Instructor’s Manual and Test Bank
G For
Elementary and Middle School
S
Mathematics: N
Teaching DevelopmentallyE
Tenth Edition
E
John A. Van de Walle, Virginia Commonwealth University
Karen S. Karp, University of Louisville
Jennifer M. Bay-Williams, University of Louisville
R
Prepared by
Elizabeth Todd Brown,
Professor Emeritus, University of Louisville
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto
Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
, S G
N
__________________________________________________________________________________
Copyright © 2019, 2016, 2013 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Printed in
E
the United States of America. This publication is protected by copyright, and permission should be
obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or
transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise.
For information regarding permissions, request forms and the appropriate contacts within the Pearson
E
Education Global Rights & Permissions Department, please visit www.pearsoned.com/permissions/.
Instructors of classes using Elementary and Middle School Mathematics Teaching Developmentally, 10e,
R
by Van de Walle, Karp, Bay-Williams, may reproduce material from the Instructor’s Resource Manual and
Test Bank for classroom use.
10 9 8 7 6 5 4 3 2 1 ISBN-10: 0134802128
ISBN-13: 9780134802121
www.pearsonhighered.com
2
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
, TABLE OF CONTENTS
Introductory Thoughts...................................................................................................................................................iv
Course Designs and Options...........................................................................................................................................v
Introducing These Manual Notes...............................................................................................................................xxiv
Share Your Thoughts..................................................................................................................................................xxv
Chapter by Chapter
Chapter 1: Teaching Mathematics in the 21st Century...............................................................................................…1
Chapter 2: Exploring What It Means to Know and Do Mathematics.............................................................................4
Chapter 3: Teaching Through Problem Solving.............................................................................................................9
G
Chapter 4: Planning in the Problem-Based Classroom.................................................................................................12
Chapter 5: Creating Assessments for Learning.............................................................................................................15
Chapter 6: Teaching Mathematics Equitably to All Students.......................................................................................18
S
Chapter 7: Developing Early Number Concepts and Number Sense...........................................................................21
Chapter 8: Developing Meanings for the Operation.....................................................................................................23
N
Chapter 9 Developing Basic Fact Fluency....................................................................................................................26
Chapter 10: Developing Whole-Number Place-Value Concepts..................................................................................29
Chapter 11: Developing Strategies for Addition and E
Subtraction Computation..................................................................................................................32
Chapter 12: Developing Strategies for Multiplication and
Division Computation......................................................................................................................37
E
Chapter 13: Algebraic Thinking, Equations, and Functions.........................................................................................39
Chapter 14: Developing Fraction Concepts..................................................................................................................42
Chapter 15: Developing Fraction Operations...............................................................................................................45
R
Chapter 16: Developing Decimal and Percent Concepts and Decimal Computation...................................................48
Chapter 17: Ratios, Proportions, and Proportional Reasoning.....................................................................................53
Chapter 18: Developing Measurement Concepts..........................................................................................................57
Chapter 19: Geometric Thinking and Geometric Concepts..........................................................................................62
Chapter 20: Developing Concepts of Data and Statistics.............................................................................................66
Chapter 21: Exploring Concepts of Probability............................................................................................................72
Chapter 22: Developing Concepts of Exponents, Integers, and
Real Numbers...................................................................................................................................75
Test...............................................................................................................................................................................78
Answer Key................................................................................................................................................................159
3
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
, INTRODUCTORY THOUGHTS
There is a great deal of difference between writing a text and writing the accompanying Instructor’s Manual. On one
hand, the text, which undoubtedly reflects many personal beliefs, strengths, and weaknesses of the authors, is much
more a reflection of current thinking in mathematics education. The ideas are supported by research and the
direction and vision provided by the NCTM Standards, Curriculum Focal Points, AMTE Standards for Preparing
Teachers of Mathematics and Common Core State Standards documents. The activities are adaptations of ideas
found in journals, been borrowed from excellent teachers, and/or tested personally. The text is offered to the
instructor and pre-service and practicing teachers as a resource for teaching mathematics pre-K to 8 with reasonable
confidence that the ideas found there are solid thinking in mathematics education.
On the other hand, the concept of an instructor’s manual suggests that the authors in some way may be suggesting
how an instructor might teach the class. In talking with numerous colleagues and students around this country and
other countries about the way they conduct their pre-service or in-service methods classes, several ideas are repeated
G
and confirmed. Some of these people use (or used as a student) this text and others do not. What is abundantly clear
is that there are nearly as many ways to conduct a methods class as there are those who teach them. Quite likely,
most of these alternatives have excellent features and fit the needs of the user. The thoughts offered in this
Instructor’s Manual are therefore offered with great temerity and with the hope that they will be accepted in the
spirit of a collegial professional conversation.
