using the best of both! - prentice hall · prentice hall is proud to produce two outstanding middle...

Prentice Hall is proud to produce two outstanding middle grades mathematics curriculum,Prentice Hall Mathematics and Connected Mathematics 2 (CMP2). This guide will show howyou can use the “Best of Both” in your classroom.

Below you will find guidelines for replacing Lessons from Prentice Hall Mathematics Course 1,Course 2, Course 3, and Pre-Algebra with CMP2 units. Consider the following when implementing both texts in your classroom.

Benefits of Implementing CMP2 Units in Your Prentice Hall Mathematics Classroom• Targeted instruction on a particular math concept or strand based on assessment data

• Integration of hands-on, real-world problems for a particular math concept or strand

• Gradual implementation of CMP2 as the primary curriculum in the classroom

Guidelines for Using CMP2 Replacement UnitsIn order to develop deep, conceptual understanding of mathematics, the units found within theCMP2 curriculum build and connect from Investigation to Investigation, unit-to-unit, and grade-to-grade.

• Maintaining the Unit’s Effectiveness—It is best to implement a CMP2 unit in itsentirety, because math concepts build gradually from the beginning to the end of a unit.Implementing isolated CMP2 problems will be less effective in helping students gain adeep understanding of the math content found within the unit.

• Necessary Prerequisites—Connected Mathematics units are dependent upon eachother in developing understanding of mathematics. Refer to the “Content Connections toOther Units” feature within the CMP2 Teacher’s Guide to determine which math conceptsare prerequisites for success within the unit.

• Be Mindful of Time—Prentice Hall Mathematics Lessons and CMP2 Problems may havedifferent pacing requirements. Refer to the Prentice Hall Mathematics Teacher’s Editionand CMP2 Teacher’s Guide for guidance.

Implementing Best of Both in the ClassroomIn the following pages, there are charts indicating which Prentice Hall Mathematics lessons canbe omitted in order to implement a CMP2 unit. Use this as your initial guide in choosing whichCMP2 unit fits your students’ needs.

Go to PHSchool.com/cmp2/bestofboth to see examples of sequencing that could be imple-mented into your classroom. Use this as a guide to create an appropriate sequencing for yourclassroom based on your students’ needs.

Using the Best of Both!

Grade 6 CMP2 Replacement Unit Omit PH Math Course 1 ©2008 Lessons

Prime TimeProblem 1.1: Finding Proper FactorsProblem 1.2: Prime and Composite NumbersProblem 1.3: Finding MultiplesProblem 2.1: Rectangles and Factor PairsProblem 2.2: Reasoning with Odd and Even NumbersProblem 2.3: Classifying NumbersProblem 3.1: Choosing Common Multiples or Common

FactorsProblem 3.2: Choosing Common Multiples or Common



FactorsProblem 4.1: Finding Factor StringsProblem 4.2: Finding the Longest Factor StringProblem 4.3: Using Prime FactorizationProblem 5.1: Using Multiples and Factors

PH Math Course 1 ©2008Lesson 4-3: Prime Numbers and Prime FactorizationLesson 4-4: Greatest Common FactorLesson 4-7: Least Common Multiple

Bits & Pieces IProblem 1.1: Whole Numbers and FractionsProblem 1.2: Folding Fraction StripsProblem 1.3: Finding Fractional PartsProblem 1.4: Using Fractions to CompareProblem 2.1: Equivalent Fractions and Equal SharesProblem 2.2: Finding Equivalent FractionsProblem 2.3: Comparing Fractions to BenchmarksProblem 2.4: Fractions Between FractionsProblem 2.5: Naming Fractions Greater than 1Problem 3.1: Using Tenths and HundredthsProblem 3.2: Place Values Greater than HundredthsProblem 3.3: Decimal BenchmarksProblem 3.4: Moving from Fractions to DecimalsProblem 3.5: Ordering DecimalsProblem 4.1: Making Sense of PercentsProblem 4.2: Using Percents to CompareProblem 4.3: Expressing Data in Percent FormProblem 4.4: Moving Between Representations

PH Math Course 1 ©2008Lab 1-5a: Exploring Decimal ModelsLesson 1-5: Understanding DecimalsLesson 1-6: Comparing & Ordering DecimalsLab 1-8b: Multiplying and Dividing Decimals by 10,

100, and 1,000Lab 4-5a: Modeling FractionsLesson 4-5: Equivalent FractionsLab 4-6a: Exploring Improper FractionsLesson 4-6: Mixed Numbers and Improper FractionsLesson 4-8: Comparing & Ordering FractionsLesson 4-9: Fractions & DecimalsLab 7-6a: Modeling PercentsLesson 7-6: Percents, Fractions, & Decimals

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Shapes & DesignsProblem 1.1: Classifying PolygonsProblem 1.2: SymmetryProblem 1.3: Tiling with Regular PolygonsProblem 2.1: Understanding AnglesProblem 2.2: Developing Angle BenchmarksProblem 2.3: Using an Angle RulerProblem 2.4: Analyzing Measurement ErrorsProblem 2.5: Angles and Parallel LinesProblem 3.1: Angle Sums of Regular PolygonsProblem 3.2: Angle Sums of Any PolygonProblem 3.3: Interior Angles and TilingProblem 3.4: Exterior Angles of PolygonsProblem 4.1: Building TrianglesProblem 4.2: Building QuadrilateralsProblem 4.3: Properties of Quadrilaterals

