Massachusetts Department of Higher Education
2010 Mathematical Preparation of Elementary Teachers Module Series

|Module Title: |Geometry and Spatial Sense |
|Abstract: |In this lesson, the students will explore and analyze geometric shapes, properties of shapes and relationships; specify |
| |locations and describe spatial relationships using coordinate geometry; apply transformations to analyze mathematical |
| |situations; and use visualization, spatial reasoning, and geometric modeling to solve problems. |
|Curriculum Framework Content|Geometry & Measurement |
|Strand(s): | |
|Content Prerequisites: |Students should have informal experiences with geometric shapes, properties of shapes, and relationships. |
|Authors: |Bill Buckreis |
| |wbuckreis@framingham.edu |
| |Framingham State University |
| |Mathematics Department |

TABLE OF CONTENTS

OVERVIEW………………………………………………………………………………………………..3

LESSON OBJECTIVES…………………………………………………………………………………...3

LESSON FORMAT………………………………………………………………………………………..4

SUGGESTED ACTIVITIES, PROBLEMS, AND ASSESSMENTS……………………………………..5

RESOURCES…………………………………………………………………………………………….33
Overview
According to the National Council of Teachers of Mathematics [NCTM] Principles and Standards for School Mathematics (2000), geometry and spatial sense are fundamental components of mathematics learning. Geometry and spatial sense offer ways to interpret and reflect on our physical environment and can serve as tools for the study of other topics in mathematics and science. NCTM proposes that instructional programs from prekindergarten through grade 12 enable all students to:

• analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;

• specify locations and describe spatial relationships using coordinate geometry;

• apply transformations and use symmetry to analyze mathematical situations;

• use visualization, spatial reasoning, and geometric modeling to solve problems.

These recommendations are also echoed in the Massachusetts Mathematics Curriculum Framework.

In this lesson, the students will explore and analyze geometric shapes, properties of shapes and relationships; specify locations and describe spatial relationships using coordinate geometry; apply transformations to analyze mathematical situations; and use visualization, spatial reasoning, and geometric modeling to solve problems.

Lesson Objectives

The students will engage in problem solving, communicating, reasoning, connecting, and representing as they:

1. Put two-dimensional shapes together and take them apart.

2. Identify, describe, and compare two- and three-dimensional shapes.

3. Predict properties of and relationships between two- and three dimensional shapes and validate the results of predicting.

4. Graph points and identify coordinates of points on the