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Pacing Guide is provided to help you customize your course.Pacing Guide is provided to help you customize your course.

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It accounts for 115 standard class periods. A Daily Planner precedes each chapter and gives you lesson-by-lesson suggestions for that chapter.

Chapter 1 Arithmetic to Algebra 16 Days

LESSON TITLE LESSON TITLE

1.0 Habits of Mind 1.08 Decimals—Addresses on the Number Line

1.01 Getting Started 1.09 Number Line Addition

1.02 Thinking About Negative Numbers 1.10 Number Line Multiplication

1.03 Extending the Addition Table 1.11 Getting Started

1.04 Extending the Multiplication Table 1.12 Addition and Subtraction Algorithms

1.05 The Basic Rules of Arithmetic—Properties of Operations 1.13 Adding and Subtracting Fractions

1.06 Getting Started 1.14 Multiplication Algorithms

1.07 Numbers Besides the Integers—Fractions 1.15 Multiplying and Dividing Fractions

Chapter 2 Expressions and Equations 17 Days


2.01 Getting Started 2.10 When Backtracking Does Not Work

2.02 Modeling General Situations—Writing Expressions 2.11 The Basic Moves for Solving Equations

2.03 Evaluating Expressions 2.12 Solutions of Linear Equations

2.04 Simplifying Expressionss 2.13 Focus on the Distributive Property

2.05 Rephrasing the Basic Rules 2.14 Getting Started

2.06 Getting Started 2.15 Building Equations

2.07 Reversing Operations 2.16 Solving Word Problems

2.08 Solving Equations by Backtracking 2.17 More Than One Variable—Solving in Terms of Each Other

2.09 Getting Started

This Pacing Guide is provided to help you customize your course.

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Chapter 3 Graphs 13 Days


3.01 Getting Started 3.08 Two Basic Graphs: Direct and Inverse

3.02 Transformations 3.09 Four More Basic Graphs

3.03 Equations as Point-Testers 3.10 Getting Started

3.04 Graphing by Plotting 3.11 Pitch and Slope

3.05 Graphing Related Quantities 3.12 Rates of Change

3.06 Intersections of Graphs 3.13 Collinearity


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Chapter 4 Lines 14 Days


4.01 Getting Started 4.07 Slope and Parallel Lines

4.02 Equations of Lines 4.08 Solving Systems: Elimination

4.03 Jiffy Graphs: Lines—Day 1 4.09 Getting Started

4.03 Jiffy Graphs: Lines—Day 2 4.10 Solving by Graphing

4.04 Overtaking—Slope in Distance-Time Graphs 4.11 Inequalities with One Variable

4.05 Getting Started 4.12 Inequalities with Two Variables

4.06 Solving Systems: Substitution 4.13 Graphing Linear Inequalities

Chapter 5 Exponents and Functions 17 Days


5.01 Getting Started 5.10 Zero and Negative Exponents

5.02 Building Functions 5.11 Scientifi c Notation

5.03 Is It a Function? 5.12 Getting Started

5.04 Naming Functions 5.13 Constant Differences

5.05 Function Inputs and Outputs 5.14 Recursive Rules

5.06 Graphing Functions 5.15 Constant Ratios

5.07 Getting Started 5.16 Compound Interest

5.08 Squares, Cubes, and Beyond—Some Basic Rules of Exponents 5.17 Graphs of Exponential Functions

5.09 More Basic Rules of Exponents

Chapter 6 Statistics and Fitting Lines 10 Days


6.01 Getting Started 6.06 Two-Variable Data

6.02 Mean, Median, and Mode 6.07 Getting Started

6.03 Data Displays 6.08 Linear Trends in Data

6.04 Paired Comparisons—Box-and-Whisker Plots 6.09 Fitting Lines to Data

6.05 Categorical Data 6.10 The Line of Best Fit



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Chapter 7 Introduction to Geometry 13 Days


