Using the Best of Both!

Transcription

1 Using the Best of Both! A Guide to Using Connected Mathematics 2 with Prentice Hall Mathematics Courses 1, 2, , and Algebra Readiness MatBro111707BestOfBothPH10&CMP2.indd 1 6/7/11 11:59 AM

2 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 Units In 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 Classroom In 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. 2

3 Grade 6 Grade 6 CMP2 Replacement Unit Omit PH Math Course Lessons Prime Time Problem 1.1: Problem 1.2: Problem 1.3: Problem 2.1: Problem 2.2: Problem 2.3: Problem 3.1: Problem 3.2: Problem 3.3: Problem 3.4: Problem 4.1: Problem 4.2: Problem 4.3: Problem 5.1: Finding Proper Factors Prime and Composite Numbers Finding Multiples Rectangles and Factor Pairs Reasoning with Even and Odd Numbers Classifying Numbers Choosing Common Multiples or Common Factors Choosing Common Multiples or Common Factors Choosing Common Multiples or Common Factors Choosing Common Multiples or Common Factors Finding Factor Strings Finding the Longest Factor String Using Prime Factorization Using Multiples and Factors PH Math Course Lesson 4-3: Prime Numbers and Prime Factorization Lesson 4-4: Greatest Common Factor Lesson 4-7: Least Common Multiple Bits and Pieces I Problem 1.1: Whole Numbers and Fractions Problem 1.2: Folding Fraction Strips Problem 1.3: Finding Fractional Parts Problem 1.4: Using Fractions to Compare Problem 2.1: Equivalent Fractions and Equal Shares Problem 2.2: Finding Equivalent Fractions Problem 2.3: Comparing Fractions to Benchmarks Problem 2.4: Fractions Between Fractions Problem 2.5: Naming Fractions Greater than 1 Problem 3.1: Using Tenths and Hundredths Problem 3.2: Place Values Greater than Hundredths Problem 3.3: Decimal Benchmarks Problem 3.4: Moving from Fractions to Decimals Problem 3.5: Ordering Decimals Problem 4.1: Making Sense of Percents Problem 4.2: Using Percents to Compare Problem 4.3: Expressing Data in Percent Form Problem 4.4: Moving Between Representations PH Math Course Lab 1-5a: Exploring Decimal Models Lesson 1-5: Understanding Decimals Lesson 1-6: Comparing and Ordering Decimals Lab 1-8b: Multiplying and Dividing Decimals by 10, 100, and 1,000 Lab 4-5a: Modeling Fractions Lesson 4-5: Equivalent Fractions Lab 4-6a: Exploring Improper Fractions Lesson 4-6: Mixed Numbers and Improper Fractions Lesson 4-8: Comparing and Ordering Fractions Lesson 4-9: Fractions and Decimals Lab 7-6a: Modeling Percents Lesson 7-6: Percents, Fractions, and Decimals 3

4 Grade 6 CMP2 Replacement Unit Omit PH Math Course Lessons Shapes and Designs Problem 1.1: Classifying Polygons Problem 1.2: Symmetry Problem 1.3: Tiling with Regular Polygons Problem 2.1: Understanding Angles Problem 2.2: Developing Angle Benchmarks Problem 2.3: Measuring Angles Problem 2.4: Analyzing Measurement Errors Problem 2.5: Angles and Parallel Lines Problem 3.1: Angle Sums of Regular Polygons Problem 3.2: Angle Sums of Any Polygon Problem 3.3: Interior Angles and Tilings Problem 3.4: Exterior Angles of Polygons Problem 4.1: Building Triangles Problem 4.2: Building Quadrilaterals Problem 4.3: Properties of Quadrilaterals PH Math Course Lab 8-2a: Using Angle Benchmarks Lesson 8-2: Angles Lab 8-3b: Exploring Parallel Lines Lab 8-4a: Investigating Angles in a Triangle Lesson 8-4: Classifying Triangles Lab 8-5a: Angles in a Quadrilateral Lesson 8-5: Exploring and Classifying Polygons Lesson 8-7: Line Symmetry Lab 8-8b: Tessellations Bits and Pieces II Problem 1.1: Using Benchmarks Problem 1.2: Estimating Problem 2.1: Writing Addition and Subtraction Sentences Problem 2.2: Using Addition and Subtraction Problem 2.3: Fact Families Problem 2.4: Designing Algorithms for Addition and Subtraction Problem 3.1: A Model for Multiplication Problem 3.2: Another Model for Multiplication Problem 3.3: Modeling More Multiplication Situations Problem 3.4: Multiplication with Mixed Numbers Problem 3.5: Writing a Multiplication Algorithm Problem 4.1: Dividing a Whole Number by a Fraction Problem 4.2: Dividing a Fraction by a Whole Number Problem 4.3: Dividing a Fraction by a Fraction Problem 4.4: Writing a Division Algorithm PH Math Course Lesson 5-1: Estimating Sums and Differences Lab 5-2a: Modeling Fraction Operations Lesson 5-2: Fractions with Like Denominators Lab 5-3a: Modeling Unlike Denominators Lesson 5-3: Fractions with Unlike Denominators Lab 5-4a: Using Mixed Numbers Lesson 5-4: Adding Mixed Numbers Lesson 5-5: Subtracting Mixed Numbers Lesson 5-6: Equations with Fractions Lab 6-1a: Modeling Fraction Multiplication Lesson 6-1: Multiplying Fractions Lesson 6-2: Multiplying Mixed Numbers Lab 6-3a: Fraction Division Lesson 6-3: Dividing Fractions Lesson 6-4: Dividing Mixed Numbers Lesson 6-5: Solving Fraction Equations by Multiplying 4