PH Math Course 1 ©2008Lab 8-2a: Using Angle BenchmarksLesson 8-2: AnglesLab 8-3b: Exploring Parallel LinesLab 8-4a: Investigating Angles in a TriangleLesson 8-4: Classifying TrianglesLab 8-5a: Angles in a QuadrilateralLesson 8-5: Exploring and Classifying PolygonsLesson 8-7: Line SymmetryLab 8-8b: Tessellations

Bits & Pieces IIProblem 1.1: Using Fraction BenchmarksProblem 1.2: Estimating Fraction SumsProblem 2.1: Writing Addition and Subtraction

Sentences with FractionsProblem 2.2: Using Addition and Subtraction with

FractionsProblem 2.3: Fraction Fact FamiliesProblem 2.4: Designing Algorithms for Adding and

Subtracting FractionsProblem 3.1: A Model for Multiplication of FractionsProblem 3.2: Another Model for the Multiplication of

FractionsProblem 3.3: Modeling More Multiplication Situations

with FractionsProblem 3.4: Multiplication with Mixed NumbersProblem 3.5: Writing an Algorithm for Multiplication of

FractionsProblem 4.1: Dividing a Whole Number by a FractionsProblem 4.2: Dividing a Fraction by a Whole NumberProblem 4.3: Dividing a Fraction by a FractionProblem 4.4: Writing a Division Algorithm for Fractions

PH Math Course 1 ©2008Lesson 5-1: Estimating Sums and DifferencesLab 5-2a: Modeling Fraction OperationsLesson 5-2: Fractions with Like DenominatorsLab 5-3a: Modeling Unlike DenominatorsLesson 5-3: Fractions with Unlike DenominatorsLab 5-4a: Using Mixed NumbersLesson 5-4: Adding Mixed NumbersLesson 5-5: Subtracting Mixed NumbersLesson 5-6: Equations with FractionsLab 6-1a: Modeling Fraction MultiplicationLesson 6-1: Multiplying FractionsLesson 6-2: Multiplying Mixed NumbersLab 6-3a: Fraction DivisionLesson 6-3: Dividing FractionsLesson 6-4: Dividing Mixed NumbersLesson 6-5: Solving Fraction Equations by Multiplying

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Covering & SurroundingProblem 1.1: Understanding Area and PerimeterProblem 1.2: Finding Area and PerimeterProblem 1.3: Finding Area and Perimeter of RectanglesProblem 2.1: Constant Area, Changing PerimeterProblem 2.2: Perimeter and Irregular ShapesProblem 2.3: Constant Perimeter, Changing AreaProblem 2.4: Increasing Area and PerimeterProblem 3.1: Finding Area and Perimeter of TrianglesProblem 3.2: Identifying Base and HeightProblem 3.3: Triangle FamiliesProblem 3.4: Designing Triangle under ConstraintsProblem 4.1: Finding Measures of ParallelogramsProblem 4.2: Parallelograms from TrianglesProblem 4.3: Designing Parallelograms Under

ConstraintsProblem 4.4: Finding Areas and PerimetersProblem 5.1: Estimating Areas and PerimetersProblem 5.2: Finding CircumferenceProblem 5.3: Exploring Area and CircumferenceProblem 5.4: Finding Area of a Circle

PH Math Course 1 ©2008Lesson 9-3: Perimeters and Areas of RectanglesLab 9-4a: Comparing AreasLesson 9-4: Areas of Parallelograms and TrianglesLab 9-5a: Exploring CirclesLesson 9-5 Circles and CircumferenceLesson 9-6: Area of a Circle

Bits & Pieces IIIProblem 1.1: Estimating with DecimalsProblem 1.2: Adding and Subtracting DecimalsProblem 1.3: Using Fractions to Add and Subtract

DecimalsProblem 1.4: Decimal Sum and Difference AlgorithmsProblem 2.1: Relating Fraction and Decimal

MultiplicationProblem 2.2: Missing FactorsProblem 2.3: Finding Decimal ProductsProblem 2.4: Factor-Product Relationships with DecimalsProblem 3.1: Deciphering Decimal SituationsProblem 3.2: Using Common Denominators to Divide

FractionsProblem 3.3: Exploring Dividing FractionsProblem 3.4: Representing Fractions as DecimalsProblem 4.1: Determining TaxProblem 4.2: Computing TipsProblem 4.3: Using DiscountsProblem 5.1: Finding Percent DiscountsProblem 5.2: Solving Percent ProblemsProblem 5.3: Making Circle Graphs

PH Math Course 1 ©2008Lab 1-7a: Using ModelsLesson 1-7: Adding & Subtracting DecimalsLab 1-8a: Modeling Decimal MultiplicationLesson 1-8: Multiplying DecimalsLesson 1-9: Dividing DecimalsLesson 7-7: Finding the Percent of a NumberLesson 7-8: Circle GraphsLesson 7-9: Estimating with PercentsExtension: Percents Under 1% and Over 100%

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How Likely Is It?Problem 1.1: Finding Probabilities With a CoinProblem 1.2: Finding More ProbabilitiesProblem 1.3: Finding Experimental ProbabilitiesProblem 1.4: Understanding Equally Likely EventsProblem 2.1: Finding Theoretical ProbabilitiesProblem 2.2: Exploring ProbabilitiesProblem 2.3: Using Strategies to Find Theoretical

