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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