# Geometric Measurement Formulas - A Teacher's Perspective

This module provides a systematic and coherent development of the measurement formulas for computing distances, area and volume of geometric figures in the plane and in space including all of the formulas discussed in high school geometry. It also discusses a variety of problems and results in plane and solid geometry that relate to distance, area and volume as well as the rich history of geometric measurements.

The required textbook for this module is Mathematics For High School Teachers by Usiskin, Peressini, Marchisotto and Stanley. The corresponding content for this module is drawn from Chapters 8 and 10 of the text and the module is written so that it can be completed without reference to other chapters of the book.

This module is divided into the following units:

• Unit 1: Measuring distance in ordinary and unusual ways.
• Unit 2: Understanding the area formulas of plane geometry.
• Unit 3: Understanding the volume and surface area formulas of solid geometry.

These units deal with topics that are either in the typical high school geometry curriculum or are closely related to topics taught high school geometry. However, these topics are treated from a more advanced standpoint that assumes some of the collegiate background that prospective high school mathematics teachers take as undergraduates. This module complements the textbook treatment of this content with web-based resources and dynamic geometric sketches that are not available in any print textbook.

Common Core Standards for Mathemtical Practice that are emphasized include:

• 1. Make sense of problems and persevere in solving them.
• 3. Construct viable arguments.
• 4. Model with mathematics.
• 5. Use appropriate tools strategically.