Belle Vernon Area Math Curriculum Guide K – 12 2007 -2008 ...€¦ · a. Kindergarten Mathematics 6 b. First Grade Mathematics 9 c. Second Grade Mathematics 12 d. Third Grade Mathematics

Belle Vernon Area

Math Curriculum Guide

K – 12

2007 -2008 School Year

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Table of Contents:Page

1) Cover page of why and how the checklists were developed. 3

2) User Guide (defining terms found in the checklist). 4

3) Elementary Checklists:a. Kindergarten Mathematics 6b. First Grade Mathematics 9c. Second Grade Mathematics 12d. Third Grade Mathematics 16e. Fourth Grade Mathematics 20f. Fifth Grade Mathematics 26

4) Middle School Checklists:a. Sixth Grade Mathematics 31b. Seventh Grade Mathematics 34c. Pre- Algebra Mathematics 37

5) High School Checklists:a. Alignment to PSSA Anchors Grid 42b. Algebra/Geometry Part A 48c. Algebra/Geometry Part B 51d. Algebra/Geometry Part C 55e. Algebra I 58f. Geometry 61g. Algebra II 66h. Algebra III/Trigonometry 68i. Introduction to Calculus 73j. Accelerated Geometry 75k. Accelerated Algebra II 78l. Honors Pre-Calculus 81m. Honors Calculus 85n. AP Calculus 87o. Statistics 90p. PSSA Prep 9th grade 93q. PSSA Enhancement Grade 11 94

Notes: 1) Every checklist was correlated to the PSSA anchors by the teachers going through

the anchors and making sure all of the topics on the 2007 anchors were covered in the checklist. At the high school, a matrix was created due to the fact there are not anchors every single year after grade 8.

2) These checklists are a work in progress. They were completed as of the date of 5/18/2007.

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Belle Vernon Area School DistrictMath Curriculum Topic Checklists

During the 2005-2006 school year a team of math teachers from Kindergarten through 12th grade came together to review the curriculum at each grade level within the district. Each grade level worked together as a team and created a checklist of the topics to be taught in alignment with the PSSA Assessment anchors, PSSA Standards, and any additional skills needed to be successful in the next math course. Emphasis was placed on creating a seamless K-12 Math Curriculum without gaps or unnecessary repetition.

The intentions of these checklists are to:• Provide a resource for all staff, parents, and students that shows what is

being taught in each course.• Insure that all PSSA Anchors, PA Standards, and other necessary skills are

being taught when they are needed, so that our students are not taking a standardized test with many items that they have never seen or do not learn until a year after the test. Also, insure that students will have the necessary background skills to be successful in other subject areas.

• Serve as a guide for any new teacher or long term substitute as to what needs to be taught.

• Enable communication and collaboration among math teachers • Provide a usable document that can be reviewed and updated each year. • Serve to strengthen our math department. For each course or grade level a

timeline should be established on how long to spend on each topic. Eventually common lesson plans incorporating best teaching practices can be created to help strengthen areas of weakness.

Every math teacher and new teacher will be given a copy of this document. Each new teacher should be assigned a Mentor teacher that is familiar with the topic checklists for their course and can assist the new teacher in how to effectively use the checklist to guide instruction.

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User Guide:

Definition of columns used in the topic checklists

Content Is the main mathematical or general topic to be covered such as a chapter title like using fractions.

Chapter/Section Tells where this item can be found in the textbook, workbook, oror lesson or other Supplemental Material (listed as SM). The name of the

textbook, workbook, and other resources that are used will be listed at the end of the Checklist. For example 1.5 would be Chapter 1 section or lesson 5.

Calculator In grades K-3 calculators are not used. This column will be used starting with grade 4 and above. C means that a calculator will be allowed on this objective.

Anchor/Standard Displays which PSSA Anchor or PA Standard will be covered. If the objective is not a PSSA Anchor (testable item) then the Pennsylvania Standard that is covered by the objective will be listed. Pennsylvania Standards will have the letters PA in front of them. Some objectives may have neither an Anchor nor PA standard number but still be a required skill needed for the next math course.

Objective Clearly states the specific topic to be taught. As an example if the general Content is using fractions the objective may be “Adding like fractions.”

Days/Lessons This column lists the suggested number of days/lessons spent teaching this objective.

Resources

After each Topic Checklist, the textbook name, workbooks, and any additional resources that may be used should be listed such as video, manipulatives, or teacher made worksheets. List all supplemental resources listed in the topic checklist.

Assessment

Teachers do not have to list all assessments that they use individually, just list the common assessments that all teachers of the same course should administer with some targeted time line.Example:

Chapter 1 test, Chapter 2 test, 4sight, Chapter 3 test (end 1st 9weeks)Chapter 4 test, Chapter 5 test, Chapter 6 then Midterm (end 2nd 9weeks)

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Belle Vernon Area

Elementary


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Kindergarten MathematicsChecklist of Objectives

Content Chapter/Section

ObjectiveSORTING &

CLASSIFYING 1.1 To identify positions top, middle, bottom

1.2 Compare and identify positions of objects, using before, after, between.

1.3 Compare and identify positions of objects, using inside and outside.

1.4 Compare and identify positions right and left.1.5 Compare objects and describe how they are the same or different.1.6 Identify, sort, and classify objects and shapes by color.1.7 Identify, sort, and classify objects by size.1.8 Identify, sort, and classify items by shape.1.9 Use logical thinking to solve sorting problems.1.10 Sort objects by shape & color to make real graphs1.11 Sort & graph coins by kind (pennies, nickels, dimes, quarters)1.12 Sort objects by various attributes into picture graphs 1.13 Use a graph to gather & interpret data

NUMBERS 0-5 3.1 Match objects one to one3.2 Match & identify equal sets of objects3.3 Identify sets with more objects 3.4 Identify sets with less objects

3.6 Count, recognize, print, and name examples of one and two; identify and read words one and two.

3.7 Count, recognize, print, and name examples of three; identify and read word three.

3.8 Count, recognize, print, and name examples of four; identify and read word four.

3.9 Count, recognize, print, and name examples of five; identify and read word five.

3.10 Count, recognize, print, and name examples of zero; identify and read word zero.

3.11 Count, recognize, print, and name examples of numbers zero through five

3.12 Use ordinal number from first through fifth to show positions

3.13 Solve problems by interpreting graphs using numbers zero though five

NUMBERS 6-12 4.1 Count, recognize, print, and name examples of six; identify and read word six.

4.2 Count, recognize, print, and name examples of seven; identify and read word seven.

4.3 Count, recognize, print, and name examples of eight; identify and read word eight.

4.4 Count, recognize, print, and name examples of nine; identify and read word nine.

4.5 Count, recognize, print, and name examples of six through nine

4.6 Count, recognize, print, and name examples of ten; identify and read word ten.

4.7 Count, recognize, print, and name examples of eleven4.8 Count, recognize, print, and name examples of twelve

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4.9 Count, recognize, print, and name examples of numbers ten through twelve

4.10 Order numbers for sets of one through twelve objects4.13 Use more and less to compare sets of objects 4.15 Answer questions about information shown on a picture graph

ADDITION 7.2 Add one to the numbers zero through five7.3 Add one to the numbers six through nine7.4 Identify plus and equals sign; Add one in a number sentence7.5 Use a picture to solve and check addition problems7.6 Add two to the numbers zero through five7.7 Add two to the numbers six through eight7.8 Identify and add doubles7.9 Add numbers in vertical form7.10 Write number sentences for addition facts through ten7.11 Use pictures to represent number sentences

SUBTRACTION 8.2 Model subtraction of one from one through five and record the results

8.3 Model subtraction of one from six through ten and record the results

8.4 Use number sentences to record subtraction of one8.5 Act out subtraction stories using concrete objects

8.6 Model and record subtraction of two from numbers two through five

8.7 Model and record subtraction of two from numbers six through ten

8.8 Subtract numbers in vertical form

8.9 Use manipulatives and pictures to model subtraction facts from 10 or less

GREATER NUMBERS 10.1 Count & identify teen numbers (overview)

10.2 Identify and write numbers ten through twelve10.3 Identify and write numbers thirteen through fifteen10.4 Identify and write numbers sixteen through nineteen

10.6 Order numbers ten through nineteen & identify numbers missing from an order

10.7 Interpret graphs with numbers in the teens10.8 Count, identify and write number twenty10.9 Count, identify and write numbers 21 through 2510.10 Count, identify and write numbers twenty-six through thirty10.11 Identify and write numbers, in order, to thirty

10.14 Use logical thinking to estimate twenty, more than, and less than twenty

CALENDARS 5.1 Identify times of dayCLOCKS 5.9 Use analog clocks to tell time to the hour

5.10 Read and match times on digital and analog clocks5.11 Identify the times on the hour of everyday events5.12 Determine elapsed time

MEASUREMENT 6.1 Compare objects to identify which one is taller, longer or shorter6.2 Classify objects by length6.3 Identify which object is longest, tallest or shortest6.4 Measure length of objects in nonstandard units6.5 Estimate & measure length in nonstandard units6.6 Solve a problem by making & using a graph about lengths6.7 Determine which object is heavier or lighter , using a scale

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6.8 Compare pictures of objects to determine heaviest & lightest

6.9 Compare capacities of containers & determine which holds more or less

6.10 Determine which container holds the most and leastMONEY 6.13 Identify & count pennies

6.14 Identify the nickel and its value and count on from the nickel using pennies

6.15 Identify the dime and its value and count on from the dime using pennies

PATTERNS 2.1 Model, describe & extend rhythmic patterns2.2 Recognize, describe & extend color patterns2.3 Identify, describe & extend size patterns2.4 Identify, describe & extend shape patterns2.6 Identify, describe & extend position patterns2.9 Identify & extend patterns to solve problems

GEOMETRY 9.1 Identify and describe squares & circles9.2 Identify and describe rectangles and triangles9.3 Identify and sort plane figures by shapes9.5 Identify, and describe three -dimensional shapes9.6 Sort three-dimensional shapes9.8 Match the surfaces of three-dimensional shapes to plane shapes9.9 Count & compare numbers of plane & solid shapes

FRACTIONS 9.10 Identify symmetry9.12 Identify & divide pictures in halves

Addendum: The listed curriculum must be completed for the kindergarten school year. Any lesson not addressed above should be taught, as applicable, in the remaining time.

Resources:

Houghton Mifflin Mathematics Grade KIncluding: Practice Masters WorkbookTeacher Created Worksheets and Supplemental Worksheets

Assessments:Quick Checks, Chapter Tests, and Teacher Created Tests.

(Note: Curriculum tests need to be adapted according to the lessons taught.)

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First Grade MathematicsChecklist of Objectives


Objective

Comparing and Counting

Ch 1 PreviewPP. A and B

Review number concepts.

Counting/Number Words

Ch 1 Preview

PP. C and D

Match the word name with the appropriate whole number.

Addition concepts 1.1Model the concept of addition as increasing.

Model Addition 1.2Model the concept of addition as putting together.

Use symbols to add 1.3 Solve addition sentences, using + and =.Write Addition Sentences 1.4 Write addition sentences for problem situations.

Add with Zero 1.5 Solve addition problems with zero.Problem Solving 1.6 Use models to act out addition problems.Add in any order 1.7 Add numbers in any order.(Commutative Property)Ways to make 7 1.8 Write addition sentences with the sum of 7.Ways to make 8 1.9 Write addition sentences that have the sum 8.Algebra Readiness: the Equals Sign 1.10 Write addition sentences with the sum on either side

of the equals sign.Add in Vertical Form 1.11 Write addition sentences in vertical format.Problem Solving 1.12 Solve problems by using addition.Subtraction Concepts 2.1 Show the meaning of subtraction.Model Subtraction 2.2 Show the meaning of subtraction by taking away.Symbols to subtract 2.3 Solve subtraction sentences using symbols.Write subtraction sentences 2.4 Write subtraction sentences with operational symbols.

Zero in subtraction 2.5 Subtract 0 or find a difference of 0.Problem Solving 2.6 Draw pictures to solve problems.Subtract from 7 or less 2.7 Write number sentences to find the difference.Subtract from 8 or less 2.8 Write subtraction sentences to find the difference.

Subtract in vertical form 2.9 Subtract in vertical form.

Problem Solving 2.10 Solve problems by choosing the correct operation.Count On to Add 3.1 Write sums to 10 by counting on 1, 2, or 3.Add in Any Order 3.2 Add using the commutative property.Number Line to Add 3.3 Find sums to 10 using a number line. Doubles to Add 3.4 Add using doubles and doubles plus one.Draw a Picture to Add 3.5 Add by drawing a picture.

Different Ways to Add 3.6 Add using different strategies.

Count Back to Subtract 3.7 Write differences by counting back 1, 2, or 3.

Number line To Subtract 3.8 Subtract using a number line.

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Draw a Picture to Subtract 3.9 Draw a picture to subtract.

Subtract to Compare 3.10 Show the meaning of subtraction by comparing.Problem Solving: Subtraction 3.11 Use subtraction to solve problems.

Relate Addition and Subtraction 3.12 Write and solve number sentences using related

addition and subtraction facts.Fact Families 3.13 Write fact families using related facts.Different Ways to Subtract 3.14 Subtract using different strategies.

Problem Solving 3.15 Use number sentences to solve problems.Make A Tally Chart 4.2 Represent data with tally marks on a chart.Read a Picture Graph 4.3 Read and use a picture graph to compare information.

Make a Picture Graph 4.4 Make and use a picture graph to compare and use

information.Problem Solving 4.5 Use logical reasoning to solve a problem.Read a Bar Graph 4.6 Read a bar graph and use it to compare informationMake a Bar Graph 4.7 Make a bar graph and use it to compare information.Different Ways to Show Data 4.8 Use a tally chart to make a bar graph and compare

information.Problem Solving 4.9 Use a graph to solve a problem.Teen Numbers 5.1 Count, write, and order numbers to 19.Count by Tens 5.2 Count and write decade numbers.Tens and Ones 5.3 Regroup ten ones as one ten.Numbers to 50 5.4 Recognize and write numbers to 50.Numbers to 99 5.5 Identify and write numbers to 99.One Hundred 5.6 Identify and order numbers to 100.Different Ways to Show Numbers 5.7 Show two-digit numbers in different ways.

Count by Twos 5.8 Skip count by twos to 100.Count by fives 5.9 Skip count by fives to 100.

Number Patterns 5.10 Identify 1 more, 1 less, 10 more, and 10 less than a given number.

Ordinal Numbers 5.11 Identify ordinal numbers from first through tenth.Problem Solving 5.12 Use patterns to solve a problem.Use ten to estimate SM Estimate how many using a group of ten.

Compare Numbers 5.14 Compare two numbers, using is greater than and is less than.

Use Symbols to Compare Numbers 5.15 Compare two-digit numbers using >, <, and =.

Order Numbers 5.16 Compare and order numbers to 100.

Value of Coins 7.1 Identify coins-pennies, nickels, and dimes-and their values.

Nickels 7.2 Find the value of a group of nickels.Nickels and Pennies 7.3 Find the value of a group of nickels and pennies.Dimes 7.4 Find the value of groups of dimes.Dimes and Pennies 7.5 Find the value of dimes and pennies.

Count Coins 7.6 Find the value of a group of dimes, nickels, and pennies.

Equal Amounts 7.7 Find different ways to show the same amount of money.

Position Words 8.18.2

Give and follow directions about position and location of objects in space.

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Plane Shapes 8.3 Identify and describe attributes of triangles, rectangles, squares and circles.

Sorting Shapes 8.4 Classify plane shapes by common attributes.Solid Shapes 8.5 Identify, describe and compare solid shapes.Identify faces of a solid shape. 8.6 Identify the faces of a solid shape.

Problem Solving 8.7 Use patterns to solve problems.Symmetry 8.8 Identify symmetric shapes.Equal Parts 8.9 Identify and count equal parts.One Half 8.10 Use fractions to name parts of a whole.Compare Length and Height 10.1 Compare lengths and heights of objects.

Nonstandard Units 10.2 Estimate length by using non-standard units.Inches 10.3 Measure an object in inches using a ruler.

Compare Weight 10.6 Compare the weights of objects using non-standard units and direct comparison.

Pounds 10.7 Compare the weight of an object to one pound by direct comparison.

Compare Capacity 10.9 Compare the capacity/volume of containers.Cup, Gallon and Quart SM Identify gallon, cups, and quarts.Order Events 11.1 Order Events.Compare Time 11.2 Compare time.Hour 11.3 Tell time to the hour.Half Hour 11.4 Tell time to the half hourTell Time 11.5 Write time another way.Digital Clocks 11.6 Tell time on digital clocks.

Practice Telling Time 11.7 S M3.E.1.1.2how the time in different ways.Calendar 11.10 Read a calendar.Use a Calendar 11.11 Use a calendar.

Do the following at the end of the year if time allows:

Count on to Add 6.1 Write sums to 12 by counting on 1, 2, or 3.

Sums to 11 6.2 Identify equivalent forms of the same number and write sums to 11.

Sums to 12 6.3 Identify equivalent forms of the same number and write sums to 12.

Add Three Numbers 6.4 Find the sum of three one-digit numbers.Problem Solving

6.6Make a table to solve problems.

Count Back to Subtract 6.7 Solve subtraction facts.

Resources:Houghton Mifflin Mathematics Grade 1Including: Practice Masters, Spiral Review, WorkbookAdditional Resources: Math Minutes, Teacher Created Worksheets

Assessments:Quick Checks and Chapter Tests; Teacher Created Tests

(Note: Curriculum tests need to be adapted according to the lessons taught.)Local Assessments-End of the Year Computation Review-May

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Second Grade MathematicsChecklist of Objectives


ObjectiveAddition & Subtraction Facts

1.1Use the order property to find the sum.

1.2 Use a number line to count on to find the sum.1.3 Use doubles to find the sum of whole numbers.

1.4 Use doubles and doubles plus one facts to find the sum of whole numbers.

1.5 To find the sum of whole numbers by adding ten to one digit numbers.

1.6 Find the sum of whole numbers by making ten to add seven, eight, or nine.

1.7 Add three addends using the associative rule.

1.8 Use a number line to count back to find the difference of two whole numbers.

1.9 Subtract from numbers to twelve using addition (inverse relationship).

1.10 Subtract from numbers to fifteen using addition (inverse relationship).

1.11 Use the inverse relationship between addition and subtraction to subtract from numbers to twenty.

1.12 Write number sentences to solve problems.1.13 Model the meaning of subtraction as comparing.1.14 Identify and write names for numbers.1.15 Identify and write fact families (inverse relationship).