ProbabilitiesProblem 2.4: Pondering Possible and ProbableProblem 3.1: Finding Probabilities with a SpinnerProblem 3.2: Analyzing FairnessProblem 3.3: Using a SimulationProblem 4.1: Applying Experimental ProbabilityProblem 4.2: Applying Theoretical ProbabilityProblem 4.3: Analyzing a Game

PH Math Course 1 ©2008Lesson 10-1: Tree Diagrams and the Counting PrincipleLesson 10-2: ProbabilityLab 10-3b: Experimental and Theoretical ProbabilitiesLesson 10-3: Experimental ProbabilityLesson 10-4: Making Predictions from Data

Data About UsProblem 1.1: Organizing and Interpreting DataProblem 1.2: Useful StatisticsProblem 1.3: Experimenting with MedianProblem 1.4: Using Different Data TypesProblem 1.5: Vertical Bar Graphs and Horizontal Bar

GraphsProblem 2.1: Making a Stem-and-Leaf PlotProblem 2.2: Comparing DistributionsProblem 2.3: Making and Reading Coordinate GraphsProblem 2.4: Using Coordinate Graphs to Find

RelationshipsProblem 3.1: Finding the MeanProblem 3.2: Data with the Same MeanProblem 3.3: Using the Mean

PH Math Course 1 ©2008Lab 2-1a: Exploring the MeanLesson 2-1: Finding the MeanLesson 2-2: Median and ModeLesson 2-3: Frequency Tables and Line PlotsLesson 2-4: Bar Graphs and Line Graphs

(Bar Graphs Only)Lesson 2-6: Stem-and-Leaf PlotsLesson 2-7: Misleading Graphs and StatisticsLesson 11-8: Graphing in a Coordinate Plane

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Variables & PatternsProblem 1.1: Interpreting GraphsProblem 1.2: Making GraphsProblem 1.3: Interpreting GraphsProblem 1.4: Reading Data from GraphsProblem 1.5: Finding Average SpeedProblem 2.1: Analyzing a Table and a GraphProblem 2.2: Making and Analyzing a GraphProblem 2.3: Interpreting GraphsProblem 3.1: Equations with One OperationProblem 3.2: Equations with Two OperationsProblem 3.3: Equations for Revenue, Expenses, and

ProfitProblem 4.1: Making and Using Calculator TablesProblem 4.2: Making and Using Calculator GraphsProblem 4.3: Comparing Relationships

PH Math Course 2 ©2008Lab 2-6a: Using Tables to Compare DataLab 4-1a: Describing PatternsLesson 4-1: Evaluating and Writing Algebraic

ExpressionsLab 4-3a: Modeling EquationsLesson 4-3: Solving Equations by Adding or

SubtractingLesson 4-4: Solving Equations by Multiplying or

DividingLesson 4-5: Solving Two-Step ProblemsLab 9-1a: Choosing Scales and IntervalsLesson 9-1: Patterns and GraphsLesson 9-3: Patterns and TablesLesson 9-6: Interpreting GraphsLesson 10-4: Graphing Nonlinear RelationshipsLab 11-7a: Two-Variable Data CollectionLesson 11-7: Exploring Scatterplots

Stretching & ShrinkingProblem 1.1: Introduction to SimilarityProblem 1.2: Comparing Similar FiguresProblem 1.3: Corresponding Sides and AnglesProblem 2.1: Enlarging a FigureProblem 2.2: Changing a Figure’s Size and LocationProblem 2.3: Scale FactorsProblem 3.1: Rep-Tile QuadrilateralsProblem 3.2: Rep-Tile TrianglesProblem 3.3: Scale Factors and Similar ShapesProblem 4.1: Ratios within Similar ParallelogramsProblem 4.2: Ratios within Similar TrianglesProblem 5.1: Using Shadows to Find HeightsProblem 5.2: Using Mirrors to Find HeightsProblem 5.3: Finding Lengths within Similar Triangles

PH Math Course 2 ©2008Lesson 2-3: Simplifying FractionsLab 5-5a: Exploring Similar FiguresLesson 5-5: Using Similar FiguresLab 5-6a: Scale Drawings and ModelsLesson 5-6: Maps and Scale DrawingsLab 10-1b: Geometry in a Coordinate PlaneLesson 10-5: Translations

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Comparing & ScalingProblem 1.1: Exploring Ratios and RatesProblem 1.2: Analyzing Comparison StatementsProblem 1.3: Writing Comparison StatementsProblem 2.1: Developing Comparison StrategiesProblem 2.2: Developing Comparison StrategiesProblem 2.3: Scaling RatiosProblem 3.1: Making and Using a Rate TableProblem 3.2: Finding RatesProblem 3.3: Unit Rates and EquationsProblem 3.4: Two Different RatesProblem 4.1: Setting Up and Solving ProportionsProblem 4.2: Applications of ProportionsProblem 4.3: Developing Strategies for Solving

Proportions

PH Math Course 2 ©2008Lesson 2-4: Comparing & Ordering FractionsLesson 5-1: RatiosLesson 5-2: Unit Rates and Proportional ReasoningLesson 5-3: ProportionsLab 5-4a: Using Proportions with DataLesson 5-4: Solving ProportionsLesson 11-5: Estimating Population Size

Accentuate the NegativeProblem 1.1: Using Positive and Negative NumbersProblem 1.2: Comparing and Ordering Positive and