5 Grade 6 CMP2 Replacement Unit Omit PH Math Course Lessons Covering and Surrounding Problem 1.1: Understanding Area and Perimeter Problem 1.2: Finding Area and Perimeter Problem 1.3: Finding Area and Perimeter of Rectangles Problem 2.1: Constant Area, Changing Perimeter Problem 2.2: Perimeters and Irregular Shapes Problem 2.3: Constant Perimeter, Changing Area Problem 2.4: Increasing Area and Perimeter Problem 3.1: Finding Area and Perimeter Problem 3.2: Identifying Base and Height Problem 3.3: Triangle Families Problem 3.4: Designing Triangle under Constraints Problem 4.1: Finding Measures of Parallelograms Problem 4.2: Parallelograms from Triangles Problem 4.3: Designing Parallelograms under Constraints Problem 4.4: Finding Areas and Perimeters Problem 5.1: Estimating Perimeter and Area Problem 5.2: Finding Circumference Problem 5.3: Exploring Area and Circumference Problem 5.4: Finding Area PH Math Course Lesson 9-3: Perimeters and Areas of Rectangles Lab 9-4a: Comparing Areas Lesson 9-4: Areas of Parallelograms and Triangles Lab 9-5a: Exploring Circles Lesson 9-5 Circles and Circumference Lesson 9-6: Area of a Circle Bits and Pieces III Problem 1.1: Estimating with Decimals Problem 1.2: Adding and Subtracting Decimals Problem 1.3: Using Fractions to Add and Subtract Decimals Problem 1.4: Decimal Sum and Difference Algorithms Problem 2.1: Relating Fraction and Decimal Multiplication Problem 2.2: Missing Factors Problem 2.3: Finding Decimal Products Problem 2.4: Factor-Product Relationships Problem 3.1: Deciphering Decimal Situations Problem 3.2: Using Common Denominators to Divide Fractions Problem 3.3: Exploring Dividing Decimals Problem 3.4: Representing Fractions as Decimals Problem 4.1: Determining Tax Problem 4.2: Computing Tips Problem 4.3: Using Discounts Problem 5.1: Finding Percent Discounts Problem 5.2: Solving Percent Problems Problem 5.3: Making Circle Graphs PH Math Course Lab 1-7a: Using Models Lesson 1-7: Adding and Subtracting Decimals Lab 1-8a: Modeling Decimal Multiplication Lesson 1-8: Multiplying Decimals Lesson 1-9: Dividing Decimals Lesson 7-7: Finding the Percent of a Number Lesson 7-8: Circle Graphs Lesson 7-9: Estimating with Percents Extension: Percents Under 1% or Over 100% 5

6 Grade 6 CMP2 Replacement Unit Omit PH Math Course Lessons How Likely Is It? Problem 1.1: Finding Probabilities with a Coin Problem 1.2: Finding More Probabilities Problem 1.3: Finding Experimental Probabilities Problem 1.4: Understanding Equally Likely Events Problem 2.1: Finding Theoretical Probabilities Problem 2.2: Exploring Probabilities Problem 2.3: Using Strategies to Find Theoretical Probabilities Problem 2.4: Pondering Possible and Probable Problem 3.1: Finding Probabilities with a Spinner Problem 3.2: Analyzing Fairness Problem 3.3: Using a Simulation Problem 4.1: Applying Experimental Probability Problem 4.2: Applying Theoretical Probability Problem 4.3: Analyzing a Game PH Math Course Lesson 10-1: Tree Diagrams and the Counting Principle Lesson 10-2: Probability Lesson 10-3: Experimental Probability Lab 10-3b: Experimental and Theoretical Probabilities Lesson 10-4: Making Predictions from Data Data About Us Problem 1.1: Organizing and Interpreting Data Problem 1.2: Useful Statistics Problem 1.3: Experimenting with Median Problem 1.4: Using Different Data Types Problem 1.5: Vertical Bar Graphs and Horizontal Bar Graphs Problem 2.1: Making a Stem-and-Leaf Plot Problem 2.2: Comparing Distributions Problem 2.3: Making and Reading Coordinate Graphs Problem 2.4: Using Coordinate Graphs to Find Relationships Problem 3.1: Finding the Mean Problem 3.2: Data with the Same Mean Problem 3.3: Using the Mean PH Math Course Lab 2-1a: Exploring the Mean Lesson 2-1: Finding the Mean Lesson 2-2: Median and Mode Lesson 2-3: Frequency Tables and Line Plots Lesson 2-4: Bar Graphs and Line Graphs (Bar Graphs Only) Lesson 2-6: Stem-and-Leaf Plots Lesson 2-7: Misleading Graphs and Statistics Lesson 11-8: Graphing in the Coordinate Plane 6