1.16 Interpret and solve problems involving addition and subtraction.

Numbers and Patterns to 100 2.1 Count, read, and write decade numbers.

2.2 Use tens and ones models to show numbers to 100.2.3 Identify the value of the tens and ones digits of numbers.

2.5 Represent numbers in different forms (words, models, expanded form).

2.6 Identify unnecessary information in a word problem.2.7 Identify even and odd numbers.

2.8

Identify patterns on a hundred chart by counting by 2s, 3s, and 5s.

2.9 Compare whole numbers to 100 by using the symbols greater than, less than, and equal to.

2.10 Order whole numbers2.11 Round numbers to the nearest ten.2.12 Use patterns to solve problems.

Data and Graphing 3.1 Record data using tally marks.

3.2 Compare data using tables.3.3 Read a pictograph.3.4 Use logical reasoning to solve a problem.

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3.5 Interpret data on a bar graph.

3.6 Represent and compare data from a bar graph and tally chart.

3.7 Find range and mode.3.8 Use a bar graph to solve a problem.

Two-Digit Addition 5.1 Use basic addition facts to add multiples of ten.

5.2 Add numbers without regrouping.5.3 Demonstrate how to regroup ten ones as one ten.

5.5 Add a 1-digit number to a 2-digit number, with and without regrouping.

5.6 Add 1- and 2- digit numbers with and without regrouping.5.7 Regroup 10, 11, or 12 ones to add 2-digit numbers.5.8 Regroup 13, 14, or 15 ones to add 2-digit numbers.5.9 Regroup 16, 17, or 18 ones to add 2-digit #5.10 Round to the nearest ten to estimate sums.5.11 Use guess and check to solve problems.5.12 Recognize and use different addition methods.5.13 Rewrite and solve horizontal addition exercises.5.14 Add money amounts.5.15 Add three 2-digit numbers.5.16 Use data from a picture to solve problems.

Time and Calendar 10.1 Estimate the length of one minute.

10.2 Tell time to the hour.10.3 Tell time to the half-hour.10.4 Tell time to the five minutes.10.5 Tell time to the quarter-hour.

10.6 Determine how much time has passed.(Add supplemental material to cover A.M. and P.M.)

10.7 Solve problems involving elapsed time.10.8 Read and understand information on a calendar.10.9 Compare periods of time.10.10 Use schedules to solve problems.

Subtracting 2-Digit Numbers 6.1 Use basic facts to subtract tens.

6.2 Subtract numbers without regrouping.6.3 Demonstrate how to regroup one ten as ten ones.

6.5 Subtract 1-digit numbers from 2-digit numbers, with and without regrouping.

6.6 Subtract 2-digit numbers from 2-digit numbers, with and without regrouping.

6.7 Use base-ten models to act out and solve problems.

6.8 Subtract 2-digit numbers; practice subtracting from 10 and 11.

6.9 Subtract 2-digit numbers; practice subtracting from 12, 13, and 14.

6.10 Subtract 2-digit numbers; practice subtracting from 15, 16, 17, and 18.

6.11 Estimate differences by rounding to the nearest ten.6.12 Subtract using different methods.6.13 Rewrite horizontal subtraction problems in vertical form.6.14 Add and subtract money amounts less than $16.15 Check subtraction by using addition.

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6.16 Solve problems using data from a table.Money 4.1 Write the value of a group of dimes, nickels, and pennies.

4.2 Identify a quarter and write the value of a group of coins.4.3 Write the value of a group of coins.4.4 Show equal amounts with different coin combinations.4.5 Compare amounts of money.4.6 Use coins to act out a problem.

4.7 Identify a half-dollar and write the value of a group of coins.

4.8 Use coins to show a given amount.4.9 Use coins to show a given exact amount.4.10 Identify coin combinations that equal one dollar.4.11 Count on to make change.4.12 Solve two step problems using money.

Geometry, Fractions, and Probability

7.1Identify and classify circles, squares, triangles, and rectangles.

7.2 Identify sides and vertices on plane shapes.

7.3 Identify the number of faces, edges, and vertices for solid shapes.

7.4 Identify congruent shapes.7.5 Create congruent shapes with pattern blocks.7.6 Identify and draw lines of symmetry.7.7 Identify, describe, and extend patterns.7.8 Identify and write unit fractions.7.9 Identify and write fractions.

7.10 Identify fractions that show one whole or more than one whole.

7.11 Compare fractions using symbols.

7.12 Identify and write fractions that represent parts of a group or a set.

7.13 Identify fractional parts of a group.7.14 Predict and record the outcome of an event.7.15 Solve problems using data from a picture.

Measurement 9.1 Estimate and measure length using nonstandard units.

9.2 Compare the measurements of objects with different nonstandard units.

9.3 Estimate and measure to the nearest inch or foot.9.4 Estimate and measure in centimeters and meters.9.5 Measure centimeters and add to find perimeter.9.6 Use guess and check to solve problems.9.7 Estimate the weight of objects using pounds.9.8 Estimate the mass of objects using kilograms.

9.9 Use cups, pints, and quarts to measure capacity and identify equivalent measures.

9.10 Estimate whether containers hold more than, less than, or the same as one liter.

9.11 Read a Fahrenheit thermometer.

9.12 Choose the best tool and unit to measure distance, weight, capacity, temperature.

9.13 Use measurement to solve a problem.Numbers and Patterns to 1,000

11.1Count by 100s and read and write the numbers.

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11.2 Use models to count by 100s, tens, and ones and write numbers through 999.

11.3 Count, read, and write numbers through 500.11.4 Count, read, and write numbers through 1,000.

11.5 Identify place value, represent numbers using expanded form.

11.6 Use models to identify and regroup tens as hundreds.11.7 Use tables to extend number patterns and solve problems.

11.8 Use words, models, and expanded form to show 3-digit numbers in different ways.

11.9 Compare 3-digit numbers using the symbols less than, greater than, and equal to.

11.10 Identify 3-digit numbers to determine what comes before, after, and between.

11.11 Use place value to order 3-digit numbers.11.12 Count dollars and coins to determine value.11.13 Solve problems using combinations of bills and coins.

ResourcesMathematics by Houghton Mifflin 2002;

If time allows and students have mastered necessary skills, teachers may teach Chapter 8 (Multiply and Divide) and Chapter 12 (Add and Subtract 3-digit) at their discretion

AssessmentLocal Assessments at start and end of school year; All Chapter Quick-Checks and Tests

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Third Grade MathematicsChecklist of Objectives


Objective

Numbers Through 999 1.1 Write numbers to 999 in standard form, expanded

form, and word form. Identify the place and value of a digit.

Round Two-Digit Numbers 1.2 Round to the nearest ten or to the nearest ten cents.

Round Three –Digit Numbers 1.3 Round to the nearest hundred, dollar, or ten cents.

Place Value to Thousands 1.6 Write the numbers to 9,999 in different forms.

Identify the place and value of a digit in a number.

Compare Numbers 1.7 Use inequality symbols to compare numbers through

9,999.Ordering Numbers 1.8 Order groups of whole numbers through 9,999.

Round Four Digit Numbers (age 27 only)

1.9Identifying even and odd numbers.

Problem-Solving Strategy: Find a Pattern

1.10 Solve a problem by finding a pattern.

Problem-Solving Application:Read a Graph

1.13 Read a graph to solve problems.

Addition Properties 3.1 Use the Commutative Property, the Zero Property, and

the Associative Property to add.Regroup Ones 3.2 Add by regrouping ten one as one ten.Regroup Ones and Tens 3.3 Add by regrouping both ones and tens.Estimate Sums 3.4 Estimate sums by rounding numbers.Problem Solving Skill:Exact Answer or Estimate

3.5 Decide whether a problem needs an exact answer or an estimate.

Column Add 3.6 Add three or more addends.

Add Greater Numbers 3.7 Find the sum of 2 four-digit addends.

Problem Solving Strategy: Guess and Check

3.8 Use the guess and check strategy to solve.

Subtraction Strategies and 3.9 Use properties of subtraction and counting to find

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Properties differences.Regroup Tens 3.10 Subtract by regrouping 1 ten as 10 ones.Regroup Tens and Hundreds 3.11 Subtract by regrouping tens and hundreds.Estimate Differences 3.12 Estimate numbers by rounding numbers.

Problem Solving Application: Use Operations

3.15 Use addition and subtraction to solve problems.

Modeling Multiplication 5.1 Model multiplication by grouping counters.

Arrays and Multiplication 5.2 Multiply numbers in any order.

Multiply with 2 5.3 Learn ways to multiply when 2 is a factor.Multiply with 5 5.4 Learn to find the product of a factor and 5.Problem-Solving Skills: Too Much Information

5.6 Distinguish necessary from extraneous information when solving problems.

Multiply with 1 and 0 5.7 Multiply when a factor is 1 or 0.

Multiply with 3 5.8 Learn ways to multiply when 3 is a factor.Multiply with 4 5.10 Learn to find the product of a factor and 4.Line, Line Segments, Rays, and Angles

7.1 Identify and compare lines, line segments, rays, and angles.

Plane Figures 7.2 Describe and compare characteristics of plane figures.Quadrilaterals 7.3 Identify the characteristics of quadrilaterals.Triangles 7.4 Identify triangles as equilateral, isosceles, or right.Problem-Solving: Visual Thinking 7.5 Solve visual thinking problems.

Congruent Figures 7.6

Develop an understanding and recognition of congruence.

Line of Symmetry 7.7 Recognize possible lines of symmetry.

Find Area 7.9 Determine the area of a figure.Estimating Area 7.10 Use square units to estimate the area of a figure.Problem-Solving Strategy: Find a Pattern

7.11 Recognize and complete patterns.

Solid Figures 7.12 Name and describe the characteristics of solid figures.Estimating Volume 7.13 Estimate volume by counting unit cubes that fill a box.

Find Volume 7.14 Determine the volume of a solid figure.Problem-Solving Application: Use

7.15Determine whether a problem is asking for area or volume and then find the solution.

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Measurement

Value of Money 2.1 Write amounts of money, using dollars, dimes and pennies.

Count Coins and Bill 2.2 Write money amounts and count bills and coins.

Equivalent Amounts 2.3 Identify equivalent amounts of money.

Count Change 2.4 Make change by counting.Choose the Operation 2.5 Determine whether a problem requires addition or

subtraction to find the solution.

Hour, Half-Hour, Quarter Hour

2.6 Tell time to the hour, half-hour, and quarter hour. Include A.M. and P.M.

Time to the Minute 2.8 Tell time to the minute.

Elapsed Time 2.10 Find elapsed time shown on clocks.Multiply with 6 6.2 Find the product of a number and 6.Multiply with 8 6.3 Find the product of a number and 8.Problem-Solving Skills: Multi-step Problems

6.4

Solve problems that have more than one step.

Multiply with 7 6.5 Find the product of a number and 7.Multiply with 9 6.6 Find the product of a number and 9.Problem-Solving Strategy: Choose a Strategy

6.7 Decide what strategy to use to solve a problem.

Multiply Three Numbers 6.9 Find the product of 3 or more factors.Problem-Solving Application: Use Operations

6.10 Use operations to solve problems.

Measuring Length

4.1Estimate and measure lengths of objects to the nearest inch.

Measure to the Nearest Half Inch

4.2Measure objects to the nearest half inch.

Customary Units of Length 4.3 Use customary units to measure the lengths.

Estimating and Measuring Capacity

4.4 Estimate and measure capacity by using customary units.

Customary Units of Capacity

4.5 Estimate and choose appropriate units of capacity.

Customary Units of Weight 4.6 Measure the weight of objects by using customary

units of weight.Strategy: Work Backwards

4.8 Determine a beginning measurement by working backward from a final measurement.

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Collecting and Organizing Data

10.1 Collect data in the form of a survey and record the results.

Problem-Solving Skills: Use a Bar Graph

10.4 Locate and use data from a bar graph.

Make a Bar Graph 10.5 Read and make bar graphs.

Problem-Solving Strategy: Make a Table

10.7 Solve a problem by organizing data into a table.

Recording Outcomes 10.9 Experiment with probability and record the data.

Fractions and Regions 11.1 Read and write fractions.

Fractions and Groups 11.2

Name equal parts of a group, using fractions.

Fractional Parts of a Group 11.8 Find a fractional part of a group.Problem-Solving Skills: Multi-StepProblems

11.11 Determine how to solve problems with more than one step.

Add and Subtract Decimals

11.16 Find the sums and differences of two decimals.

Problem-Solving Application: Use Money

11.18 Solve problems that involve addition and subtraction of money.

Related Multiplication and Division

8.2 Use multiplication to divide.

Problem-Solving Application: Use Money

9.10 Solve problems that use money.

Problem-Solving Application: Use Operations

12.15 Determine whether to use addition, subtraction, multiplication, or division to solve problems.

Algebraic Concepts

Supplement material Determine the missing number or symbol in a number

sentence.Resources

Mathematics 3 by Houghton Mifflin Houghton Mifflin practice workbook, reteaching masters, challenge masters, refreshers masters, spiral review, fast facts, teaching transparencies, and teaching tools.AssessmentThird grade local assessment (twice a year), Chapter Tests, End of year computation assessment

19

Fourth Grade MathematicsChecklist of Objectives


ObjectivePlace Value through 100,000 1.1 Read and write numbers through one-hundred

thousandsCompare and Order Numbers 1.2 Compare and order numbers through one hundred

thousandsRounding Numbers 1.3 Estimate a number by rounding it

Estimated or Exact Amounts 1.4 Decide whether a number represents an exact

amount or an estimateProblem Solving: Use Logical Thinking

1.9Solve problems by using logical thinking

Compare Money Amounts 1.10 Count and compare amounts of money

Problem Solving Application: Use Money

1.12Solve problems involving money

Addition Properties 2.1 Recognize and apply properties of addition

Add Whole Numbers 2.2 Find whole number sums

Subtract Whole Numbers 2.3 Find whole number differences

Estimate Sums and Differences 2.4 Round numbers to estimate sums and differences

Estimated or Exact Answers 2.5 Decide whether a problem needs an exact answer

or an estimateSubtract Across Zeros 2.6 Subtract when some digits are zeros

Problem Solving Applications: Use Operations

2.7Decide when to use addition or subtraction to solve problems

Expressions and Equations 2.8 Simplify and write equations and inequalities

Write and Evaluate Algebraic Expressions

2.9

Write and evaluate expressions containing variables

Write and Solve Equations 2.10 Write and solve algebraic equations

Solving Adding Equations 2.11 Add the same number to or subtract the same

number from both sides of an equationEquations with Two Variables 2.12 Relate equations with two variables to function

tablesProblem Solving Strategy: Guess and Check

2.13Use the guess and check strategy to solve problems

Venn Diagrams 2p. 101

Describe, interpret, and/or answer questions based on a Venn diagram

Guess My Rule 2 Determine rule for function table; Guess My Rule

20

p. 147Use Doubles to Multiply

3.1p. 104-105

Use doubles to multiply when 2,3,4,6,or 8 is a factor

Multiplication Properties 3.2 Use multiplication properties to find products

Use Patterns to Multiply 3.3 Use patterns to find products

Multiples

3p. 115

SupplementalMaterials

List and identify multiplies of a number where the multiples do not exceed 100

Relate Multiplication and Division

3.4Use known multiplication facts to divide

Factors 3p. 109

List and identify all factors through 10 of any given number

Use doubles to Divide 3.5 Use doubles to divide

Division Rules 3.6 Apply rules to find quotientsDivide by 5, 7, 9, or 10 3.7 Use related multiplication facts to divide by 5, 7,

9, or 10Division with Remainders 3.8 Find a quotient with remainders

Problem Solving Skill: Multi-step Problem

3.9Solve multi-step problems

Problem Solving Application: Using Patterns

3.12Use patterns to solve problems

Two-Step Functions 3.14 Describe functions with operations and solve for

one variable when the value is known

Multiply Multiples of 10, 100, and 1,000

4.1p. 164 & 165

Use basic facts and patterns of zeros to multiply multiples of 10, 100, or 1,000

1Modeling Multiplication by One-digit Numbers

4.2

Use base-ten blocks to model multiplication

Multiply Two-Digit Numbers by One-digit Numbers

4.3

Multiply two-digit numbers by one-digit numbers with one regrouping

Estimate Products 4.4

Estimate products by rounding the factors

Problem Solving Strategy:Find a Pattern

4.5

Solve a problem by finding a pattern

21

Multiply Three-Digit Numbers by One-Digit Numbers

4.6

Multiply three-digit numbers by one-digit numbers with regrouping

Multiply Greater Numbers 4.7

Multiply four-digit numbers by one-digit numbers with regrouping

Multiply with Zeros 4.8 Multiply three-and – four digit factors with zeros

Choose the Operation 4.9 Decide what operation is necessary to solve a

given problemMultiply Multiples of 10 and 100

4.10Multiply mentally when both factors are multiples of 10 or 100

Multiply Two 2-Digit Numbers 4.11 Multiply by two-digit numbers when regrouping

Multiply Three-Digit Numbers by Two-Digit Numbers

4.12

Multiply three-digit numbers by two-digit numbers with regrouping

Problem Solving Application: Use a Pictograph

4.13

Use a pictograph to solve problems

Modeling Division

5.1p. 216 - 217

Model regrouping in division

Two-Digit Quotients 5.2 Divide two-digit dividends by one-digit divisors,

with and without remainders (no regrouping)

Regrouping in Division 5.3

Divide two-digit dividends by one-digit divisors, with and without remainders when regrouping is necessary

Interpreting Remainders 5.4 Determine a reasonable answer by interpreting

remainders when solving division problemsMental Math:Divide Multiples of 10, 100, and 1,000

5.5

Divide mentally using basic facts and patterns

Three-digit Quotients 5.6

Divide three-digit dividends by one digit divisors (three-digit quotients with and without remainders.