7.01 Getting Started 7.06 Compasses, Angles, and Circles—Day 2

7.02 Drawing 3-D Objects 7.07 Getting Started—Day 1

7.03 Drawing and Describing Shapes 7.07 Getting Started—Day 2

7.04 Drawing from a Recipe—Reading and Writing Directions 7.08 Drawings vs. Constructions

7.05 Getting Started—Day 1 7.09 Drawing UnMessUpable Figures—Building Constructions—Day 1

7.05 Getting Started—Day 2 7.09 Drawing UnMessUpable Figures—Building Constructions—Day 2

7.06 Compasses, Angles, and Circles—Day 1

Chapter 8 Congruence and Transformations 16 Days


8.01 Getting Started 8.07 Translations—Day 2

8.02 Length, Measure, and Congruence 8.08 Rotations

8.03 Corresponding Parts 8.09 Congruence and Isometry

8.04 Triangle Congruence—Day 1 8.10 Getting Started

8.04 Triangle Congruence—Day 2 8.11 Midpoint and Distance Formulas—Day 1

8.05 Getting Started 8.11 Midpoint and Distance Formulas—Day 2

8.06 Refl ections 8.12 Parallel Lines and Collinear Points

8.07 Translations—Day 1 8.13 Perpendicular Lines


Pacing Guide is provided to help you customize your course.



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It accounts for 149 standard class periods. A Daily Planner precedes each chapter and gives you lesson-by-lesson suggestions for that chapter.

