Mathematics for Elementary Teachers plus Activities Manual

by Beckmann, Sybilla

• ISBN13: 9780321447173
• ISBN10: 0321447174
• Edition: 3rd
• Format: Package
• Copyright: 2011-01-01
• Publisher: Addison Wesley

Summary

Elementary school classrooms are increasingly relying on a discovery method for the teaching of mathematics.Mathematics for Elementary Teachersthoroughly 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. Students, as a result, engage, explore, discuss, and ultimately reach true understanding of the approachandof mathematics.

Table of Contents

Problem Solving

Solving Problems

Explaining Solutions

Numbers and the Decimal System

Overview of the Number Standards

The Decimal System and Place Value

Representing Decimal Numbers

Comparing Decimal Numbers

Rounding Decimal Numbers

Fractions

The Meaning of Fractions

Fractions as Numbers

Equivalent Fractions

Comparing Fractions

Percent

Addition and Subtraction

Interpretations of Addition and Subtraction

Why the Standard Algorithms for Adding and Subtracting Decimal Numbers Work

Adding and Subtracting Fractions

When Do We Add Percentages?

Percent Increase and Percent Decrease

The Commutative and Associative Properties of Addition and Mental Math

Multiplication

The Meaning of Multiplication and Ways to Show Multiplication

Why Multiplying Decimal Numbers by 10 is Easy

The Commutative Property of Multiplication and Areas of Rectangles

The Associative Property of Multiplication and Volumes of Boxes

The Distributive Property

Mental Math, Properties of Arithmetic, and Algebra

Why the Procedure for Multiplying Whole Numbers Works

Multiplication of Fractions, Decimals, and Negative Numbers

Multiplying Fractions

Multiplying Decimals

Multiplying Negative Numbers

Scientific Notation

Division

The Meaning of Division

Understanding Long Division

Fractions and Division

Dividing Fractions

Dividing Decimals

Ratio and Proportion

Geometry

Visualization

Angles

Circles and Spheres

Triangles, Quadrilaterals, and Other Polygons

Constructions with Straightedge and Compass

Polyhedra and Other Solid Shapes

Geometry of Motion and Change

Reflections, Translations, and Rotations

Symmetry

Congruence

Similarity

Measurement

Fundamentals of Measurement

Length, Area, Volume, and Dimension

Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes

Error and Accuracy in Measurements

Converting from One Unit of Measurement to Another

More About Area and Volume

The Moving and Additivity Principles About Area

Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

Areas of Triangles

Areas of Parallelograms

Cavalieri's Principle About Shearing and Area

Areas of Circles and the Number Pi

Approximating Areas of Irregular Shapes

Relating the Perimeter and Area of a Shape

Principles for Determining Volumes

Volumes of Prisms, Cylinders, Pyramids, and Cones

Areas, Volumes, and Scaling

Number Theory

Factors and Multiples

Greatest Common Factor and Least Common Multiple

Prime Numbers

Even and Odd

Divisibility Tests

Rational and Irrational Numbers

Functions and Algebra

Mathematical Expressions, Formulas, and Equations

Solving Equations Using Number Sense, Strip Diagrams, and Algebra

Sequences

Series

Functions

Linear Functions

Statistics

Formulating Questions, Designing Investigations, and Gathering Data

Displaying Data and Interpreting Data Dis

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