# Mathematics for Elementary and Middle School Teachers with Activities, 6th edition

Published by Pearson (May 21, 2021) © 2022

**Sybilla Beckmann**

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## MyLab

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For courses in Mathematics for Teachers.

### Fosters deep understanding that leads to effective teaching

**Mathematics for Elementary and Middle School Teachers, 6th Edition** connects the foundations of K-8 mathematics to the "why" behind procedures and formulas. Known for her contributions to mathematics education, Beckmann helps future teachers explain why the standard procedures and formulas of elementary and middle school mathematics are valid, why nonstandard methods can also be valid, and more. The Classroom Activities, Problems and narrative foster active student engagement in mathematical practices. The text also addresses the K-8 CCSS for Mathematical Content from a teacher's perspective.

### Hallmark features of this title

**Organization around operations**instead of different types of numbers offers a more advanced and unified perspective; fractions, decimals and percents (traditional weak spots) can be studied repeatedly throughout the course rather than only at the end.**Emphasis on key concepts and principles**guides prospective teachers in giving explanations.**CCSS Standards for Mathematical Practice**and**CCSSM content standards:**CCSS References in the margin connect content to specific CCSS standards.**Visual representations**such as number lines, double number lines, strip diagrams and base-ten drawings are used throughout and help prospective teachers learn to explain mathematical ideas, solution methods and standard notation.- Many resources are available for download
**.**

### New and updated features of this title

**Revised Classroom Activities**are now available to students in multiple places. The**6th Edition**adds a wealth of new activities, and a new activities Materials list details any resources needed outside of the worksheet itself.**Narrative is simplified and revised throughout**to make mathematical ideas clear and accessible.**Revised introductions to many sections**provide a better rationale for the material and engage the ideas that future teachers may already have about the material.**Several new From the Field Research entries**have been added, many of which connect the material to research with students in elementary and middle school.**From the Field**also has been expanded with**Indexes and Bibliographies.****Additional entries**link material in the text to research**Correlations to State Standards;**a web page contains correlations of the content of this book to major K-8 state standards. Correlations are continually updated.**Chapter Review Problems**replace the Chapter Summary and provide more unique assistance to students, rather than simply repeating information from each section. These problems pull together ideas from the chapter as a whole and prepare students more effectively for chapter tests.

### Features of MyLab Math for the 6th Edition

- The MyLab course is a special
**Skills Review**course including the eText, video library and skills review exercises to help students practice basic skills. All Activities from the manual, along with additional activities, are included. **Exercise review and fine-tuning**: Burak Ölmez (University of Southern California) reviewed all MyLab exercises and suggested revisions to better align the content to support the text.**Extensive video program****specific to this text**includes Demonstration Videos, where the author or faculty demonstrate math processes and why they work. Conceptual Understanding Videos build conceptual understanding of key concepts. Many include corresponding exercises.**Integrated Mathematics and Pedagogy (IMAP) videos and video exercises:**The popular IMAP video exercises show elementary and middle school students working through problems, providing insight into student thinking. All IMAP videos now have at least 1**assignable exercise**, enabling instructors to check that students watched the video.**More Interactive Figures**in editable GeoGebra format serve as teaching and learning tools. Instructors can assign them as part of homework via MyLab Math.