Negative NumbersProblem 1.3: Using a Number Line ModelProblem 1.4: Using a Chip ModelProblem 2.1: Introducing Addition of IntegersProblem 2.2: Introducing Subtraction of IntegersProblem 2.3: Addition and Subtraction RelationshipsProblem 2.4: Coordinate GraphingProblem 3.1: Introducing Multiplication of IntegersProblem 3.2: Multiplication PatternsProblem 3.3: Introducing Division of IntegersProblem 3.4: Multiplying IntegersProblem 4.1: Order of OperationsProblem 4.2: Distributing OperationsProblem 4.3: The Distributive Property and Subtraction

PH Math Course 2 ©2008Lesson 1-6: Comparing and Ordering IntegersLab 1-7a: Modeling Integer Addition and SubtractionLesson 1-7: Adding and Subtracting IntegersLab 1-8a: Modeling Integer MultiplicationLesson 1-8: Multiplying and Dividing IntegersLesson 1-9: Order of Operations and the Distributive

PropertyLab 1-9b: Properties and EqualityLesson 2.1: Exponents and Order of OperationsLesson 2.7: Rational NumbersLesson 10-1: Graphing Points in Four Quadrants

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Moving Straight AheadProblem 1.1: Finding and Using RatesProblem 1.2: Linear Relationships in Tables, Graphs, and

EquationsProblem 1.3: Using Linear RelationshipsProblem 1.4: Recognizing Linear RelationshipsProblem 2.1: Finding the Point of IntersectionProblem 2.2: Using Tables, Graphs, and EquationsProblem 2.3: Comparing EquationsProblem 2.4: Connecting Tables, Graphs, and EquationsProblem 3.1: Solving Equations Using Tables and GraphsProblem 3.2: Exploring EqualityProblem 3.3: Writing EquationsProblem 3.4: Solving Linear EquationsProblem 3.5: Finding the Point of IntersectionProblem 4.1: Using Rise and RunProblem 4.2: Finding the Slope of a LineProblem 4.3: Exploring Patterns with LinesProblem 4.4: Writing Equations with Two Variables

PH Math Course 2 ©2008Lab 4-2b: Keeping the BalanceLesson 4-2: Using Number Sense to Solve EquationsLab 4-3a: Modeling EquationsLab 4-6a: Modeling Two-Step EquationsLesson 4-6: Solving Two-Step EquationsLab 5-3b: Interpreting Rates VisuallyLesson 9-5: Using Tables, Rules, and GraphsLab 9-5b: Three Views of a FunctionLesson 10-2: Graphing Linear EquationsLab 10-2b: Representing DataLesson 10-3: Finding the Slope of a LineLab 10-3b: Exploring Slope

Filling and WrappingProblem 1.1: Making Cubic BoxesProblem 1.2: Making Rectangular BoxesProblem 1.3: Testing NetsProblem 14: Flattening a BoxProblem 2.1: Finding Surface AreaProblem 2.2: Finding the Least Surface AreaProblem 2.3: Finding Volume of a Rectangular PrismProblem 3.1: Finding the Volumes of Other PrismsProblem 3.2: Finding Volumes of CylindersProblem 3.3: Finding the Surface Area of Cylinders and

PrismsProblem 3.4: Comparing VolumesProblem 4.1: Comparing Spheres and CylindersProblem 4.2: Cones and Cylinders, Pyramids

and CubesProblem 4.3: Comparing Volumes of Spheres, Cylinders,

and ConesProblem 5.1: Doubling the Volume of a Rectangular

PrismProblem 5.2: Applying Scale Factor to Rectangular

PrismsProblem 5.3: Similarity and Scale Factors

PH Math Course 2 ©2008Lab 8-8a: Three Views of an ObjectLesson 8-8: Three-Dimensional FiguresLesson 8-9: Surface Area of Prisms and CylindersLesson 8-10: Volume of Prisms and CylindersLab 8-10b: Generating Formulas for Volume

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What Do You Expect?Problem 1.1: Experimental and Theoretical ProbabilityProblem 1.2: Using an Organized ListProblem 1.3: Determining Whether a Game Is FairProblem 2.1: Area Models and ProbabilityProblem 2.2: Using an Area ModelProblem 2.3: Finding the Best ArrangementProblem 3.1: Simulating a Probability SituationProblem 3.2: Finding Expected ValueProblem 3.3: Comparing Expected ValuesProblem 4.1: Finding More Expected ValuesProblem 4.2: Binomial ProbabilityProblem 4.3: Expanding Binomial Probability

PH Math Course 2 ©2008Lesson 12-1: ProbabilityLab 12-2a: Exploring ProbabilityLesson 12-2: Experimental ProbabilityLab 12-3b: Exploring Multiple EvensLab 12-4a: Exploring Multiple EventsLesson 12-4: Compound Events

Data DistributionsProblem 1.1: Variability in Categorical DataProblem 1.2: Variability in Numerical CountsProblem 1.3: Variability in Numerical MeasurementsProblem 1.4: Two Kinds of VariabilityProblem 2.1: The Mean as an Equal ShareProblem 2.2: The Mean as a Balance Point in

DistributionProblem 2.3: Repeated Values in a DistributionProblem 2.4: Median and Mean and Shapes of

DistributionProblem 3.1: Measuring and Describing Reaction TimesProblem 3.2: Comparing Reaction TimesProblem 3.3: Comparing More Than a Few StudentsProblem 3.4: Comparing Fastest and Slowest TrialsProblem 4.1: Representing Survey DataProblem 4.2: Comparing Speed

PH Math Course 2 ©2008Lesson 1-10: Mean, Median, Mode, and RangeLesson 11-1: Reporting Frequency