Place the First Digit of the Quotient

5.7Divide three-digit dividends by one-digit divisors (two-digit quotients with and without remainders)

Divide Money 5.8 Divide money amounts by whole numbersZeros in the Quotient 5.9 Divide three-digit dividends by one-digit divisors

(zeros in the quotient)

Problem Solving Strategy:Work Backward

5.10

Solve problems by working backward

Divisibility Rules 5.11 Identify numbers divisible by 2,5, or 10Prime and Composite

5.12Add p. 161

Identify a number as prime or composite

22

Problem Solving Applications: Use Operations 5.17

Solve problems by choosing an operation

Represent Fractions

7.1p. 322 - 323

Write a fraction for a part of a region or a part of a group

Fractional Parts of a Number 7.2 Find the fractional part of a number, using models

or computationCompare Fractions with Like Denominators

Refer to 7.6p. 339

Supplemental Materials

Locate and identify fractions on a number line – ONLY fractions with like denominators

Write Mixed Numbers 7.7 Write equivalent improper fractions and mixed

numbers

Add with Like Denominators 7.9

Add fractions and mixed numbers with like denominators

Subtract with Like Denominators

7.10Subtract fractions an mixed numbers with like denominators

Fractions and Decimals

8.1p. 370 -371

Demonstrate the relationship between fractions and decimals

Mixed Numbers and Decimals 8.2 Read, write , and model decimals greater than one

Fraction and Decimal Equivalents

8.3Supplemental

Materials

Write equivalent fractions and decimals thru 10ths

Compare and Order Decimals

8.4p. 380


Compare and order decimals on a number line thru 10ths

Problem Solving Strategy: Find a Pattern

8.6Recognize and use patterns to solve problems

Add and Subtract Decimals

8.7Add p. 377

Find sums and differences of decimals

Problem Solving Applications: Use Decimals

8.8Solve problems by finding decimal sums and differences;

Inch, Half Inch, and Quarter Inch

6.1p. 276 - 277

Measure to the nearest inch, half inch, and quarter inch

Customary Units of Capacity and Weight

6.3Change customary units of capacity and weight

Centimeter and Millimeter 6.5 Measure, using centimeters and millimeters

Metric Units of Capacity and Mass

6.7Change metric units of capacity and mass

Problem Solving Strategy: Make a Table

6.8Supplemental

Materials

Solve a problem by organizing information in a table

23

Digital and Analog Time

6Supplemental

Materials

Match/construct analog time (a picture of a clock), to the same time written in digital

Identify Time6


Identify time(analog or digital) as the amount of minutes before and/or after the hour

Determine Elapsed Time

6Supplemental

Materials

Determine the beginning or ending time, given the elapsed time (limited to 2 adjacent hours)

Collect and Organize Data 9.1

Conduct a survey and collect and organize information;Vocabulary – data, bar graph, line plot

Use a Bar Graph 9.3 Read and interpret bar graphs and double gar graphs

Problem Solving Skill: Interpret a Line Graph

9.4Interpret line graph data

Read and Understand Line Graphs

9.5Read and interpret a line graph

Problem Solving: Choose a Strategy

9.6Choose a strategy to solve problems

Probability and Outcomes 9.7 Describe the probability of an event

Find Probability 9.8 Write the probability of an eventMaking Predictions 9.9 Use probability to make predictions

Problem Solving Applications: Use Data and Probability 9.11

Use data and probability to solve problems

Create a Graph

9SupplementMaterials

Graph data or complete a graph given the data (bar graph, or pictograph – grid is provided)

Interpret Data from a Graph

9 Supplement Materials

Translate information based on data or chance (data my be shown in tables, charts, line graphs, bar graphs or pictographs)

Points, Lines, and Line Segments

10.1p. 458 - 549

Name and describe the characteristics of points, lines, line segments, parallel, perpendicular lines

Rays and Angles 10.2 Name and describe the characteristics of rays and angles

Polygons and Quadrilaterals 10.3 Name and describe the characteristics of polygons

and quadrilateralsClassify Triangles 10.4 Name and classify triangles: right, obtuse, and

acute

Circles 10.5 Identify parts of a circle and turns about the center of a circle

Symmetry 10.7 Identify line and rotational symmetry

Problem Solving 10.12 Solve problems that require visual thinking

24

Skill:Analyze Visual Problems


Solid Figures(No Nets) 10.13 Name and identify the characteristics of solid

figures: cube, sphere, rectangular prism, pyramidLocate Points on a Grid Using Whole Numbers

11.1p. 522 - 523

Name points on a grid, using ordered pairs

Graph Ordered Pairs 11.2 Plot points on a graph, using ordered pairs

Resources:

Houghton Mifflin Mathematics Book 4Including: Practice Masters, Spiral Review, Workbook

Additional Resources:Math Minutes

Teacher Created Worksheets

Assessments: Quick Checks, Chapter Tests, and Teacher Created Tests

(Note: Curriculum tests need to be adapted according to the lessons taught.)Local Assessments – September & JanuaryEnd of Year Computation Review - May

25

Fifth Grade MathematicsChecklist of Objectives

*Topic is taught without the use of a calculator at first and then the students are shown how to solve problems with a calculator


Objective

Whole Numbers Decimals and Integers

1.1

Use expanded notation to represent whole numbers and decimals.Identify the place value of a digit.

1.2 Read and write numbers through hundred thousands with exponents

1.3 Compare whole numbers through 9 digits using >, <, =

1.3

Round whole numbers through millions and decimals through hundredths.

1.4 Solve problems involving whole numbers and decimals using estimation.

1.5 Use expanded notations to represent whole numbers and decimals.

1.5 Identify the place value of a digit.

1.6 Round whole numbers through millions and decimals through hundredths.

1.8Read and write decimals in standard and word forms.Identify the place value of a digit

1.9 Compare whole numbers through 9 digits and decimals through hundredths using <, >, =

1.10

Round whole numbers through millions and decimals through hundredths.

1.11 Compare whole numbers through 9 digits and decimals through hundredths using <, >, =

1.12Locate integers on a number line (greater than or equal to -20)

Supplemental Identify negative numbers on a thermometerAddition Subtraction and Equations

2.1 Addition of whole numbers

2.2 Subtraction of whole numbers 2.4 Addition of decimals to thousandths 2.5 Subtraction of decimals to thousandths 2.6 Solve problems by working backwards

2.9 Solve for a missing number in an equation – single operation (whole numbers)

2.10 Solve addition and subtraction equations using a function table

26

Multiplication 3.2 Multiply by a one digit number

3.3 Multiplying numbers that contain zeros by a one-digit number

3.4 Using estimation to solve problems involving whole numbers and decimals

3.5Use patterns or mental math to multiply by multiples of 10, 100, 1000

3.6 Multiply by multiples of 10 3.8 Multiply by two digit numbers

3.9 Choose an operation to solve a problemDivision and Equations 4.1 Use place value to divide by one-digit divisors

4.2 Problems with zeros in the quotient4.3 Using basic multiplication facts to estimate quotients4.4 Calculate the mean, median and range of a set of data

6.5 Identify the mode of a set of a dataCalculate the mean, median and range of a set of data

4.13 Write and solve multiplication and division equations4.14 Use counters to solve equations

4.15 Solve equations involving multiplication and division using function tables

4.16 Write equations to solve word problems

Measurement and Integers 5.1

Measure to the nearest fraction of an inch.Use a ruler to measure to the nearest 1/8 inch or centimeter

5.2

Select appropriate unit for calculating perimeter and area.Calculate and label perimeter and area of a square or rectangle

5.3

Select appropriate unit for measuring weight and capacityConverting capacity and weight measurements in customary and metricSolve problems of weight, length and capacity

5.4 Solve problems involving more than one step

5.5

Measure in metric units and make conversions

Use a ruler to measure to the nearest 1/8 inch or centimeter

5.6

Change from one metric unit of capacity or mass to anotherConversion of metric units of mass and capacitySolving problems of metric units of weight, mass and capacity

5.7Use addition and subtraction to solve problems involving times and schedules

Number Theory and Addition and Subtraction of Fractions

7.1

Identify prime and composite numbers

27

7.2 Write the prime factorization of a number

7.3 Determine when 2, 3, 4, 5, 9, or 10 is a factor of a number

7.4 Find common factors and the greatest common factors of 2 or more numbers

7.5 Find common multiples and the least common multiple

7.7 Write a fraction to represent some part of a whole amount or a part of a group of objects

7.8 Use multiplication to find equivalent fractions

7.9 Using division or prime factorization to write fractions in simplest form

7.10 Compare fractions, mixed numbers and decimals7.11 Compare unlike fractions7.13 Add and subtract fractions with like denominators7.14 Add fractions with unlike denominators

7.15 Use the least common denominator to add fractions with unlike denominators

7.16 Add mixed numbers having like or unlike denominators

7.17 Rename mixed numbers to find differences

7.18 Subtract fractions and mixed numbers with unlike denominators

7.19 Use renaming to subtract mixed numbers7.20 Use patterns to solve fraction problems

Data, Statistics and Probability 6.2 Compare data sets by using a double bar graph

6.3 Make and interpret a histogram6.4 Analyze data from graphs to solve word problems

6.6Use a line plot to find the mean, median and mode of a set of data

6.7 Analyze line graphs without numbers6.8 Interpret and make line and double line graphs

6.9 Choose an appropriate graph according to the data given

6.10 Solve a problem by using a table6.12 Predict an determine outcomes6.13 Use fractions to find probability6.14 Use data to make predictions

Multiplication and Division of Decimals

9.1Find the product of a whole number and a decimal

9.2 Use rounding to estimate products of decimal factors9.3 Find the product of two decimal factors

9.4 Write zeros in the product of decimal factors when needed

9.5 Recognize and apply patterns to solve problemsGeometry and Measurement 10.1 Identify and draw points, lines, line segment and rays

10.5 Classify quadrilaterals and find missing angle measures

10.6 Solve problems by thinking about a simpler problem10.10 Identify rotational and line symmetry

28

10.16Identify solid figures from different perspectives and find surface area of rectangular prisms and cubes (faces, vertices, edges)

Integers and the Coordinate Plane

12.1Identify transformations such as translations, reflections and rotations

After PSSADivision and Equations 4.5 Interpret remainders

4.7 Divide by a two digit number4.8 Estimated quotient is too large4.9 Estimated quotient is too small

Multiplication and Division of Fractions

8.2 Multiply Fractions

8.3 Multiply Fractions and Mixed Numbers8.4 Use the Operation8.8 Divide by a Fraction8.5 Divide by a Unit Fraction8.6 Divide by a Counting Number8.7 Solve a Simpler Problem8.9 Divide with Mixed Numbers8.10 Use Circle Graphs

Ratio and Percent 11.1 Meaning of Ratios

11.2 Equivalent Ratios11.3 Rates11.6 Understand Percent11.7 Ratio and Percent11.8 Decimals and Percents

11.9 Use Fractions, Decimals, and Percents for Comparisons

11.10 Choose a Strategy11.12 Percent of a Number11.13 Compare Data Sets11.14 Use Percent

Resources

Mathematics 5 by Houghton MifflinHoughton Mifflin practice workbook, reteaching masters, challenge masters, refresher

masters, spiral review and teaching toolsPSSA Coach

Assessment

Fifth grade local assessment (twice a year)End of year computation assessment

29

Belle Vernon Area

Middle School


30

Sixth Grade MathematicsChecklist of Objectives


Calculator Objective

Place Value 1.1 NC Learn how to read, write, and understand whole number and decimal place value.

Ordering numbers 1.2 NC Compare/Order numbers and decimals from millions

to hundred thousandths using a number lineRounding numbers 1.3 NC Round whole numbers and decimals by using place

valueCompute Decimals and Whole numbers

1.5 NCAdd and subtract decimals and whole numbers

1.7-1.9 NC Multiply whole numbers and decimals1.11-1.13 NC Divide whole numbers and decimals

3.13 NC Divide with terminating or repeating quotients

Estimation SUP NC Estimate and compute value of whole numbers and decimals. (up to 2-digit divisors)

Exponents 3.2/1.15 NC Comprehension of exponential value and powers of 103.2 NC Computation of exponents

Number Theory 3.4 NC Use and know the divisibility rules for 2, 3, 5, 10

3.1 NC Understand the difference between prime and composite numbers and factoring.

3.3 NC Compute prime factorization

3.5 NC Find the greatest common factor of numbers up to 33.6 NC Find the least common multiple of numbers up to 3

Data Analysis 2.1 C Definition analysis and application of mean, median, mode, range.

2.2 NC Analyze and comprehend single and double bar graphs.

2.3 NC Analyze and comprehend frequency tables and histograms.

2.4 NC Analyze and comprehend single and double line graphs and line plots.

SUP NC Analyze and comprehend circle graphs using percents. (center point and tic marks)

SUP NC Choose the appropriate representation for a specific set of data from the same type of graph.

Fractions 3.8 NC Understand the value of fractions and compare their equivalency.

3.9 NC Reduce the value to its simplest form

3.10 NC Compare and order the differences in value of fractions

SUP NC Conversion of mixed numbers to improper and vice versa

4.1-4.2 NC Add fractions and mixed numbers4.3 NC Subtract fractions and mixed numbers

4.5-4.6 NC Multiply fractions and mixed numbers4.7-4.10 NC Divide fractions and mixed numbers (reciprocal)

Measurement SUP NC Use or read a ruler to measure to the nearest 1/16 in.SUP NC Use or read a ruler to measure to the nearest

31

millimeter.

SUP NCChoose the most precise measurement (length, capacity, weight/customary and metric) of a given object (smaller measurements are more precise).

SUP NC Find the amount of elapsed time for an event.Fractions, Decimals, Percents

SUP NCModel percents using drawings, graphs, and/or sets. (circle graphs)

7.7-7.11 NC Understand the value of decimals, fractions, and percents,

7.11 NC The conversion among decimals, fractions, and percents.

Midterm

Geometry 9.1 NC Identify, draw and label points, planes, lines, line segments, rays, angles, and vertices.

SUP NC Identify, describe and label parallel, perpendicular and intersecting lines.

9.2 NC Define, label and identify right, straight, acute and obtuse angles.

9.3 NC Measure angles using a protractor up to 180

9.7 NC Identify and describe properties of all 6 triangles (obtuse, right, acute, scalene, isosceles, equilateral)

9.7 NC Total number of degrees in a triangle.9.8 NC Identify and classify and compare quadrilaterals.9.8 NC Identify the total number of degrees in a quadrilateral.9.12 NC Identify and classify and compare polygons (10 sided)

10.1 NC Find the perimeter of any polygon (regular and irregular)

10.5 NC Identify the parts of a circle and find the diameter and radius of a circle.

Algebra 6.1-6.4 NC Complete equations by using the following properties: associative, commutative, distributive, and identity.

6.3 NC Understand the order of operations.

6.11 NC Identify the inverse operation needed to solve a one-step equation.

6.11/6.12 NC Solve a one-step equations using all 4 operations (whole numbers)

6.7-6.8 NC Match or write and equation involving a variable to a verbal situation.

12.1 NC Plot, locate or identify points in Quadrant 1 (intervals:1,2,5,10)

6.12/12.5 NC Create, extend, find a missing element in a pattern using X/Y charts, In(put)/Out(put) and graphs

12.6 NC Determine a rule based on a pattern or illustrate a pattern based on a given rule (in a chart or graph)

Probability 11.2/ NC Define and find the probability of a simple event.

11.7 NCDetermine and show all possible combinations involving no more than 20 total arrangements (tree diagram, table, grid)

After PSSAIntegers 5.1-5.2 NC Identify integers and compare and order integers.

5.4-5.5 NC Add and subtract integers.5.6-5.7 NC Multiply and divide integers

6.11 NC Solve one-step equations with addition and subtraction

32

6.12 NC Solve one-step equations with multiplication and division

Ratios, Proportions, Percents

7.1 NCRepresent ratios in all 3 forms

7.2 NC Solve for unit rates7.3 NC Solve ratios7.4 NC Solve problems on Distance, Rate, and Time7.7 NC Scale drawings.7.11 NC Review converting fractions, decimals, and percents

8.1-8.2 NC Find the percent of number and a missing percents.8.7 NC Find interest rates8.9 NC Find sales tax and sales discounts

Geometry 10.1-10.2-10.3 NC Find area of quadrilaterals, triangles, and circles.

10.5 NC Find circumference of circles

Measurement 4.12-4.13 NC Conversions of customary units of measurement (length, capacity, and weight)

1.16 NC Conversions of metric units of measurements (length, capacity, and weight)

FinalResources: Textbook: Mathematics Houghton Mifflin; Finish Line Workbook; Supplemental WorksheetsAssessment: Tests, quizzes, midterm and final exams, PSSA

33

Seventh Grade MathematicsChecklist of Objectives

C =Calculator, NC = No Calculators


Calculator ObjectiveOrder of Operations 2.1 NC Solve mathematical expressions using the order of operations.

2.1 NC Evaluate a variable expression using the order of operations.2.1 NC Find patterns in a series of order of operations problems.

Exponents 2.2 NC Use exponents to write powers, including evaluating expressions.

2.2 NC Find patterns in exponent problems.GCF & LCM 2.5, 3.1 NC Find the GCF and LCM for two and three numbers.Fractions and Decimals 2.6 NC Write fractions in simplest form.

2.7 NC Convert fractions to decimals.2.8 NC Order fractions and decimals on a number line.3.2 NC Convert mixed numbers to improper fractions, vice versa.

3.3, 3.4 NC Add and subtract fractions and mixed numbers.3.5 NC Multiply fractions and mixed numbers.3.7 NC Dividing fractions and mixed numbers.

Supp. C Perform all fraction functions and operations with the use of a calculator.

X-Y Axis Relationship 4.1 NC Describe the relationship between two variables using x-y

tables. 4.1 NC Create expressions based on the information in tables.

4.2 NC Plot points from data tables in Quadrant 1.

4.2 NC Draw lines on a coordinate plane using information from an x-y table.

Integers 4.3 NC Compare and order and plot integers on a number line.4.3 NC Find patterns given a series of integers.

4.4, 4.5 NC Add and subtract integers.

4.4, 4.5 NC Evaluate integers using addition and subtraction problems using variables.

10.6, 10.7 NC Multiply and divide integers.

