new a guide to using connected mathematics...

Using the Best of Both!

A Guide to UsingConnected Mathematics 2

withPrentice Hall Mathematics

Courses 1, 2, 3 ©2012, and Algebra Readiness

MatBro111707BestOfBothPH10&CMP2.indd 1 6/7/11 11:59 AM

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Using the Best of Both!Pearson is proud to produce two outstanding middle grades mathematics curriculums, Prentice Hall Mathematics and Connected Mathematics 2 (CMP2). This guide will show how you can use the “Best of Both” programs in your classroom.

Below you will find guidelines for replacing lessons from Prentice Hall Mathematics Course 1, Course 2, Course 3, and Algebra Readiness 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 the CMP2 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 its entirety, 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 a deep understanding of the math content found within the unit.

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

• Be Mindful of Time—Prentice Hall Mathematics lessons and CMP2 problems may have different pacing requirements. Refer to the Prentice Hall Mathematics Teacher’s Edition and CMP2 Teacher’s Guide for guidance.

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

MatBro111707BestOfBothPH10&CMP2.indd 2 6/7/11 12:00 PM

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PHSchool.com/cmp2/bestofboth

Grade 6 CMP2 Replacement Unit Omit PH Math Course 1 ©2012 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 Even and Odd 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 ©2012Lesson 4-3: Prime Numbers and Prime FactorizationLesson 4-4: Greatest Common FactorLesson 4-7: Least Common Multiple

Bits and 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 ©2012Lab 1-5a: Exploring Decimal ModelsLesson 1-5: Understanding DecimalsLesson 1-6: Comparing and 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 and Ordering FractionsLesson 4-9: Fractions and DecimalsLab 7-6a: Modeling PercentsLesson 7-6: Percents, Fractions, and Decimals

GRade 6


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Shapes and 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: Measuring AnglesProblem 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 TilingsProblem 3.4: Exterior Angles of PolygonsProblem 4.1: Building TrianglesProblem 4.2: Building QuadrilateralsProblem 4.3: Properties of Quadrilaterals

PH Math Course 1 ©2012Lab 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 and Pieces IIProblem 1.1: Using BenchmarksProblem 1.2: EstimatingProblem 2.1: Writing Addition and Subtraction SentencesProblem 2.2: Using Addition and Subtraction Problem 2.3: Fact FamiliesProblem 2.4: Designing Algorithms for Addition

and SubtractionProblem 3.1: A Model for MultiplicationProblem 3.2: Another Model for Multiplication Problem 3.3: Modeling More Multiplication SituationsProblem 3.4: Multiplication with Mixed NumbersProblem 3.5: Writing a Multiplication AlgorithmProblem 4.1: Dividing a Whole Number by a FractionProblem 4.2: Dividing a Fraction by a Whole NumberProblem 4.3: Dividing a Fraction by a FractionProblem 4.4: Writing a Division Algorithm

PH Math Course 1 ©2012Lesson 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 and 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: Perimeters and Irregular ShapesProblem 2.3: Constant Perimeter, Changing AreaProblem 2.4: Increasing Area and PerimeterProblem 3.1: Finding Area and PerimeterProblem 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 Perimeter and AreaProblem 5.2: Finding CircumferenceProblem 5.3: Exploring Area and CircumferenceProblem 5.4: Finding Area

PH Math Course 1 ©2012Lesson 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 and 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 RelationshipsProblem 3.1: Deciphering Decimal SituationsProblem 3.2: Using Common Denominators

to Divide FractionsProblem 3.3: Exploring Dividing DecimalsProblem 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 ©2012Lab 1-7a: Using ModelsLesson 1-7: Adding and 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% or 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 ©2012Lesson 10-1: Tree Diagrams and the Counting PrincipleLesson 10-2: ProbabilityLesson 10-3: Experimental ProbabilityLab 10-3b: Experimental and Theoretical ProbabilitiesLesson 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 ©2012Lab 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 the Coordinate Plane


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GRade 7


Variables and PatternsProblem 1.1: Interpreting TablesProblem 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 ©2012Lab 2-6b: Using Tables to Compare DataLab 4-1a: Describing PatternsLesson 4-1: E valuating 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: Exploring 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 Scatter Plots

Stretching and ShrinkingProblem 1.1: Introduction to SimilarityProblem 1.2: Comparing Similar FiguresProblem 1.3: Corresponding Sides and AnglesProblem 2.1: Making Similar FiguresProblem 2.2: Changing a Figure’s Size and LocationProblem 2.3: Scale FactorsProblem 3.1: Forming Rep-Tiles with Similar

QuadrilateralsProblem 3.2: Forming Rep-Tiles with Similar 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 with Similar Triangles

PH Math Course 2 ©2012Lesson 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 the Coordinate PlaneLesson 10-5: Translations


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Comparing and ScalingProblem 1.1: Exploring Ratios and RatesProblem 1.2: Analyzing Comparison StatementsProblem 1.3: Writing Comparison StatementsProblem 2.1: Developing Comparison StrategiesProblem 2.2: More 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 ©2012Lesson 2-4: Comparing and 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 2.5: 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 ©2012Lesson 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 ©2012Lab 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 1.4: 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 Factors to Rectangular PrismsProblem 5.3: Similarity and Scale Factors

PH Math Course 2 ©2012Lab 8-8a: Three Views of an ObjectLesson 8-8: Three-Dimensional FiguresLesson 8-9: Surface Areas of Prisms and CylindersLesson 8-10: Volumes 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 ©2012Lesson 12-1: ProbabilityLab 12-2a: Exploring ProbabilityLesson 12-2: Experimental ProbabilityLab 12-3b: Using Data to PredictLab 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 Many Data ValuesProblem 3.4: Comparing Larger DistributionsProblem 4.1: Representing Survey DataProblem 4.2: Comparing Speed