7 Grade 7 Grade 7 CMP2 Replacement Unit Omit PH Math Course Lessons Variables and Patterns Problem 1.1: Interpreting Tables Problem 1.2: Making Graphs Problem 1.3: Interpreting Graphs Problem 1.4: Reading Data from Graphs Problem 1.5: Finding Average Speed Problem 2.1: Analyzing a Table and a Graph Problem 2.2: Making and Analyzing a Graph Problem 2.3: Interpreting Graphs Problem 3.1: Equations with One Operation Problem 3.2: Equations with Two Operations Problem 3.3: Equations for Revenue, Expenses, and Profit Problem 4.1: Making and Using Calculator Tables Problem 4.2: Making and Using Calculator Graphs Problem 4.3: Comparing Relationships PH Math Course Lab 2-6b: Using Tables to Compare Data Lab 4-1a: Describing Patterns Lesson 4-1: E valuating and Writing Algebraic Expressions Lab 4-3a: Modeling Equations Lesson 4-3: Solving Equations by Adding or Subtracting Lesson 4-4: Solving Equations by Multiplying or Dividing Lesson 4-5: Exploring Two-Step Problems Lab 9-1a: Choosing Scales and Intervals Lesson 9-1: Patterns and Graphs Lesson 9-3: Patterns and Tables Lesson 9-6: Interpreting Graphs Lesson 10-4: Graphing Nonlinear Relationships Lab 11-7a: Two-Variable Data Collection Lesson 11-7: Exploring Scatter Plots Stretching and Shrinking Problem 1.1: Introduction to Similarity Problem 1.2: Comparing Similar Figures Problem 1.3: Corresponding Sides and Angles Problem 2.1: Making Similar Figures Problem 2.2: Changing a Figure s Size and Location Problem 2.3: Scale Factors Problem 3.1: Forming Rep-Tiles with Similar Quadrilaterals Problem 3.2: Forming Rep-Tiles with Similar Triangles Problem 3.3: Scale Factors and Similar Shapes Problem 4.1: Ratios within Similar Parallelograms Problem 4.2: Ratios within Similar Triangles Problem 5.1: Using Shadows to Find Heights Problem 5.2: Using Mirrors to Find Heights Problem 5.3: Finding Lengths with Similar Triangles PH Math Course Lesson 2-3: Simplifying Fractions Lab 5-5a: Exploring Similar Figures Lesson 5-5: Using Similar Figures Lab 5-6a: Scale Drawings and Models Lesson 5-6: Maps and Scale Drawings Lab 10-1b: Geometry in the Coordinate Plane Lesson 10-5: Translations 7

8 Grade 7 CMP2 Replacement Unit Omit PH Math Course Lessons Comparing and Scaling Problem 1.1: Exploring Ratios and Rates Problem 1.2: Analyzing Comparison Statements Problem 1.3: Writing Comparison Statements Problem 2.1: Developing Comparison Strategies Problem 2.2: More Comparison Strategies Problem 2.3: Scaling Ratios Problem 3.1: Making and Using a Rate Table Problem 3.2: Finding Rates Problem 3.3: Unit Rates and Equations Problem 3.4: Two Different Rates Problem 4.1: Setting Up and Solving Proportions Problem 4.2: Applications of Proportions Problem 4.3: Developing Strategies for Solving Proportions PH Math Course Lesson 2-4: Comparing and Ordering Fractions Lesson 5-1: Ratios Lesson 5-2: Unit Rates and Proportional Reasoning Lesson 5-3: Proportions Lab 5-4a: Using Proportions with Data Lesson 5-4: Solving Proportions Lesson 11-5: Estimating Population Size Accentuate the Negative Problem 1.1: Using Positive and Negative Numbers Problem 1.2: Comparing and Ordering Positive and Negative Numbers Problem 1.3: Using a Number Line Model Problem 1.4: Using a Chip Model Problem 2.1: Introducing Addition of Integers Problem 2.2: Introducing Subtraction of Integers Problem 2.3: Addition and Subtraction Relationships Problem 2.5: Coordinate Graphing Problem 3.1: Introducing Multiplication of Integers Problem 3.2: Multiplication Patterns Problem 3.3: Introducing Division of Integers Problem 3.4: Multiplying Integers Problem 4.1: Order of Operations Problem 4.2: Distributing Operations Problem 4.3: The Distributive Property and Subtraction PH Math Course Lesson 1-6: Comparing and Ordering Integers Lab 1-7a: Modeling Integer Addition and Subtraction Lesson 1-7: Adding and Subtracting Integers Lab 1-8a: Modeling Integer Multiplication Lesson 1-8: Multiplying and Dividing Integers Lesson 1-9: Order of Operations and the Distributive Property Lab 1-9b: Properties and Equality Lesson 2-1: Exponents and Order of Operations Lesson 2-7: Rational Numbers Lesson 10-1: Graphing Points in Four Quadrants 8

