# Cpm Homework Help Int 1/X

**Chapter 1: Functions**

Opening | 1.OP | Chapter Opening |

Section 1.1 | 1.1.1 | Solving Puzzles in Teams |

1.1.2 | Investigating the Growth of Patterns | |

1.1.3 | Multiple Representations of Functions | |

Section 1.2 | 1.2.1 | Function Machines |

1.2.2 | Functions | |

1.2.3 | Domain and Range | |

Section 1.3 | 1.3.1 | Rewriting Expressions with Exponents |

1.3.2 | Zero and Negative Exponents | |

Closure | 1.CL | Chapter Closure |

**Chapter 2: Linear Functions**

Opening | 2.OP | Chapter Opening |

Section 2.1 | 2.1.1 | Seeing Growth in Linear Functions |

2.1.2 | Comparing Δy and Δx | |

2.1.3 | Slope | |

2.1.4 | y = mx + b and More on Slope | |

Section 2.2 | 2.2.1 | Modeling Linear Functions |

2.2.2 | Rate of Change | |

2.2.3 | Equations of Lines in a Situation | |

2.2.4 | Dimensional Analysis | |

Section 2.3 | 2.3.1 | Writing the Equation of a Line Given the Slope and a Point |

2.3.2 | Writing the Equation of a Line Through Two Points | |

2.3.3 | Writing y = mx + b from Graphs and Tables | |

Closure | 2.CL | Chapter Closure |

**Chapter 3: Transformations and Solving**

Opening | 3.OP | Chapter Opening |

Section 3.1 | 3.1.1 | Spatial Visualization and Reflections |

3.1.2 | Rotations and Translations | |

3.1.3 | Slopes of Parallel and Perpendicular Lines | |

3.1.4 | Defining Rigid Transformations | |

3.1.5 | Using Transformations to Create Polygons | |

3.1.6 | Symmetry | |

Section 3.2 | 3.2.1 | Modeling Area and Perimeter with Algebra Tiles |

3.2.2 | Exploring an Area Model | |

3.2.3 | Multiplying Polynomials and the Distributive Property | |

Section 3.3 | 3.3.1 | Multiple Methods for Solving Equations |

3.3.2 | Fraction Busters | |

3.3.3 | Solving Exponential and Complex Equations | |

Closure | 3.CL | Chapter Closure |

**Chapter 4: Modeling Two-Variable Data**

Opening | 4.OP | Chapter Opening |

Section 4.1 | 4.1.1 | Line of Best Fit |

4.1.2 | Residuals | |

4.1.3 | Upper and Lower Bounds | |

4.1.4 | Least Squares Regression Line | |

Section 4.2 | 4.2.1 | Residual Plots |

4.2.2 | Correlation | |

4.2.3 | Association is Not Causation | |

4.2.4 | Interpreting Correlation in Context | |

Closure | 4.CL | Chapter Closure |

**Chapter 5: Sequences**

Opening | 5.OP | Chapter Opening |

Section 5.1 | 5.1.1 | Representing Exponential Growth |

5.1.2 | Rebound Ratios | |

5.1.3 | The Bouncing Ball and Exponential Decay | |

Section 5.2 | 5.2.1 | Generating and Investigating Sequences |

5.2.2 | Generalizing Arithmetic Sequences | |

5.2.3 | Recursive Sequences | |

Section 5.3 | 5.3.1 | Comparing Growth in Tables and Graphs |

5.3.2 | Using Multipliers to Solve Problems | |

5.3.3 | Comparing Sequences to Functions | |

Closure | 5.CL | Chapter Closure |

**Chapter 6: Systems of Equations**

Opening | 6.OP | Chapter Opening |

Section 6.1 | 6.1.1 | Working with Multi-Variable Equations |

6.1.2 | Summary of Solving Equations | |

6.1.3 | Solving Word Problems by Using Different Representations | |

6.1.4 | Solving Word Problems by Writing Equations | |

Section 6.2 | 6.2.1 | Solving Systems of Equations Using the Equal Values Method |

