure of an arc or an angle formed by intersecting chords or a chord that intersects a tangent to a circleObj. 64 - Determine the measure of an arc or an angle formed by two tangents, two secants, or a tangent and a secant that intersect outside a circleObj. 65 - Determine a length using intersecting chords, two secants that intersect outside a circle, or a tangent and a secant that intersect outside a circleObj. 66 - Solve a problem involving intersecting chords, tangents, and/or secants of a circleObj. 67 - Determine an equation of a circleObj. 68 - Determine the radius, center, or diameter of a circle given an equationObj. 69 - Determine the area or circumference of a circle given an equation of the circle


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NC 2.04 - Develop and apply properties of solids to solve problems.

Topic 10 - Surface Area and Volume

Obj. 87 - Determine a length given the surface area of a right cylinder or a right prism that has a rectangle or a right triangle as a base

Obj. 88 - Solve a problem involving the surface area of a cone or a pyramid that has a rectangle or right triangle as a baseObj. 89 - Determine a length given the surface area of a right prism or a right pyramid that has a regular polygon as its baseObj. 90 - Determine the volume of an oblique prism or an oblique cylinder

Obj. 91 - Determine the volume of a right pyramid or a right coneObj. 92 - Solve a problem involving the volume of a right pyramid or a right coneObj. 93 - Determine the volume of an oblique pyramid or an oblique cone

Obj. 94 - Determine the surface area of a sphereObj. 95 - Determine the radius, diameter, or circumference of a sphere given its surface areaObj. 96 - WP: Solve a problem involving the surface area of a sphere

Obj. 97 - Determine the surface area of a complex solid figureObj. 98 - Solve a problem involving the surface area of a complex solid figureObj. 99 - Determine the volume of a sphere or hemisphereObj. 100 - WP: Determine the volume of a sphere or hemisphereObj. 101 - Determine the volume of a complex solid figureObj. 102 - WP: Solve a problem involving the volume of a complex solid figureObj. 103 - Solve a problem involving the surface areas of similar solid figures


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Obj. 104 - Solve a problem involving the volumes of similar solid figures

Obj. 105 - Solve a problem involving two solid figures that have the same surface area or volumeObj. 106 - WP: Solve a problem involving two solid figures that have the same surface area or volume

NC 3 - The learner will transform geometric figures in the coordinate plane algebraically.NC 3.01 - Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

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

NC 3.02 - Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to describe the transformation of polygons in the coordinate plane.


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Standard Topic Description Objective DescriptionNC 1 - The learner will perform operations with complex numbers, matrices, and polynomials.NC 1.01 - Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems.

Topic 6 - Roots, Radicals, and Complex Numbers

Obj. 70 - Simplify expressions with fractional exponents

Obj. 73 - Simplify expressions with rational exponents

Topic 9 - Exponents and Logarithms

Obj. 129 - Exponential equations to logarithmic formObj. 130 - Logarithmic equations to exponential formObj. 131 - Find logarithms by converting to exponential formObj. 132 - Find natural logarithms of numbersObj. 133 - Properties of logarithms, simplify expressionsObj. 134 - Properties of logs, find equivalent logsObj. 135 - Solve logarithmic equationsObj. 136 - Solve exponential equationsObj. 137 - Solve equations involving natural logarithmsObj. 138 - WP: Interest problemsObj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems

NC 1.02 - Define and compute with complex numbers.


Obj. 80 - Write imaginary numbers: bi

Obj. 81 - Raise i to powersObj. 82 - Factor expressions using complex numbersObj. 83 - Add and subtract complex numbersObj. 84 - Operations on complex numbersObj. 85 - Rationalize denominators with complex numbersObj. 86 - Solve equations involving complex numbers

NC 1.03 - Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.

Topic 8 - Polynomials Obj. 110 - Add polynomials

Obj. 111 - Subtract polynomials

Standards List with Aligned Product SkillsProduct NameAccelerated Math Algebra 2


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Obj. 112 - Add and subtract polynomialsObj. 113 - Square a binomial, ax + by

Obj. 114 - Multiply 2 binomialsObj. 115 - Multiply monomials by polynomialsObj. 116 - Multiply binomials by trinomialsObj. 117 - Square trinomialsObj. 118 - Simplify polynomial expr using multiplicationObj. 119 - Divide polynomials by monomialsObj. 120 - Divide polynomialsObj. 128 - WP: Polynomials

Topic 10 - Rational Expressions and Equations

Obj. 143 - Rational expressions, domainsObj. 145 - Simplify rational expressionsObj. 148 - Multiply and simplify rational expressionsObj. 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

Obj. 154 - Simplify complex rational expressions

NC 1.04 - Operate with matrices to model and solve problems.