9 Grade 7 CMP2 Replacement Unit Omit PH Math Course Lessons Moving Straight Ahead Problem 1.1: Problem 1.2: Problem 1.3: Problem 1.4: Problem 2.1: Problem 2.2: Problem 2.3: Problem 2.4: Problem 3.1: Problem 3.2: Problem 3.3: Problem 3.4: Problem 3.5: Problem 4.1: Problem 4.2: Problem 4.3: Problem 4.4: Finding and Using Rates Linear Relationships in Tables, Graphs, and Equations Using Linear Relationships Recognizing Linear Relationships Finding the Point of Intersection Using Tables, Graphs, and Equations Comparing Equations Connecting Tables, Graphs, and Equations Solving Equations Using Tables and Graphs Exploring Equality Writing Equations Solving Linear Equations Finding the Point of Intersection Using Rise and Run Finding the Slope of a Line Exploring Patterns with Lines Writing Equations with Two Variables PH Math Course Lab 4-2b: Keeping the Balance Lesson 4-2: Using Number Sense to Solve Equations Lab 4-3a: Modeling Equations Lab 4-6a: Modeling Two-Step Equations Lesson 4-6: Solving Two-Step Equations Lab 5-3b: Interpreting Rates Visually Lesson 9-5: Using Tables, Rules, and Graphs Lab 9-5b: Three Views of a Function Lesson 10-2: Graphing Linear Equations Lab 10-2b: Representing Data Lesson 10-3: Finding the Slope of a Line Lab 10-3b: Exploring Slope Filling and Wrapping Problem 1.1: Making Cubic Boxes Problem 1.2: Making Rectangular Boxes Problem 1.3: Testing Nets Problem 1.4: Flattening a Box Problem 2.1: Finding Surface Area Problem 2.2: Finding the Least Surface Area Problem 2.3: Finding Volume of a Rectangular Prism Problem 3.1: Finding the Volumes of Other Prisms Problem 3.2: Finding Volumes of Cylinders Problem 3.3: Finding the Surface Area of Cylinders and Prisms Problem 3.4: Comparing Volumes Problem 4.1: Comparing Spheres and Cylinders Problem 4.2: Cones and Cylinders, Pyramids and Cubes Problem 4.3: Comparing Volumes of Spheres, Cylinders, and Cones Problem 5.1: Doubling the Volume of a Rectangular Prism Problem 5.2: Applying Scale Factors to Rectangular Prisms Problem 5.3: Similarity and Scale Factors PH Math Course Lab 8-8a: Three Views of an Object Lesson 8-8: Three-Dimensional Figures Lesson 8-9: Surface Areas of Prisms and Cylinders Lesson 8-10: Volumes of Prisms and Cylinders Lab 8-10b: Generating Formulas for Volume 9

10 Grade 7 CMP2 Replacement Unit Omit PH Math Course Lessons What Do You Expect? Problem 1.1: Experimental and Theoretical Probability Problem 1.2: Using an Organized List Problem 1.3: Determining Whether a Game Is Fair Problem 2.1: Area Models and Probability Problem 2.2: Using an Area Model Problem 2.3: Finding the Best Arrangement Problem 3.1: Simulating a Probability Situation Problem 3.2: Finding Expected Value Problem 3.3: Comparing Expected Values Problem 4.1: Finding More Expected Values Problem 4.2: Binomial Probability Problem 4.3: Expanding Binomial Probability PH Math Course Lesson 12-1: Probability Lab 12-2a: Exploring Probability Lesson 12-2: Experimental Probability Lab 12-3b: Using Data to Predict Lab 12-4a: Exploring Multiple Events Lesson 12-4: Compound Events Data Distributions Problem 1.1: Variability in Categorical Data Problem 1.2: Variability in Numerical Counts Problem 1.3: Variability in Numerical Measurements Problem 1.4: Two Kinds of Variability Problem 2.1: The Mean as an Equal Share Problem 2.2: The Mean as a Balance Point in Distribution Problem 2.3: Repeated Values in a Distribution Problem 2.4: Median and Mean and Shapes of Distribution Problem 3.1: Measuring and Describing Reaction Times Problem 3.2: Comparing Reaction Times Problem 3.3: Comparing Many Data Values Problem 3.4: Comparing Larger Distributions Problem 4.1: Representing Survey Data Problem 4.2: Comparing Speed PH Math Course Lesson 1-10: Mean, Median, Mode, and Range Lesson 11-1: Reporting Frequency 10

11 Grade 8 Grade 8 CMP2 Replacement Unit Omit PH Math Course Lessons Thinking with Math Models Problem 1.1: Finding Patterns and Making Predictions Problem 1.2: Finding Patterns and Making Predictions Problem 1.3: Extending Patterns Problem 2.1: Linear Models Problem 2.2: Equations for Linear Relationships Problem 2.3: Solving Linear Equations Problem 2.4: Intersecting Linear Models Problem 3.1: Relating Length and Width Problem 3.2: Inverse Variation Patterns Problem 3.3: Inverse Variation Patterns PH Math Course Lab 2-6b: Using Formulas Lab 3-5a: Tables and Graphs Lesson 3-5: Equations, Tables, and Graphs Lab 4-1b: Finding Rates Lesson 6-1: Solving Two-Step Equations Lesson 9-4: Reading Graphs Critically Lab 9-4b: Making Graphs Tell a Story Lesson 9-7: Making Predictions from Scatter Plots Lab 9-7b: Plotting a Strategy Lesson 11-2: Relating Graphs to Events Lesson 11-4: Understanding Slope Lab 11-5a: Graphing Equations Lesson 11-5: Graphing Linear Functions Lesson 11-6: Writing Rules for Linear Functions Looking for Pythagoras Problem 1.1: Locating Points and Finding Distances Problem 1.2: Shapes on a Coordinate Grid Problem 1.3: Finding Areas Problem 2.1: Looking for Squares Problem 2.2: Square Roots Problem 2.3: Using Squares to Find Lengths Problem 3.1: The Pythagorean Theorem Problem 3.2: A Proof of the Pythagorean Theorem Problem 3.3: Finding Distances Problem 3.4: Lengths that Form a Right Triangle Problem 4.1: Analyzing the Wheel of Theodorus Problem 4.2: Finding Unknown Side Lengths Problem 4.3: Analyzing Triangles Problem 4.4: Finding the Perimeter PH Math Course Lab 2-2b: Repeating Decimals Lesson 3-1: Exploring Square Roots and Irrational Numbers Lab 3-2a: Exploring the Pythagorean Theorem Lesson 3-2: The Pythagorean Theorem Lesson 3-3: Using the Pythagorean Theorem Extension: Analyzing Triangles Lesson 3-4: Graphing in the Coordinate Plane Lesson 7-6: Areas of Polygons Lab 7-7a: Estimating Area 11