PH Math Course 2 ©2012Lesson 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 ©2012 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 Scatter PlotsLab 9-7b: Plotting a StrategyLesson 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 ©2012Lab 2-2b: Repeating DecimalsLesson 3-1: Exploring Square Roots and

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

GRade 8


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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 ©2012 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 ©2012Lesson 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 ©2012Lesson 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 Sides Lesson 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 ©2012Lab 3-4b: Finding the MidpointLab 3-5b: Matching GraphsLab 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 Dividing


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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 Scatter PlotsProblem 4.2: Writing an Equation to Describe

a RelationshipProblem 4.3: Analyzing a Relationship

PH Math Course 3 ©2012Lesson 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


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GRade 7

Grade 7 CMP2 Replacement Unit Omit PH Math algebra Readiness ©2010 Lessons

Variables and PatternsProblem 1.1: Interpreting TablesProblem 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 Algebra Readiness ©2010Lesson 1-1: Variables and ExpressionsLesson 1-3: Writing and Evaluating ExpressionsLesson 1-8: Look for a PatternLesson 2-4: Variables and EquationsLesson 2-5: Solving Equations by Adding or SubtractingLesson 2-6: Solving Equations by Multiplying or DividingLesson 3-4: Solving Equations by Adding or

Subtracting DecimalsLesson 3-5: Solving Equations by Multiplying or

Dividing DecimalsLesson 6-10: Make a TableLab 8-3: Graphing Lines

Stretching and ShrinkingProblem 1.1: Introduction to SimilarityProblem 1.2: Comparing Similar FiguresProblem 1.3: Corresponding Sides and AnglesProblem 2.1: Making Similar FiguresProblem 2.2: Changing a Figure’s Size and LocationProblem 2.3: Scale FactorsProblem 3.1: Forming Rep-Tiles with Similar QuadrilateralsProblem 3.2: Forming Rep-Tiles with Similar 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 with Similar Triangles

PH Math Algebra Readiness ©2010Lesson 6-3: Similar Figures and Scale DrawingsLab 6-3: DilationsLab 9-8: Dilations in the Coordinate PlaneLab 10-1: Perimeter and Area of Similar FiguresLesson 11-4: Write a Proportion

Comparing and ScalingProblem 1.1: Exploring Ratios and RatesProblem 1.2: Analyzing Comparison StatementsProblem 1.3: Writing Comparison StatementsProblem 2.1: Developing Comparison StrategiesProblem 2.2: More 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 Algebra Readiness ©2010Lesson 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 2.5: 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 Algebra Readiness ©2010Lesson 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)

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 Algebra Readiness ©2010Lab 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-intercept

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 Factors to Rectangular PrismsProblem 5.3: Similarity and Scale Factors

PH Math Algebra Readiness ©2010Lesson 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 SpheresLesson 10-10: Scale Factors and Solids


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GRade 8


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 Algebra Readiness ©2010Lesson 3-3: Using FormulasLesson 7-1: Solving Two-Step EquationsLesson 7-2: Solving Multi-Step EquationsLesson 7-3: Two-Step Equations with Fractions

and DecimalsLesson 7-5: Solving Two-Step InequitiesLesson 7-6: Transforming FormulasLab 8-1: Relations and 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 Algebra Readiness ©2010Lesson 1-10: The Coordinate PlaneLesson 5-2: Fractions and DecimalsLesson 11-1: Square Roots and Irrational NumbersLesson 11-2: The Pythagorean TheoremLesson 11-3: Distance and Midpoint Formulas


18


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 Algebra Readiness ©2010Lab 4-2: Patterns and ExponentsLesson 4-2: ExponentsLesson 4-7: Exponents and MultiplicationLesson 4-8: Exponents and DivisionLesson 4-9: Scientific NotationLesson 5-9: Powers of Products and QuotientsLesson 6-7: Percent of ChangeLesson 7-7: Simple and Compound Interest

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 Algebra Readiness ©2010Lesson 9-5: CongruenceLesson 9-8: TranslationsLesson 9-9: Symmetry and ReflectionsLesson 9-10: Rotations

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 Scatter PlotsProblem 4.2: Writing an Equation to Describe

a RelationshipProblem 4.3: Analyzing a Relationship

PH Math Algebra Readiness ©2010Lesson 12-1: Mean, Median, and ModeLesson 12-2: Frequency Tables, Line Plots,

and HistogramsLesson 12-3: Box-and-Whisker PlotsLesson 12-5: Scatter Plots


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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 Algebra Readiness ©2010Lesson 1-1: Variables and ExpressionsLesson 1-2: The Order of OperationsLesson 1-3: Writing and Evaluating ExpressionsLesson 2-1: Properties of NumbersLesson 2-3: Simplifying Algebraic ExpressionsLesson 2-4: Variables and Equations Lesson 4-2: ExponentsLesson 7-2: Solving Multi-Step EquationsLesson 7-3: Two-Step Equations with Fractions

and Decimals

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 Algebra Readiness ©2010Lesson 2-8: Inequalities and their GraphsLesson 2-9: Solving One-Step Inequalities by

Adding or SubtractingLesson 2-10: Solving One-Step Inequalities by

Multiplying or DividingLesson 7-5: Solving Two-Step InequalitiesLesson 8-6: Solving Systems of Linear EquationsLesson 8-7: Graphing Linear Inequalities Lesson 11-3: Distance and Midpoint Formulas


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