Goals and Values
S
N
As you make choices and decisions for your classes, you may find it helpful to focus on a few large ideas that you
want your students to take from the course. If we gathered all your choices, your main agendas may be somewhat
different but equally valuable. Here are three ideas you might keep in mind:
1. A View of Good School Mathematics: Students in your methods class should view school mathematics as
E
a science and process of making sense of things—to understand what it means to do mathematics. The pre-K–8
students we teach in school should come to know mathematics as a discipline involving investigating, verifying,
exploring, explaining, discovering, conjecturing, describing, reasoning, and sense making. It is an active subject that
requires engagement in thinking about important ideas. Prospective teachers should abandon the view that school
E
mathematics is a collection of lock-step rules and procedures for answer-getting. For most teacher candidates this
constitutes a major paradigm shift. It is important to be appreciative of their backgrounds and prior experiences,
while continually stressing that mathematics is a science of pattern and order. R
2. Problem-Based, Student-Centered Approaches: The most significant factor in P-8 students’ learning,
regardless of the content area, is reflective thought. The best way that we know to cause reflective thinking in the
area of mathematics is to use problem-based tasks that require students to struggle with ideas using the mental tools
they currently own. It is neither the manipulatives nor the wonderful explanations that alone can cause learning, but
rather active minds working to make sense of a new idea. The Common Core State Standards go beyond
mathematics content and include eight Standards for Mathematical Practices. These “processes and proficiencies”
must be developed in all students. Your teacher candidates or in-service teachers in your methods class need to
understand why a classroom of lively and productive discourse is to be highly valued and how they can incorporate
the Mathematical Practices to get the students in their future or current classrooms to do the thinking.
3. Mathematics that is Intrinsically Rewarding: Mathematics in school is enjoyable and motivating, both to
learn and to teach. Not all teachers will come to enjoy mathematics equally and very few will get as excited about it
as much as the authors of this text. However, all can learn that it is not routine or boring and that it does not consist
of mindless and tediously repetitious tasks. Most importantly, the enjoyment comes from the mathematics, not from
some external reward. Pre-service and practicing teachers need to experience this level of passion for the subject
matter to enhance their positive disposition toward teaching mathematics.
From the perspective of the authors, the specific content that is selected and even the methods that you choose for
conducting your class are never as important as the big ideas you select and your enthusiasm and passion for
teaching the subject of mathematics.
4
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
G For
Elementary and Middle School
S
Mathematics: N
Teaching DevelopmentallyE
Tenth Edition
E
John A. Van de Walle, Virginia Commonwealth University
Karen S. Karp, University of Louisville
Jennifer M. Bay-Williams, University of Louisville
R
Prepared by
Elizabeth Todd Brown,
Professor Emeritus, University of Louisville
Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto
Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
, S G
N
__________________________________________________________________________________
Copyright © 2019, 2016, 2013 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Printed in
E
the United States of America. This publication is protected by copyright, and permission should be
obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or
transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise.
For information regarding permissions, request forms and the appropriate contacts within the Pearson
E
Education Global Rights & Permissions Department, please visit www.pearsoned.com/permissions/.
Instructors of classes using Elementary and Middle School Mathematics Teaching Developmentally, 10e,
R
by Van de Walle, Karp, Bay-Williams, may reproduce material from the Instructor’s Resource Manual and
Test Bank for classroom use.