6.2.2 | Solving Systems of Equations Using Substitution | |

6.2.3 | Making Connections: Systems and Multiple Representations | |

Section 6.3 | 6.3.1 | Solving Systems Using Elimination |

6.3.2 | More Elimination | |

6.3.3 | Making Connections: Systems, Solutions, and Graphs | |

Section 6.4 | 6.4.1 | Choosing a Strategy for Solving a System |

6.4.2 | Pulling it all Together | |

Closure | 6.CL | Chapter Closure |

**Chapter 7: Congruence and Coordinate Geometry**

Opening | 7.OP | Chapter Opening |

Section 7.1 | 7.1.1 | Defining Congruence |

7.1.2 | Conditions for Triangle Congruence | |

7.1.3 | Creating a Flowchart | |

7.1.4 | Justifying Triangle Congruence Using Flowcharts | |

7.1.5 | More Conditions for Triangle Congruence | |

7.1.6 | Congruence of Triangles Through Rigid Transformations | |

7.1.7 | More Congruence Flowcharts | |

Section 7.2 | 7.2.1 | Studying Quadrilaterals on a Coordinate Grid |

7.2.2 | Coordinate Geometry and Midpoints | |

7.2.3 | Identifying Quadrilaterals on a Coordinate Grid | |

Closure | 7.CL | Chapter Closure |

**Chapter 8: Exponential Functions**

Opening | 8.OP | Chapter Opening |

Section 8.1 | 8.1.1 | Investigating y = b^{x} |

8.1.2 | Multiple Representations of Exponential Functions | |

8.1.3 | More Applications of Exponential Functions | |

8.1.4 | Exponential Decay | |

8.1.5 | Graph → Equation | |

8.1.6 | Completing the Multiple Representations Web | |

Section 8.2 | 8.2.1 | Curve Fitting |

8.2.2 | Curved Best-Fit Models | |

8.2.3 | Solving a System of Exponential Functions Graphically | |

Closure | 8.CL | Chapter Closure |

**Chapter 9: Inequalities**

Opening | 9.OP | Chapter Opening |

Section 9.1 | 9.1.1 | Solving Linear, One-Variable Inequalities |

9.1.2 | More Solving Inequalities | |

9.1.3 | Solving Absolute Value Equations and Inequalities | |

Section 9.2 | 9.2.1 | Graphing Two-Variable Inequalities |

9.2.2 | Graphing Linear and Nonlinear Inequalities | |

Section 9.3 | 9.3.1 | Systems of Inequalities |

9.3.2 | More Systems of Inequalities | |

9.3.3 | Applying Inequalities to Solve Problems | |

Closure | 9.CL | Chapter Closure |

**Chapter 10: Functions and Data**

Opening | 10.OP | Chapter Opening |

Section 10.1 | 10.1.1 | Association in Two-Way Tables |

10.1.2 | Investigating Data Representations | |

10.1.3 | Comparing Data | |

10.1.4 | Standard Deviation | |

Section 10.2 | 10.2.1 | Transforming Functions |

10.2.2 | Arithmetic Operations with Functions | |

10.2.3 | Proving Linear and Exponential Growth Patterns | |

Closure | 10.CL | Chapter Closure |

**Chapter 11: Constructions and Closure**

Opening | 11.OP | Chapter Opening |

Section 11.1 | 11.1.1 | Introduction to Constructions |

11.1.2 | Constructing Bisectors | |

11.1.3 | More Explorations with Constructions | |

Section 11.2 | 11.2.1 | Solving Work and Mixing Problems |

11.2.2 | Solving Equations and Systems Graphically | |

11.2.3 | Using a Best-Fit Line to Make a Prediction | |

11.2.4 | Treasure Hunt | |

11.2.5 | Using Coordinate Geometry and Constructions to Explore Shapes | |

11.2.6 | Modeling with Exponential Functions and Linear Inequalities | |

Closure | 11.CL | Chapter Closure |

**Appendix: Solving Equations**

Opening | A.OP | Chapter Opening |

Section A.1 | A.1.1 | Exploring Variables and Expressions |

A.1.2 | Using Zero to Simplify Algebraic Expressions | |

A.1.3 | Using Algebra Tiles to Compare Expressions | |

A.1.4 | Justifying and Recording Work | |

A.1.5 | Using Algebra Tiles to Solve for x | |

A.1.6 | More Solving Equations | |

A.1.7 | Checking Solutions | |

A.1.8 | Determining the Number of Solutions | |

A.1.9 | Using Equations to Solve Problems | |

Closure | A.CL | Appendix Closure |

**Checkpoint Materials**

CP 1: | Solving Linear Equations, Part 1 (Integer Coefficients) |

CP 2: | Evaluating Expressions and the Order of Operations |

CP 3: | Operations with Rational Numbers |

CP 4: | Laws of Exponents and Scientific Notation |

CP 5: | Writing the Equation of a Line |

CP 6A: | Solving Linear Equations, Part 2 (Fractional Coefficients) |

CP 6B: | Multiplying Polynomials and Solving Equations with Parentheses |

CP 7: | Interpreting Associations |

CP 8A: | Rewriting Equations with More Than One Variable |

CP 8B: | Solving Problems by Writing Equations |

CP 9: | Solving Linear Systems of Equations |

CP 10: | Determining Congruent Triangles |

CP 11: | The Exponential Web |

**Glossary**

**Index**

Chapters are divided into sections that are organized around core topics. Within each section, lessons include activities, challenging problems, investigations and practice problems. Teacher notes for each lesson include a “suggested lesson activity” section with ideas for lesson introduction, specific tips and strategies for lesson implementation to clearly convey core ideas, and a means for bringing the lesson to closure. Read More...

Core ideas are synthesized in “Math Notes” boxes throughout the text. These notes are placed in a purposeful fashion, often falling one or more lessons after the initial introduction of a concept. This approach allows students time to explore and build conceptual understanding of an idea before they are presented with a formal definition or an algorithm or a summary of a mathematical concept. “Math Notes” boxes include specific vocabulary, definitions and instructions about notation, and occasionally interesting extensions or real-world applications of mathematical concepts.

Learning Log reflections appear periodically at the end of lessons to allow students to synthesize what they know and identify areas that need additional explanation. Toolkits are provided as working documents in which students write Learning Logs, interact with Math Notes and create other personal reference tools.

Each chapter offers review problems in the chapter closure: typical problems that students can expect on an assessment, answers, and support for where to get help with the problem. Chapter closure also includes lists of Math Notes and Learning Logs, key vocabulary in the chapter, and an opportunity to create structured graphic organizers.

The books include “Checkpoints” that indicate to students where fluency with a skill should occur. Checkpoints offer examples with detailed explanations, in addition to practice problems with answers.

In addition, CPM provides a *Parent Guide with Extra Practice* available for free download cpm.org of in booklet form for purchase. In addition to practice problems with answers, the *Parent Guide with Extra Practice* provides examples with detailed explanations and guidance for parents and tutors.

Each chapter comes with an assessment plan to guide teachers into choosing appropriate assessment problems. CPM provides a secure online test generator and sample tests. The Assessment Guidebook contains guidance for a wide variety of assessment strategies.

Technology is used in the course to allow students to see and explore concepts after they have developed some initial conceptual understanding. The course assumes that classes have access to at least one of these three technology setups: a set of graphing calculators and whole-class display technology for the teacher, a full computer lab with computers that have graphing software for each student, or a classroom computer with graphing software equipped with projection technology. Read Less...

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