12 Grade 8 CMP2 Replacement Unit Omit PH Math Course Lessons Growing, Growing, Growing Problem 1.1: Introducing Exponential Relationships Problem 1.2: Representing Exponential Relationships Problem 1.3: Growth Factors Problem 1.4: Comparing Growth Factors Problem 2.1: y-intercepts Other Than 1 Problem 2.2: Interpreting Exponential Equations Problem 2.3: Interpreting Exponential Graphs Problem 3.1: Fractional Growth Factors Problem 3.2: Growth Rates Problem 3.3: Connecting Growth Rate and Growth Factor Problem 4.1: Introducing Exponential Decay Problem 4.2: Representing Exponential Decay Problem 4.3: Modeling Exponential Decay Problem 5.1: Predicting the Ones Digit Problem 5.2: Operating with Exponents Problem 5.3: Exploring Exponential Equations PH Math Course Lesson 2-7: Powers and Exponents Lab 2-8a: Multiplying by Powers of 10 Lesson 2-8: Scientific Notation Lab 5-5a: Describing Change Lesson 5-5: Percent of Change Lab 12-3a: Exploring Exponents Lesson 12-3: Exponents and Multiplication Lesson 12-5: Exponents and Division Extension: Power Rules Kaleidoscopes, Hubcaps, and Mirrors Problem 1.1: Reflection Symmetry Problem 1.2: Rotation Symmetry Problem 1.3: Analyzing Symmetries Problem 1.4: Translation Symmetry Problem 2.1: Describing Line Reflections Problem 2.2: Describing Rotations Problem 2.3: Describing Translations Problem 2.4: Using Symmetry to Think About Tessellations Problem 3.1: Relating Symmetry and Congruence Problem 3.2: Congruent Triangles Problem 3.3: Congruent Triangles Problem 3.4: Side Lengths and Congruence Problem 4.1: Finding Distances without Measuring Problem 4.2: Using Symmetry to Find Properties of Shapes Problem 5.1: Coordinate Rules for Reflections Problem 5.2: Coordinate Rules for Translations Problem 5.3: Coordinate Rules for Rotations Problem 5.4: Coordinate Rules for Transformation Combinations PH Math Course Lesson 3-6: Translations Lab 3-7a: Exploring Reflections Lesson 3-7: Reflections and Symmetry Lab 3-8a: Exploring Rotations Lesson 3-8: Rotations Extension: Tessellations Lesson 7-3: Congruent Polygons Lesson 7-5: Angles and Polygons 12

13 Grade 8 CMP2 Replacement Unit Omit PH Math Course Lessons Say It With Symbols Problem 1.1: Writing Equivalent Expressions Problem 1.2: Determining Equivalence Problem 1.3: Interpreting Expressions Problem 1.4: Revisiting the Distributive Property Problem 2.1: Adding Expressions Problem 2.2: Substituting Equivalent Expressions Problem 2.3: Using Equations Problem 3.1: Solving Linear Equations Problem 3.2: Solving More Linear Equations Problem 3.3: Factoring Quadratic Expressions Problem 3.4: Solving Quadratic Equations Problem 4.1: Looking at Patterns of Change Problem 4.2: Linear, Exponential, Quadratic Problem 4.3: Sorting Functions Problem 5.1: Using Algebra to Solve a Puzzle Problem 5.2: Odd and Even Revisited Problem 5.3: Squaring Odd Numbers PH Math Course Lesson 1-1: Algebraic Expressions and the Order of Operations Lesson 1-5: Properties of Numbers (Distributive Property Only) Lesson 2-7: Powers and Exponents (Evaluating Expressions Only) Lab 6-2a: Modeling Expressions Lesson 6-2: Simplifying Algebraic Expressions Lesson 6-3: Solving Multi-Step Equations Lesson 6-4: Solving Equations with Variables on Both Sides Lesson 11-7: Quadratic and Other Nonlinear Functions Lab 11-7b: Changing Representations Lesson 12-2: Adding and Subtracting Polynomials Lesson 12-4: Multiplying Polynomials Shapes of Algebra Problem 1.1: Equations for Circles Problem 1.2: Parallels and Perpendiculars Problem 1.3: Finding Midpoints Problem 2.1: Graphs of Linear Systems Problem 2.2: Linear Inequalities Problem 2.3: Solving Linear Inequalities Problem 3.1: Solving Equations with Two Variables Problem 3.2: Connecting y = mx + b and ax + by= c Problem 3.3: Intersections of a Line Problem 4.1: The y = mx + b Case Problem 4.2: Solving Systems by Writing Equivalent Forms Problem 4.3: Solving Systems by Substitution Problem 4.4: Solving Systems by Combination Problem 5.1: Graphing No More Than Situations Problem 5.2: Solving Linear Inequalities by Graphing Problem 5.3: Graphs of Linear Inequalities Problem 5.4: Systems of Linear Inequalities PH Math Course Lab 3-4b: Finding the Midpoint Lab 3-5b: Matching Graphs Lab 6-5a: Graphing Inequalities Lesson 6-5: Solving Inequalities by Adding or Subtracting Lab 6-6a: Inequalities and Negative Numbers Lesson 6-6: Solving Inequalities by Multiplying or Dividing 13

