Geometric measurement formulas; that is, formulas for computing:
- the area or perimeter of geometric figures in the plane such as triangles, polygons and circles,
- the volume or surface area of various geometric solids such as pyramids, cylinders and spheres, and
- the distance between geometric objects such as the distance between two points or between a point and a line,
are important topic in high school geometry.
The discussion of basic area and perimeter formulas usually begins in middle school or even earlier when students begin to identify and classify geometric figures. From that point on, geometric measurement formulas are important tools in all mathematics courses.
The first objective of this module is to provide mathematics teachers with a systematic development of all of the standard geometric measurement formulas with careful attention to their rich history and their numerous applications. The second objective is to help teachers to explore the many connections that exist between these formulas and the rest of geometry, algebra, precalculus and calculus.
We will help teachers achieve these instructional objectives through the guided individual study of text and internet-based course resources, four required problem assignments and the preparation of an approved final classroom project.
Textbook and prerequisite skills for this module.
The required textbook for this module is Mathematics for High School Teachers by Usiskin, Peressini, Marchisotto and Stanley. This book is a very good professional development resource for high school mathematics teachers. If you do not wish to purchase it yourself, it may be available in your school library or you may ask your school librarian to order a copy.
All four assignments for this module will require you to produce accurate geometric sketches and constructions and insert them into the Microsoft Word documents that you will prepare for the four assignments of this module. Consequently, you will need access to and some facility with a geometric construction program such as Geometer's Sketchpad to do the assignments. Math Teacher Link offers a Tutorial for math teachers (Module 4: Using the Geometer's Sketchpad) that you can take for free as an MTL Guest or for credit (SeeRegistration , Fees and Getting Started for more details.)
You will submit these assignments and retrieve your graded assignments electronically through the MTL Module Working Environment (also referred to as Moodle)..
Structure of the Module:
This module is divided into the following units and parts:
Unit 1: Measuring Distance in Ordinary and Unusual Ways
- Part 1: What is distance?
- Part 2: Minimum distance problems in plane geometry.
Unit 2: Understanding the Area Formulas of Plane Geometry.
- Part 1: Area formulas for polygonal figures
- Part 2: Area formula for curvilinear figures.
Unit 3: Understanding the Volume and Surface Area formulas of Solid Geometry
- Part 1:Volume formulas for Polyhedra.
- Part 2: Volume and Surface Area formulas for cylinders, spheres, cones and other "curvy" solids.
Module Completion Requirements:
You wil have an enrollment period of three months from the date that you are e-mailed your MTL log-in, password and 800-Help number to complete all of your work for this module. A three month extension is possible for unforeseen circumstances provided that you are making reasonable progress with your work.
There are a total of four assignments: Assignment 1.1 for Unit 1, Assignments 2.1 and 2.2 for Unit 2, and Assignment 3.1 for Unit 3. You should do each assignment as soon as you complete the parts of the unit required by the assignment. You will be asked to place the solutions of all of the problems in a given assignment into a single Microsoft Word document and then submit the document electronically through the MTL Module Working Environment (also referred to as the ClassComm system). The module instructor will evaluate your work on each assignment and return your graded assignment through ClassComm and /or e-mail the results to you.
Teachers enrolled in this module for University of Illinois Continuing Education Units are required to satisfactorily complete these four assignments.
Teachers enrolled for University of Illinois graduate credit, or undergraduate prospective mathematics teachers enrolled for University of Illinois undergraduate credit, must also complete an approved Final Project.