Topic 5 - Matrices and Determinants

Obj. 58 - Matrices, multiply by a constant (2 x 2)Obj. 59 - Matrices, sums and differences (3 x 3)Obj. 60 - Matrices, products (3 x 3)

Obj. 63 - Matrices, inversesObj. 66 - Matrices, solve systems of equationsObj. 67 - WP: Matrices

NC 1.05 - Model and solve problems using direct, inverse, combined and joint variation.

Topic 7 - Quadratic Obj. 98 - Solve variation problems

Obj. 99 - WP: Variation problemsNC 2 - The learner will use relations and functions to solve problems.


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NC 2.01 - Use the composition and inverse of functions to model and solve problems; justify results.

Topic 3 - Relations, Functions, and Graphs

Obj. 32 - Find compositions of 2 functions

Obj. 33 - Find inverses of functionsNC 2.02 - Use quadratic functions and inequalities to model and solve problems; justify results.

Topic 7 - Quadratic Obj. 105 - Solve quadratic inequalities


Topic 7 - Quadratic Obj. 96 - Graph quadratic functions

Obj. 97 - WP: Graph quadratic functionsObj. 106 - Graph quadratic inequalities

NC 2.02.b - Interpret the constants and coefficients in the context of the problem.NC 2.03 - Use exponential functions to model and solve problems; justify results.NC 2.03.a - Solve using tables, graphs, and algebraic properties.

Topic 9 - Exponents and Logarithms

Obj. 138 - WP: Interest problems

Obj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems

Obj. 141 - Graph exponential functions

NC 2.03.b - Interpret the constants, coefficients, and bases in the context of the problem.NC 2.04 - Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.NC 2.04.a - Interpret the constants, coefficients, and bases in the context of the data.NC 2.04.b - Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.NC 2.05 - Use rational equations to model and solve problems; justify results.NC 2.05.a - Solve using tables, graphs, and algebraic properties.

Topic 10 - Rational Expressions and Equations

Obj. 147 - Graph rational functions and equationsObj. 155 - Solve equations containing rational expressionsObj. 156 - Solve rational equations (no solution)


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NC 2.05.b - Interpret the constants and coefficients in the context of the problem.NC 2.05.c - Identify the asymptotes and intercepts graphically and algebraically.NC 2.06 - Use cubic equations to model and solve problems.

Topic 7 - Quadratic Obj. 104 - Solve cubic equations

Obj. 107 - Solve cubic inequalities with 1-variable

NC 2.06.a - Solve using tables and graphs.NC 2.06.b - Interpret constants and coefficients in the context of the problem.NC 2.07 - Use equations with radical expressions to model and solve problems; justify results.


Obj. 75 - Rationalize denominators



Obj. 74 - Add and subtract radical expressionsObj. 76 - Solve equations containing radicals

NC 2.07.b - Interpret the degree, constants, and coefficients in the context of the problem.NC 2.08 - Use equations and inequalities with absolute value to model and solve problems; justify results.NC 2.08.a - Solve using tables, graphs, and algebraic properties.


Obj. 22 - Graph absolute value inequalities (number line)Obj. 23 - Graph absolute value ineq (coordinate plane)Obj. 25 - WP: Absolute value and inequalities

NC 2.08.b - Interpret the constants and coefficients in the context of the problem.NC 2.09 - Use the equations of parabolas and circles to model and solve problems; justify results.NC 2.09.a - Solve using tables, graphs, and algebraic properties.

Topic 11 - Conics and Second-Degree Equations

Obj. 158 - Graph circles

Obj. 171 - Graph parabolas (y = x^2)

Obj. 172 - Graph parabolas (x = y^2)

NC 2.09.b - Interpret the constants and coefficients in the context of the problem.

