Mathematics for Elementary Teachers plus Activities Manual

  • ISBN13:


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  • Edition: 3rd
  • Format: Package
  • Copyright: 2011-01-01
  • Publisher: Addison Wesley
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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
The Meaning of Fractions
Fractions as Numbers
Equivalent Fractions
Comparing Fractions
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
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
The Meaning of Division
Understanding Long Division
Fractions and Division
Dividing Fractions
Dividing Decimals
Ratio and Proportion
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
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
Linear Functions
Formulating Questions, Designing Investigations, and Gathering Data
Displaying Data and Interpreting Data Dis
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