10.6, 10.7 NC Evaluate integers using multiplication and division problems

using variables.Mean, Median, Mode, Range

5.1 CCalculate the mean, median, mode and range of a set of data.

5.1 NC Determine which of the central tendencies are most appropriate given a situation.

Data Analysis 5.2, 5.5, Supp. NC Analyze data in histograms, double bar graphs, multiple line

graphs and stem-and-leaf plots.

Supp. NC Formulate predictions and/or draw conclusions based on data in bar graphs, circle graphs or line graphs.

MIDTERM

Plotting Points 5.4 NC

Plot and/or identify ordered pairs on a coordinate plane in all 4 Quadrants. Identify all part of a coordinate plane. (Quadrants, Axes, Origin)

34

Probability 5.7 C Find the theoretical probability of a simple and/or compound event.

5.7 C Find the theoretical probability of an event not occurring.5.7 C Find the experimental probability.

Supp. NC Formulate predictions and/or draw conclusions based on data of probability.

Measurement Conversions Supp. C Convert units of measurement.

Supp. NC Add and subtract measurements with or without regrouping.Ratios and Proportions 6.1 C Write ratios to compare quantities.

6.2 C Calculate and apply unit rates or unit prices.6.3, 6.4 C Solve for a variable in a given proportion.6.3, 6.4 C Use proportions to determine if two quantities are equivalent.Supp. C Use ratios or proportions to solve problems.

6.7 C Interpret and apply scales and blueprints using proportions. Percents 7.1 NC Convert between decimals, fractions, and percents.

7.3 C Use proportions to solve for percentages of numbers.

Estimation Supp. NC Estimate answers to problems using whole numbers, decimals, fractions, mixed numbers and percents.

Geometry 8.1 NC Identify parallel, perpendicular and skew lines.

8.1 NC Identify vertical, adjacent, complimentary and supplementary angles.

Area, Perimeter, Circumference

Supp. NCIdentify, describe or define the radius, diameter or chords of circles.

8.3 CSolve problems involving relationships between the radius and diameter of circles. Find, use, and apply the circumference of circles.

8.6 C Find the area of a circle.Supp. C Find the perimeter of single and compound figures.

8.4 C Find the area of a parallelogram.8.5 C Find the area of a trapezoid.

Congruent Figures Supp. NC Identify congruent polygons given measurements and/or tic

and angle marks.Supp. NC Identify corresponding sides and angles of congruent figures.

Similar Figures 6.6 NC Identify similar polygons given measurements and/or tic and

angle marks.6.6 NC Identify corresponding sides and angles of similar figures.

6.6 C Use proportions to find the missing length of a side in similar figures.

One-Step Equations Supp. NC Use appropriate strategies to solve one-step equations.

Algebraic Expressions and Inequalities

Supp. NC

Identify expressions and equations that model mathematical situations and real life word problems. (Using whole numbers and decimals)

Supp. NC Identify inequalities that model mathematical situations and real life word problems. (Using whole numbers and decimals)

PSSAIf Time Allows After PSSATwo-Step Supp. NC Solve one- or two-step equations.

35

Equations

Supp. NC Use substitution to check the accuracy of a given value for an equation.

Supp. C Determine the value of an algebraic expression by simplifying and/or substituting a number for the variable.

One-Step Inequalities Supp. NC Solve one-step inequalities. (No division or multiplication of

negatives) Graph solution on a number line.

Supp. NC Solve one-step inequalities when dividing or multiplying by negative numbers. Graph solutions on a number line.

Angles and Intersecting Lines

Supp. NCSolve for missing angles of intersecting lines, parallel lines cut by a transversal and in different polygons.

Nets and Polyhedral Supp. NC Match the net and it’s characteristics with the respective 3-

Dimensional FigureFINAL

Resources

Passport to Mathematics by McDougal LittellMcDougal practice workbook, Finish Line, Supplemental Worksheets

Assessment

Midterm and Final ExamsLocal Assessments (twice a year)

36

Pre-AlgebraChecklist of Objectives

C = Calculator, NC = No Calculator


Calculator ObjectiveUsing A Problem Solving Plan

1-1 NCWhen is it appropriate to round up or down.Identify when an exact answer is needed or when an estimate is appropriate.

Numbers & Expressions 1-2 NC Use the order of operations to evaluate expressions.

Translate verbal phrases into numerical expressions.Variables & Expressions 1-3 NC Evaluate expressions containing variables.

Translate verbal phrases into algebraic expressions.

Properties 1-4 NC Identify and use properties of addition and multiplication and to simplify algebraic expressions.

Variables & Equations 1-5 NC Identify and solve open sentences.

Translate verbal sentences into equations.Ordered Pairs & Relations 1-6 NC Use ordered pairs to locate points.

Use tables and graphs to represent relations.Scatter Plots 1-7 NC Construct and interpret scatter plots.Integers &Absolute Value

2-1 NCCompare and order integers.Find the absolute value of an expression.

Adding Integers 2-2 NC Add integers.

SubtractingIntegers 2-3 NC Subtract integers.

MultiplyingIntegers 2-4 NC Multiply integers.

Dividing Integers 2-5 NC Divide integers.

DistributiveProperty 3-1 NC Use the Distributive Property to write equivalent numerical

and algebraic expressions.Simplifying Algebraic Expressions

3-2 NCUse the Distributive Property to simplify algebraic expressions.

Solving Equations by Adding or Subtracting

3-3 CSolve equations by the Substitution Property of Equality and Addition Property of Equality.

Solving Equations by Multiplying or Dividing

3-4 CSolve equations by using Division and Multiplication Property of Equality.

Solving Two-Step Equations

3-5 CSolve two-step equations.

Writing Two-Step Equations

3-6 CWrite verbal sentences as two step equations.

Using Formulas 3-7 C Solve problems by using formulas and problems involving

perimeter and area of rectangles.Mid-TermFactors & 4-1 NC Determine whether one number is a factor of another and

37

Monomials determine whether an expression is a monomial.Powers & Exponents 4-2 NC Write expressions using exponents.

Evaluate expressions containing exponents.Simplifying Algebraic Fractions

4-5 NCSimplify fractions using the GCF and simplify algebraic fractions.

Multiply & Divide Monomials

4-6 NCMultiply monomials.Divide monomials.

Negative Exponents 4-7 NC Write expressions using negative exponents.

Scientific Notations 4-8 NC Express numbers in standard form and scientific notation.

Multiplying Rational Numbers

5-3 NCMultiply fractions.

Dividing Rational Numbers

5-4 NCDivide fractions using multiplicative inverses.

Measures of Central Tendency

5-8 CUse the mean, median, and mode measures of central tendency.

Stem-and-Leaf Plots 12-1 C Display and interpret data in stem-and-leaf plots.

Box-and-Whisker Plot 12-3 C Display and interpret data in a box-and-whisker plot.

Metric Measure-ment

Supp. CConvert Metric Measurements

Fahrenheit to Celcius Supp. C Convert Fahrenheit temperatures to Celcius temperatures.

Solving Equations with Rational Numbers

5-9 CSolve equations containing rational numbers.

Arithmetic & Geometric Sequences

5-10 CFind missing elements in numeric or geometric sequences.

Solving Equations with Variables on Each Side

7-1 CSolve equations with variables on each side.

Solving Equations with Grouping Symbols

7-2 CSolve equations that involve grouping symbols.

Inequalities 7-3 C Write and graph inequalities.Solving Inequalities by Adding or Subtracting

7-4 CSolve inequalities by using the Addition and Subtraction Property of Inequality.

Solving Inequalities by Multiplying or Dividing

7-5 CSolving inequalities by multiplying or dividing by a positive or negative number.

Solving Multi-Step Inequalities

7-6 CSolve inequalities that involve more than one operation.

The Coordinate System 2-6 NC Graph points on a coordinate plane.

38

Functions 8-1 NC Determine whether relations are functions.Linear Equations in Two Variables

8-2 CSolve linear equations with two variables.Graph linear equations using ordered pairs.

Graphing Linear Equations Using Intercepts

8-3 C

Find the x- and y-intercepts of graphs.Graph linear equations using x- and y- intercepts.

Slope 8-4 C Find the slope of a line.Slope-Intercept Form 8-6 C Determine slope and y-intercept of lines and graph.

Solving Systems of Equations 8-9 C Solve system of linear equations by graphing.

Graphing Inequalities 8-10 C Graph linear inequalities.

Squares and Square Roots 9-1 C Find squares and square roots.

Angles 9-3 NC Classify angles as obtuse, right, acute, or straight.

Triangles 9-4 C Find the missing angle of a triangle.Classify triangles by angles and by sides.

The Pythagorean Theorem

9-5 C

Use the Pythagorean Theorem to find the length of a side of a right triangle.Solve word problems involving the Pythagorean Theorem.Use converse of the Pythagorean Theorem to determine if a triangle is a right triangle.

Line and Angle Relationships 10-1 C

Identify the relationships of angles formed by two parallel lines and the transversal.Identify the relationships of vertical, adjacent, complementary, and supplementary angles.

Quadrilaterals 10-4 C Find the missing angle measure of a quadrilateral.Classify quadrilaterals.

Area: Parallelograms, Triangles, and Trapezoids

10-5 CFind area of parallelograms, triangles, and trapezoids.

Polygons 10-6 C

Classify polygons.Determine the sum of the measures of the interior and exterior angles of a polygon.Determine the measure of one interior angle of a polygon.

Circumference and Area: Circle 10-7 C Find the circumference and area of a circle.

Volume: Prisms and Cylinders

11-2 CFind the volume of prisms. Find the volumes of circular cylinders.

Surface Area: Prisms & Cylinders

11-4 CFind the surface area of prisms and cylinders.

Permuta-tions andCombina-tions

Supp. C

Use permutations and combinations.

PSSARatios and Rates 6-1 C Write ratios as fractions in simplest form.

Determine unit rates.Using Propor-tions 6-2 C Solve proportions.

Use proportions to solve real world problems.

39

Scale Drawings & Models

6-3 CUse scale drawings.

Fractions, Decimals, & Percents

6-4 CExpress fractions as percents and vice versa.Express percents as decimals and vice versa.

Using Percent Equations 6-7 C Solve percent problems using percent equations.

Percent of Change 6-8 C Find percent of increase.

Find percent of decrease.Probability & Predictions 6-9 C Find the probability of simple events.

FINAL

ResourcesPre-Algebra by Glencoe

Glencoe Practice Workbook, Supplemental Worksheets

AssessmentMid-Term and Final Exam

Local Assessments (twice a year)

40

Belle Vernon Area

High School


41

Anchor A NUMBER SYSTEMS

Anchor Eligible Content

Alg/Geom A

Alg/Geom

B

Alg/Geom C

Alg I Alg II Geom Alg III

A.1.1.1

Find the square root of an integer to the nearest tenth using either a

calculator or estimation.X X X X X X

A.1.1.2

Express numbers and/or simplify expressions using scientific

notation (in numbers <1)X X X

A.1.1.3 Simplify square roots. X X X X X X

A.1.2.1

Find the GCF and/or the LCM for sets of monomials. X X X O O O

A.1.3.1

Locate/identify irrational numbers at the approximate location on a

number line.X X X X X X

A.1.3.2

Compare and/or order any real numbers (rational and irrational

mixed).X X X X X X

A.2.1.1

Solve problems using rates and percents (ex. distance, work,

mixture)X X

A.2.1.2 Use direct and inverse proportion. X X X X

A.2.1.3

Identify and/or use proportional relationships in problem solving. X X X X

A.2.2.1

Simplify/evaluate expressions with positive and negative exponents

(up to 10) or absolute value.X X X X X X

A.2.2.2

Simplify/evaluate expressions involving multiplying with

exponents, powers of powers, and powers of products.

X X X X X X

A.3.1.1

Simplify/evaluate using order of operations. X X X X X X

A.3.2.1 Use estimation to solve problems. X O O

X Represents a topic that is taught in the course listed

O Represents a topic that is incorporated or applied as a part of

a lesson The alignment to anchor chart was developed to ensure that all students taking different math courses or academic sequences still had the opportunity to learn the material being tested on the 11th grade PSSA test. In addition this chart can be used once we identify strength or weaknesses on year to year test results to identify where each topic is being taught and how many times each topic is covered.

42

Anchor B MEASUREMENT


Alg/Geom

A

Alg/Geom B

Alg/Geom

CAlg I Alg II Geo

m Alg III

B.2.1.1

Measure or compare angles in degrees (up to 360°). (Protractor

must be provided or drawn.)X X X X

B.2.2.1

Calculate the surface area of prisms, cylinders, cones,

pyramids, or spheres using formula sheet.

X X X X X X

B.2.2.2

Calculate the volume of prisms, cylinders, cones, pyramids or

spheres using the formula sheet.X X X X X X

B.2.2.3

Estimate area, perimeter or circumference of an irregular

figure.X X X

B.2.2.4

Find the measurement of a missing length given the perimeter,

circumference, area, or volume.X X X X X

B.2.3.1

Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area

or volume.

X X X X

* How does changing the length of the radius affect the

circumference?X X X X

* How does changing the length of the edge of a cube affect the

volume of the cube?X X X X

* How does changing the length of the base of a triangle affect the

area of the triangle?X X X X

43

Anchor C GEOMETRY


Alg/Geom

A

Alg/Geom

B

Alg/Geom

CAlg I Alg II Geom Alg

III

C.1.1.1

Identify or use the properties of a radius, diameter, or tangent of a circle (given whole numbers).

X X X O

C.1.1.2

Identify or use the properties of arcs, semicircles, inscribed angles,

or central angles.X X X

C.1.2.1

Identify or use properties of triangles (medians, altitudes, angle bisectors, side/angle relationships,

Triangle Inequality theorem).

X X

C.1.2.2

Identify or use properties of isosceles and equilateral triangles. X X

C.1.3.1

Identify or use properties of congruent and similar polygons or

solids.X X X

C.1.4.1

Find the measure of a right triangle using the Pythagorean Theorem (on formula sheet).

X X X X X X X

C.3.1.1

Calculate the distance or midpoint on a number line or on a

coordinate plane (on formula sheet)

X X X X

C.3.1.2

Relate slope to perpendicular or parallelism (limit to linear

algebraic expressions – slope formula on sheet).

X X X X X X

44

Anchor D ALGEBRAIC CONCEPTS


Alg/Geom A

Alg/Geom B

Alg/Geom

CAlg I Alg II Geom Alg III

D.1.1.1

Analyze a set of data for the existence of a pattern and

represent the pattern algebraically or geometrically.

X X X X X

D.1.1.2

Determine if a relation is a function given a set of points or a

graph.X X X X X X

D.1.1.3

Identify the domain, range or inverse of a relation (may be

presented as ordered pairs or a table).

X X X X X

D.2.1.1

Solve compound inequalities and/or graph their solution sets on

a number line (may include absolute value inequalities).

X X X X X X

D.2.1.2

Identify or graph functions, linear equations or linear inequalities on

a coordinate plane.X X X X X X X

D.2.1.3

Write, solve and/ or apply a linear equation (including problem

situations).X X X X X O

D.2.1.4

Write and/or solve systems of equations using graphing,

substitution, and/or elimination (limit: 2 equations).

X X X O X

D.2.1.5

Solve quadratic equations using factoring (integers only). X X O X

D.2.2.1

Add, subtract, and/or multiply polynomial expressions. X X X X X O

D.2.2.2

Factor algebraic expressions including difference of squares

and trinomial (limited to ax²+bx+c).

X X X X X

D.2.2.3 Simplify algebraic fractions. X X X X X O

D.3.1.1

Identify, describe and/or use constant or varying rates of

change.X

D.3.1.2

Describe how a change in one variable relates to a change in a

second variable.X X

D.3.2.1

Apply the formula for the slope of a given line to solve a problem. X X X X X X

45

D.3.2.2

Given the graph of a line, two points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope

form, standard form, and/or slope-intercept form.

X X X X X X X

D.3.2.3

Compute the slope and/or y-intercept represented by an

equation or graph.X X X X X O X

D.4.1.1

Match the graph of a given function to its table or equation. X X X X X X

46

Anchor E DATA AND PROBABILITY


Alg/Geom

A

Alg/Geom

B

Alg/Geom

CAlg I Alg II Geo

m Alg III

E.1.1.1

Create or use appropriate graphical representations of data including box-and-whisker plots, stem-and-

leaf plots, or scatter plots.

X X X X X

E.1.1.2

Analyze data or answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots,

or scatter plots).

X X X X X

E.2.1.1

Calculate or select the appropriate measure of central tendency

(mean, median, or mode) of a set of data given or represented on a table, line plot, or stem-and-leaf

plot).

X X X X X

E.2.1.2

Calculate/and or interpret the range, quartiles, and interquartile

range.X O X

E.2.1.3

Describe how outliers affect measures of central tendency. X X X

E.3.1.1

Find probabilities for independent, dependent or compound events

and represent as a fraction, decimal, or percent).

X X X X X X

E.3.1.2

Find, convert or compare the probability and/or odds of a simple

event.X X X X X

E.3.2.1

Determine the number of permutations and/or combinations or apply the fundamental counting principle (formula given on sheet).

X X X X

E.4.1.1

Estimate or calculate to make predictions based on a circle, line,

bar graph, or given situation.X O O

E.4.1.2

Use probability to predict outcomes. X X X

E.4.2.1

Draw, find, and/or write an equation for a line of best-fit for a

scatter plot.X X X

E.4.2.2

Make predictions using equations or graphs of best-fit lines or scatter

plots.X X X X X

47

ALGEBRA/GEOMETRY AChecklist of Objectives

Content Chapter/Section C/NC ObjectiveMean, Median, Mode, and Range

1.2 C Calculate measures of central tendency (mean, median, and mode) and the measure of dispersion (range).

Stem-and-Leaf Plot 1.3 C

Calculate mean, median, mode, quartiles, interquartile, range, outliers, clusters, and gaps from a stem-and leaf plot.

Circle Graphs 1.3 C Interpret circle graphs. Frequency Tables and Pictographs

1.4 C Interpret frequency tables and pictographs.

Bar Graphs and Line Graphs 1.6 C Estimate or calculate to make predictions based on a line

or bar graph.Scatter Plots and Lines of Best Fit

1.7 C Make predictions using graphs of lines of best-fit and correlation.Identify the type of correlation.

Box-and Whisker Plots 1.8 C Create and analyze data from box-and-whisker plots.