Topic 11 - Conics and Second-Degree Equations

Obj. 159 - Circles, general form equations


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Obj. 160 - Circles, write equations given centers and radiiObj. 161 - Circles, write equations using given factsObj. 162 - WP: CirclesObj. 170 - Parabolas, find vertex from equation

NC 2.10 - Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

Topic 4 - Systems of Equations and Inequalities

Obj. 45 - Solve systems, substitution

Obj. 46 - Solve systems, elimination

Obj. 48 - Graph systems of equations

Obj. 49 - Verify ordered triples are solutions to systemsObj. 50 - Solve systems, three equationsObj. 51 - WP: Solve systems, number problemsObj. 52 - WP: Solve systems, motion and distance problemsObj. 53 - WP: Solve systems, age problemsObj. 54 - WP: Solve systems, coin problemsObj. 55 - WP: Solve systems, mixture and investment problemsObj. 56 - Solve systems of linear inequalities by graphingObj. 57 - Solve linear programming problems

Topic 5 - Matrices and Determinants

Obj. 64 - Cramer's Rule, solve systems of 2 equationsObj. 65 - Cramer's Rule, solve systems of 3 equations


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Agency Tag Set NameNorth Carolina, Math, 2003, Precalculus, Standard Course of Study, State Department of EducationStandard Topic Description Objective DescriptionNC 1 - The learner will describe geometric figures in the coordinate plane algebraically.NC 1.01 - Transform relations in two dimensions; describe the results algebraically and geometrically.

Topic 1 - Review of Fundamental Concepts of Algebra

Obj. 18 - Add, subtract, multiply, & divide functions

Obj. 22 - Use rigid & nonrigid transformations to graph func

NC 1.02 - Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.


Obj. 15 - WP: Quadratic equations

Topic 2 - Polynomials Obj. 37 - WP: Quadratic functionsTopic 7 - Conic Sections Obj. 105 - WP: Conic sections



Obj. 11 - Solve quad eqns, square root rule

Obj. 12 - Solve quad eqns, factor (real roots)Obj. 13 - Solve quad eqns, quadratic formulaObj. 14 - Solve high degree eqns in quad form

Topic 2 - Polynomials Obj. 35 - Parabolas, find vertex from equationObj. 36 - Graph quadratic functions

Obj. 42 - Descartes' Rule of SignsObj. 43 - Rational Zeros TheoremObj. 44 - Intermediate Value TheoremObj. 45 - Upper & Lower Bounds Test

Topic 7 - Conic Sections Obj. 91 - Parabolas, graph given equationsObj. 96 - Circle, graph given equationsObj. 99 - Ellipses, graph given equationsObj. 102 - Hyperbola, graph given equationsObj. 106 - Solve systems of second-degree equations

NC 1.02.b - Interpret the constants and coefficients in the context of the problem.

Topic 7 - Conic Sections Obj. 94 - Circles, determine centers & radii from eqns

Obj. 97 - Ellipses, find centers, vertices, & fociObj. 101 - Hyperbolas, find vertices, asymptotes, & foci

Standards List with Aligned Product SkillsProduct NameAccelerated Math Pre-Calculus


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Agency Tag Set NameNorth Carolina, Math, 2003, Precalculus, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description


NC 1.03 - Operate with vectors in two dimensions to model and solve problems.

Topic 11 - Vectors Obj. 151 - Linear combinations of 2 vectors

Obj. 152 - Given 2 points, find a vector & its magnitudeObj. 153 - Find unit vectors in the same direction as vectorsObj. 154 - Dot products of 2 vectors

Obj. 155 - Angles between 2 vectors

Obj. 156 - Projections of 1 vector onto anotherObj. 157 - Cross products of 2 vectorsObj. 158 - Find the distance between 2 points in spaceObj. 159 - Direction angles of vectors in spaceObj. 160 - Area of parallelograms from adj side vectorsObj. 161 - Find equations of planes normal to vectorsObj. 162 - WP: Navigational problems w/ vectors

NC 2 - The learner will use relations and functions to solve problems.

NC 2.01 - Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.


Obj. 5 - WP: Linear Equations

Obj. 15 - WP: Quadratic equationsObj. 34 - WP: Rational equations

Topic 3 - Exponential and Logarithmic Functions

Obj. 57 - WP: Exponential functions

Obj. 60 - WP: Compound interestObj. 61 - WP: Radioactive decay

Topic 8 - Systems of Linear Equations and Inequalities

Obj. 117 - WP: Systems of linear equations

NC 2.01.a - Solve using graphs and algebraic properties.


