Mathematics for Elementary Teachers with Activities

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-01-01
  • Publisher: Addison Wesley
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The goal of this text is to provide prospective elementary teachers with a deep understanding of the mathematics they will be called on to teach. Through a careful, mathematically precise development of concepts, this text asks that students go beyond simply knowing how to carry out mathematical procedures. Students must also be able to explain why mathematics works the way it does. Being able to explain why is a vital skill for teachers. Through activities, examples and applications, the author expects students to write and solve problems, make sense of the mathematics, and write clear, logical explanations of the mathematical concepts. The accompanying Activities Manual promotes engagement, exploration, and discussion of the material, rather than passive absorption. Both students and instructors should find this material fun, interesting, and rewarding.

Table of Contents

Problem Solving
Solving Problems
Explaining Solutions
Numbers and the Decimal System
Introduction to the Number Systems
The Decimal System and Place Value
Representing Decimal Numbers
Comparing Sizes of Decimal Numbers
Rounding Decimal Numbers
The Meaning of Fractions
Equivalent Fractions
Fractions as Numbers
Comparing Sizes of Fractions
Addition and Subtraction
Interpretations of Addition and Subtraction
The Algorithms for Adding and Subtracting
Adding and Subtracting Fractions
When Do We Add Percentages
Percent Increase and Percent Decrease
The Commutative and Associative Properties and Mental Math
The Meaning of Multiplication
Why Multiplying Decimal Numbers by 10 Is Easy
Multiplication and Areas of Rectangles
The Commutative Property of Multiplication
Multiplication and Volumes of Boxes
The Associative Property of Multiplication
The Distributive Property
Mental Math, Properties of Arithmetic, and Algebra
Why the Procedure for Multiplying Works
Multiplication of Fractions, Decimals, and Negative Numbers
Multiplying Fractions
Multiplying Decimals
Multiplying Negative Numbers
Scientific Notation
The Meaning of Division
Understanding Long Division
Fractions and Division
Dividing Fractions
Dividing Decimals
Ratio and Proportion
Circles and Spheres
Quadrilaterals and Other Polygons
Constructions With Straightedge and Compass
Polyhedra and Other Solid Shapes
Geometry of Motion and Change
Reflections, Translations, and Rotations
The Concept of Measurement
Error and Accuracy in Measurements
Length, Area, Volume, and Dimension
Calculating Perimeter, Area, and Volume
Comparing Sizes of Objects
Converting From one Unit of Measurement to Another
More About Area and Volume
The Moving and Combining Principles About Area
The Pythagorean Theorem
Approximating Areas of Irregular Shapes
Cavalieri's Principle About Shearing and Area
Areas of Triangles
Areas of Parallelograms
Areas of Circles and the Number Pi
Relating the Perimeter and Area of a Shape
Principles for Determining Volumes
Volumes of Solid Shapes
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 With Pictures and With Algebra
Linear Functions
Designing Investigations and Gathering Data
Displaying Data and Interpreting Data Displays
The Center of Data: Mean, Median and Mode
The Spread of Data: Percentiles
Basic Principles and Calculation Methods of Probability
Calculating Probabilities by considering the Ideal Outcome
Table of Contents provided by Publisher. All Rights Reserved.

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