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Thinking with Math ModelsProblem 1.1: Finding Patterns and Making PredictionsProblem 1.2: Finding Patterns and Making PredictionsProblem 1.3: Extending PatternsProblem 2.1: Linear ModelsProblem 2.2: Equations for Linear RelationshipsProblem 2.3: Solving Linear EquationsProblem 2.4: Intersecting Linear ModelsProblem 3.1: Relating Length and WidthProblem 3.2: Inverse Variation PatternsProblem 3.3: Inverse Variation Patterns

PH Math Course 3 ©2008 Lab 2-6b: Using FormulasLab 3-5a: Tables and GraphsLesson 3-5: Equations, Tables, and GraphsLab 4-1b: Finding RatesLesson 6-1: Solving Two-Step EquationsLesson 9-4: Reading Graphs CriticallyLab 9-4b: Making Graphs Tell a StoryLesson 9-7: Making Predictions from ScatterplotsLab 9-7b: Line of Best FitLesson 11-2: Relating Graphs to EventsLesson 11-4: Understanding SlopeLab 11-5a: Graphing EquationsLesson 11-5: Graphing Linear FunctionsLesson 11-6: Writing Rules for Linear Functions

Looking for PythagorasProblem 1.1: Locating Points and Finding DistancesProblem 1.2: Shapes on a Coordinate GridProblem 1.3: Finding AreasProblem 2.1: Looking for SquaresProblem 2.2: Square RootsProblem 2.3: Using Squares to Find LengthsProblem 3.1: The Pythagorean TheoremProblem 3.2: A Proof of the Pythagorean TheoremProblem 3.3: Finding DistancesProblem 3.4: Lengths That Form a Right TriangleProblem 4.1: Analyzing the Wheel of TheodorusProblem 4.2: Finding Unknown Side LengthsProblem 4.3: Analyzing TrianglesProblem 4.4: Finding the Perimeter

PH Math Course 3 ©2008Lab 2-2b: Repeating DecimalsLesson 3-1: Exploring Square Roots and Irrational

NumbersLab 3-2a: Expressions and Square RootsLesson 3-2: The Pythagorean TheoremLesson 3-3: Using the Pythagorean TheoremExtension: Analyzing TrianglesLesson 3-4: Graphing in a Coordinate PlaneLesson 7-6: Areas of PolygonsLab 7-7a: Estimating Area

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Growing, Growing, GrowingProblem 1.1: Introducing Exponential RelationshipsProblem 1.2: Representing Exponential RelationshipsProblem 1.3: Growth FactorsProblem 1.4: Comparing Growth FactorsProblem 2.1: Y-Intercepts Other Than 1Problem 2.2: Interpreting Exponential EquationsProblem 2.3: Interpreting Exponential GraphsProblem 3.1: Fractional Growth FactorsProblem 3.2: Growth RatesProblem 3.3: Connecting Growth Rate and Growth

FactorProblem 4.1: Introducing Exponential DecayProblem 4.2: Representing Exponential DecayProblem 4.3: Modeling Exponential DecayProblem 5.1: Predicting the Ones DigitProblem 5.2: Operating with ExponentsProblem 5.3: Exploring Exponential Equations

PH Math Course 3 ©2008 Lesson 2-7: Powers and ExponentsLab 2-8a: Multiplying by Powers of 10Lesson 2-8: Scientific NotationLab 5-5a: Describing ChangeLesson 5-5: Percent of ChangeLab 12-3a: Exploring ExponentsLesson 12-3: Exponents and MultiplicationLesson 12-5: Exponents and DivisionExtension: Power Rules

Kaleidoscopes, Hubcaps, and MirrorsProblem 1.1: Reflection SymmetryProblem 1.2: Rotation SymmetryProblem 1.3: Analyzing SymmetriesProblem 1.4: Translation SymmetryProblem 2.1: Describing Line ReflectionsProblem 2.2: Describing RotationsProblem 2.3: Describing TranslationsProblem 2.4: Using Symmetry to Think About

TessellationsProblem 3.1: Relating Symmetry and CongruenceProblem 3.2: Congruent TrianglesProblem 3.3: Congruent TrianglesProblem 3.4: Side Lengths and CongruenceProblem 4.1: Finding Distances Without MeasuringProblem 4.2: Using Symmetry to Find Properties of

ShapesProblem 5.1: Coordinate Rules for ReflectionsProblem 5.2: Coordinate Rules for TranslationsProblem 5.3: Coordinate Rules for RotationsProblem 5.4: Coordinate Rules for Transformation

Combinations

PH Math Course 3 ©2008Lesson 3-6: TranslationsLab 3-7a: Exploring ReflectionsLesson 3-7: Reflections and SymmetryLab 3-8a: Exploring RotationsLesson 3-8: RotationsExtension: TessellationsLesson 7-3: Congruent PolygonsLesson 7-5: Angles and Polygons

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Say It With SymbolsProblem 1.1: Writing Equivalent ExpressionsProblem 1.2: Determining EquivalenceProblem 1.3: Interpreting ExpressionsProblem 1.4: Revisiting the Distributive PropertyProblem 2.1: Adding ExpressionsProblem 2.2: Substituting Equivalent ExpressionsProblem 2.3: Using EquationsProblem 3.1: Solving Linear EquationsProblem 3.2: Solving More Linear EquationsProblem 3.3: Factoring Quadratic ExpressionsProblem 3.4: Solving Quadratic EquationsProblem 4.1: Looking at Patterns of ChangeProblem 4.2: Linear, Exponential, QuadraticProblem 4.3: Sorting FunctionsProblem 5.1: Using Algebra to Solve a PuzzleProblem 5.2: Odd and Even RevisitedProblem 5.3: Squaring Odd Numbers