Perimeter 2.3 C Find and estimate the perimeter of regular and irregular figures.Find the measurement of a missing length given the perimeter.

Area of Parallelograms and Triangles

2.4 C Find the area of parallelograms and triangles.

Circumference and Area of a Circle

2.7 C Calculate the circumference and area of circles and the area of irregular figures involving circles.

Proportions 2.8 CDetermine if a statement is a proportion and solve proportions. Use proportional relationships in problem solving.

Addition and Subtraction of Signed Numbers

3.1 NC Add and subtract signed numbers.

Use absolute value to simplify expressions.Multiplication and Division of Signed Numbers

3.2 NC Multiply/divide signed numbers.

Order of Operations 3.3 NC Perform order of operations with signed numbers.

Real Number properties 3.4 NC Use number set vocabulary and the commutative,

associative, and distributive properties.Evaluating Variable expressions

3.5 C Write and evaluate variable expressions.

Patterns 3.6 C Analyze a set of data for the existence of patterns and represent the pattern algebraically or graphically.

Scientific Notation 3.7 C Write numbers in exponential form and standard form.

Simplify expressions using scientific notation.

48

Laws of Exponents 3.8 C Use the Product, Quotient, and Power Rules of Exponents.

Squares and Square Roots 3.9 C Calculate the square or square root rounded to a given

place value when needed.

Lines, Rays, Angles, Planes 4.1 C

Identify and name points, rays, line segments, lines, angles, and planes. Measure and compare angles in degrees with a protractor or from a diagram.

Polygons and Polyhedra 4.2 C

Identify and classify polygons. Identify triangles by sides, and angles. Identify the faces, edges, and vertices of polyhedra.

Solids 4.3 C Name polyhedra and 3-dimensional figures with curved surfaces...

Volume of Prisms and Cylinders

4.7 C Calculate the volume of prisms and cylinders.

Find the measurement of a missing length given the volume.

Volume of Pyramids and Cones

4.8 C Calculate the volume of pyramids and cones.


Surface Area 4.9 C Calculate the surface area of prisms and cylinders.Solutions to Equations 5.1 C Determine if a given value for a variable is a solution to an

equation.Solving Equations 5.2 C Use addition and subtraction transformations to solve

equations.Solving Equations 5.3 C Use multiplication and division transformations to solve

equations.2-Step Equations 5.4 C Solve 2-step equations and use means-extremes to solve

proportions.MidtermLike Terms 5.5 C Solve an equation by combining like terms.

Formulas 5.6 C Solve problems using formulas and isolate specific variables in formulas.

Graphing 1-Step Inequalities

5.8 C Solve simple inequalities and graph their solution sets on a number line.

Graphing 2-Step Inequalities

5.9 C Solve 2-step inequalities and graph their solution sets on a number line.

Coordinate Plane 7.2 C Identify the parts of a coordinate plane and graph points.

Relations and Functions 7.3 C Determine if a relation is a function given a set of points or

a graph.Identify the domain and range of a relation.

Linear Graphs 7.4 C Graph linear functions using a table of points.Calculate the intercepts for linear functions.

Slope 7.5 C Calculate the slope given two points on a line.Compute the slope represented by an equation or graph and identify it as +, -, 0, or undefined.

Slope-Intercept Form 7.6 C Graph a linear equation given the slope-intercept form of a

line. Given the graph of a line a linear equation in slope-intercept form, identify the slope and y-intercept.Compute the y-intercept represented by an equation or

49

graph.Distance Formula and Pythagorean Theorem

7.7 C Draw a diagram and use the Pythagorean Theorem to find the distance between the points.

Calculate the distance between two points by using the Distance formula.

Solutions of Equations and Inequalities

7.8 CIdentify whether a point is a solution of a linear or nonlinear equation or inequality from the graph or from the equation or inequality.

Angles and Transversals 8.1 C

Classify angles as complementary, supplementary, or neither. Identify transversals. Identify adjacent angles. Use vertical and corresponding angles to find missing angle measurements.

Diagonals and Angle Sum of Polygons

8.3 C Determine the number of diagonals and interior angle sum of polygons.

Standard Form 9.1 C Simplify and write polynomials in standard form.Addition and Subtraction of Polynomials

9.2 C Add and subtract polynomials.

Multiplication of Monomials 9.3 C Multiply monomials. Use the Product, Power, and Power

of a Power Rules of Exponents.Distributive Property 9.4 C Use the distributive property to simplify expressions.GCF 9.5 C Use the GCF to factor polynomials.Division by a Monomial 9.6 C Divide monomials and polynomials by a monomial. Use

the Quotient Rule of Exponents.

Probability 10.1 C Find the probability of an event and represent it as a fraction, decimal, or percent.

Experimental Probability 10.2 C Find experimental probability.Sample Spaces 10.3 C Use tree diagrams to help list sample spaces.Counting Principle 10.4 C Use the Counting Principle to find the number of

outcomes.Independent and Dependent Events

10.5 C Find probabilities of independent and dependent events.

FINAL

Resources:Text book is Math Matters I, by Glencoe which includes all teacher materials, practice worksheets, tests, and other resources.Prealgebra by Glencoe; Algebra I by Holt; Bridges to Algebra and Geometry by Cord; Basic Geometry by McDougal Little/ Houghton Mifflin

Assessment: Quizzes, Chapter Tests, Mid-Term and Final Exam

50

ALGEBRA/GEOMETRY BChecklist of Objectives



Measures of central tendency and range

1.2 CCalculate the mean, median, mode, and range working backwards.

Histogram and stem-and-leaf plots

1.3 CCalculate mean, median, mode, quartiles, and interquartile range from a stem-and leaf plot.

1.3 C Describe how outliers affect measures of central tendency.

Scatter plots and lines of best fit

1.4 CCreate or use scatter plots.

Analyze data or answer questions based on displayed data (scatter plots).

Coefficients and correlation 1.5 C Analyze data or answer questions based on

displayed data (scatter plots).Quartiles and percentiles 1.6 C Create or use box-and-whisker.

Analyze data or answer questions based on displayed data (box-and-whisker).

Graphs and statistics 1.7 C Make predictions using graphs of best-fit

lines and correlation.Matrices to organize data 1.8 C Analyze data based on box-and-whisker

plots.

Real numbers 2.1 C Locate/identify irrational numbers at the approximate location on a number line.Compare and/or order any real numbers (rational and irrational mixed).

Order of operations 2.2 C Simplify/evaluate using order of

operations.Variable expressions 2.3 C This section: write variable expressions.

Addition and subtraction 2.4 C

This section: add and subtract variable expressions.

Multiplication and division 2.5 C This section: multiply and divide variable

expressions.Simplify 2.6 C This section: simplify variable expressions.

Properties of exponents 2.7 C

Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.

Zero and 2.8 C Simplify/evaluate expressions with

51

negative exponents

positive and negative exponents (up to 10) or absolute value.Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.

Patterns 2.9 CAnalyze a set of data for the existence of a pattern and represent the pattern algebraically or geometrically.

Equations 3.1 C This section: solve equations and formulas.One step equations 3.2 C This section: solve equations (one-step).

Two or more operation equations

3.4 CThis section: solve equations with two or more operations.

Proportions 3.5 C Identify and/or use proportional relationships in problem solving.

Graph inequalities 3.6 C Graph linear inequalities on a number line.

Solve inequalities 3.7 C Solve linear inequalities

Squares and square roots 3.8 C

Find the square root of an integer to the nearest tenth using either a calculator or estimation. This section solves equations with square roots.

Probability 4.3 C Find, convert or compare the probability and/or odds of a simple event.

Compound events 4.4 C

Find probabilities for independent, dependent or compound events and represent as a fraction, decimal, or percent).

Independent and dependent 4.5 C

Find probabilities for independent, dependent or compound events and represent as a fraction,decimal, or %

Permutations 4.6 CDetermine the number of permutations or apply the fundamental counting principle (formula given on sheet).

Combinations 4.7 CDetermine the number of combinations or apply the fundamental counting principle (formula given on sheet).

Angles and perpendicular lines

5.2 CMeasure or compare angles in degrees (up to 360°). (Protractor must be provided or drawn.)

Triangles 5.4 C Identify or use properties of isosceles and equilateral triangles.

Congruency 5.5 C Identify or use properties of congruent polygons or solids.

52

Quadrilaterals and parallelograms

5.6 CThis section: know properties of quadrilaterals and parallelograms.

Angles of Polygons 5.7 C This section: find angle measures of

polygons.

Circles 5.8 CIdentify or use the properties of a radius, diameter, or tangent of a circle (given whole numbers).Identify or use the properties of arcs, semicircles, inscribed angles, or central angles.

Distance 6.1 CCalculate the distance or midpoint on a number line or on a coordinate plane (on formula sheet)

Slope of a line 6.2 C Compute the slope by an equation or graph.

Linear equations 6.3 C Identify or linear equations on a coordinate

plane.Given the graph of a line, two points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope form, standard form, and/or slope-intercept form.Compute the slope and y-intercept represented by an equation or graph.

Linear inequalities 6.4 C Identify or graph linear equations or linear

inequalities on a coordinate plane.

Functions 6.5 C Determine if a relation is a function given a set of points or a graph.

Patterns 6.7 C Match the graph of a given function to its table or equation.

Direct variation 6.8 C Use direct and inverse proportion.Inverse variation 6.9 C Use direct and inverse proportion.

Parallel and perpendicular lines

8.1 CRelate slope to perpendicular or parallelism (limit to linear algebraic expressions – slope formula on sheet).

Graph systems 8.2 C Write and/or solve systems of equations using graphing. (limit: 2 equations).

Substitution 8.3 C Write and/or solve systems of equations using substitution. ( limit: 2 equations)

Linear combination 8.4 C Write and/or solve systems of equations

using elimination (limit: 2 equations).

Systems of inequalities 8.7 C

Identify or graph linear inequalities on a coordinate plane. This section does systems.

53

Polynomials 9.1 C Add and subtract polynomial expressions.

Multiply monomials 9.2 C

Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products.

Divide monomials 9.3 C Simplify algebraic fractions.

Multiply 9.4 C This section: multiply a polynomial by a monomial.

Multiply binomials 9.5 C Multiply polynomial expressions.

Greatest common factor 9.7 C Find the GCF for sets of monomials.

Difference of two squares 9.8 C

Factor algebraic expressions including difference of squares and trinomial (limited to ax²+bx+c).

Surface area 10.2 CCalculate the surface area of prisms, cylinders, cones, pyramids, or spheres using formula sheet.

3-dimensional figures 10.3 C

Calculate the surface area of prisms, cylinders, cones, pyramids, or spheres using formula sheet.

Volume of pyramids 10.7 C Calculate the volume of prisms and

pyramids using the formula sheet.Find the measurement of a missing length given the volume.Describe how a change in the linear dimension of a figure affects its volume. * How does changing the length of the edge of a cube affect the volume of the cube?

Volume of cylinders, cones or spheres

10.8 CCalculate the volume of cylinders, cones, or spheres using the formula sheet.


Similar polygons 11.1 C Identify or use properties of similar

polygons or solids.Indirect measurement 11.2 C Identify or use properties of similar

polygons or solids.

Pythagorean theorem 11.3 C

Find the measure of a right triangle using the Pythagorean Theorem (on formula sheet).

Resources:Textbook is Math Matters II, by Glencoe, Practice worksheets, Resource Masters, teacher materials. Supplemental Materials include textbook from Cord Algebra and worksheets,

54

Basic Geometry by McDougal Littell and Algebra I (Structure Method) by Houghton Mifflin.

Assessment:

Chapter Tests, Mid-Term, and Final Exam.

Algebra/Geometry CChecklist of Objectives

Content Chapter/ Section


Real Numbers 1.2 Identify, compare, and graph real and irrational numbers

Order of Operations 1.41.5

Simplify / evaluate expressions including fractions using order of operations

Properties of Exponents 1.7 Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products

Exponents and Scientific Notation

1.8 Simplify/evaluate expressions with positive and negative exponents or absolute value and scientific notation

Patterns 2.13.5

Analyze a set of data for the existence of a pattern and represent the pattern algebraically or geometrically

Relations and Functions 2.2 C Identify relations and their domains and ranges. Identify and evaluate functions

One-Step Equations 2.4 C Solve one-step equationsMulti-Step Equations 2.5 C Solve multi-step equationsLinear Inequalities 2.6 C Solve simple inequalities and graph their

solution on a number lineMeasures of Central Tendency

2.7 C Calculate the appropriate measure of central tendency of a set of data given or represented on a table.

Display Data 2.8 C Create and analyze data using box and whisker plots and stem and leaf plots

Linear Functions 2.3 C Graph linear functions through table of values. Match the graph of a given function to its table or equation.

Linear Inequalities 2.6 C Graph linear inequalities on a coordinate plane.

Slope of a Line 6.1 C Find the slope of a line. Write the slope-intercept form of an equation and graph the equation.

Parallel and Perpendicular Lines

6.2 C Relate slope to parallel and perpendicular lines.

Writing Equations of Lines

6.3 C Given the graph of a line, two points on a line, or the slope and point on a line, write or identify the linear equation in point-slope form, standard form, and/or slope-intercept form.

Scatter Plots and Box and Whisker Plots

9.6 C Interpret and make scatter plots. Write the equations for the line of best fit.

Systems of Equations 6.4 C Solve a system of equations by graphing.

55

Solve Systems by Substitution

6.5 C Solve a system of equations by substitution.

Solve Systems by Adding and Multiplying

6.6 C Solve a system of equations by elimination.

Systems of Inequalities 6.8(Optional)

C Use graphing to solve systems of linear inequalities.

Points, Lines, and Planes 3.1 C Define basic terms and apply postulates for points, lines, and planes.

Types of Angles 3.2 C Classify and measure angles.Segments and Angles 3.3 C Identify and apply theorems about midpoints,

angle bisectors, and vertical anglesTriangles and Triangle Theorems

4.1 C Solve equations to find measures of angles. Classify angles.

Congruent Triangles 4.24.3

C Identify and use properties of congruent triangles.

Altitudes, Medians, and Perpendicular Bisectors

4.4 C Identify and use properties of triangles. (medians, altitudes, bisectors)

Polygons and Angles 4.7 C Find the measures of interior and exterior angles of polygons.

Special Quadrilaterals: Parallelograms and Trapezoids

4.84.9

C Apply properties of quadrilaterals to find the missing lengths and angle measurements.

Irrational Numbers 10.1 C Simplify square roots Pythagorean Theorem 10.2 C Apply the Pythagorean theorem to problems.Perimeter, Circumference, and Area

5.2 C Find perimeter, circumference and area and missing lengths. Describe how a change in the linear dimension of a figure affects it perimeter, circumference, or area.

Irregular Shapes 5.4 C Find the area, perimeter, or circumference of irregular figures.

Surface Area of Three-Dimensional Figures

5.6 C Find the surface area of prisms, cylinders, cones, pyramids, or spheres using formula sheet.

Volume of Three Dimensional Figures

5.7 C Find the volume of prisms, cylinders, cones, pyramids, or spheres using formula sheet.

Ratios and Proportions 7.1 C Use ratios and proportions to solve problemsSimilar Polygons 7.2

7.7C Find the missing measures of similar

polygons.Percents and Probability 9.1 C Find, convert, or compare the probability

and/or odds of a simple event.Compound, Independent, and Dependent Events

9.39.4

C Find probabilities of compound, dependent, and independent events.

Permutations and Combinations

9.5 C Find the number of permutations and combinations of a set.

10.410.6

C Identify and use properties of tangent, arcs, semicircles, inscribed angles, or central angles of circles.