Chapter 1 Real Numbers 11 Days


1.01 Getting Started 1.07 Getting Started

1.02 Defi ning Square Roots 1.08 Laws of Exponents

1.03 Arithmetic With Square Roots 1.09 Zero and Negative Exponents

1.04 Conventions for Roots—Simplifi ed Formss 1.10 Sequences and Operations

1.05 Rational and Irrational Numbers 1.11 Defi ning Rational Exponents

1.06 Roots, Radicals, and the nth Root

Chapter 2 Polynomials 12 Days


2.01 Getting Started 2.07 Normal Form

2.02 Form and Function—Showing Expressions are Equivalent 2.08 Arithmetic With Polynomials

2.03 The Zero Product Property 2.09 Getting Started

2.04 Transforming Expressions 2.10 Factoring a Difference of Squares

2.05 Getting Started 2.11 Factoring Sums and Products

2.06 Anatomy of a Polynomial 2.12 Factoring by Completing the Square


Chapter 3 Quadratics and Complex Numbers 13 Days


3.01 Getting Started 3.08 Jiffy Graphs: Parabolas

3.02 Making it Formal—Deriving the Quadratic Formula 3.09 Getting Started

3.03 Building a Quadratic Equation from its Roots 3.10 Extending the Number System

3.04 Factoring Nonmonic Quadratics 3.11 Making the Extension: The Square Root of -1

3.05 Getting Started 3.12 Extension to Complex Numbers

3.06 Optimization 3.13 Reciprocals and Division

3.07 Graphing Quadratic Equations

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Chapter 4 Functions 17 Days


4.01 Getting Started 4.10 Graphing Functions

4.02 Two Types of Defi nitions—Closed Form and Recursive 4.11 Getting Started

4.03 Constant Differences 4.12 Graphs of Exponential Functions

4.04 Tables and Slope 4.13 Tables of Exponential Functions

4.05 Difference Tables for Polynomial Functions 4.14 Getting Started

4.06 Getting Started 4.15 More Basic Graphs

4.07 Getting Precise About Functions 4.16 Translating Graphs

4.08 Algebra With Functions 4.17 Scaling and Refl ecting Graphs

4.09 Inverses: Doing and Undoing

Chapter 5 Applications of Probability 8 Days


5.0 Binomials and Pascal’s Triangle 5.04 Probabilities of Compound Events

5.01 Getting Started 5.05 Polynomial Powers and Counting

5.02 Probability and Pascal’s Triangle 5.06 Expected Value

5.03 Conditional Probability 5.07 Lotteries

Chapter 6 Congruence and Proof 29 Days


6.0 Triangle Congruence—Day 1 6.08 Getting Started

6.0 Triangle Congruence—Day 2 6.09 What Does a Proof Look Like?—Day 1

6.01 Getting Started 6.09 What Does a Proof Look Like?—Day 2

6.02 Numerical Invariants in Geometry—Day 1 6.10 Analyzing the Statement to Prove

6.02 Numerical Invariants in Geometry—Day 2 6.11 Analysis of a Proof—Day 1

6.02 Numerical Invariants in Geometry—Day 3 6.11 Analysis of a Proof—Day 2

6.03 Spatial Invariants—Shape, Concurrence, and Collinearity—Day 1 6.12 The Reverse List

6.03 Spatial Invariants—Shape, Concurrence, and Collinearity—Day 2 6.13 Practicing Your Proof-Writing Skills

6.03 Spatial Invariants—Shape, Concurrence, and Collinearity—Day 3 6.14 Getting Started

6.04 Getting Started 6.15 General Quadrilaterals

6.05 Deduction and Proof 6.16 Properties of Quadrilaterals

6.06 Parallel Lines—Day 1 6.17 Parallelograms—Day 1

6.06 Parallel Lines—Day 2 6.17 Parallelograms—Day 2

6.07 The Parallel Postulate—Day 1 6.18 Classifying Quadrilaterals

6.07 The Parallel Postulate—Day 2



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Chapter 7 Similarity 23 Days


7.01 Getting Started 7.10 Nested Triangles—One Triangle Inside Another—Day 1

7.02 Scale Factors—Day 1 7.10 Nested Triangles—One Triangle Inside Another—Day 2

7.02 Scale Factors—Day 2 7.11 Proving the Side-Splitter Theorems

7.03 What is a Well-Scaled Drawing? 7.12 The Side-Splitter Theorems (continued)

7.04 Testing for Scale 7.13 Getting Started

7.05 Checking for Scaled Copies—Day 1 7.14 Similar Figures

7.05 Checking for Scaled Copies—Day 2 7.15 Tests for Similar Triangles—Day 1

7.06 Getting Started 7.15 Tests for Similar Triangles—Day 2

7.07 Making Scaled Copies 7.15 Tests for Similar Triangles—Day 3

7.08 Ratio and Parallel Methods—Day 1 7.16 Areas of Similar Triangles—Day 1

7.08 Ratio and Parallel Methods—Day 2 7.16 Areas of Similar Triangles—Day 2


Chapter 8 Circles 17 Days



8.02 Area and Perimeter—Day 1 8.09 Arcs and Central Angles—Day 1

8.02 Area and Perimeter—Day 2 8.09 Arcs and Central Angles—Day 2

8.03 Connecting Area, Circumference—Day 1 8.10 Chords and Inscribed Angles—Day 1

8.03 Connecting Area, Circumference—Day 2 8.10 Chords and Inscribed Angles—Day 2

8.04 Getting Started 8.11 Circumscribed and Inscribed Circles

8.05 An Area Formula for Circles 8.12 Secants and Tangents

8.06 Circumference 8.13 Power of a Point, Part 1

8.07 Arc Length

Chapter 9 Using Similarity 14 Days


9.01 Getting Started 9.08 Some Special Ratios

9.02 An Inequality of Means 9.09 Finding Triangle Areas

9.03 Similarity in Ancient Greece 9.10 Volumes of Solids

9.04 Concurrence of Medians 9.11 Getting Started

9.05 Midpoint and Distance Formulas 9.12 Cavalieri’s Principle

9.06 Getting Started 9.13 Proving Volume Formulas

9.07 Some Special Triangles 9.14 Volume of a Sphere

Chapter 10 Analytic Geometry 5 Days


10.0 Equations of Circles 10.03 Coordinates and Proof

10.01 Getting Started 10.04 The Power of a Point, Part 2

10.02 Equations as Point-Testers



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CMEProject•Mathematics III v

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Table of Contents v CME Project • Mathematics II v

National Advisory Board The National Advisory Board met early in the project, providing critical feedback on the instructional design and the overall organization. Members include