PH Math Course 3 ©2008Lesson 1-1: Algebraic Expressions and the Order of

OperationsLesson 1-5: Properties of Numbers (Distributive

Property Only)Lesson 2-7: Powers and Exponents (Evaluating

Expressions Only)Lab 6-2a: Modeling ExpressionsLesson 6-2: Simplifying Algebraic ExpressionsLesson 6-3: Solving Multi-Step EquationsLesson 6-4: Solving Equations with Variables on Both

SidesLesson 11-7: Quadratic and Other Nonlinear FunctionsLab 11-7b: Changing RepresentationsLesson 12-2: Adding and Subtracting PolynomialsLesson 12-4: Multiplying Polynomials

Shapes of AlgebraProblem 1.1: Equations for CirclesProblem 1.2: Parallels and PerpendicularsProblem 1.3: Finding MidpointsProblem 2.1: Graphs of Linear SystemsProblem 2.2: Linear InequalitiesProblem 2.3: Solving Linear InequalitiesProblem 3.1: Solving Equations with Two VariablesProblem 3.2: Connecting y = mx + b and ax + by= cProblem 3.3: Intersections of a LineProblem 4.1: The y = mx + b CaseProblem 4.2: Solving Systems by Writing Equivalent

FormsProblem 4.3: Solving Systems by SubstitutionProblem 4.4: Solving Systems by CombinationProblem 5.1: Graphing “No More than” SituationsProblem 5.2: Solving Linear Inequalities by GraphingProblem 5.3: Graphs of Linear InequalitiesProblem 5.4: Systems of Linear Inequalities

PH Math Course 3 ©2008Lab 3-4b: Finding the MidpointLab 3-5b: Graphing Linear Equations in Standard

FormLab 6-5a: Graphing InequalitiesLesson 6-5: Solving Inequalities by Adding or

SubtractingLab 6-6a: Inequalities and Negative NumbersLesson 6-6: Solving Inequalities by Multiplying or

DividingLab 6-6b: Systems of Linear Equations

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Samples and PopulationsProblem 1.1: From Line Plots to HistogramsProblem 1.2: Using HistogramsProblem 1.3: Box-and-Whisker PlotsProblem 1.4: Analyzing DataProblem 2.1: Using a Sample to Make PredictionsProblem 2.2: Selecting a SampleProblem 2.3: Choosing Random SamplesProblem 2.4: Choosing a Sample SizeProblem 3.1: Comparing and Analyzing DataProblem 3.2: Using a Simulation to Make a DecisionProblem 4.1: Interpreting ScatterplotsProblem 4.2: Writing an Equation to Describe a

RelationshipProblem 4.3: Analyzing a Relationship

PH Math Course 3 ©2008Lesson 9-1: Finding Mean, Median, and ModeLab 9-1b: Comparing Mean and MedianLesson 9-2: Displaying FrequencyLab 9-2b: Making HistogramsLesson 9-6: Box-and-Whisker PlotsLab 9-6b: Making Box-and-Whisker PlotsLab 9-7a: Scatter PlotsLesson 10-3: Conducting a SurveyLab 10-3b: Simulations with Random Numbers

CMP2 Replacement Unit Omit PH Math Pre-Algebra ©2007 Lessons

Variables & PatternsProblem 1.1: Interpreting GraphsProblem 1.2: Making GraphsProblem 1.3: Interpreting GraphsProblem 1.4: Reading Data from GraphsProblem 1.5: Finding Average SpeedProblem 2.1: Analyzing a Table and a GraphProblem 2.2: Making and Analyzing a GraphProblem 2.3: Interpreting GraphsProblem 3.1: Equations with One OperationProblem 3.2: Equations with Two OperationsProblem 3.3: Equations for Revenue, Expenses, and

ProfitProblem 4.1: Making and Using Calculator TablesProblem 4.2: Making and Using Calculator GraphsProblem 4.3: Comparing Relationships

PH Math Pre-Algebra ©2007Lesson 1-1: Variables and ExpressionsLesson 1-8: Look for a PatternLesson 6-10: Make a TableLab 8-3: Graphing Lines

Stretching & ShrinkingProblem 1.1: Introduction to SimilarityProblem 1.2: Comparing Similar FiguresProblem 1.3: Corresponding Sides and AnglesProblem 2.1: Enlarging a FigureProblem 2.2: Changing a Figure’s Size and LocationProblem 2.3: Scale FactorsProblem 3.1: Rep-Tile QuadrilateralsProblem 3.2: Rep-Tile TrianglesProblem 3.3: Scale Factors and Similar ShapesProblem 4.1: Ratios within Similar ParallelogramsProblem 4.2: Ratios within Similar TrianglesProblem 5.1: Using Shadows to Find HeightsProblem 5.2: Using Mirrors to Find HeightsProblem 5.3: Finding Lengths within Similar Triangles

PH Math Pre-Algebra ©2007Lesson 6-3: Similar Figures and Scale DrawingsLab 6-3: DilationsLab 9-8: Dilations on a Coordinate PlaneLab10-1: Perimeter and Area of Similar FiguresLesson 11-4: Write a Proportion