Add and Subtract Polynomials

11.1 C Add and subtract polynomial expressions.

Multiply by a Monomial 11.2 C Multiply polynomial expressionsDivide and Find Factors 11.3 C Divide and find factors of polynomialsMultiplication of 11.4 C Multiply two binomials

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BinomialsFactoring Trinomials 11.7

11.9C Factor trinomials

Final

Resources:

This curriculum is formatted to the textbook Math Matters 3.Additional resources as follows: Basic Geometry by McDougal Littell , Algebra I by McDougal Littell, Algebra I (Structure Method) by Houghton Mifflin

Assessment:

Quizzes, Chapter Tests, Midterm, Final, 4-sight tests

57

ALGEBRA IChecklist of Objectives


Calculator

Objective

Evaluate Expressions 1.1 C Evaluate a variable expression1.1 C Evaluate a geometric expression1.2 C Evaluate expressions containing exponents and

absolute value1.3 C Use order of operations to evaluate expressions1.4 C Check solutions to equations and inequalities1.5 C Translate verbal phrases into algebraic

expressionsEvaluate Functions 1.7 C Identify a function from a table

1.7 C Identify a function from a set of points1.7 C Identify a function from a graph1.7 C Make an input-output table for a function4.8 C Use function notation4.8 C Evaluate a function for a given value

Use Tables and Graphs

1.6 C Use tables to organize data

1.6 C Use graphs to organize data1.6 C Draw and interpret bar and line graphs and double

bar graphsPutting Data In Order 6.6 C Make and use a stem-and-leaf plot to put data in

order6.6 C Find the mean, median and mode of data6.7 C Find the five-number summary6.7 C Draw a box-and-whiskers plot6.7 C Read and interpret a box-and-whisker plot4.1 C Draw a scatter plot and make predictions4.1 C Determine the correlation of x and y

Properties of Real Numbers

2.1 C Graph and compare real numbers on a number line

2.1 C Find the opposite of a number2.1 C Find the absolute value of a number and evaluate

expressions with absolute value2.2 C Add real numbers using a number line

Properties of Real Numbers

2.2 NC Add real numbers using a addition rule

2.3 NC Subtract real numbers using subtraction rule2.5 NC Multiply real numbers using multiplication rules2.7 NC Divide real numbers using division rules2.6 C Use the distributive property2.7 C Use division to simplify expressions

Probability and Odds 2.8 C Find the probability of one and multiple event(s)2.8 C Find the odds of one and multiple event(s)2.8 C Find the odds given the probability2.8 C Determine if an event is dependent or independent

Solve Linear Equations

3.1 C Solve equations using addition and subtraction

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3.2 C Solve equations using multiplication and division 3.3 C Solve multi-step equations3.4 C Solve equations with variables on both sides3.6 C Solve decimal equations3.8 C Calculate unit rates and use to solve problems3.8 C Calculate average rates and use to solve problems3.8 C Find percents and use to solve problems11.1 C Solve proportions11.2 C Solve percent problems

Solving a Formula For one of Its Variables

3.7 C Area formulas(use formula page from PSSA)

3.7 C Distance formulas3.7 C Work formulas backwards3.7 C Solve formulas for all variables

Write Equations in Function Form

3.7 C Rewrite and equations so y is a function of x

3.7 C Rewrite and equation so x is a function of yGraph Linear Equations

4.1 C Plot points in a coordinate plane

4.2 C Graph a linear equation using a table or a list4.2 C Graph a horizontal line4.2 C Graph a vertical line4.3 C Graph by finding the x and y-intercepts4.4 C Find the slope of a line using two points4.4 C Find the slope of a line from a graph4.6 C Graph in slope-intercept form

Solve Linear Equations

4.7 C Solve equations using graphs

Write Linear Equations

5.1 C Write the equation of the line given the slope and y-intercept

5.1 C Write the equation of the line given a graph of the line

5.2 C Write the equation of the line given the slope and a point

Write Linear Equations

5.3 C Write an equation of the line given two points

5.3 C Write an equation of the line that is vertical or horizontal

5.3 C Write an equation of the line that is parallel or perpendicular to another line

Solve and Graph Linear Inequalities

6.1 C Graph linear inequalities in one variable

6.1 C Solve one-step linear inequalities6.2 C Solve multi-step linear inequalities6.3 C Solve compound inequalities6.4 C Solve absolute-value equations6.4 C Solve absolute-value inequalities6.5 C Graph linear inequalities in two variables

Use Properties of Exponents

8.1 C Multiply exponential expressions

8.1 C Product of powers property8.1 C Power of a power property8.1 C Power of a product property8.2 C Evaluate expressions that have negative and zero

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exponents8.3 C Divide exponential expressions

Polynomials 10.1 C Add and subtract polynomials10.1 C Classify polynomials10.2 C Multiply two binomials(FOIL)10.2 C Multiply a binomial by a trinomial10.3 C Square a binomial by writing out the expression

Polynomials 10.3 C Use sum and difference pattern to multiply binomials

10.5 C Factor a trinomial(x2 + bx + c)

10.6 C Factor a trinomial(ax2 + bx + c)

10.7 C Factor special productsSimplifying Radicals 9.1 NC Find the square roots of numbers

9.2 NC Simplify square roots using the product property9.2 NC Simplify square roots by using the quotient

property9.2 C Simplify square roots by rationalizing the

denominator9.2 C Add, subtract, multiply, and divide radical

expressions

Resources:

Algebra 1 by McDougal Littell, a Houghton Mifflin Company andCopyrighted in 2001. Supplemental Workbooks, Teacher-Created Worksheets, and Test Generator.

Assessment:

Observation, Quick Checks, Quizzes, Chapter Tests, 4Sight, Mid-Term, and Final Exam.

60

GEOMETRYChecklist of Objectives


Calculator

Objective

Patterns/ Inductive Reasoning

1.1 C Find and describe patterns of numbers. Find next number in a sequence.

Geometric Terms.

1.2 C Discuss terminology of geometry. Name points, lines, planes, collinear, coplanar, segment, ray.

Segments and angles

1.3 C Use ruler postulate, segment addition postulate, and distance formula.

1.4 C Name an angle by 3 letters, 1 letter, or 1 number. Name parts of angles (vertex and sides).

1.4 C Use a protractor to draw or measure an angle.1.4 C Use protractor postulate, and angle addition

postulate.1.5 C Define midpoint, bisector (both angle and

segment), and find missing measures.1.5 C Use midpoint formula (given 2 points find

midpoint, and given a point and midpoint find the other point).

1.6 C Identify vertical angles, linear pairs, supplementary, and complementary angles. Find missing measures.

Perimeter and Area

1.7 C Find perimeter, area, and circumference of common figures. Solve word problems.

Supplement C Estimate area, perimeter or circumference of an irregular figure

Proof and Deductive Reasoning

2.1 C Analyze a conditional statement and its parts. Know converse, inverse, contra-positive and bi-conditional.

2.2 C Convert statements to if-then form, only-if form, and if and only if form.

2.3 C Use symbolic notation to represent logical expressions (p→q).

2.3 C Use the law of syllogism and detachment in deductive reasoning.

2.4 C Use properties of Algebra to solve equations (add, subtract, multiply, divide, distributive, associative, reflexive, symmetric, transitive, substitution).

2.5 C Justify statements about congruent segment.

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Write reasons for steps in geometric proofs.2.6 C Write 2 column proofs to prove statements

about segments and angles and special properties of segments and angles.

Lines and angles

3.1 C Identify relationships between lines: parallel, perpendicular, skew.

3.1 C Identify angles formed by transversals (alternate interior, alt. ext, corresponding, same side int., same side exterior).

3.2 C Write proofs in various forms (show paragraph proof, do 2 column proof) also prove results about ┴ lines.

3.3 C Find missing angle measures of angles formed by transversals.

3.4-5 C Prove lines parallel by angles formed by transversals.

Supplement C Graph lines by plotting points, using slope intercept, using x and y intercepts. (give 4sight)

3.6 C Find slopes of lines from equations, graphs, and points. Identify parallel and perpendicular lines.

3.6 C Write equations of lines using slope intercept formula. (given slope and y-int., given point and slope, 2 points).

3.7 C Write equations of parallel lines and perpendicular lines to a given line.

Triangles 4.1 C Classify triangles by sides and angles (acute, obtuse, right, scalene, isosceles, and equilateral).

4.1 C Find angle measures in a triangle using triangle sum theorem and exterior angle theorem.

4.2 C Identify congruent figures and corresponding parts. Find missing measures of sides and angles in congruent figures.

4.3-5 C Prove triangles are congruent by SSS,SAS,ASA,AAS,and HL.

4.5 C Use CPCTC to find missing measures, prove missing parts congruent, or prove triangles congruent.

4.6 C Use properties of isosceles and equilateral triangles to find missing measures.

4.7 C Use the distance formula and coordinate geometry to show triangle congruence.

Triangle Properties

5.1 C Use properties of angle bisectors and perpendicular bisectors to find missing

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measures.5.2-3 C Differentiate between altitudes, medians, angle

bisectors, and perpendicular bisectors.5.2-3 C Use slope, midpoint, and distance formulas to

find coordinates of angle bisectors, ┴ bis., medians, altitudes.

5.4 C Identify the midsegment of a triangle and use it to find missing measures.

5.5 C Use triangle inequality theorem to determine if a triangle can be drawn with given measures.

5.5 C Find shortest and longest sides of a triangle based on shortest and longest angles and vice versa.

Quadri-laterals

6.1 C Identify and name polygons based on number of sides.

6.1 C Find missing measures in a quadrilateral.11.1 C Find measure of interior and exterior angles of

polygons.6.2 C Use properties of parallelograms to find

missing measure.6.3 C Prove a quadrilateral is a parallelogram.6.4 C Use properties of sides and angles of

rhombuses, rectangles, and squares.6.5 C Determine if information given classifies a

quadrilateral as a parallelogram, rhombus, square, rect. discuss kite.

6.6 C Use properties of trapezoids and kites to find missing measures.

6.7 C Find areas of triangles and quadrilaterals using formulas (refer to pssa formula sheet).

MIDTERMSimilarity 8.1 C Simplify the ratio of 2 numbers.

8.1 C Solve and use proportions to solve real life problems.

8.2 C Find geometric and arithmetic mean of 2 numbers.

8.2 C Use properties of proportions (reciprocal, switching means, adding denominators) to find equivalent proportions.

8.3 C Identify similar polygons.8.4 C Identify similar triangles by AA, SAS, and

SSS.8.5 C Find missing measures in similar polygons.8.6 C Use proportionality statements to find segment

lengths.

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AlgReview C Simplify radicals and radical expressions (adding/subtracting/dividing/multiplying).

Right Triangles

9.1 C Solve problems involving similar right triangles drawn from an altitude of a triangle from the right angle.

9.1 C Write a similar triangle statement of the 3 triangles formed.

9.1 C Use geometric mean to find missing measures.9.2 C Use the Pythagorean theorem to find missing

measures. Apply this to real-life problems.9.3 C Determine if a triangle is acute, right, or obtuse

based on the measure of the 3 sides.9.4 C Find the missing side lengths of a 30-60-90

and 45-45-90 triangle.9.5 C Find the Sine, Cosine, and Tangent of a right

triangle’s acute angle.Circles 10.1 C Identify parts of a circle

(chord,radius,secant,tangent,diameter).10.1 C Use properties of tangents to a circle.

10.2-4 C Use properties of arcs and chords of a circle (central angle, inscribed angle, 2 segments meeting inside, 2 on outside) to find missing measures (arcs or angles).

10.2 C Use arc addition postulate to find missing arc measures.

10.5 C Find lengths of segments of chords, secants, and tangents.

10.6 C Find the equation of a circle in standard form.Areas of Circles

11.4 C Find circumference of circle, and arc length of arcs.

11.5 C Find the area of sectors.11.6 C Find geometric probability, and use this to

solve word problems.Solids 12.1 C Use properties of polyhedra.Surface Area 12.2-3 C Find surface area of cylinders, cones, prisms,

spheres, and pyramids. (Refer to pssa formula sheet). Stress units of measure.

Volume 12.4-6 C Find volume of cylinders, cones, prisms, spheres, and pyramids.

Supplement&

11.3

C Describe how a change in the linear dimension affects the perimeter, circumference, area, and volume. How does radius affect circumference? How does length affect area of triangles, etc? How does length affect volume of cube, etc?

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Final

Resources:Geometry by Larson, Boswell, and Stiff, a McDougal Littell Company (skipped 5.6,8.7,9.6,9.7,10.7,11.2,12.6,12.7, Chapter 7)

“Challenge: Skills and Applications” exercises found in the resource chapter books should be assigned frequently, so that Algebra skills are stressed to allow for a smooth transition into Algebra II.

Geometry Plane and Simple (Creative Publications)

Assessment:

Quizzes, Chapter Tests, Mid-term, Final Exam, and 4-sight tests

65

ALGEBRA IIChecklist of Objectives


Calculator

Objective

Equations and Inequalities

1.1 C Use and identify properties of real numbers

1.2 NC Evaluate powers both in and outside of parenthesis1.3 C Solve linear equations with variables on both sides and with

fractions1.4 C Rewrite equations and formulas with more than one variable1.6 C Solve simple and compound inequalities1.7 C Solve absolute value equations and inequalities

Linear Equations and Functions

2.1 C Represent relations and functions by mapping and table and identify functions from graphs

2.2 C Find slopes of lines and classify as parallel or perpendicular2.3 C Use slope-intercept form and x and y intercept form to graph

linear equations2.4 C Write an equation of a line in slope-intercept form, point-

slope form and standard form. Be able to switch from one to the other.

2.5 C Use a scatter plot to identify correlation and approximate the line of best fit using a graphics calculator and from a graph

2.6 C Graph linear inequalities in two variables, include multiple choice questions from graphs

2.7 C Evaluate piecewise functions for a given value of x, no graphing

Systems of Linear Equations and Inequalities

3.1 C Graph and solve systems of linear equations in two variables

3.2 C Solve systems of linear equations using the substitution and the linear combination methods

3.3 C Graph and solve systems of linear inequalities to find the solutions of the system

Probability and Statistics

7.7 C Use measures of central tendency to describe data sets. Draw and use box-and-whiskers plot and histograms to represent data graphically

12.1 C Use the fundamental counting principle and permutations to count the number of ways an event can happen

12.2 C Use combinations to count the number of ways an event can happen

12.3 C Find theoretical and experimental probabilities12.4 C Find probabilities of compound and mutually exclusive

events

12.5 C Find the probability of dependent and independent eventsRational Equations and Functions

9.1 C Classify direct and inverse variation, write an inverse variation equation and check data for variation

Quadratic Functions

5.1 C Graph quadratic functions

5.2 C Solve quadratic equations by factoring

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5.3 C Solve quadratic equations by finding square roots. Rationalize the denominator

Quadratic Functions

5.4 C Add, subtract, multiply and divide complex numbers. Solve quadratic equations with complex solutions

5.5 C Solve quadratic equations by completing the square and write quadratic equations in vertex form

5.6 C Solve quadratic equations using the quadratic formula and use the discriminant to determine roots

Polynomials and Polynomial Functions

6.1 C Use properties of exponents to evaluate and simplify expressions with powers including scientific notation(HW on page 914)

6.2 C Classify and evaluate polynomial functions using direct substitution.

6.3 C Add, subtract and multiply polynomials6.5 C Use long and synthetic division to Divide polynomials and

relate the result to the remainder and factor theoremsPowers, Roots and Radicals

7.1 NC Evaluate the nth root of real numbers using both radical notation and rational exponent notation

7.2 C Use properties of rational exponents to evaluate and simplify expressions

7.3 C Perform operations with functions including power functions(Add, subtract, multiply, divide, and composition)

7.4 C Find the inverses of linear and nonlinear functionsRational Equations and Functions

9.4 C Multiply, divide, and simplify rational expressions(This section is optional. To be completed if time allows)

Matrices and Determinants

4.1 C Add and subtract matrices, multiply by a scalar and solve matrix equations (This section is optional. To be completed if time allows)

Resources:

Algebra 2 by McDougal Littell, a Houghton Mifflin Company andCopyrighted in 2001. Supplemental Workbooks, Teacher-Created Worksheets,

and Test Generator.

Assessment:

Observation, Quizzes, Quick Checks, Chapter Tests, 4Sights, Mid-term, and Final Exam.

67

ALGEBRA III / TRIGONOMETRYChecklist of Objectives

All topics are taught without a calculator at first, then the students are shown how to solve the problems with a calculator.

Content Chapter/Section Calculator

Objective

Real numbers P.1 * Interval notation, distance, absolute value, and algebraic properties

Exponents and Radicals

P.2 Exponential properties, radicals, nth roots, properties of radicals, combining radicals, rationalizing, and the use of conjugates

Polynomials and special products P.3

Perform operations with polynomials, difference of squares, square of a binomial, cubes of binomials

Factoring P.4 Difference of squares, perfect square trinomials, sum and difference of cubes, factoring by grouping, factoring trinomials

Rational expressions

P.5 Finding the domain, simplifying rational expressions, operations with rational expressions

Errors to avoid P.6 Algebraic errors to avoidGraphical Represen-tation of Data

P.7Cartesian plane, scatter plots, distance formula, midpoint formula, translation of points

Graphs of Equations

1.1 Sketch equations using the point-plotting technique

1.1 Find intercepts of a graph, use the fundamental theorem of algebra

1.1 Test for symmetry in the x-axis, y-axis, and origin

1.1 Use intercepts and symmetry as sketching aids

1.1 Find the equation of a circle, write an equation for a circle

Linear equations in one variable

1.2 Solve linear equations and check solutions with and without fractional expressions

1.2 Perform operations on equations with extraneous solutions

Modeling with linear equations

1.3 Use a verbal model to compose an algebraic equation

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1.3 Use common formulas in algebraic models and equations

Quadratic Equations

1.4 Solve quadratic equations by factoring, extracting square roots, completing the square, and using the quadratic formula

1.4 Perform operations on word problems with applications of the quadratic formula

Complex Numbers

1.5 Perform operations with complex numbers and imaginary units, use complex conjugates

Other types of equations

1.6 Solve polynomial equations of a high degree, solve equations with radicals, solve equations with fractions

1.6 Solve equations with absolute values1.6 Use the formula for compound interest to

solve equationsLinear Inequalities

1.7 Solve inequalities, recognize bounded and unbounded intervals

1.7 Solve double inequalities, solve absolute value inequalities

Other types of inequalities

1.8 Solve polynomial inequalities by testing intervals and using critical numbers

1.8 Find the domain and range of an expression

Linear equations in two variables

2.1 Use slope intercept form to graph a line, find the slope of a line, use slope as a ratio, use slope as a rate of change

2.1 Use point slope form to write an equation of a line in two variables

2.1 Find parallel and perpendicular lines2.1 Use general form for the equation of a

line, define vertical and horizontal lines by given equation

2.1 Find the intersection of lines, graphically, algebraically, and with a graphing calculator

Functions 2.2 Find the domain and range of functions, test for functions

Analyze graphs of functions

2.3 Perform the vertical line test, find zeros of a function

Shifting, reflecting, and stretching graphs

2.4 Shift graphs vertically and horizontally

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2.4 Reflect graphs in the x-axis, y-axis, and origin

2.4 Stretch and shrink graphsCombination of functions

2.5 Find the sum, difference, product, quotient and composites of functions

Inverse functions 2.6 Find inverses of functions informally and graphically, graph the inverse of a function

2.6 Perform and apply the horizontal line test

Polynomial functions

3.1 Graph parabolas from general and standard form of a quadratic equation, find vertex, find intercepts, apply with word problems

Polynomial functions of a higher degree

3.2 Sketch cubic functions with and without a graphing calculator

Polynomial and synthetic division

3.3 Perform long division on polynomials, perform synthetic division on polynomials

3.3 Use the factor theoremMath modeling 3.5 Use direct variation, direct variation as

an nth power, inverse variation, and joint variation

3.5 Find the intersection of two lines, of a parabola and a line, of a circle and a line, and of a circle and a parabola algebraically and graphically

Conics 4.4 Graph ellipses with and without a graphing calculator, find foci, major axis, minor axis, and intercepts, write the standard form for the equation of an ellipse

4.4 Graph hyperbolas with and without a graphing calculator, write the standard form for the equation of a hyperbola, find foci and asymptotes

4.5 Be able to find standard form for the equation of a circle, ellipse, and hyperbola when given the algebraic equation or graph

Exponential functions

5.1 Define and graph exponential functions

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5.1 Define, graph, and use logarithmic and natural logarithmic functions, use formulas for compound interest

