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Mathematics for Elementary Teachers - With Activities Manual

Mathematics for Elementary Teachers - With Activities Manual - 2nd edition

Mathematics for Elementary Teachers - With Activities Manual - 2nd edition

ISBN13: 9780321447173

ISBN10: 0321447174

Mathematics for Elementary Teachers - With Activities Manual by Sybilla Beckmann - ISBN 9780321447173
Edition: 2ND 08
Copyright: 2008
Publisher: Addison-Wesley Longman, Inc.
International: No
Mathematics for Elementary Teachers - With Activities Manual by Sybilla Beckmann - ISBN 9780321447173

ISBN13: 9780321447173

ISBN10: 0321447174

Edition: 2ND 08

Other Editions of Mathematics for Elementary Teachers - With Activities Manual

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Elementary school classrooms are increasingly relying on a discovery method for the teaching of mathematics. Mathematics for Elementary Teachers thoroughly prepares preservice teachers to use this approach as it has been proven to increase their depth of understanding of mathematics. In this text, topics are organized by operation, rather than number type, and time is spent explaining why the math works, rather than just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics.


  • The table of contents is organized according to operation instead of by number type, making the learning process more intuitive and easier.
  • Class Activities are integral to learning and are designed to be done in class or in small groups outside of class. They promote critical thinking, discussion, and give students depth of understanding and perspective on the concepts.
  • Practice Problems are an opportunity for students to work through problems with solutions immediately following. This prompt feedback prepares them for homework questions that count.
  • Problems are opportunities for practice without available solutions, typically assigned as homework. Answers appear in the Instructor's Solutions Manual and can be provided online for students at the discretion of the instructor.
  • Unique content in Chapter 13: Functions and Algebra introduces U.S. teachers to the impressive diagrammatic method presented in grade 3 - 6 math texts used in Singapore, where children score top in the world in math. This method helps students make sense of, and solve, a variety of algebra and other word problems without using variables. The text helps students see the relationship between the Singaporean diagrammatic method and standard algebraic problem solving methods.

Table of Contents

Table of Contents

Chapter 1 Problem Solving

1.1 Solving Problems
1.2 Explaining Solutions

Chapter 2 Numbers and the Decimal System

2.1 Overview of the Number Standards
2.2 The Decimal System and Place Value
2.3 Representing Decimal Numbers
2.4 Comparing Decimal Numbers
2.5 Rounding Decimal Numbers

Chapter 3 Fractions

3.1 The Meaning of Fractions
3.2 Fractions as Numbers
3.3 Equivalent Fractions
3.4 Comparing Fractions
3.5 Percent

Chapter 4 Addition and Subtraction

4.1 Interpretations of Addition and Subtraction
4.2 Why the Standard Algorithms for Adding and Subtracting Decimal Numbers Work
4.3 Adding and Subtracting Fractions
4.4 When Do We Add Percentages?
4.5 Percent Increase and Percent Decrease
4.6 The Commutative and Associative Properties of Addition and Mental Math

Chapter 5 Multiplication

5.1 The Meaning of Multiplication and Ways to Show Multiplication
5.2 Why Multiplying Decimal Numbers by 10 is Easy
5.3 The Commutative Property of Multiplication and Areas of Rectangles
5.4 The Associative Property of Multiplication and Volumes of Boxes
5.5 The Distributive Property
5.6 Mental Math, Properties of Arithmetic, and Algebra
5.7 Why the Procedure for Multiplying Whole Numbers Works

Chapter 6 Multiplication of Fractions, Decimals, and Negative Numbers

6.1 Multiplying Fractions
6.2 Multiplying Decimals
6.3 Multiplying Negative Numbers
6.4 Scientific Notation

Chapter 7 Division

7.1 The Meaning of Division
7.2 Understanding Long Division
7.3 Fractions and Division
7.4 Dividing Fractions
7.5 Dividing Decimals
7.6 Ratio and Proportion

Chapter 8 Geometry

8.1 Visualization
8.2 Angles
8.3 Circles and Spheres
8.4 Triangles, Quadrilaterals, and Other Polygons
8.5 Constructions with Straightedge and Compass
8.6 Polyhedra and Other Solid Shapes

Chapter 9 Geometry of Motion and Change

9.1 Reflections, Translations, and Rotations
9.2 Symmetry
9.3 Congruence
9.4 Similarity

Chapter 10 Measurement

10.1 Fundamentals of Measurement
10.2 Length, Area, Volume, and Dimension
10.3 Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes
10.4 Error and Accuracy in Measurements
10.5 Converting from One Unit of Measurement to Another

Chapter 11 More About Area and Volume

11.1 The Moving and Additivity Principles About Area
11.2 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem
11.3 Areas of Triangles
11.4 Areas of Parallelograms
11.5 Cavalieri's Principle About Shearing and Area
11.6 Areas of Circles and the Number Pi
11.7 Approximating Areas of Irregular Shapes
11.8 Relating the Perimeter and Area of a Shape
11.9 Principles for Determining Volumes
11.10 Volumes of Prisms, Cylinders, Pyramids, and Cones
11.11 Areas, Volumes, and Scaling

Chapter 12 Number Theory

12.1 Factors and Multiples
12.2 Greatest Common Factor and Least Common Multiple
12.3 Prime Numbers
12.4 Even and Odd
12.5 Divisibility Tests
12.6 Rational and Irrational Numbers

Chapter 13 Functions and Algebra

13.1 Mathematical Expressions, Formulas, and Equations
13.2 Solving Equations Using Number Sense, Strip Diagrams, and Algebra
13.3 Sequences
13.4 Series
13.5 Functions
13.6 Linear Functions

Chapter 14 Statistics

14.1 Formulating Questions, Designing Investigations, and Gathering Data
14.2 Displaying Data and Interpreting Data Displays
14.3 The Center of Data: Mean, Median, and Mode
14.4 Percentiles and the Distribution of Data

Chapter 15 Probability

15.1 Basic Principles and Calculation Methods of Probability
15.2 Using Fraction Arithmetic to Calculate Probabilities

Other Editions of Mathematics for Elementary Teachers - With Activities Manual

Mathematics for Elementary Teachers - With Activity Manual by Sybilla Beckmann - ISBN 9780321654274
Mathematics for Elementary Teachers by Sybilla Beckmann - ISBN 9780321357731