# Mathematics for Elementary Teachers with Activity Manual

**by**Beckmann, Sybilla

### 9780321654274

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## Summary

**Mathematics for Elementary Teachers, Third Edition **offers an inquiry-based approach to this course, which helps students reach a deeper understanding of mathematics.

**Sybilla Beckmann**, known for her contributions in math education, writes a text that encourages future teachers to find answers through exploration and group work. Fully integrated activities are found in her accompanying Activities Manual, which comes with every new copy of the text. As a result, students engage, explore, discuss, and ultimately reach a true understanding of mathematics.

The new Active Teachers, Active Learners DVD helps instructors enrich their classroom by expanding their knowledge of teaching using an inquiry-based approach. The DVD shows Beckmann and her students discovering various concepts, along with voiceover commentary from Beckmann. This DVD is the ideal resource for instructors who are teaching with an inquiry-based approach for the first time, and for instructors who seek new ideas to integrate into their course.

The table of contents is organized by operation rather than number type to foster a more unified understanding of the math concepts. Throughout the text, students learn why the math works, rather than just the mechanics of how it works. In this new edition the contents have been updated and rearranged for a more natural organization.

As a result, readers engage, explore, discuss, and ultimately reach a true understanding of mathematics. Numbers & the Decimal System; Fractions; Addition & Subtraction; Multiplication; Multiplication of Fractions, Decimals & Negative Numbers; Division; Combining Multiplication & Division: Proportional Reasoning; Number Theory; Algebra; Geometry; Measurement; Area of Shapes; Solid Shapes and their Volume and Surface Area; Geometry of Motion & Change; Statistics; Probability.

For all readers interested in mathematics for elementary school teachers

## Author Biography

**Sybilla Beckmann**earned her undergraduate degree in mathematics from Brown University and a PhD in mathematics from the University of Pennsylvania. She taught and did research in mathematics at Yale University for two years. Since then, she has been at the University of Georgia. When she had children, she became very interested in helping prospective teachers understand and appreciate the mathematics they will teach. This interest led to her book. In her spare time, she enjoys playing the piano, weaving, attending classical music concerts, and traveling with her family.

## Table of Contents

**Chapter 1:** **Numbers and the Decimal System**

1.1 The Counting Numbers

1.2 Decimals and Negative Numbers

1.3 Comparing Numbers in the Decimal System

1.4 Rounding Numbers

**Chapter 2:** **Fractions**

2.1 The Meaning of Fractions

2.2 Interlude: Solving Problems and Explaining Solutions

2.3 Fractions as Numbers

2.4 Fractions as numbers

2.4 Equivalent Fractions

2.5 Comparing Fractions

2.6 Percent

**Chapter 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 Common Algorithms for Adding and Subtracting Numbers in the Decimal System Work

3.4 Adding and Subtracting Fractions

3.5 Adding and Subtracting Negative Numbers

**Chapter 4:** **Multiplication**

4.1 Interpretations of Multiplication

4.2 Why multiplying Numbers by 10 is Easy in the Decimal System

4.3 The Commutative and Associative Properties of Multiplication

4.4 The Distributive Property

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

4.6 Why the Common Algorithm for Multiplying Whole Numbers Works

**Chapter 5:** **Multiplication of Fractions,** **Decimals, and Negative Numbers**

5.1 Multiplying Fractions

5.2 Multiplying decimals

5.3 Multiplying Negative numbers

5.4 Powers and Scientific Notation

**Chapter 6:** **Division**

6.1 Interpretations of Division

6.2 Division and Fractions and Division with Remainder

6.3 Why the Common Long Division Algorithm Works

6.4 Fraction Division from the “How Many Groups?” Perspective

6.5 Fraction Division from the “How Many in One Group?” Perspective

6.6 Dividing Decimals

**Chapter 7:** **Combining Multiplication and** **Division: Proportional Reasoning**

7.1 The Meanings of Ratio, Rate, and Proportion

7.2 Solving Proportion Problems by Reasoning with Multiplication and Division

7.3 Connecting Ratios and Fractions

7.4 When You Can Use a Proportion and When You Cannot

7.5 Percent Revisited: Percent Increase and Decrease

**Chapter 8:** **Number Theory**

8.1 Factors and Multipliers

8.2 Greatest Common Factor and Least Common Multiple

8.3 Prime Numbers

8.4 Even and Odd

8.5 Divisibility Tests

8.6 Rational and Irrational Numbers

8.7 Looking Back at the Number Systems

**Chapter 9:** ** Algebra**

9.1 Mathematical Expressions and Formulas

9.2 Equations

9.3 Solving Equations

9.4 Solving Algebra Story Problems with Strip Diagrams and with Algebra

9.5 Sequences

9.6 Series

9.7 Functions

9.8 Linear Functions

**Chapter 10:** **Geometry**

10.1 Visualization

10.2 Angles

10.3 Angles and Phenomena in the World

10.4 Circles and Spheres

10.5 Triangles, Quadrilaterals, and Other Polygons

10.6 Constructions with Straightedge and Compass

**Chapter 11:** **Measurement**

11.1 Fundamentals 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 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 Cavalieri’s Principle about Shearing and Area

12.6 Areas of Circles and the Number Pi

12.7 Approximating Areas of Irregular Shapes

12.8 Contrasting and Relating the Perimeter and Area of Shape

12.9 Using moving and Additivity Principles to Prove the Pythagorean Theorem

**Chapter 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 14:** **Geometry of Motion and Change**

14.1 Reflections, Translations, and Rotations

14.2 Symmetry

14.3 Congruence

14.4 Similarity

14.5 Areas, Volumes, and Scaling

**Chapter 15:** ** Statistics**

15.1 Formulating Questions, Designing Investigations, and Gathering Data

15.2 Displaying Data and Interpreting Data Displays

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

15.4 The Distribution of Data

**Chapter 16:** **Probability**

16.1 Basic Principles of Probability

16.2 Counting the Number of Outcomes

16.3 Calculating Probabilities in Multi-Stage Experiments

16.4 Using Fraction Arithmetic to Calculate Probabilities