14 Grade 8 CMP2 Replacement Unit Omit PH Math Course Lessons Samples and Populations Problem 1.1: From Line Plots to Histograms Problem 1.2: Using Histograms Problem 1.3: Box-and-Whisker Plots Problem 1.4: Analyzing Data Problem 2.1: Using a Sample to Make Predictions Problem 2.2: Selecting a Sample Problem 2.3: Choosing Random Samples Problem 2.4: Choosing a Sample Size Problem 3.1: Comparing and Analyzing Data Problem 3.2: Using a Simulation to Make a Decision Problem 4.1: Interpreting Scatter Plots Problem 4.2: Writing an Equation to Describe a Relationship Problem 4.3: Analyzing a Relationship PH Math Course Lesson 9-1: Finding Mean, Median, and Mode Lab 9-1b: Comparing Mean and Median Lesson 9-2: Displaying Frequency Lab 9-2b: Making Histograms Lesson 9-6: Box-and-Whisker Plots Lab 9-6b: Making Box-and-Whisker Plots Lab 9-7a: Scatter Plots Lesson 10-3: Conducting a Survey Lab 10-3b: Simulations with Random Numbers 14

15 Grade 7 Grade 7 CMP2 Replacement Unit Variables and Patterns Problem 1.1: Interpreting Tables Problem 1.2: Making Graphs Problem 1.3: Interpreting Graphs Problem 1.4: Reading Data from Graphs Problem 1.5: Finding Average Speed Problem 2.1: Analyzing a Table and a Graph Problem 2.2: Making and Analyzing a Graph Problem 2.3: Interpreting Graphs Problem 3.1: Equations with One Operation Problem 3.2: Equations with Two Operations Problem 3.3: Equations for Revenue, Expenses, and Profit Problem 4.1: Making and Using Calculator Tables Problem 4.2: Making and Using Calculator Graphs Problem 4.3: Comparing Relationships Omit PH Math Algebra Readiness 2010 Lessons Lesson 1-1: Variables and Expressions Lesson 1-3: Writing and Evaluating Expressions Lesson 1-8: Look for a Pattern Lesson 2-4: Variables and Equations Lesson 2-5: Solving Equations by Adding or Subtracting Lesson 2-6: Solving Equations by Multiplying or Dividing Lesson 3-4: Solving Equations by Adding or Subtracting Decimals Lesson 3-5: Solving Equations by Multiplying or Dividing Decimals Lesson 6-10: Make a Table Lab 8-3: Graphing Lines Stretching and Shrinking Problem 1.1: Introduction to Similarity Problem 1.2: Comparing Similar Figures Problem 1.3: Corresponding Sides and Angles Problem 2.1: Making Similar Figures Problem 2.2: Changing a Figure s Size and Location Problem 2.3: Scale Factors Problem 3.1: Forming Rep-Tiles with Similar Quadrilaterals Problem 3.2: Forming Rep-Tiles with Similar Triangles Problem 3.3: Scale Factors and Similar Shapes Problem 4.1: Ratios within Similar Parallelograms Problem 4.2: Ratios within Similar Triangles Problem 5.1: Using Shadows to Find Heights Problem 5.2: Using Mirrors to Find Heights Problem 5.3: Finding Lengths with Similar Triangles Lesson 6-3: Similar Figures and Scale Drawings Lab 6-3: Dilations Lab 9-8: Dilations in the Coordinate Plane Lab 10-1: Perimeter and Area of Similar Figures Lesson 11-4: Write a Proportion Comparing and Scaling Problem 1.1: Exploring Ratios and Rates Problem 1.2: Analyzing Comparison Statements Problem 1.3: Writing Comparison Statements Problem 2.1: Developing Comparison Strategies Problem 2.2: More Comparison Strategies Problem 2.3: Scaling Ratios Problem 3.1: Making and Using a Rate Table Problem 3.2: Finding Rates Problem 3.3: Unit Rates and Equations Problem 3.4: Two Different Rates Problem 4.1: Setting Up and Solving Proportions Problem 4.2: Applications of Proportions Problem 4.3: Developing Strategies for Solving Proportions Lesson 6-1: Ratios and Unit Rates Lesson 6-2: Proportions 15