Obj. 4 - Solve linear equations

Obj. 6 - Solve absolute value eqns with 1-variableObj. 11 - Solve quad eqns, square root ruleObj. 12 - Solve quad eqns, factor (real roots)


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Obj. 13 - Solve quad eqns, quadratic formulaObj. 14 - Solve high degree eqns in quad formObj. 20 - Find compositions of 2 functionsObj. 21 - Find inverses of functionsObj. 23 - Graph rational functionsObj. 24 - Graph piecewise-defined functionsObj. 30 - Solve radical equationsObj. 31 - Solve eqns w/ neg or frac exponents in quad formObj. 33 - Solve rational equations

Topic 2 - Polynomials Obj. 46 - Graph nth-degree polynomialsObj. 49 - Find zeros of polynomials

Topic 3 - Exponential and Logarithmic Functions

Obj. 55 - Graph exponential functions

Obj. 56 - Graph log functionsObj. 58 - Solve log equationsObj. 59 - Solve exponential equations

Topic 7 - Conic Sections Obj. 91 - Parabolas, graph given equations

NC 2.01.b - Interpret the constants, coefficients, and bases in the context of the problem.


Obj. 16 - Domains & range, functions

NC 2.02 - Use trigonometric and inverse trigonometric functions to model and solve problems; justify results.

Topic 5 - Applications in Trigonometry

Obj. 73 - WP: Right triangles

NC 2.02.a - Solve using graphs and algebraic properties.

Topic 4 - Trigonometric Functions

Obj. 66 - Graph sin & cos using amp, period, & phase shiftObj. 67 - Graph tan & cot functions

Obj. 68 - Graph sec & csc functions

Obj. 69 - Apply sum & diff formula for sin & cosObj. 70 - Apply double-angle formulas for sin & cosObj. 71 - Apply product-sum formulas


Obj. 78 - Find values of inverse trig functionsObj. 79 - Solve trig equationsObj. 80 - Solve eqns involving inverse trig functions


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NC 2.02.b - Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.NC 2.02.c - Develop and use the law of sines and the law of cosines.


Obj. 74 - Law of Sines

Obj. 75 - Law of Sines (ambiguous case)Obj. 76 - Law of CosinesObj. 77 - Find areas of non-right triangles

NC 2.03 - For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.NC 2.03.a - Interpret the constants, coefficients, and bases in the context of the data.NC 2.03.b - Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions.NC 2.04 - Use the composition and inverse of functions to model and solve problems.NC 2.05 - Use polar equations to model and solve problems.NC 2.05.a - Solve using graphs and algebraic properties.

Topic 6 - Polar Coordinates Obj. 85 - Graph polar equations

NC 2.05.b - Interpret the constants and coefficients in the context of the problem.NC 2.06 - Use parametric equations to model and solve problems.

NC 2.07 - Use recursively-defined functions to model and solve problems.NC 2.07.a - Find the sum of a finite sequence.

Topic 9 - Sequences and Series Obj. 127 - Find sums of arithmetic seriesObj. 133 - Find sums of finite geometric seriesObj. 135 - Evaluate geometric series in sigma notationObj. 136 - WP: Geometric series

NC 2.07.b - Find the sum of an infinite sequence.

Topic 9 - Sequences and Series Obj. 134 - Find sums of infinite geometric series

NC 2.07.c - Determine whether a given series converges or diverges.


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NC 2.07.d - Translate between recursive and explicit representations.NC 2.08 - Explore the limit of a function graphically, numerically, and algebraically.

Topic 12 - Introduction to Calculus

Obj. 163 - Limits, use graphs

Obj. 164 - Limits, polynomial functionsObj. 165 - Limits, rational functions

Obj. 166 - Limits, rational functions (x incr or decr)Obj. 167 - Limits, rationalization techniquesObj. 168 - Find one-sided limits


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Agency Tag Set NameNorth Carolina, Math, 2003, Advanced Placement Statistics, Standard Course of Study, State Department of EducationStandard Topic Description Objective DescriptionNC 1 - The learner will analyze univariate data to solve problems.NC 1.01 - Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplots, and effects of changing units on summary measures.