Preface

Solving Problems and Explaining Solutions

**1. Numbers and the Base-Ten System **

1.1 The Counting Numbers

1.2 Decimals and Negative Numbers

1.3 Reasoning to Compare Numbers in Base Ten

1.4 Reasoning about Rounding

CHAPTER REVIEW PROBLEMS

**2. Fractions and Problem Solving**

2.1 Defining and Reasoning about Fractions

2.2 Reasoning about Equivalent Fractions

2.3 Reasoning to Compare Fractions

2.4 Reasoning about Percent

CHAPTER REVIEW PROBLEMS

**3. Addition and Subtraction**

3.1 Interpretations of Addition and Subtraction

3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts

3.3 Why the Standard Algorithms for Addition and Subtraction in Base Ten Work

3.4 Reasoning about Fraction Addition and Subtraction

3.5 Why We Add and Subtract with Negative Numbers the Way We Do

CHAPTER REVIEW PROBLEMS

**4. Multiplication **

4.1 Interpretations of Multiplication

4.2 Why Multiplying by 10 Is Special in Base Ten

4.3 The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes ofBoxes

4.4 The Distributive Property

4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts

4.6 Why the Standard Algorithm for Multiplying Whole Numbers Works

CHAPTER REVIEW PROBLEMS

**5. Multiplication of Fractions, Decimals, and Negative Numbers**

5.1 Making Sense of Fraction Multiplication

5.2 Making Sense of Decimal Multiplication

5.3 Extending Multiplication to Negative Numbers

5.4 Powers and Scientific Notation

CHAPTER REVIEW PROBLEMS

**6. Division**

6.1 Interpretations of Division

6.2 Division and Fractions and Division with Remainder

6.3 Why Division Algorithms Work

6.4 Fraction Division from the How-Many-Groups Perspective

6.5 Fraction Division from the How-Many-Units-in-1-Group Perspective

6.6 Dividing Decimals

CHAPTER REVIEW PROBLEMS

**7. Ratio and Proportional Relationships **

7.1 Motivating and Defining Ratio and Proportional Relationships

7.2 Solving Proportion Problems by Reasoning with Multiplication and Division

7.3 The Values of a Ratio: Unit Rates and Multipliers

7.4 Proportional Relationships

7.5 Proportional Relationships versus Inversely Proportional Relationships

7.6 Percent Revisited: Percent Increase and Decrease

CHAPTER REVIEW PROBLEMS

**8. Number Theory**

8.1 Factors and Multiples

8.2 Even and Odd

8.3 Divisibility Tests

8.4 Prime Numbers

8.5 Greatest Common Factor and Least Common Multiple

8.6 Rational and Irrational Numbers

CHAPTER REVIEW PROBLEMS

**9. Algebra**

9.1 Numerical Expressions

9.2 Expressions with Variables

9.3 Equations

9.4 Solving Algebra Word Problems with Strip Diagrams and with Algebra

9.5 Sequences

9.6 Functions

9.7 Linear and Other Relationships

CHAPTER REVIEW PROBLEMS

**10. Geometry **

10.1 Lines and Angles

10.2 Angles and Phenomena in the World

10.3 Circles and Spheres

10.4 Triangles, Quadrilaterals, and Other Polygons

CHAPTER REVIEW PROBLEMS

**11. Measurement **

11.1 Concepts of Measurement

11.2 Length, Area, Volume, and Dimension

11.3 Error and Precision in Measurements

11.4 Converting from One Unit of Measurement to Another

CHAPTER REVIEW PROBLEMS

**12. Area of Shapes **

12.1 Areas of Rectangles Revisited

12.2 Moving and Additivity Principles About Area

12.3 Areas of Triangles

12.4 Areas of Parallelograms and Other Polygons

12.5 Shearing: Changing Shapes Without Changing Area

12.6 Area and Circumference of Circles and the Number Pi

12.7 Approximating Areas of Irregular Shapes

12.8 Contrasting and Relating the Perimeter and Area of Shapes

12.9 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

CHAPTER REVIEW PROBLEMS

**13. Solid Shapes and Their Volume and Surface Area**

13.1 Polyhedra and Other Solid Shapes

13.2 Patterns and Surface Area

13.3 Volumes of Solid Shapes

13.4 Volume of Submersed Objects versus Weight of Floating Objects

CHAPTER REVIEW PROBLEMS

**14. Geometry of Motion and Change**

14.1 Reflections, Translations, and Rotations

14.2 Symmetry

14.3 Congruence

14.4 Constructions with Straightedge and Compass

14.5 Similarity

14.6 Dilations and Similarity

14.7 Areas, Volumes, and Similarity

CHAPTER REVIEW PROBLEMS

**15. Statistics **

15.1 Formulating Statistical Questions, Gathering Data, and Using Samples

15.2 Displaying Data and Interpreting Data Displays

15.3 The Center of Data: Mean, Median, and Mode

5.4 Summarizing, Describing, and Comparing Data Distributions

CHAPTER REVIEW PROBLEMS

**16. Probability**

16.1 Basic Principles of Probability

16.2 Counting the Number of Outcomes

16.3 Calculating Probabilities of Compound Events

16.4 Using Fraction Arithmetic to Calculate Probabilities

CHAPTER REVIEW PROBLEMS

Downloads

Bibliography

Index

Credits

### About our author

**Sybilla Beckmann** is a Josiah Meigs Distinguished Professor of Mathematics, Emeritus at the University of Georgia. She received her PhD in mathematics from the University of Pennsylvania and taught at Yale University as a J.W. Gibbs Instructor of Mathematics. Her early research was on Arithmetic Geometry, but her current research is in mathematical cognition, education of teachers, and mathematics content for students at all levels, particularly for PreK through the middle grades. She has developed mathematics courses for prospective elementary and middle grades teachers at the University of Georgia and wrote this book for such courses.

A member of the writing teams for the Common Core State Standards for Mathematics* *and for NCTM's **Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics**, she has worked on the development of several state mathematics standards. She was a member of the Committee on Early Childhood Mathematics of the National Research Council and coauthor of its report **Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity.** She has also been a member on other national panels and committees working to improve mathematics education. Several years ago she taught an average 6th-grade mathematics class every day at a local public school in order to better understand school mathematics teaching. Sybilla has won numerous awards, including the Louise Hay Award for Contributions to Mathematics Education for the Association of Women in Mathematics and the Mary P. Dolciani Award from the Mathematical Association of America.

Sybilla enjoys playing piano, running, singing, dancing, weaving, and traveling with her family. She and her husband Will Kazez live in Athens, Georgia. They look forward to visits from their 2 children who are now away working and in graduate school.

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