Core Connections, Course 3 - Weebly

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 Kensington, CA

Misty Nikula (Second Edition)

CPM Educational Program 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, 9498 Little Rapids Way, Elk Grove, CA 95758. 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

5

1.1.3 Writing Equations Using the 5-D Process

6

1.2.1 Proportional Relationships

7

1.2.2 Solving Proportions

8

Chapter 2 Simplifying with Variables

9

Learning Log Entries

9

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

17

2.1.1 Non-Commensurate

17

2.1.2 Mathematics Vocabulary

17

2.1.3 Combining Like Terms

18

2.1.4 Evaluating Expressions and the Orders of Operations

19

2.1.5 Commutative Property

20

2.1.6 Simplifying an Expression ("Legal Moves")

20

2.1.7 Associative and Identity Properties

21

2.1.8 Inverse Properties

21

2.1.9 Using an Equation Mat

22

Chapter 3 Graphs and Equations

23

Learning Log Entries

23

3.1.6 Qualities of a Complete Graph

3.1.7 Graphing Errors

3.2.2 How Many Solutions?

Math Notes

26

3.1.1 Patterns in Nature

26

3.1.3 Discrete and Continuous Graphs

26

3.1.4 Parabolas

27

3.1.5 Independent and Dependent Variables

28

3.2.1 Complete Graph

28

3.2.2 Circular Vocabulary, Circumference, and Area

29

3.2.3 Solving a Linear Equation

30

3.2.4 Solutions to an Equation with One Variable

30

3.2.5 The Distributive Property

31

Chapter 4 Multiple Representations

32

Learning Log Entries

32

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

37

4.1.7 Representations of Patterns

37

Chapter 5 Systems of Equations

38

Learning Log Entries

38

5.1.2 Solving Equations with Fractions

5.2.1 Points of Intersection

5.2.3 Equal Values Method

Math Notes

41

5.1.1 Linear Equations

41

5.1.2 Equivalent Equations

41

5.2.1 Solving Equations with Fractions (also known as the Fraction Buster Method) 42

5.2.2 System of Equations Vocabulary

42

5.2.3 The Equal Values Method

43

5.2.4 Solutions to a System of Equations

43

Chapter 6 Transformations and Similarity

44

Learning Log Entries

44

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

49

6.1.3 Rigid Transformations

49

6.2.2 Corresponding Parts of Similar Shapes

50

6.2.6 Scale Factor

51

Chapter 7 Slope and Association

52

Learning Log Entries

52

7.1.3 Associations

7.2.3 Slope and Steepness

7.3.1 Line From Data Points

7.3.2 Describing Association

Math Notes

57

7.1.1 Circle Graphs

57

7.1.2 Line of Best Fit

57

7.1.3 Describing Association ? Part 1

58

7.2.4 Slope of a Line

59

7.2.5 Proportional Equations

60

7.3.2 Describing Association ? Part 2

60

Chapter 8 Exponents and Functions

61

Learning Log Entries

61

8.1.3 Simple and Compound Interest

8.2.1 Scientific Notation

8.2.3 Simplifying Exponent Expressions

8.3.1 Functions

Math Notes

66

8.1.1 Simple Interest

66

8.1.2 Exponents

66

8.1.3 Compound Interest

67

8.2.3 Scientific Notation

67

8.2.4 Laws of Exponents

68

8.3.1 Functions

68

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