Topic 4 - Descriptive statistics Obj. 27 - Mean

Obj. 28 - MedianObj. 29 - ModeObj. 30 - Choose best measure of central tendencyObj. 31 - RangeObj. 32 - PercentilesObj. 33 - Expected valueObj. 34 - OutliersObj. 35 - Box-and-whisker plotsObj. 36 - Trimmed meanObj. 37 - VarianceObj. 38 - Standard deviation

NC 1.02 - Analyze distribution of continuous univariate data (both normal and non-normal).NC 2 - The learner will construct and interpret displays of univariate data to solve problems.NC 2.01 - Construct and interpret graphical displays of univariate data.

Topic 3 - Sample spaces Obj. 17 - Venn diagrams

Obj. 19 - Circle graphsTopic 4 - Descriptive statistics Obj. 23 - Frequency histograms

Obj. 24 - Relative frequency histogramsObj. 25 - Stem-and-leaf plotsObj. 26 - Misleading graphsObj. 35 - Box-and-whisker plots

NC 2.02 - Compare distributions among sets of univariate data.NC 3 - The learner will collect and analyze date to solve problems.

Topic 7 - Data collection Obj. 64 - Experimental probability - predict using sample resultsObj. 65 - Capture/recapture experiments

NC 3.01 - Analyze categorical data.

NC 3.02 - Use and compare methods of data collection.NC 3.03 - Apply statistical principles and methods in sample surveys; identify difficulties.

Topic 7 - Data collection Obj. 62 - Sampling techniques

Obj. 63 - Identify bias

Standards List with Aligned Product SkillsProduct NameAM Probability & Statistics


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Agency Tag Set NameNorth Carolina, Math, 2003, Advanced Placement Statistics, Standard Course of Study, State Department of EducationStandard Topic Description Objective Description


NC 3.04 - Apply principles and methods in designed experiments; identify difficulties.

Topic 3 - Sample spaces Obj. 16 - Sample space of experiment

NC 3.05 - Apply concepts of probability to solve problems.

Topic 3 - Sample spaces Obj. 13 - Probability of simple events

Obj. 14 - Probability of compound eventsObj. 15 - Complement of eventsObj. 18 - Mutually exclusive (disjoint) eventsObj. 20 - Bayes' formula for conditional probabilityObj. 22 - Independent events

Topic 4 - Descriptive statistics Obj. 33 - Expected valueTopic 5 - Discrete probability distributions

Obj. 39 - Discrete uniform distribution

Obj. 40 - WP: Discrete uniform distributionObj. 41 - Bernoulli distributionObj. 42 - WP: Bernoulli trialsObj. 43 - Binomial distributionObj. 44 - WP: Binomial experiments

Obj. 45 - Game theoryObj. 46 - Geometric distributionObj. 47 - WP: Geometric distribution

Obj. 48 - Negative binomial distributionObj. 49 - WP: Negative binomial distributionObj. 50 - Hypergeometric distribution

Obj. 51 - WP: Hypergeometric distributionObj. 52 - Poisson distributionObj. 53 - WP: Poisson distribution

Topic 6 - Continuous probability distributions

Obj. 54 - Continuous uniform distributionObj. 55 - WP: Continuous uniform distributionObj. 56 - Chi-square distributionObj. 58 - Student's t distributionObj. 59 - WP: Student's t distribution

Topic 7 - Data collection Obj. 64 - Experimental probability - predict using sample resultsObj. 65 - Capture/recapture experiments

NC 3.06 - Use normal distributions as a model for distribution.


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NC 3.06.a - Investigate the properties of the normal distribution.

NC 3.06.b - Use the table of standard normal distribution (Z).


Obj. 57 - Normal distribution

Topic 9 - Confidence intervals Obj. 74 - z-scoresObj. 75 - Areas in tailsObj. 76 - Areas between tails

NC 3.07 - Simulate sampling distributions.NC 3.08 - Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance.NC 3.09 - Recognize, construct and interpret results using confidence intervals in the context of a problem.

Topic 9 - Confidence intervals Obj. 73 - Chebyshev's inequality

Obj. 74 - z-scoresObj. 75 - Areas in tailsObj. 76 - Areas between tailsObj. 77 - Confidence coefficientsObj. 78 - Standard error of the mean

Obj. 79 - Sample sizeObj. 80 - Confidence intervals for meansObj. 81 - Confidence intervals for difference of means

Topic 10 - Hypothesis testing Obj. 83 - Single-sample testObj. 84 - Two-sample testObj. 85 - Small-sample test

NC 3.10 - Perform tests of significance and interpret results in the context of a problem.