Logarithmic functions and their graphs

5.2 Graph logarithmic functions, use the properties of logarithms

5.2 Evaluate logarithms with and without calculators

Properties of logarithms

5.3 Use properties of logarithms and natural logarithms, rewrite logarithms

Exponential /logarithmic equations

5.4 Solve logarithmic equations, solve exponential equations

Exponential and logarithmic models

5.5 Solve problems involving exponential growth and decay

Angles and their measure

6.1 Define angles in standard position, find coterminal angles in terms of degrees

6.1 Define one radian, define central angle, find coterminal angles in terms of radians

6.1 Convert from radians to degrees and from degrees to radians

6.1 Use the formula for arc lengthRight triangle trigonometry

6.2 Use the right triangle definitions for the six trigonometric functions

6.2 Evaluate trigonometric functions of 30, 45, and 60 degrees, use the cofunction relationships

6.2 Use the reciprocal identities, quotient identities, and Pythagorean identities

6.2 Evaluate trig functions with and without a calculator

6.2 Solve right trianglesTrigonometric functions of any angle

6.3Evaluate trig functions of any angle

6.3 Use reference angles6.3 Define and use the unit circle6.3 Define and use a periodic function, use

even and odd trig functionsGraphs of sine and cosine 6.4

graph sine and cosine curves

6.4 Give the amplitude and period of the

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graph or an equation6.4 Stretch and shrink trig graphs

horizontally and vertically6.4 Translate trig graphs

Graphs of other trig functions

6.5 Graph the tangent, cotangent, secant, and cosecant

Inverse trig functions

6.6 Graph the arcsine, arccos, and arc tan

6.6 Evaluate inverse trig functions with and without calculators

6.6 Find composites of trig and inverse trig functions

Applications involving right triangles

6.7 Solve right triangles and use harmonic motion

Using fundamental identities

7.1 Use fundamental trig identities to evaluate a function

7.1 Simplify a trig expression7.1 Factor, simplify, add, subtract, and

rewrite trig expressionsVerify trig identities

7.2 Verify identities

Solve trig equations

7.3 Solve trig equations by combining like terms, extracting square roots, factoring, and using quadratic methods

Sum and difference formulas

7.4 Use the sum and difference formulas for sine, cosine, and tangent, find exact values without a calculator

7.4 Prove cofunction identities, derive reduction formulas

Multiple angle and product to sum formulas

7.5 Use the double angle formulas for sine, cosine, and tangent

7.5 Use the half angle formulas for sine, cosine, and tangent

Law of sines 8.1 Use the law of sines to solve a triangleLaw of cosines 8.2 Use the law of cosines to solve a triangleSupplemental n/aArea of a triangle K = ½ ab sin CArea of sectors of circles

K = ½ (radius)(radius)(angle)K = ½ r s

Resources:Algebra and Trigonometry – Structure and Method Book 2 by Mcdougal LittleAlgebra and Trigonometry – Larson Hostetler Teacher made materialsAssessment:Mid-term, Final Exam, and 4-sight tests for 11th grade students

72

Introduction to CalculusChecklist of Objectives


Calculator

Objective

Real numbers and the real line

p-1 C Locate/identify/compare real numbers; simplify/evaluate using order of operations

Cartesian plane p-2 C Identify and use properties of circle; calculate the distance or midpoint on a coordinate plane

Graphs of equations

p-3 C Review intercepts of a graph, systems of equations and symmetry

Lines in a plane p-4 C Review linear equations, slope, parallel and perpendicular lines

Functions p-5 C Study function and function notation, domain, range and combinations of functions

Trigonometric functions

p-6 C Review of trigonometric functions, angles, degree and radian measure

Limits 1-1 C Introduction to limitsProperties of limits

1-2 C Limits of algebraic functions; properties of limits

Evaluation of limits

1-3 C Cancellation and rationalization techniques for evaluating limits

Continuity and one sided limits

1-4 C Determining continuity at a point and on an open interval

Infinite limits 1-5 C Study infinite limits and vertical asymptotes

Derivatives, tangent line

2-1 C Finding the derivative using the limit process

Differentiation rules

2-2 C Finding the derivative using the constant and power rules

Product and quotient rules

2-3 C Finding the derivative using the product and quotient rules; higher order derivatives

Chain rule 2-4 C Finding the derivative using the chain rule; simplifying derivatives

Implicit differentiation

2-5 C Finding the derivative using implicit differentiation

Related rates 2-6 C Applying the derivative to finding related rates

Extrema on an 3-1 C Finding the extrema of a function on an

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interval interval; critical numbersRolle and mean value theorem

3-2 C Applying Rolle’s and the Mean Value Theorem

First derivative test

3-3 C Applying the first derivative test to increasing and decreasing functions

Indefinite integration

4-1 C Apply the basic integration rules

Area, summations 4-2 C Apply the basic rules for sigma notation; area under a curve

Fundamental theorem of calculus

4-4 C Apply the fundamental theorem of calculus to evaluate a definite integral and find area

Integration by substitution

4-5 C Apply the general power rule for integration; integration by substitution

Resources:

Calculus, McDougal Littell, a Houghton Mifflin Company Copyrighted in 2001.

Assessment:

Chapter Tests, Mid-Term, and Final Exam.

74

Accelerated Geometry Checklist of Objectives


Calculator

Objective

Points, lines and planes

1-2 C Identify points lines and planes

Segments, rays and distance

1-3 C Identify segments lines and distance; calculate the distance or midpoint on a number line or on a coordinate plane.

Angles 1-4 C Measure or compare angles in degrees up to 360) protractor provided or drawn.

Postulates and theorems

1-5 C Postulates and theorems relating to points, lines and planes.

If-then statements

2-1 C Compare inductive and deductive reasoning; conditionals, hypothesis, converse and counterexamples.

Properties from Algebra

2-2 C Simplify/evaluate expressions using the properties of algebra

Proving theorems

2-3 C Prove and apply the midpoint and angle bisector theorems

Special pairs of angles

2-4 C Apply definitions of complementary, supplementary and vertical angles

Perpendicular lines

2-5 C Apply definition and theorems about perpendicular lines

Planning a proof

2-6 C Apply theorems for complementary and supplementary angles

Definitions 3-1 C Define parallel lines and angles formed by transversal

Parallel lines 3-2 C Identify and use properties of parallel linesProving lines parallel

3-3 C Proving and applying theorems of parallel lines

Angles of a triangle

3-4 C Classify triangles according to sides and angles; apply theorems using angle measure

Angles of a polygon

3-5 C Use the interior and exterior angle formulas for polygons

Inductive reasoning

3-6 C Compare inductive and deductive reasoning

Congruent figures

4-1 C Identify corresponding parts of congruent figures

Prove triangles congruent

4-2 C Use properties of congruent triangles(SSS, SAS, ASA)

Use congruent triangles

4-3 C Deduce information about angles and segments of congruent triangles

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Isosceles triangle theorems

4-4 C Identify and use properties of isosceles and equilateral triangles

Prove triangles congruent

4-5 C Apply theorems for congruent triangles(AAS, HL)

Using several congruent triangles

4-6 C Apply properties and theorems for congruent triangles in proofs

Medians, altitudes and perpendicular bisectors

4-7 C Identify and use properties of triangles(medians, altitudes and perpendicular bisectors)

Properties of parallelogram

5-1 C Apply the definitions and properties of parallelograms

Prove quadrilaterals are parallelogram

5-2 C Prove quadrilaterals are parallelograms

Parallel line theorems

5-3 C Apply theorems about parallel lines

Special parallelogram

5-4 C Identify and apply properties of special parallelograms

Trapezoids 5-5 C Identify and apply properties of trapezoidsRatio and proportion

7-1 C Use proportional relationships in problem solving

Properties of proportions

7-2 C Apply the properties of proportions in problem solving

Similar polygons

7-3 C Identify similar polygons

Similar triangles postulate

7-4 C Apply properties for similar triangles(AA)

Similar triangle theorems

7-5 C Apply theorems for similar triangles(SAS, SSS)

Proportional lengths

7-6 C Using proportional length properties to solve for missing segments and angles

Similarity in right triangles

8-1 C Similarity in right triangles; using the geometric mean

Pythagorean theorem

8-2 C Apply the Pythagorean Theorem to solve right triangles

Circle terms 9-1 C Identify radius, tangent, chord, diameter and secant of a circle

Tangents 9-2 C Apply theorems for tangents of a circleArcs and central angles

9-3 C Apply theorems for arcs and central angles of a circle

Arcs and chords 9-4 C Identify and use properties of arcs and chords

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of a circleInscribed angles 9-5 C Identify and use properties of inscribed

anglesAreas of rectangles

11-1 C Calculate the area of an irregular figure; find the measurement of a missing length given the perimeter or area

Areas of parallelogram triangles, and rhombuses

11-2 C Find area of parallelograms, triangles, and rhombuses and missing lengths given the area

Circumferenc and area of circle

11-5 C Calculate area and circumference of circles and find missing lengths given the area or circumference

Ratios of areas 11-7 C Use the ratios of areas to describe how a change in the linear dimension affects perimeter, circumference or area

Resources:

Geometry by McDougal Littell, a Houghton Mifflin Company and Copyrighted in 2001.

Assessment:

Chapter Tests, Mid-Term and Final Exam.

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ACCELERATED ALGEBRA IIChecklist of Objectives

Content Chapter/Section C/NC Objective

Real Numbers 1.1 NC Locate and identify rational and irrational numbers at the approxi-mate location on a number line.

NC Compare and order any real numbers (rational and irrational mixed).

Algebraic Expressions 1.2 NC Simplify and evaluate using order of operations.

Linear Equations 1.3 NC Write and solve a linear equation.

Word Problems 1.4 NC Write, solve and apply a linear equation (including problem situations).

Literal Equations 1.5 NC Isolate variables.

C Find the measurement of a missing length given the perimeter, circumference, area, or volume.

Simple and Compound Inequalities

1.6 C Solve compound inequalities and graph the solution sets on a number line.

Absolute Value Equations/ Inequalities

1.7 C Solve absolute value inequalities and graph the solution sets on a number line.

Tables/Graphs 1.8 C Estimate or calculate to make predictions based on a circle, line or bar graph.

Graphing Linear

Equations 2.1 NC Graph linear equations on a coordinate plane.

NC Match the graph of a given function to its table or equation.Slope 2.2 NC Compute the slope given 2 points.

Identify the slope from a graph.NC Identify slopes as parallel, perpendicular, or neither.

Slope-intercept Form 2.3 NC Graph linear equations on a coordinate plane.

NC Identify the slope and y-intercept represented by an equation or graph.

NC Write and solve linear equations for word problem situations.Writing

Equations of Lines

2.4 NCGiven the graph of a line, two points on the line, or the slope and a point on a line, write the linear equation in point-slope form, standard form, or slope-intercept form.Find the equation of a line parallel or perpendicular to a given line through a given point.

C Use direct proportion.Graphing

Linear Inequalities

2.5 C Graph linear inequalities on a coordinate plane.

Best-Fitting Lines and

Correlation2.7 C Write an equation for a line of best-fit for a scatter plot.

C Make predictions using equations or graphs of best-fit lines.

Graphing Systems 3.1 C Estimate a solution given a graph of a system of equations.

C Graph a system of linear equations on a coordinate plane.C Write and solve systems graphically to represent word problems.

C Write and solve systems of equations using graphing (limit: 2 equations).

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Substitution and Elimination 3.2 C Write and solve systems of equations using substitution or

elimination (limit: 2 equations).Word Problems using Systems 3.3 C Write and solve systems of equations using substitution or

elimination (limit: 2 equations) for word problems.Systems of

Linear Inequalities

3.4 C Graph systems of linear inequalities on a coordinate plane.

Radicals Intro to Chapter 5 C Simplify square roots and rationalize denominators including

conjugates.Solving

Quadratics 5.1 C Find the square root of an integer to the nearest tenth using either a calculator or estimation. Solve quadratics by finding square roots.)

Graphing Quadratics 5.2 C Graph quadratics.

Quadratics and the Zero Product Property

9.3 C Factor algebraic expressions including difference of squares and trinomials (limited to ax²+bx+c).

Solve quadratic equations using factoring (Zero Product Property). Factoring for polynomials of other degrees will be done later with the Chapter 9 topics.Midterm

Completing the Square 5.3 C Solve quadratics by completing the square.

Quadratic Formula 5.4 C Solve quadratics by the quadratic formula.Complex Numbers 5.5 C Add, subtract, and multiply imaginary and complex numbers.Quadratic

Formula with Complex Solutions

5.6 C Solve quadratics having real and complex-number solutions.

Graphing Quadratic

Inequalities5.7 C Graph quadratic inequalities.

Functions 6.1 C Determine if a relation is a function given a set of points or a graph.

C Identify the domain and range of a relation (may be presented as ordered pairs or a table).

Composition 6.2 C Find the composition of two functions.Inverse

Functions 6.3 C Identify the inverse of a relation (may be presented as ordered pairs or a table).

Statistics 6.7 C Create graphical representations of data including box-and-whisker plots, stem-and-leaf plots, or scatter plots.

CAnalyze data or answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots, or scatter plots).

CCalculate or select the appropriate measure of central tendency (mean, median, or mode) of a set of data given or represented on a table, line plot, or stem-and-leaf plot).

C Calculate/and or interpret the range, quartiles, and interquartile range.

C Describe how outliers affect measures of central tendency.Probability 15.1 C Find the probability of dependent and independent events.

Find theoretical and experimental probability.Fundamental

Counting Principle /

Permutations15.2 C Use the Fundamental Counting Principle and permutations to

identify the number of ways an event can happen.

Combinations 15.3 C Use combinations to identify the number of ways an event can happen.

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Properties of Exponents 7.1 NC Use the properties of Exponents to simplify exponential

expressions.NC Use scientific notation.

Rational and Radical Notation

7.3 NC Evaluate expressions with radical notation for nth roots and rational exponent notation

Expressions with Radical and Rational

Notation

7.4 NC Use Properties of Exponents to simplify expressions written in radical and rational exponent notation.

Radical Equations 7.5 NC Solve radical equations.Graphing

Square and Cube Roots

7.6 NC Graph square and cube roots.

Identify the domain and range of square root and cube root equations.

Polynomials 9.1 C Add, subtract, and multiply polynomial expressions.Special

Factoring Patterns

9.3 CSolve polynomials using special factoring patterns and the Zero product property (sum and difference of cubes, factoring by grouping). Find both real and imaginary roots.

Polynomial Long and Synthetic Division

9.4 C Divide polynomials using long division and synthetic division and relate to the remainder and factor theorems.

Fundamental Theorem of

Algebra9.6 C Connect the zeros, factors, solutions, x-intercepts, and the

Fundamental Theorem of Algebra.Algebraic Fractions 10.3 C Multiply and divide rational expressions.

Final Exam

Resources:

Algebra and Trigonometry Structure and Method Book2, by Houghton Mifflin.Algebra 2 by McDougal Littell.

Assessment:Quizzes, Chapter Tests, Midterm, Final

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Honors Pre-Calculus / TrigonometryChecklist of Objectives

All topics are taught without a calculator at first, then the students are shown how to solve the problems with a calculator.


Calculator

Objective

Linear functions 1.1 * Sketch equations using the point-plotting technique

1.1 Use point-slope form, general form, intercept form and slope-intercept form for the equation of a line

1.1 Find parallel and perpendicular lines, define vertical and horizontal lines by equation

1.1 Find the intersection of two lines algebraically, graphically, and with a graphing calculator

1.1 Use the distance and midpoint formulasSlopes of lines 1.2 Find the slope of a line, be able to find the

slope of parallel and perpendicular linesFind equations of lines

1.3 Find equations of lines given various pieces of information, be able to use 4 different forms of equations for lines discussed in 1.1

Linear Functions and Models

1.4 Model real-world situations by means of linear functions

Quadratic Functions 1.5 Add, subtract, multiply and divide complex numbers

1.6 Solve quadratic equations by factoring, completing the square, and using the quadratic formula

Quadratic Functions and their graphs

1.7 Define and graph quadratic functions, use standard forms for the equation of a parabola

Quadratic Models 1.8 Model real-world situations using quadratic functions

Polynomial Functions 2.1 Identify polynomial functions, use synthetic substitution, find zeros

2.2 Apply the remainder theorem and the factor theorem

2.3 Graph cubic, quartic, and quintic functions with and without a calculator.

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2.4 Find maximum and minimum values of polynomial functions

2 .5 Find roots of polynomial functions2.6 Solve cubic and quartic equations by

factoring and using a quadratic term2.7 Apply the fundamental theorem of

algebra, the complex conjugates theorem, the rational coefficients theorem, even / odd theorem, and the sum and product of roots.

Inequalities 3.1 Solve and graph linear and absolute value inequalities in one variable

3.2 Solve and graph polynomial inequalities in one variable

3.3 Solve and graph polynomial inequalities in two variables

3.4 Solve applied problems using linear programming, use the corner-point principle

Functions 4.1 Identify domain, range, zeros, and graph a function

4.2 Find the sum, difference, product, quotient, and composite of functions

4.3 Reflect graphs and use symmetry to sketch graphs

4.4 Stretch, shrink, and translate graphs4.5 Find the inverse of a function, perform

and apply the horizontal line test

Exponents and logarithms

5.1 Define and apply integral exponents

5.2 Define and apply rational exponents5.3 Define and use exponential functions, use

the rule of 72

5.4 Use compound interest formula and the number e

5.5 Define and apply logarithms5.6 Prove and apply the laws of logarithms5.7 Solve exponential equations with and

without changing basesCoordinate Proofs 6.1 Prove theorems from geometry by using

coordinates6.2 Find equations of circles, graph circles,

find intersection of a line and a circle algebraically, graphically, and with a

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graphing calculator6.3 Find equations of ellipses and graph them6.4 Find equations of hyperbolas and graph

them, use and define asymptotes

Angles, Arcs, and Sectors

7.1 Find the measure of an angle in degrees or radians and find coterminal angles

Sectors of Circles 7.2 Find the arc length and area of a sector of a circle

The Sine and Cosine Functions

7.3Define sine and cosine, graph sine and cosine without a graphing calculator, solve simple trigonometric equations

Evaluating and graphing sine and cosine

7.4Use reference angles, find values of sine and cosine, sketch graphs of functions

The other trigonometric functions

7.5 Find values of tangent, cotangent, secant, and cosecant, also graph each of these functions without a graphing calculator

The inverse trigonometric functions

7.6 Find the values of the inverse trigonometric functions, graph the inverse trig functions

Simple trigonometric equations

8.1 Solve simple trigonometric equations and apply them

Sine and Cosine Curves

8.2 Find equations of different size sine and cosine curves and apply equations, use amplitude and period

Modeling periodic behavior

8.3 Use trigonometric functions to model periodic behavior

Relationships among the functions

8.4 Simplify trigonometric expressions, prove trig identities, use reciprocal relationships, use Pythagorean identities, use negative trig relationships, use the cofunction relationships

Solving more difficult trigonometric equations

8.5 Use trigonometric identities and technology to solve more difficult trigonometric equations

Solving right triangles

9.1 Use trigonometry to find unknown sides or angles of a right triangle

Area of a triangle 9.2 Find the area of a triangle given the lengths of two sides and the measure of the included angle

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The law of sines 9.3 Use the law of sines to find the unknown parts of a triangle

The law of cosines 9.4 Use the law of cosines to find the unknown parts of a triangle

Sum and difference formulas for sine and cosine

10.1 Derive and apply formulas for the sum and difference of the sine and cosine

Sum and difference formula for the tangent

10.2 Derive and apply the sum and difference formula for the tangent

Double-angle and half-angle formulas

10.3 Derive and apply the double-angle and half-angle formulas for the sine, cosine, and tangent

Resources:

Advanced Mathematics – Pre-calculus with Discrete Mathematics and DataAnalysis by Richard G. Brown, a McDougal Littell / Houghton Mifflin company copyrighted 1997. Teacher made supplements.