10 9 8 7 6 5 4 3 2 1 ISBN-10: 0134802128
ISBN-13: 9780134802121
www.pearsonhighered.com
2
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
, TABLE OF CONTENTS
Introductory Thoughts...................................................................................................................................................iv
Course Designs and Options...........................................................................................................................................v
Introducing These Manual Notes...............................................................................................................................xxiv
Share Your Thoughts..................................................................................................................................................xxv
Chapter by Chapter
Chapter 1: Teaching Mathematics in the 21st Century...............................................................................................…1
Chapter 2: Exploring What It Means to Know and Do Mathematics.............................................................................4
Chapter 3: Teaching Through Problem Solving.............................................................................................................9
G
Chapter 4: Planning in the Problem-Based Classroom.................................................................................................12
Chapter 5: Creating Assessments for Learning.............................................................................................................15
Chapter 6: Teaching Mathematics Equitably to All Students.......................................................................................18
S
Chapter 7: Developing Early Number Concepts and Number Sense...........................................................................21
Chapter 8: Developing Meanings for the Operation.....................................................................................................23
N
Chapter 9 Developing Basic Fact Fluency....................................................................................................................26
Chapter 10: Developing Whole-Number Place-Value Concepts..................................................................................29
Chapter 11: Developing Strategies for Addition and E
Subtraction Computation..................................................................................................................32
Chapter 12: Developing Strategies for Multiplication and
Division Computation......................................................................................................................37
E
Chapter 13: Algebraic Thinking, Equations, and Functions.........................................................................................39
Chapter 14: Developing Fraction Concepts..................................................................................................................42
Chapter 15: Developing Fraction Operations...............................................................................................................45
R
Chapter 16: Developing Decimal and Percent Concepts and Decimal Computation...................................................48
Chapter 17: Ratios, Proportions, and Proportional Reasoning.....................................................................................53
Chapter 18: Developing Measurement Concepts..........................................................................................................57
Chapter 19: Geometric Thinking and Geometric Concepts..........................................................................................62
Chapter 20: Developing Concepts of Data and Statistics.............................................................................................66
Chapter 21: Exploring Concepts of Probability............................................................................................................72
Chapter 22: Developing Concepts of Exponents, Integers, and
Real Numbers...................................................................................................................................75
Test...............................................................................................................................................................................78
Answer Key................................................................................................................................................................159
3
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
, INTRODUCTORY THOUGHTS
There is a great deal of difference between writing a text and writing the accompanying Instructor’s Manual. On one
hand, the text, which undoubtedly reflects many personal beliefs, strengths, and weaknesses of the authors, is much
more a reflection of current thinking in mathematics education. The ideas are supported by research and the
direction and vision provided by the NCTM Standards, Curriculum Focal Points, AMTE Standards for Preparing
Teachers of Mathematics and Common Core State Standards documents. The activities are adaptations of ideas
found in journals, been borrowed from excellent teachers, and/or tested personally. The text is offered to the
instructor and pre-service and practicing teachers as a resource for teaching mathematics pre-K to 8 with reasonable
confidence that the ideas found there are solid thinking in mathematics education.
On the other hand, the concept of an instructor’s manual suggests that the authors in some way may be suggesting
how an instructor might teach the class. In talking with numerous colleagues and students around this country and
other countries about the way they conduct their pre-service or in-service methods classes, several ideas are repeated
G
and confirmed. Some of these people use (or used as a student) this text and others do not. What is abundantly clear
is that there are nearly as many ways to conduct a methods class as there are those who teach them. Quite likely,
most of these alternatives have excellent features and fit the needs of the user. The thoughts offered in this
Instructor’s Manual are therefore offered with great temerity and with the hope that they will be accepted in the
spirit of a collegial professional conversation.
Goals and Values
S
N
As you make choices and decisions for your classes, you may find it helpful to focus on a few large ideas that you
want your students to take from the course. If we gathered all your choices, your main agendas may be somewhat
different but equally valuable. Here are three ideas you might keep in mind:
1. A View of Good School Mathematics: Students in your methods class should view school mathematics as
E
a science and process of making sense of things—to understand what it means to do mathematics. The pre-K–8
students we teach in school should come to know mathematics as a discipline involving investigating, verifying,
exploring, explaining, discovering, conjecturing, describing, reasoning, and sense making. It is an active subject that
requires engagement in thinking about important ideas. Prospective teachers should abandon the view that school
E
mathematics is a collection of lock-step rules and procedures for answer-getting. For most teacher candidates this
constitutes a major paradigm shift. It is important to be appreciative of their backgrounds and prior experiences,
while continually stressing that mathematics is a science of pattern and order. R
2. Problem-Based, Student-Centered Approaches: The most significant factor in P-8 students’ learning,
regardless of the content area, is reflective thought. The best way that we know to cause reflective thinking in the
area of mathematics is to use problem-based tasks that require students to struggle with ideas using the mental tools
they currently own. It is neither the manipulatives nor the wonderful explanations that alone can cause learning, but
rather active minds working to make sense of a new idea. The Common Core State Standards go beyond
mathematics content and include eight Standards for Mathematical Practices. These “processes and proficiencies”
must be developed in all students. Your teacher candidates or in-service teachers in your methods class need to
understand why a classroom of lively and productive discourse is to be highly valued and how they can incorporate
the Mathematical Practices to get the students in their future or current classrooms to do the thinking.
3. Mathematics that is Intrinsically Rewarding: Mathematics in school is enjoyable and motivating, both to
learn and to teach. Not all teachers will come to enjoy mathematics equally and very few will get as excited about it
as much as the authors of this text. However, all can learn that it is not routine or boring and that it does not consist
of mindless and tediously repetitious tasks. Most importantly, the enjoyment comes from the mathematics, not from
some external reward. Pre-service and practicing teachers need to experience this level of passion for the subject
matter to enhance their positive disposition toward teaching mathematics.
From the perspective of the authors, the specific content that is selected and even the methods that you choose for
conducting your class are never as important as the big ideas you select and your enthusiasm and passion for
teaching the subject of mathematics.
4
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All rights reserved.