16 16 Grade 7 CMP2 Replacement Unit Accentuate the Negative Problem 1.1: Using Positive and Negative Numbers Problem 1.2: Comparing and Ordering Positive and Negative Numbers Problem 1.3: Using a Number Line Model Problem 1.4: Using a Chip Model Problem 2.1: Introducing Addition of Integers Problem 2.2: Introducing Subtraction of Integers Problem 2.3: Addition and Subtraction Relationships Problem 2.5: Coordinate Graphing Problem 3.1: Introducing Multiplication of Integers Problem 3.2: Multiplication Patterns Problem 3.3: Introducing Division of Integers Problem 3.4: Multiplying Integers Problem 4.1: Order of Operations Problem 4.2: Distributing Operations Problem 4.3: The Distributive Property and Subtraction Moving Straight Ahead Problem 1.1: Finding and Using Rates Problem 1.2: Linear Relationships in Tables, Graphs, and Equations Problem 1.3: Using Linear Relationships Problem 1.4: Recognizing Linear Relationships Problem 2.1: Finding the Point of Intersection Problem 2.2: Using Tables, Graphs, and Equations Problem 2.3: Comparing Equations Problem 2.4: Connecting Tables, Graphs, and Equations Problem 3.1: Solving Equations Using Tables and Graphs Problem 3.2: Exploring Equality Problem 3.3: Writing Equations Problem 3.4: Solving Linear Equations Problem 3.5: Finding the Point of Intersection Problem 4.1: Using Rise and Run Problem 4.2: Finding the Slope of a Line Problem 4.3: Exploring Patterns with Lines Problem 4.4: Writing Equations with Two Variables Filling and Wrapping Problem 1.1: Making Cubic Boxes Problem 1.2: Making Rectangular Boxes Problem 1.3: Testing Nets Problem 14: Flattening a Box Problem 2.1: Finding Surface Area Problem 2.2: Finding the Least Surface Area Problem 2.3: Finding Volume of a Rectangular Prism Problem 3.1: Finding the Volumes of Other Prisms Problem 3.2: Finding Volumes of Cylinders Problem 3.3: Finding the Surface Area of Cylinders and Prisms Problem 3.4: Comparing Volumes Problem 4.1: Comparing Spheres and Cylinders Problem 4.2: Cones and Cylinders, Pyramids and Cubes Problem 4.3: Comparing Volumes of Spheres, Cylinders, and Cones Problem 5.1: Doubling the Volume of a Rectangular Prism Problem 5.2: Applying Scale Factors to Rectangular Prisms Problem 5.3: Similarity and Scale Factors Omit PH Math Algebra Readiness 2010 Lessons Lesson 1-2: The Order of Operations Lesson 1-4: Integers and Absolute Value Lab 1-5: Modeling Integers Lesson 1-5: Adding Integers Lesson 1-6: Subtracting Integers Lesson 1-9: Multiplying and Dividing Integers Lesson 1-10: The Coordinate Plane Lesson 2-2: The Distributive Property Lesson 4-2: Exponents (Using Order of Operations Only) Lab 2-5: Lesson 2-5: Lesson 2-6: Lesson 7-1: Lesson 7-4: Lesson 8-2: Lesson 8-3: Using Models with Equations Solving Equations by Adding or Subtracting Solving Equations by Multiplying or Dividing Solving Two-Step Equations Write an Equation Equations with Two Variables Slope and y-intercept Lesson 10-4: Space Figures Lab 10-5: Wrapping Cylinders Lesson 10-5: Surface Area: Prisms and Cylinders Lesson 10-6: Surface Area: Pyramids, Cones, and Spheres Lesson 10-7: Volume: Prisms and Cylinders Lesson 10-8: Make a Model Lesson 10-9: Volume: Pyramids, Cones, and Spheres Lesson 10-10: Scale Factors and Solids

17 Grade 8 Grade 8 CMP2 Replacement Unit Thinking with Math Models Problem 1.1: Finding Patterns and Making Predictions Problem 1.2: Finding Patterns and Making Predictions Problem 1.3: Extending Patterns Problem 2.1: Linear Models Problem 2.2: Equations for Linear Relationships Problem 2.3: Solving Linear Equations Problem 2.4: Intersecting Linear Models Problem 3.1: Relating Length and Width Problem 3.2: Inverse Variation Patterns Problem 3.3: Inverse Variation Patterns Omit PH Math Algebra Readiness 2010 Lessons Lesson 3-3: Using Formulas Lesson 7-1: Solving Two-Step Equations Lesson 7-2: Solving Multi-Step Equations Lesson 7-3: Two-Step Equations with Fractions and Decimals Lesson 7-5: Solving Two-Step Inequities Lesson 7-6: Transforming Formulas Lab 8-1: Relations and Functions Looking for Pythagoras Problem 1.1: Locating Points and Finding Distances Problem 1.2: Shapes on a Coordinate Grid Problem 1.3: Finding Areas Problem 2.1: Looking for Squares Problem 2.2: Square Roots Problem 2.3: Using Squares to Find Lengths Problem 3.1: The Pythagorean Theorem Problem 3.2: A Proof of the Pythagorean Theorem Problem 3.3: Finding Distances Problem 3.4: Lengths that Form a Right Triangle Problem 4.1: Analyzing the Wheel of Theodorus Problem 4.2: Finding Unknown Side Lengths Problem 4.3: Analyzing Triangles Problem 4.4: Finding the Perimeter Lesson 1-10: The Coordinate Plane Lesson 5-2: Fractions and Decimals Lesson 11-1: Square Roots and Irrational Numbers Lesson 11-2: The Pythagorean Theorem Lesson 11-3: Distance and Midpoint Formulas 17