Assessment:

Mid-Term, Final Exam, Projects, and (2) 4-Sights Tests

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Honors CalculusChecklist of Objectives



Real Numbers and the Real Line


Cartesian Plane p-2 C Identify and use properties of circle; calculate the distance or midpoint on a coordinate plane

Graphs of Equations


Lines in the Plane p-4 C Review linear equations, slope, parallel and perpendicular lines


Trigonometry p-6 Review of trigonometric functions, angles, degree and radian measure

Introduction to Limits

1-1 C Introduction to limits

Properties of Limits

1-2 C Limits of algebraic functions; properties of limits

Techniques for Evaluating Limits


Continuity and One-sided Limits


Infinite Limits 1-5 C Study infinite limits and vertical asymptotesDerivative and the Tangent Line Problem


Basic Differentiation Rules


Rates of Change 2-2, 2-3 C Using a derivative to determine the rate of change of one variable with respect to another

Product and Quotient Rules and Higher Order Derivatives


Chain Rule 2-4 C Finding the derivative using the chain rule; simplifying derivatives

Implicit Differentiation


Related Rates 2-6 C Applying the derivative to finding related ratesExtrema on an Interval

3-1 C Finding the extrema of a function on an interval; critical numbers

Rolle’s Theorem and Mean ValueTheorem


Increasing and Decreasing Functions and the First Derivative Test


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Concavity and the Second Derivative Test

3-4 C Finding concavity and points of inflection of a function; Applying the second derivative test

Infinite Limits 3-5 C Study limits at infinity and horizontal asymptotes

Summary of Curve sketching

3-6 C Analyze a function to determine its graph

Optimization Problems

3-7 C Problem solving strategies for applied maximum and minimum problems

Antiderivative and Indefinite Integration


Fundamental Theorem of Calculus

4-4 C Apply the fundamental theorem of calculus to evaluate a definite integral, find the area and the average value of a function.

Integration by Substitution


Logarithmic Functions and Derivatives

5-1 C Review the properties and find the derivative of a natural logarithmic function

Natural Logarithmic Function and Integration

5-2 C Apply the log rule for integration; apply the basic trigonometric formulas

Exponential Functions

5-4 C Review properties and find the derivative and integrals of natural exponential functions

Differential Equations: Growth and Decay

5-6 C Solving differential equations; applications of exponential functions involving growth, decay and interest

Inverse Trig Functions and Differentiation

5-7 NC Properties and derivatives of inverse trig functions

Inverse Trig Functions and Integration

5-8 NC Integrals involving inverse trig functions

Area Between Two Curves

6-1 C Find the area of the region between two curves

Volume: The Disc Method

6-2 C Use the disc and washer method to find the volume of the solid formed by revolving the region around an axis

Volume: The Shell Method

6-3 C Use the shell method of find the volume of the solid formed by revolving the region around an axis

Resources:This curriculum is formatted to the textbook Calculus – Larson, Hostetler, Edwards, 5th edition

Assessment:Quizzes, Tests, Midterm, Final

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Advanced Placement CalculusChecklist of Objectives



Real Numbers and the Real Line


Cartesian Plane p-2 C Identify and use properties of circle; calculate the distance or midpoint on a coordinate plane

Graphs of Equations


Lines in the Plane p-4 C Review linear equations, slope, parallel and perpendicular lines


Trigonometry p-6 NC Review of trigonometric functions, angles, degree and radian measure

Introduction to Limits

1-1 C Introduction to limits

Properties of Limits 1-2 C Limits of algebraic functions; properties of limits

Techniques for Evaluating Limits


Continuity and One-sided Limits


Infinite Limits 1-5 C Study infinite limits and vertical asymptotesDerivative and the Tangent Line Problem


Basic Differentiation Rules


Rates of Change 2-2, 2-3 C Using a derivative to determine the rate of change of one variable with respect to another

Product and Quotient Rules and Higher Order Derivatives


Chain Rule 2-4 C Finding the derivative using the chain rule; simplifying derivatives

Implicit Differentiation


Related Rates 2-6 C Applying the derivative to finding related ratesExtrema on an Interval

3-1 C Finding the extrema of a function on an interval; critical numbers

Rolle’s Theorem and Mean ValueTheorem


Increasing and Decreasing Functions and the First Derivative Test


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Concavity and the Second Derivative Test

3-4 C Finding concavity and points of inflection of a function; Applying the second derivative test

Infinite Limits 3-5 C Study limits at infinity and horizontal asymptotes

Summary of Curve Sketching

3-6 C Analyze a function to determine its graph

Optimization Problems

3-7 C Problem solving strategies for applied maximum and minimum problems

Linear Approximation

3-9 C Use the equation of a tangent line to estimate the value of a function

Antiderivative and Indefinite Integration


Area 4-2 C Apply the basic rules for sigma notation; area under a curve

Riemann Sums and Definite Integrals

4-3 C Apply properties of Riemann Sums and definite integrals

Fundamental Theorem of Calculus

4-4 C Apply the fundamental theorem of calculus to evaluate a definite integral, find the area and the average value of a function.

Integration by Substitution


Numerical Integration

4-6 C Approximate the area under the curve with the trapezoidal rule

Logarithmic Functions and Derivatives

5-1 C Review the properties and find the derivative of a natural logarithmic function

Natural Logarithmic Function and Integration

5-2 C Apply the log rule for integration; apply the basic trigonometric formulas

Exponential Functions

5-4 C Review properties and find the derivative of natural exponential functions

Differential Equations: Growth and Decay

5-6 C Solving differential equations; applications of exponential functions involving growth, decay and interest

Inverse Trig Functions and Differentiation

5-7 C Properties and derivatives of inverse trig functions

Inverse Trig Functions and Integration

5-8 C Integrals involving inverse trig functions

Area Between Two Curves

6-1 C Find the area of the region between two curves

Volume: The Disc Method

6-2 C Use the disc and washer method to find the volume of the solid formed by revolving the

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region around an axisVolume: The Shell Method

6-3 C Use the shell method of find the volume of the solid formed by revolving the region around an axis

Note: This curriculum is formatted to the textbook Calculus – Larson, Hostetler, Edwards, 5th edition

Additional Resources: Advanced Placement Examination Questions

Assessment: Chapter test, AP problems, Midterm, AP Exam, Final

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StatisticsChecklist of Objectives



What is Statistics? 1-1 C Introduce basic terms concerning population and sample; discuss methods of acquiring data and levels of measurement

Random Samples 2-1 C Discuss types of random samples and generate random numbers through a table and calculator

Graphs 2-2 C Create and use bar graphs, pareto charts, pictograms, circle graphs, time plots, and time series

Histograms and Frequency Distributions

2-3 C Create histograms and frequency distribution tables

Stem and Leaf Displays

2-4 C Create and use data in stem and leaf plots

Measures of Central Tendency

3-1 C Determine mean, median, and mode

Measures of Variation

3-2 C Discuss Measures of variation; range, variance, standard deviation, coefficient of variation, Chebyshev’s Theorem

Analysis of Grouped Data

3-3 C Compute the mean and standard deviation of group data; compute weighted averages

Percentiles and Box and Whisker Plots

3-4 C Compute percentiles and create box and whisker plots

What is Probability ?

4-1 C Find simple probabilities

Compound Events 4-2 C Find the probability of compound eventsTrees and Counting Techniques

4-3 C Determine the number of permutations or combinations and apply the fundamental counting principle.

Introduction to Random Variables and Probability Distributions

5-1 C Introduce random variables and probability distributions

Binomial Probabilities

5-2 C Find the probability of a binomial distribution

Properties of the Binomial Distribution

5-3 C Find the mean and standard deviation of the binomial distribution

Geometric and Poisson Probability Distributions

5-4 C Geometric and poisson probability distributions

Graphs of Normal Probability Distributions

6-1 C Graph the normal probability distribution

Area under the 6-2 C Convert to standard units and apply the standard

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Standard Normal Distribution

normal distribution

Area Under Any Normal Curve

6-3 C Find the area under any normal curve

Normal Approximation

6-4 C Normal Approximation to the Binomial Distribution

Sampling Distributions

7-1 C Discuss sampling distributions

Central Limit Theorem

7-2 C Apply the Central Limit Theorem

Estimating μ with Large Samples

8-1 C Find the confidence interval for the mean with large samples

Estimating μ with Small Samples

8-2 C Find the confidence interval for the mean with small samples

Estimating p in the Binomial Distribution

8-3 C Find the confidence interval for p in the binomial distribution

Choosing the Sample Size

8-4 C Determine the sample size for a large sample estimate of the mean and for an estimate of p in a binomial experiment

Estimating μ1 – μ2

and p1 – p2

8-5 C Find the confidence interval for the difference in population means using large independent samples; confidence interval for the difference in population means using small independent samples; confidence interval for the difference in population proportions

Introduction to Hypothesis Testing

9-1 C Introduce hypothesis testing including level of significance and critical values

Tests Involving the Mean

9-2 C Hypothesis tests involving the mean

The P Value in Hypothesis Testing

9-3 C P value in hypothesis testing

Tests Involving the Mean

9-4 C Hypothesis tests involving the mean with large samples

Tests Involving a Proportion

9-5 C Hypothesis tests involving a proportion

Tests Involving Paired Differences

9-6

C Hypothesis tests involving paired differences with dependent samples

Testing Differences of Two Means or Two Proportions

9-7 C Hypothesis tests involving the difference means for large and small samples and the difference between population proportions

Introduction to Paired Data and Scatter Diagrams

10-1 C Construct a scatter plot; discuss types of correlations and linear regression

Linear Regression 10-2 C Draw, find, and write an equation for the line of best fit for a scatter plot; make predictions using equations or graphs of best fit lines or scatter plots

Linear Correlation Coefficient

10-3 C Determine the linear correlation coefficient and the coefficient of determination

Chi Square: Tests of Independence

11-1 C Hypothesis tests involving chi-square and independence of variables

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Chi-Square: Goodness of Fit

11-2 C Hypothesis tests involving chi-square and the goodness of fit

Resources:

This curriculum is formatted to the textbook Understandable Statistics – Brase / Brase 6th edition

Assessments:

Chapter tests, Midterm and Final

92

PSSA PREP 9th GradeChecklist of Objectives

This course is a review and tutorial of 8th grade PSSA topics.

Content Chapter/Section Calculator Anchor/Standard

Objective

PSSA Practice Test

C All A-EStudents will review old 8th grade PSSA Practice test, including open ended problems

Number Systems PSSA Coach C

APA

2.1+2

Use fractions, decimals, and percents and find percent of a number. Simplify exponents and solve problems with exponents including scientific notation. Solve computations with and without a calculator with order of operations

Geometry and Measure-ment

PSSA Coach C B and CPA 2.3

Use measurement in U.S. and Metric systems to find perimeter, area, and volume of geometric figures. Solve problems with ratio, rates, and scale drawings. Use protractor to find and name angles.

Problem Solving PSSA Coach C

All A-EPA

2.4+5

Student will use steps to problem solving and mathematical reasoning for word problems

Data and Probability

PSSA Coach C EPA 2.6

Solve problems using mean, median, mode, and types of graphs. Find the probability of an event

Algebraic Concepts PSSA Coach C D

PA 2.8

Find the algebraic rule from a pattern. Solve algebraic equations. Use formulas from the formula page to solve problems.

Graphing PSSA Coach C C and DPA 2.8

Plot point in the coordinate system and graph linear equations using the slope intercept form

Geometry PSSA Coach CC

PA 2.9+10

Use the Pythagorean Theorem to solve problems. Use line of symmetry and begin review of open ended problems for 8th grade practice test.

Practice Test PSSA TEST C All A-E Review then 8th Grade PSSA Practice

Test as a Final Exam.Resources:

PSSA Mathematics Coach Workbooks Grade 8 by Educational Design.PSSA Practice Tests and released items.Teacher made supplemental worksheets and activities.

Assessment:8th Grade PSSA Practice Test as Final Exam.

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PSSA Enhancement Grade 11Standardized Test Practice

Checklist of Objectives


Calculator

Anchor/Standard

Objective

Number Systems C A

Write numbers as fractions, decimals, and percents. Find percent of a number. Use rules of exponents to simplify expressions and simplify square roots.

Number Systems C A Use scientific notation. Simplify expressions. Use

ratios, rates, proportions, and scale drawings.

Number Systems C A

Use absolute value, rational, and irrational numbers. Compute with and without a calculator using order of operations.

Number Systems C A Review and Test on all topics in PSSA Anchor A

Number Systems

Geometry/ Measurement C B/C

Use basic Geometric terms, label figures, find the measure of angles. Identify and use types of angles such as vertical, corresponding, and alternate interior angles.

Geometry/Measurement C B/C Find the perimeter, area, surface area, and volume of

geometric figures (including irregular shapes).

Geometry/Measurement C B/C

Name and use properties of parts of circles. Identify and use properties of types of triangles. Use triangle sum theorem to find missing angles. Solve problems with congruent and similar triangles. Use properties of quadrilaterals.

Geometry/Measurement C B/C Solve problems using Pythagorean theorem. Solve open

ended problems using geometry.Geometry/Measurement C B/C Review and Test on all Measurement and Geometry

topics that are in PSSA Anchors B and C.

Algebra C D

Construct a coordinate system, label all parts, and plot points. Graph linear equations using slope intercept form. Graph nonlinear equations using substitution chart method (just parabolas).

Algebra C DGiven 2 points find the midpoint, slope, distance, and the equation of the line containing the two points. Complete pattern and find the algebraic rule.

Algebra C D Solve algebraic equations and inequalities. Graph inequalities.

Algebra C DMultiply using distributive property and foil method to multiply binomials. Factor out monomial terms and factor out a trinomial into two binomials

Algebra C D Review and Test on all Algebraic topics from PSSA Anchor D

Data and Probability C E

Find the mean, median, mode, and range of a set of data. Construct and interpret frequency charts, normal distribution, stem and leaf, and box and whisker plots.

Data and Probability C E Find the probability of an event. Use permutations and

combinations.Data andProbability C E Review and Test on all topics from PSSA Anchor E data

and probabilityC All PSSA PRACTICE TEST AS A MIDTERM GRADE

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3days including open ended responses.Number Systems

PSSABook C A Solve released items and workbook problems using

number systems.Geometry/Measurement

PSSABook C B/C Solve released items and workbook problems using

Geometry and measurement.

Algebra PSSABook C D Solve released items and workbook problems using

Algebraic concepts.Data and Probability

PSSABook C E Solve released items and workbooks problems using data

and probability.Using the formula page C All Solve problems using the formula page from the PSSA

test.Open Ended Problems C All Solve open ended problems, show all work, and explain

answers.

PSSABook All

Solve problems without a calculator and vocabulary review. Take practice test out of Mastering the PSSA workbook.Taking the real PSSA Test and review

Venn Diagrams C Set up and use Venn diagrams to solve problems.

Trig Ratios C PA 2.10 Use basic Trig ratios to find missing parts of right triangles and use trig ratios to solve word problems.

Electrician Apprenticeship Exam

C AllTake Electrician Apprenticeship Exam as practice.

SAT Tests SAT C All SAT Preparation. Go through SAT practice test together discussing solution to each question.

SAT Tests SAT C AllSAT Preparation. Go through current SAT practice test together discussing solution to each question. Students will take a practice SAT test and discuss scoring.

SAT Tests SAT C All SAT Preparation. Go through old SAT practice test from previous year.

SAT Tests SAT C All

SAT Preparation. Go through old SAT practice test from previous year and allow students time on the computer to look over SAT websites to practice Math and English.

ACT Tests ACT C All ACT Preparation. Go through ACT Practice test with students in class and discuss scoring.

ASVAB C AllASVAB test practice. Have student take the math section of the Armed Service Vocational Aptitude Battery Test and discuss scoring.

C All Students will sample college placement tests then prepare for our final exam. Cumulative Final Exam

ResourcesMastering the PSSA by Glencoe Mathematics, McGraw Hill.SAT Preparation Booklet from College Boards.ACT Preparation Booklet from ACT.Teacher made supplemental worksheets, tests, and activities.

Assessment Teacher made tests and activities. PSSA Practice Test from Pa. Department of Education as Mid-Term. Teacher made tests using released items from the PSSA tests and opened ended. Final Exam. Several tests are used in class for practice or preparation but not graded as tests, such as the practice SAT test, practice ACT test, Electrician Apprenticeship Exam, and the ASVAB tests.

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Documents

Belle Vernon Area Math Curriculum Guide K – 12 2007 -2008 ...€¦ · a. Kindergarten Mathematics 6 b. First Grade Mathematics 9 c. Second Grade Mathematics 12 d. Third Grade Mathematics