Topic 8 - Bivariate data Obj. 72 - Difference between correlations

Topic 10 - Hypothesis testing Obj. 86 - Calculate p-valuesObj. 87 - Type I and Type II errorsObj. 88 - Large-sample hypothesis testingObj. 89 - Two-sample hypothesis testingObj. 90 - Small-sample hypothesis testingObj. 91 - Chi-square test

NC 4 - The learner will analyze bivariate data to solve problems.

Topic 5 - Discrete probability distributions

Obj. 40 - WP: Discrete uniform distributionObj. 42 - WP: Bernoulli trialsObj. 44 - WP: Binomial experiments

Obj. 45 - Game theory


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Obj. 47 - WP: Geometric distribution

Obj. 49 - WP: Negative binomial distributionObj. 51 - WP: Hypergeometric distributionObj. 53 - WP: Poisson distribution


Obj. 55 - WP: Continuous uniform distributionObj. 59 - WP: Student's t distribution

Obj. 61 - WP: F distributionTopic 11 - Linear regression Obj. 98 - Estimate the predicted

value y-hatObj. 99 - Forecasting

NC 4.01 - Analyze bivariate data. Topic 1 - Pre-requisites Obj. 2 - Bar graphsObj. 3 - Scatter plots

Topic 5 - Discrete probability distributions

Obj. 39 - Discrete uniform distribution

Obj. 41 - Bernoulli distributionObj. 43 - Binomial distributionObj. 46 - Geometric distributionObj. 48 - Negative binomial distributionObj. 50 - Hypergeometric distribution

Obj. 52 - Poisson distributionTopic 6 - Continuous probability distributions

Obj. 54 - Continuous uniform distributionObj. 56 - Chi-square distributionObj. 57 - Normal distributionObj. 58 - Student's t distributionObj. 60 - F distribution

Topic 8 - Bivariate data Obj. 69 - Stacked bar chartsObj. 70 - Calculate covariance as SxyObj. 72 - Difference between correlations

Topic 11 - Linear regression Obj. 92 - Interpret scatter plotsObj. 99 - Forecasting

NC 4.01.a - Recognize and analyze correlation and linearity.

Topic 8 - Bivariate data Obj. 71 - Calculate correlation coefficient

Topic 11 - Linear regression Obj. 93 - Linearity of dataObj. 94 - Calculate SxxObj. 95 - Calculate the slope of regression lineObj. 96 - Calculate a

NC 4.01.b - Determine the least squares regression line.

Topic 11 - Linear regression Obj. 94 - Calculate Sxx

Obj. 95 - Calculate the slope of regression line


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Obj. 96 - Calculate aObj. 97 - Calculate regression line equationObj. 98 - Estimate the predicted value y-hatObj. 99 - Forecasting

NC 4.01.c - Create residual plots and identify outliers and influential points to analyze data.NC 4.01.d - Use logarithmic and power transformations to analyze data.


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Agency Tag Set NameNorth Carolina, Math, 2003, AP Calculus, Standard Course of Study, State Department of Education

Standard Topic Description Objective DescriptionNC 1 - The learner will demonstrate an understanding of the behavior of functions.NC 1.01 - Demonstrate an understanding of limits both local and global.

Topic 2 - Limits and Continuity Obj. 30 - Limits, special trig limits

Topic 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals

Obj. 146 - Find types of indeterminate forms w/ substitution

Obj. 147 - L'Hopital's Rule, evaluate limits

NC 1.01.a - Calculate limits, including one-sided, using algebra.

Topic 2 - Limits and Continuity Obj. 26 - Limits, polynomial functions

Obj. 27 - Limits, rational functionsObj. 28 - Limits, rational functions (x incr or decr)Obj. 29 - Limits, rationalization techniquesObj. 32 - Find one-sided limits

NC 1.01.b - Estimate limits from graphs or tables of data.

Topic 2 - Limits and Continuity Obj. 25 - Limits, use graphs

NC 1.02 - Recognize and describe the nature of aberrant behavior caused by asymptotes and unboundedness.NC 1.02.a - Understand asymptotes in terms of graphical behavior.

