Core Connections: Course 3

Core Connections: Course 3

Foundations for Algebra Toolkit

Managing Editors / Authors

Leslie Dietiker, Ph.D., Director of Curriculum (Both Editions)

Boston University Boston, MA

Evra Baldinger (First Edition)

University of California, Berkeley Berkeley, CA

Barbara Shreve (First Edition)

San Lorenzo High School San Lorenzo, CA

Michael Kassarjian (Second Edition)

CPM Educational Program Dallas, TX

Misty Nikula (Second Edition)

Whatcom Day Academy Bellingham, WA

Technical Assistants: Toolkit

Hannah Coyner

Sarah Maile

Sacramento, CA

Sacramento, CA

Megan Walters

Sacramento, CA

Cover Art

Jonathan Weast

Sacramento, CA

Program Directors

Leslie Dietiker, Ph.D.

Boston University Boston, MA

Judy Kysh, Ph.D.

Departments of Education and Mathematics San Francisco State University, CA

Lori Hamada

CPM Educational Program Fresno, CA

Tom Sallee, Ph.D.

Department of Mathematics University of California, Davis

Brian Hoey

CPM Educational Program Sacramento, CA

Copyright ? 2013 by CPM Educational Program. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Requests for permission should be made in writing to: CPM Educational Program, 1233 Noonan Drive, Sacramento, CA 95822. Email: cpm@.

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Printed in the United States of America

ISBN: 978-1-60328-096-9

Core Connections: Foundations for Algebra Course 3 Toolkit

Chapter 1 Problem Solving

2

Learning Log Entries

2

1.2.1 Proportional Relationships

Math Notes

4

1.1.1 FractionDecimalPercent

4

1.1.2 Axes, Quadrants, and Graphing on an xy-Coordinate Graph

4

1.1.3 Writing Equations Using the 5-D Process

5

1.2.1 Proportional Relationships

5

1.2.2 Solving Proportions

5

Chapter 2 Fractions and Integer Addition

7

Learning Log Entries

7

2.1.1 Algebra Tiles and Variables

2.1.2 Finding Perimeter and Combining Like Terms

2.1.3 Meanings of Minus

2.1.3 Representing Expressions on an Expression Map

2.1.4 Using Zeros to Simplify

2.1.5 Legal Moves for Simplifying and Comparing Expressions

2.1.9 Solutions of an Equation

Math Notes

12

2.1.1 Non-Commensurate

12

2.1.2 Mathematics Vocabulary

13

2.1.3 Combining Like Terms

14

2.1.4 Evaluating Expressions and the Orders of Operations

14

2.1.5 Commutative Property

14

2.1.6 Simplifying an Expression ("Legal Moves")

15

2.1.7 Associative and Identity Properties

15

2.1.8 Inverse Properties

15

2.1.9 Using an Equation Mat

15

Chapter 3 Graphs and Equations

16

Learning Log Entries

16

3.1.6 Qualities of a Complete Graph

3.1.7 Graphing Errors

3.2.2 How Many Solutions?

Math Notes

21

3.1.1 Patterns in Nature

21

3.1.3 Discrete and Continuous Graphs

21

3.1.4 Parabolas

21

3.1.5 Independent and Dependent Variables

22

3.2.1 Complete Graph

22

3.2.2 Circular Vocabulary, Circumference, and Area

23

3.2.3 Solving a Linear Equation

23

3.2.4 Solutions to an Equation with One Variable

23

3.2.5 The Distributive Property

24

Chapter 4 Multiple Representations

25

Learning Log Entries

25

4.1.2 Representations of Patterns Web

4.1.3 Connecting Linear Rules and Graphs

4.1.4 y = mx + b

4.1.6 Graphing Without an x y Table

Math Notes

28

4.1.7 Representations of Patterns

28

Chapter 5 Systems of Equations

31

Learning Log Entries

31

5.1.2 Solving Equations with Fractions

5.2.1 Points of Intersection

5.2.3 Equal Values Method

Math Notes

35

5.1.1 Linear Equations

35

5.1.2 Equivalent Equations

35

5.2.1 Solving Equations with Fractions (also known as the Fraction Buster Method) 36

5.2.2 System of Equations Vocabulary

36

5.2.3 The Equal Values Method

37

5.2.4 Solutions to a System of Equations

37

Chapter 6 Transformations and Similarity

38

Learning Log Entries

38

6.1.3 Rigid Transformations

6.2.1 Dilations

6.2.3 Finding Similar Shapes

6.2.6 Finding Missing Sides of Similar Shapes

Math Notes

42

6.1.3 Rigid Transformations

42

6.2.2 Corresponding Parts of Similar Shapes

42

6.2.6 Scale Factor

42

Chapter 7 Slope and Association

45

Learning Log Entries

45

7.1.3 Associations

7.2.3 Slope and Steepness

7.3.1 Line From Data Points

7.3.2 Describing Association

Math Notes

48

7.1.1 Circle Graphs

48

7.1.2 Line of Best Fit

48

7.1.3 Describing Association ? Part 1

49

7.2.4 Slope of a Line

49

7.2.5 Proportional Equations

50

7.3.2 Describing Association ? Part 2

50

Chapter 8 Exponents and Functions

52

Learning Log Entries

52

8.1.3 Simple and Compound Interest

8.2.1 Scientific Notation

8.2.3 Simplifying Exponent Expressions

8.3.1 Functions

Math Notes

56

8.1.1 Simple Interest

56

8.1.2 Exponents

57

8.1.3 Compound Interest

57

8.2.3 Scientific Notation

58

8.2.4 Laws of Exponents

58

8.3.1 Functions

59

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