Mathematics for Elementary Teachers Volume II: Geometry and Other Topics, Preliminary Edition (with Activities Manual)

by Beckmann, Sybilla

• ISBN13: 9780321149145
• ISBN10: 0321149149
• Format: Package
• Copyright: 2003-01-01
• Publisher: Addison Wesley
• More Book Details
• Purchase Benefits

Summary

Available as a two-volume set, this text is intended to give students depth and perspective in their knowledge of the mathematics taught in elementary school. The author believes that some key elements in achieving this depth and perspective are for students to write clear, logical explanations, for students to enhance their intuition by working with examples and by looking for patterns and connections, and for students to use mathematics in a variety of applications. The book is centered around class activities, which are designed for students to work on in class in small groups. The class activities foster engagement, exploration and discussion of the material, rather than passive absorption. Many exercises and problems are included at the end of each chapter. Working on these exercises and problems and justifying their solutions carefully and clearly is crucial to achieving depth of understanding of the material. Both students and instructors should find this material fun, interesting, and rewarding.

Table of Contents

1. Geometry.

Visualization.
Angles.
Circles and Spheres.
Triangles.
Quadrilaterals and Other Polygons.
Constructions with Straightedge and Compass.
Polyhedra and Other Solid Shapes.

2. Geometry of Motion and Change.

Reflections, Translations, and Rotations.
Symmetry.
Congruence.
Similarity.

3. Measurement and Geometry.

The Concept of Measurement.
Measurable Attributes.
Converting From One Unit of Measurement to Another.
The Moving and Combining Principles About Area.
The Pythagorean Theorem.
More Ways to Determine Areas.
Areas of Triangles.
Areas of Parallelograms.
Areas of Circles and the Number Pi.
How are Perimeter and Area Related?
Principles for Determining Volumes.
Volumes of Prisms, Cylinders, Pyramids, and Cones.
Areas, Volumes, and Scaling.

4. Functions and Algebra.

Patterns, Sequences, Formulas, and Equations.
Functions.

5. Statistics.

Designing Investigations and Gathering Data.
Displaying Data.
The Center of Data: Average and Median.
The Spread of Data: Percentiles, Range.

6. Probability.

Some Basic Principles of Probability.
Fraction Multiplication and Probability.

Appendix A: Cutouts for Exercises and Problems.