Richard Askey, University of Wisconsin Edward Barbeau, University of Toronto Hyman Bass, University of MichiganCarol Findell, Boston University Arthur Heinricher, Worcester Polytechnic InstituteRoger Howe, Yale UniversityBarbara Janson, Janson AssociatesKenneth Levasseur, University of Massachusetts, LowellJames Madden, Louisiana State University, Baton RougeJacqueline Miller, Education Development CenterJames Newton, University of MarylandRobert Segall, Greater Hartford Academy of Mathematics and ScienceGlenn Stevens, Boston UniversityHerbert Wilf, University of PennsylvaniaHung-Hsi Wu, University of California, Berkeley

Core Mathematical Consultants Dick Askey, Ed Barbeau, and Roger Howe have been involved in an even more substantial way, reviewing chapters and providing detailed and critical advice on every aspect of the program. Dick and Roger spent many hours reading and criticizing drafts, brainstorming with the writing team, and offering advice on everything from the logical organization to the actual numbers used in problems. We can’t thank them enough.

Teacher Advisory Board The Teacher Advisory Board for the CME Project was essential in help ing us create an effective format for our lessons that embodies the philosophy and goals of the program. Their debates about pedagogi cal issues and how to develop mathematical top ics helped to shape the distinguishing features of the curriculum so that our lessons work effective ly in the classroom. The advisory board includes

Jayne Abbas, Richard Coffey, Charles Garabedian, Dennis Geller, Eileen Herlihy, Doreen Kilday, Gayle Masse, Hugh McLaughlin, Nancy McLaughlin, Allen Olsen, Kimberly Osborne, Brian Shoemaker, and Benjamin Sinwell

Field-Test Teachers Our field-test teachers gave us the benefit of their classroom experi ence by teaching from our draft lessons and giv ing us extensive, critical feedback that shaped the drafts into realistic, teachable lessons. They shared their concerns, questions, challenges, and successes and kept us focused on the real world. Some of them even welcomed us into their classrooms as co-teachers to give us the direct experience with students that we needed to hone our lessons. Working with these expert professionals has been one of the most gratifying parts of the development—they are “highly qualified” in the most profound sense.

California Barney Martinez, Jefferson High School, Daly City; Calvin Baylon and Jaime Lao, Bell Junior High School, San Diego; Colorado Rocky Cundiff, Ignacio High School, Ignacio; Illinois Jeremy Kahan, Tammy Nguyen, and Stephanie Pederson, Ida Crown Jewish Academy, Chicago; Massachusetts Carol Martignette, Chris Martino, and Kent Werst, Arlington High School, Arlington; Larry Davidson, Boston University Academy, Boston; Joe Bishop and Carol Rosen, Lawrence High School, Lawrence; Maureen Mulryan, Lowell High School, Lowell; Felisa Honeyman, Newton South High School, Newton Centre; Jim Barnes and Carol Haney, Revere High School, Revere; New Hampshire Jayne Abbas and Terin Voisine, Cawley Middle School, Hooksett; New Mexico Mary Andrews, Las Cruces High School, Las Cruces; Ohio James Stallworth, Hughes Center, Cincinnati; Texas Arnell Crayton, Bellaire High School, Bellaire; Utah Troy Jones, Waterford School, Sandy; Washington Dale Erz, Kathy Greer, Karena Hanscom, and John Henry, Port Angeles High School, Port Angeles; Wisconsin Annette Roskam, Rice Lake High School, Rice Lake.

Special thanks go to our colleagues at Pearson, most notably Elizabeth Lehnertz, Joe Will, and Stewart Wood. The program benefits from their expertise in every way, from the actual mathematics to the design of the printed page.

Contributors to the CME Project

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A Daily Planner precedes each chapter and gives you lesson-by-lesson suggestions for that chapter.