18 Grade 8 CMP2 Replacement Unit Growing, Growing, Growing Problem 1.1: Introducing Exponential Relationships Problem 1.2: Representing Exponential Relationships Problem 1.3: Growth Factors Problem 1.4: Comparing Growth Factors Problem 2.1: y-intercepts Other Than 1 Problem 2.2: Interpreting Exponential Equations Problem 2.3: Interpreting Exponential Graphs Problem 3.1: Fractional Growth Factors Problem 3.2: Growth Rates Problem 3.3: Connecting Growth Rate and Growth Factor Problem 4.1: Introducing Exponential Decay Problem 4.2: Representing Exponential Decay Problem 4.3: Modeling Exponential Decay Problem 5.1: Predicting the Ones Digit Problem 5.2: Operating with Exponents Problem 5.3: Exploring Exponential Equations Kaleidoscopes, Hubcaps, and Mirrors Problem 1.1: Reflection Symmetry Problem 1.2: Rotation Symmetry Problem 1.3: Analyzing Symmetries Problem 1.4: Translation Symmetry Problem 2.1: Describing Line Reflections Problem 2.2: Describing Rotations Problem 2.3: Describing Translations Problem 2.4: Using Symmetry to Think About Tessellations Problem 3.1: Relating Symmetry and Congruence Problem 3.2: Congruent Triangles Problem 3.3: Congruent Triangles Problem 3.4: Side Lengths and Congruence Problem 4.1: Finding Distances without Measuring Problem 4.2: Using Symmetry to Find Properties of Shapes Problem 5.1: Coordinate Rules for Reflections Problem 5.2: Coordinate Rules for Translations Problem 5.3: Coordinate Rules for Rotations Problem 5.4: Coordinate Rules for Transformation Combinations Samples and Populations Problem 1.1: From Line Plots to Histograms Problem 1.2: Using Histograms Problem 1.3: Box-and-Whisker Plots Problem 1.4: Analyzing Data Problem 2.1: Using a Sample to Make Predictions Problem 2.2: Selecting a Sample Problem 2.3: Choosing Random Samples Problem 2.4: Choosing a Sample Size Problem 3.1: Comparing and Analyzing Data Problem 3.2: Using a Simulation to Make a Decision Problem 4.1: Interpreting Scatter Plots Problem 4.2: Writing an Equation to Describe a Relationship Problem 4.3: Analyzing a Relationship Omit PH Math Algebra Readiness 2010 Lessons Lab 4-2: Patterns and Exponents Lesson 4-2: Exponents Lesson 4-7: Exponents and Multiplication Lesson 4-8: Exponents and Division Lesson 4-9: Scientific Notation Lesson 5-9: Powers of Products and Quotients Lesson 6-7: Percent of Change Lesson 7-7: Simple and Compound Interest Lesson 9-5: Congruence Lesson 9-8: Translations Lesson 9-9: Symmetry and Reflections Lesson 9-10: Rotations Lesson 12-1: Mean, Median, and Mode Lesson 12-2: Frequency Tables, Line Plots, and Histograms Lesson 12-3: Box-and-Whisker Plots Lesson 12-5: Scatter Plots 18

19 Grade 8 CMP2 Replacement Unit Say It With Symbols Problem 1.1: Writing Equivalent Expressions Problem 1.2: Determining Equivalence Problem 1.3: Interpreting Expressions Problem 1.4: Revisiting the Distributive Property Problem 2.1: Adding Expressions Problem 2.2: Substituting Equivalent Expressions Problem 2.3: Using Equations Problem 3.1: Solving Linear Equations Problem 3.2: Solving More Linear Equations Problem 3.3: Factoring Quadratic Expressions Problem 3.4: Solving Quadratic Equations Problem 4.1: Looking at Patterns of Change Problem 4.2: Linear, Exponential, Quadratic Problem 4.3: Sorting Functions Problem 5.1: Using Algebra to Solve a Puzzle Problem 5.2: Odd and Even Revisited Problem 5.3: Squaring Odd Numbers Omit PH Math Algebra Readiness 2010 Lessons Lesson 1-1: Variables and Expressions Lesson 1-2: The Order of Operations Lesson 1-3: Writing and Evaluating Expressions Lesson 2-1: Properties of Numbers Lesson 2-3: Simplifying Algebraic Expressions Lesson 2-4: Variables and Equations Lesson 4-2: Exponents Lesson 7-2: Solving Multi-Step Equations Lesson 7-3: Two-Step Equations with Fractions and Decimals Shapes of Algebra Problem 1.1: Equations for Circles Problem 1.2: Parallels and Perpendiculars Problem 1.3: Finding Midpoints Problem 2.1: Graphs of Linear Systems Problem 2.2: Linear Inequalities Problem 2.3: Solving Linear Inequalities Problem 3.1: Solving Equations with Two Variables Problem 3.2: Connecting y = mx + b and ax + by= c Problem 3.3: Intersections of a Line Problem 4.1: The y = mx + b Case Problem 4.2: Solving Systems by Writing Equivalent Forms Problem 4.3: Solving Systems by Substitution Problem 4.4: Solving Systems by Combination Problem 5.1: Graphing No More Than Situations Problem 5.2: Solving Linear Inequalities by Graphing Problem 5.3: Graphs of Linear Inequalities Problem 5.4: Systems of Linear Inequalities Lesson 2-8: Inequalities and their Graphs Lesson 2-9: Solving One-Step Inequalities by Adding or Subtracting Lesson 2-10: Solving One-Step Inequalities by Multiplying or Dividing Lesson 7-5: Solving Two-Step Inequalities Lesson 8-6: Solving Systems of Linear Equations Lesson 8-7: Graphing Linear Inequalities Lesson 11-3: Distance and Midpoint Formulas 19

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