Topic 2 - Limits and Continuity Obj. 31 - Find vertical asymptotes of functions

Topic 4 - Applications of Differentiation

Obj. 52 - Find horizontal asymptotes

Obj. 53 - Graph intercepts, extrema, inflect, & asymptote

NC 1.02.b - Describe asymptotic behavior in terms of limits involving infinity.NC 1.02.c - Compare relative magnitudes of functions and their rates of change.NC 1.03 - Identify and demonstrate an understanding of continuity of functions.

Topic 2 - Limits and Continuity Obj. 33 - Find intervals where functions are continuous

Obj. 36 - Solve problems using definition of continuity

NC 1.03.a - Develop an intuitive understanding of continuity. (Close values of the domain lead to close values of the range.)NC 1.03.b - Understand continuity in terms of limits.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Calculus


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NC 1.03.c - Develop a geometric understanding of graphs of continuous functions. (Intermediate Value Theorem and Extreme Value Theorem).

Topic 2 - Limits and Continuity Obj. 34 - Intermediate Value Theorem


Obj. 46 - Find extrema of continuous functions

NC 2 - The learner will use derivatives to solve problems.


Obj. 61 - Applied problems: DifferentialsObj. 62 - Applied problems: Business w/ differentiation

NC 2.01 - Explore and interpret the concept of the derivative graphically, numerically, analytically and verbally.

NC 2.01.a - Interpret derivative as an instantaneous rate of change.NC 2.01.b - Define derivative as the limit of the difference quotient.NC 2.01.c - Identify the relationship between differentiability and continuity.NC 2.02 - Apply the concept of the derivative at a point.NC 2.02.a - Find the slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.

Topic 3 - Differentiation Obj. 43 - Find slopes & equations of tangent lines

NC 2.02.b - Find the tangent line to a curve at a point and local linear approximation.

Topic 3 - Differentiation Obj. 43 - Find slopes & equations of tangent lines

NC 2.02.c - Find the instantaneous rate of change as the limit of average rate of change.NC 2.02.d - Approximate a rate of change from graphs and tables of values.NC 2.03 - Interpret the derivative as a function.NC 2.03.a - Identify corresponding characteristics of graphs of f and f'.NC 2.03.b - Identify relationship between the increasing and decreasing behavior of f and the sign of f'.


Obj. 49 - Find intervals of increase & decrease

NC 2.03.c - Investigate the Mean Value Theorem and its geometric consequences.


Obj. 48 - Mean Value Theorem


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NC 2.03.d - Translate between verbal and algebraic descriptions of equations involving derivatives.NC 2.04 - Demonstrate fluency and accuracy in the computation of derivatives.

Topic 3 - Differentiation Obj. 41 - Find higher-order derivatives

NC 2.04.a - Find the derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.

Topic 3 - Differentiation Obj. 37 - Differentiate using the Power Rule

Obj. 38 - Differentiate using the Product RuleObj. 39 - Differentiate using the Quotient RuleObj. 40 - Differentiate, trig functions

Topic 6 - Transcendental Functions

Obj. 88 - Find derivatives of log functionsObj. 96 - Find derivatives of inverse functionsObj. 102 - Differentiate exponential functionsObj. 109 - Differentiate exponent func w/ various basesObj. 110 - Differentiate log functions w/ various basesObj. 120 - Differentiate inverse trig functionsObj. 123 - Differentiate hyperbolic functionsObj. 125 - Differentiate inverse hyperbolic functions

NC 2.04.b - Use the basic rules for the derivative of sums, products, and quotients of functions.

Topic 3 - Differentiation Obj. 38 - Differentiate using the Product Rule

Obj. 39 - Differentiate using the Quotient Rule

NC 2.04.c - Use the chain rule and implicit differentiation.

Topic 3 - Differentiation Obj. 42 - Differentiate using the Chain RuleObj. 44 - Differentiate using implicit differentiation

NC 2.05 - Interpret the second derivative.NC 2.05.a - Identify the corresponding characteristics of the graphs of f, f', and f".


Obj. 54 - Graph functions with given characteristics

NC 2.05.b - Identify the relationship between the concavity of f and the sign of f".


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NC 2.05.c - Identify points of inflection as places where concavity changes.