Comparing & ScalingProblem 1.1: Exploring Ratios and RatesProblem 1.2: Analyzing Comparison StatementsProblem 1.3: Writing Comparison StatementsProblem 2.1: Developing Comparison StrategiesProblem 2.2: Developing Comparison StrategiesProblem 2.3: Scaling RatiosProblem 3.1: Making and Using a Rate TableProblem 3.2: Finding RatesProblem 3.3: Unit Rates and EquationsProblem 3.4: Two Different RatesProblem 4.1: Setting Up and Solving ProportionsProblem 4.2: Applications of ProportionsProblem 4.3: Developing Strategies for Solving

Proportions

PH Math Pre-Algebra ©2007Lesson 6-1: Ratios and Unit RatesLesson 6-2: Proportions

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Accentuate the NegativeProblem 1.1: Using Positive and Negative NumbersProblem 1.2: Comparing and Ordering Positive and

Negative NumbersProblem 1.3: Using a Number Line ModelProblem 1.4: Using a Chip ModelProblem 2.1: Introducing Addition of IntegersProblem 2.2: Introducing Subtraction of IntegersProblem 2.3: Addition and Subtraction RelationshipsProblem 2.4: Coordinate GraphingProblem 3.1: Introducing Multiplication of IntegersProblem 3.2: Multiplication PatternsProblem 3.3: Introducing Division of IntegersProblem 3.4: Multiplying IntegersProblem 4.1: Order of OperationsProblem 4.2: Distributing OperationsProblem 4.3: The Distributive Property and Subtraction

PH Math Pre-Algebra ©2007Lesson 1-2: The Order of OperationsLesson 1-4: Integers and Absolute ValueLab 1-5: Modeling IntegersLesson 1-5: Adding IntegersLesson 1-6: Subtracting IntegersLesson 1-9: Multiplying and Dividing IntegersLesson 1-10: The Coordinate PlaneLesson 2-2: The Distributive PropertyLesson 4-2: Exponents (Using Order of Operations

Only)Lesson 4-6: Rational NumbersLesson 5-1: Comparing and Ordering Rational

Numbers

Moving Straight AheadProblem 1.1: Finding and Using RatesProblem 1.2: Linear Relationships in Tables, Graphs, and

EquationsProblem 1.3: Using Linear RelationshipsProblem 1.4: Recognizing Linear RelationshipsProblem 2.1: Finding the Point of IntersectionProblem 2.2: Using Tables, Graphs, and EquationsProblem 2.3: Comparing EquationsProblem 2.4: Connecting Tables, Graphs, and EquationsProblem 3.1: Solving Equations Using Tables and GraphsProblem 3.2: Exploring EqualityProblem 3.3: Writing EquationsProblem 3.4: Solving Linear EquationsProblem 3.5: Finding the Point of IntersectionProblem 4.1: Using Rise and RunProblem 4.2: Finding the Slope of a LineProblem 4.3: Exploring Patterns with LinesProblem 4.4: Writing Equations with Two Variables

PH Math Pre-Algebra ©2007Lab 2-5: Using Models with EquationsLesson 2-5: Solving Equations by Adding or SubtractingLesson 2-6: Solving Equations by Multiplying or

DividingLesson 7-1: Solving Two-Step EquationsLesson 7-4: Write an EquationLesson 8-2: Equations with Two VariablesLesson 8-3: Slope and y-interceptLesson 8-4: Writing Rules for Linear Functions

Filling and WrappingProblem 1.1: Making Cubic BoxesProblem 1.2: Making Rectangular BoxesProblem 1.3: Testing NetsProblem 14: Flattening a BoxProblem 2.1: Finding Surface AreaProblem 2.2: Finding the Least Surface AreaProblem 2.3: Finding Volume of a Rectangular PrismProblem 3.1: Finding the Volumes of Other PrismsProblem 3.2: Finding Volumes of CylindersProblem 3.3: Finding the Surface Area of Cylinders and

PrismsProblem 3.4: Comparing VolumesProblem 4.1: Comparing Spheres and CylindersProblem 4.2: Cones and Cylinders, Pyramids and CubesProblem 4.3: Comparing Volumes of Spheres, Cylinders,

and ConesProblem 5.1: Doubling the Volume of a Rectangular

PrismProblem 5.2: Applying Scale Factor to Rectangular

PrismsProblem 5.3: Similarity and Scale Factors

PH Math Pre-Algebra ©2007Lesson 3-4: Using FormulasLesson 10-4: Space FiguresLab 10-5: Wrapping CylindersLesson 10-5: Surface Area: Prisms and CylindersLesson 10-6: Surface Area: Pyramids, Cones, and

SpheresLesson 10-7: Volume: Prisms and CylindersLesson 10-8: Make a ModelLesson 10-9: Volume: Pyramids, Cones, and SpheresLab 10-9: Scaling and Volume

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What Do You Expect?Problem 1.1: Experimental and Theoretical ProbabilityProblem 1.2: Using an Organized ListProblem 1.3: Determining Whether a Game Is FairProblem 2.1: Area Models and ProbabilityProblem 2.2: Using an Area ModelProblem 2.3: Finding the Best ArrangementProblem 3.1: Simulating a Probability SituationProblem 3.2: Finding Expected ValueProblem 3.3: Comparing Expected ValuesProblem 4.1: Finding More Expected ValuesProblem 4.2: Binomial ProbabilityProblem 4.3: Expanding Binomial Probability

