Cpm Homework Help Int 1/X

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Chapter 1: Functions

Opening1.OPChapter Opening
Section Puzzles in Teams
1.1.2Investigating the Growth of Patterns
1.1.3Multiple Representations of Functions
Section Machines
1.2.3Domain and Range
Section Expressions with Exponents
1.3.2Zero and Negative Exponents
Closure1.CLChapter Closure

Chapter 2: Linear Functions

Opening2.OPChapter Opening
Section Growth in Linear Functions
2.1.2Comparing Δy and Δx
2.1.4y = mx + b and More on Slope
Section Linear Functions
2.2.2Rate of Change
2.2.3Equations of Lines in a Situation
2.2.4Dimensional Analysis
Section the Equation of a Line Given the Slope and a Point
2.3.2Writing the Equation of a Line Through Two Points
2.3.3Writing y = mx + b from Graphs and Tables
Closure2.CLChapter Closure

Chapter 3: Transformations and Solving

Opening3.OPChapter Opening
Section Visualization and Reflections
3.1.2Rotations and Translations
3.1.3Slopes of Parallel and Perpendicular Lines
3.1.4Defining Rigid Transformations
3.1.5Using Transformations to Create Polygons
 Section Area and Perimeter with Algebra Tiles
3.2.2Exploring an Area Model
3.2.3Multiplying Polynomials and the Distributive Property
 Section Methods for Solving Equations
3.3.2Fraction Busters
3.3.3Solving Exponential and Complex Equations
Closure3.CLChapter Closure

Chapter 4: Modeling Two-Variable Data

Opening4.OPChapter Opening
Section of Best Fit
4.1.3Upper and Lower Bounds
4.1.4Least Squares Regression Line
Section Plots
4.2.3Association is Not Causation
4.2.4Interpreting Correlation in Context
Closure4.CLChapter Closure

Chapter 5: Sequences

Opening5.OPChapter Opening
Section Exponential Growth
5.1.2Rebound Ratios
5.1.3The Bouncing Ball and Exponential Decay
Section and Investigating Sequences
5.2.2Generalizing Arithmetic Sequences
5.2.3Recursive Sequences
Section Growth in Tables and Graphs
5.3.2Using Multipliers to Solve Problems
5.3.3Comparing Sequences to Functions
Closure5.CLChapter Closure

Chapter 6: Systems of Equations

Opening6.OPChapter Opening
Section with Multi-Variable Equations
6.1.2Summary of Solving Equations
6.1.3Solving Word Problems by Using Different Representations
6.1.4Solving Word Problems by Writing Equations
Section Systems of Equations Using the Equal Values Method
6.2.2Solving Systems of Equations Using Substitution
6.2.3Making Connections: Systems and Multiple Representations
Section Systems Using Elimination
6.3.2More Elimination
6.3.3Making Connections: Systems, Solutions, and Graphs
Section a Strategy for Solving a System
6.4.2Pulling it all Together
Closure6.CLChapter Closure

Chapter 7: Congruence and Coordinate Geometry

Opening7.OPChapter Opening
Section Congruence
7.1.2Conditions for Triangle Congruence
7.1.3Creating a Flowchart
7.1.4Justifying Triangle Congruence Using Flowcharts
7.1.5More Conditions for Triangle Congruence
7.1.6Congruence of Triangles Through Rigid Transformations
7.1.7More Congruence Flowcharts
Section Quadrilaterals on a Coordinate Grid
7.2.2Coordinate Geometry and Midpoints
7.2.3Identifying Quadrilaterals on a Coordinate Grid
Closure7.CLChapter Closure

Chapter 8: Exponential Functions

Opening8.OPChapter Opening
Section y = bx
8.1.2Multiple Representations of Exponential Functions
8.1.3More Applications of Exponential Functions
8.1.4Exponential Decay
8.1.5Graph → Equation
8.1.6Completing the Multiple Representations Web
Section Fitting
8.2.2Curved Best-Fit Models
8.2.3Solving a System of Exponential Functions Graphically
Closure8.CLChapter Closure

Chapter 9: Inequalities

Opening9.OPChapter Opening
Section Linear, One-Variable Inequalities
9.1.2More Solving Inequalities
9.1.3Solving Absolute Value Equations and Inequalities
Section Two-Variable Inequalities
9.2.2Graphing Linear and Nonlinear Inequalities
Section of Inequalities
9.3.2More Systems of Inequalities
9.3.3Applying Inequalities to Solve Problems
Closure9.CLChapter Closure

Chapter 10: Functions and Data

Opening10.OPChapter Opening
Section in Two-Way Tables
10.1.2Investigating Data Representations
10.1.3Comparing Data
10.1.4Standard Deviation
Section Functions
10.2.2Arithmetic Operations with Functions
10.2.3Proving Linear and Exponential Growth Patterns
Closure10.CLChapter Closure

Chapter 11: Constructions and Closure

Opening11.OPChapter Opening
Section to Constructions
11.1.2Constructing Bisectors
11.1.3More Explorations with Constructions
Section Work and Mixing Problems
11.2.2Solving Equations and Systems Graphically
11.2.3Using a Best-Fit Line to Make a Prediction
11.2.4Treasure Hunt
11.2.5Using Coordinate Geometry and Constructions to Explore Shapes
11.2.6Modeling with Exponential Functions and Linear Inequalities
Closure11.CLChapter Closure

Appendix: Solving Equations

OpeningA.OPChapter Opening
Section A.1A.1.1Exploring Variables and Expressions
A.1.2Using Zero to Simplify Algebraic Expressions
A.1.3Using Algebra Tiles to Compare Expressions
A.1.4Justifying and Recording Work
A.1.5Using Algebra Tiles to Solve for x
A.1.6More Solving Equations
A.1.7Checking Solutions
A.1.8Determining the Number of Solutions
A.1.9Using Equations to Solve Problems
ClosureA.CLAppendix 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


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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