Obj. 53 - Graph intercepts, extrema, inflect, & asymptote

NC 2.06 - Apply the derivative in graphing and modeling contexts.NC 2.06.a - Analyze curves, with attention to monotonicity and concavity.


Obj. 51 - Find intervals of concavity for functions graphs

Obj. 54 - Graph functions with given characteristics

NC 2.06.b - Optimize with both absolute (global) and relative (local) extrema.


Obj. 46 - Find extrema of continuous functions

Obj. 50 - Find relative extrema of functionsObj. 55 - Applied problems: Max & min


Obj. 103 - Find extrema & inflect points of exponential func

NC 2.06.c - Model rates of change, including related rates problems.

Topic 3 - Differentiation Obj. 45 - Solve related rates problems

NC 2.06.d - Use implicit differentiation to find the derivative of an inverse function.NC 2.06.e - Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

Topic 3 - Differentiation Obj. 45 - Solve related rates problems

NC 2.06.f - Interpret differential equations geometrically via slope fields and the relationship between slope fields and solution curves for differential equations.NC 3 - The learner will use integrals to solve problems.

Topic 5 - Integration Obj. 67 - Applied problems: Differential equations

NC 3.01 - Explore and interpret the concept of the definite integral.


Obj. 138 - Integrate by parts to evaluate integral

NC 3.01.a - Compute Riemann sums using left, right, and midpoint evaluation points.NC 3.01.b - Find the definite integral as a limit of Riemann sums over equal subdivisions.

Topic 5 - Integration Obj. 75 - Evaluate definite integrals using limit definition

NC 3.01.c - Find the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: the definite integral, from a to b, of f'(x) dx = f(b) - f(a)


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NC 3.01.d - Identify basic properties of definite integrals.

Topic 5 - Integration Obj. 74 - Use properties of definite integrals


Obj. 137 - Integrate, choose appropriate method

NC 3.02 - Apply standard techniques of anti-differentiation.

Topic 5 - Integration Obj. 66 - Antiderivatives, find differential equations

NC 3.02.a - Find anti-derivatives following directly from derivatives of basic functions.NC 3.02.b - Find anti-derivatives by substitution of variables (including change of limits for definite integrals).

NC 3.03 - Apply and interpret the Fundamental Theorem of Calculus.NC 3.03.a - Use the Fundamental Theorem to evaluate definite integrals.

Topic 5 - Integration Obj. 76 - Fundamental Theorem, evaluate integrals

NC 3.03.b - Use the Fundamental Theorem to represent a particular anti-derivative, and the analytical and graphical analysis of functions so defined.NC 3.04 - Define and use appropriate integrals in a variety of applications.

Topic 7 - Applications of Integration

Obj. 132 - Applied problems: Work of a constant force

Obj. 133 - Applied problems: Fluid force on a surfaceObj. 134 - Find center of mass of systems of point massesObj. 135 - Find centroids of plane regionsObj. 136 - Volume, Theorem of Pappus

NC 3.04.a - Interpret the integral of a rate of change to give accumulated change.NC 3.04.b - Find specific anti-derivatives using initial conditions.

Topic 5 - Integration Obj. 66 - Antiderivatives, find differential equationsObj. 67 - Applied problems: Differential equations

NC 3.04.c - Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.

Topic 5 - Integration Obj. 81 - Trapezoidal Rule, approx definite integrals

NC 3.04.d - Find the area of a region. Topic 5 - Integration Obj. 72 - Find integrals yielding areas of regionsObj. 73 - Sketch regions whose areas are given by integrals


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Obj. 127 - Area, region between two curvesObj. 131 - Area, surfaces of revolution

NC 3.04.e - Find the volume of a solid with known cross sections.


Obj. 128 - Volume, disc method

Obj. 129 - Volume, shell methodNC 3.04.f - Find the average value of a function.

Topic 5 - Integration Obj. 77 - Find average values of functions on intervals

NC 3.04.g - Find the distance traveled by a particle along a line.


Obj. 130 - Arc length of curves over intervals

NC 3.04.h - Solve separable differential equations and use them in modeling. In particular, study the equation y' = ky and exponential growth.

Topic 5 - Integration Obj. 63 - Solve separable differential equations


Obj. 113 - Solve separable differential equations


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North Carolina State Standards Alignment Grades One