chapter 1 Functions and Polynomials 13 Days

Lesson TiTLe Lesson TiTLe

1.0 Anatomy of a Polynomial 1.06 The Factor Theorem


1.02 Lagrange Interpolation—Fitting Polynomial Functions to Tables 1.08 Quadratics

1.03 Agreeing to Disagree—Finding Functions with Specific Values 1.09 Factoring Cubes

1.04 Getting Started 1.10 Pippins and Cheese—More Factoring Techniques

1.05 Polynomial Division 1.11 Rational Expressions

chapter 2 Sequences and Series 18 Days


2.0 Two Types of Definitions 2.09 Getting Started

2.01 Getting Started 2.10 Arithmetic Sequences and Series

2.02 Gauss’s Method and Euclid’s Method 2.11 Geometric Sequences and Series

2.03 Ways to Visualize Sums 2.12 Limits

2.04 The g Notation 2.13 Repeating Decimals


2.06 Definite and Indefinite Sums 2.15 Pascal’s Triangle

2.07 g Identities 2.16 The Binomial Theorem

2.08 Tables and Figurate Numbers

chapter 3 Statistical Inference 22 Days



3.02 Probability and Pascal’s Triangle 3.11 Experiments and Simulations

3.03 Polynomial Powers 3.12 Bernoulli Trials

3.04 Expected Value 3.13 Surveys, Studies, and Experiments

3.05 Lotteries 3.14 Sampling and Margin of Error


3.07 Variance and Standard Deviation 3.16 The Central Limit Theorem

3.08 Adding Variance 3.17 The Normal Distribution

3.09 Repeated Experiments


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chapter 4 Trigonometry 18 Days


4.0 Right Triangle Trigonometry 4.08 Graphing the Tangent Function

4.01 Getting Started 4.09 The Angle-Sum Identities

4.02 Extending the Domain, Part 1—0° to 360° 4.10 Getting Started

4.03 Extending the Domain, Part 2—All Real Numbers 4.11 The Area of a Triangle

4.04 The Pythagorean Identity 4.12 The Law of Sines

4.05 Solving Trigonometric Equations 4.13 The Law of Cosines

4.06 Getting Started 4.14 Heron’s Formula—Using Side Lengths to Find the Area of a Triangle

4.07 Graphing Cosine and Sine

chapter 5 Analyzing Trigonometric Functions 10 Days


5.01 Getting Started 5.05 Analyzing Graphs—The Sine and Cosine Functions

5.02 Trigonometry With Radians 5.06 Getting Started

5.03 Graphing Cosine and Sine Functions 5.07 Sinusoidal Functions—Amplitude, Period, Phase Shift

5.04 Solving Cosine and Sine Equations 5.08 Applying Trigonometric Functions

chapter 6 Complex Numbers and Polynomials 11 Days


6.01 Getting Started 6.06 Powers of Complex Numbers

6.02 The Complex Plane 6.07 Roots of Unity

6.03 Another Form for Complex Numbers— r cis u 6.08 Geometry of Roots of Unity

6.04 The Multiplication Law 6.09 Arithmetic With Roots of Unity—Regular Polygons


chapter 7 Polynomial and Rational Functions 16 DaysLesson TiTLe Lesson TiTLe

7.01 Getting Started 7.07 Graphing Rational Functions

7.02 Continuity of Polynomial Functions 7.08 Revisiting Secants and Tangents

7.03 Graphs and Secant Lines 7.09 Getting Started

7.04 Polynomials in Powers of x – a 7.10 Monthly Payments

7.05 Secants and Tangents 7.11 The Factorial Function


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chapter 8 Exponential and Logarithmic Functions 16 Days

lesson title lesson title

8.01 Getting Started 8.09 Graphing Logarithmic Functions

8.02 Graphs of Exponential Functions 8.10 The Logarithmic Scale

8.03 Tables of Exponential Functions 8.11 Getting Started

8.04 Properties of Exponential Functions 8.12 Compound Interest; the Number e

8.05 Exponential Functions, One-to-One 8.13 Another Way to Find e

8.06 Getting Started 8.14 The Natural Logarithm Function

8.07 Defining Logarithms 8.15 Analysis of f(x) = ex and g(x) = ln x

8.08 Laws of Logarithms

chapter 9 Optimization and Geometric Modeling 14 Days

lesson title lesson title

9.0 Equations as Point-Testers 9.07 Areas of Similar Polygons


9.02 Finding the Shortest Path 9.09 Slicing Cones

9.03 Reflecting to Find the Shortest Path 9.10 Conics at the Origin

9.04 Getting Started 9.11 Conics Anywhere

9.05 Maximizing Areas, Part 1 9.12 They Are All the Same—A Continuous Family of Curves

9.06 Maximizing Areas, Part 2

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