PH Math Pre-Algebra ©2007Lesson 6-4: ProbabilityLesson 12-4: Counting Outcomes and Theoretical

ProbabilityLesson 12-5: Independent and Dependent EventsLab 12-7: Simulating an EventLesson 12-7: Experimental Probability

Thinking with Math ModelsProblem 1.1: Finding Patterns and Making PredictionsProblem 1.2: Finding Patterns and Making PredictionsProblem 1.3: Extending PatternsProblem 2.1: Linear ModelsProblem 2.2: Equations RelationshipsProblem 2.3: Solving Linear EquationsProblem 2.4: Intersecting Linear ModelsProblem 3.1: Relating Length and WidthProblem 3.2: Inverse Variation PatternsProblem 3.3: Inverse Variation Patterns

PH Math Pre-Algebra ©2007Lesson 3-4: Using FormulasLesson 7-2: Solving Multi-Step EquationsLesson 7-5: Solving Equations with Variables on Both

SidesLab 8-1: Relating Graphs to EventsLesson 8-6: Solving by Graphing

Looking for PythagorasProblem 1.1: Locating Points and Finding DistancesProblem 1.2: Shapes on a Coordinate GridProblem 1.3: Finding AreasProblem 2.1: Looking for SquaresProblem 2.2: Square RootsProblem 2.3: Using Squares to Find LengthsProblem 3.1: The Pythagorean TheoremProblem 3.2: A Proof of the Pythagorean TheoremProblem 3.3: Finding DistancesProblem 3.4: Lengths That Form a Right TriangleProblem 4.1: Analyzing the Wheel of TheodorusProblem 4.2: Finding Unknown Side LengthsProblem 4.3: Analyzing TrianglesProblem 4.4: Finding the Perimeter

PH Math Pre-Algebra ©2007Lesson 5-2: Fractions and DecimalsLesson 11-1: Square Roots and Irrational NumbersLesson 11-2: The Pythagorean TheoremLesson 11-5: Special Right Triangles

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Growing, Growing, GrowingProblem 1.1: Introducing Exponential RelationshipsProblem 1.2: Representing Exponential RelationshipsProblem 1.3: Growth FactorsProblem 1.4: Comparing Growth FactorsProblem 2.1: Y-Intercepts Other Than 1Problem 2.2: Interpreting Exponential EquationsProblem 2.3: Interpreting Exponential GraphsProblem 3.1: Fractional Growth FactorsProblem 3.2: Growth RatesProblem 3.3: Connecting Growth Rate and Growth

FactorProblem 4.1: Introducing Exponential DecayProblem 4.2: Representing Exponential DecayProblem 4.3: Modeling Exponential DecayProblem 5.1: Predicting the Ones DigitProblem 5.2: Operating with ExponentsProblem 5.3: Exploring Exponential Equations

PH Math Pre-Algebra ©2007Lab 4-2: Patterns & ExponentsLesson 4-2: Exponents (Using an Exponent Only)Lesson 4-7: Exponents and MultiplicationLesson 4-8: Exponents and DivisionLesson 4-9: Scientific NotationLesson 5-9: Powers of Products and QuotientsLesson 6-8: Percent of ChangeLesson 7-8: Simple and Compound InterestLesson 13-3: Exponential Growth and Decay

Kaleidoscopes, Hubcaps, and MirrorsProblem 1.1: Reflection SymmetryProblem 1.2: Rotation SymmetryProblem 1.3: Analyzing SymmetriesProblem 1.4: Translation SymmetryProblem 2.1: Describing Line ReflectionsProblem 2.2: Describing RotationsProblem 2.3: Describing TranslationsProblem 2.4: Using Symmetry to Think About

TessellationsProblem 3.1: Relating Symmetry and CongruenceProblem 3.2: Congruent TrianglesProblem 3.3: Congruent TrianglesProblem 3.4: Side Lengths and CongruenceProblem 4.1: Finding Distances Without MeasuringProblem 4.2: Using Symmetry to Find Properties of

ShapesProblem 5.1: Coordinate Rules for ReflectionsProblem 5.2: Coordinate Rules for TranslationsProblem 5.3: Coordinate Rules for RotationsProblem 5.4: Coordinate Rules for Transformation

Combinations

PH Math Pre-Algebra ©2007Lesson 9-5: CongruenceLesson 9-8: TranslationsLesson 9-9: Symmetry and ReflectionsLesson 9-10: RotationsLab 9-10: Tessellations

Samples and PopulationsProblem 1.1: From Line Plots to HistogramsProblem 1.2: Using HistogramsProblem 1.3: Box-and-Whisker PlotsProblem 1.4: Analyzing DataProblem 2.1: Using a Sample to Make PredictionsProblem 2.2: Selecting a SampleProblem 2.3: Choosing Random SamplesProblem 2.4: Choosing a Sample SizeProblem 3.1: Comparing and Analyzing DataProblem 3.2: Using a Simulation to Make a DecisionProblem 4.1: Interpreting ScatterplotsProblem 4.2: Writing an Equation to Describe a

RelationshipProblem 4.3: Analyzing a Relationship

PH Math Pre-Algebra ©2007Lesson 3-3: Mean, Median, and ModeLesson 8-5: ScatterplotsLesson 12-1: Frequency Tables, Line Plots, and

HistogramsLesson 12-2: Box-and-Whisker PlotsLesson 12-8: Random Samples and SurveysLesson 12-9: Simulate a ProblemLab 12-9: Using Random Numbers

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