Keeping the Perimeter Constant

(1)

Overview

This is a generative activity useful for exploring basic geometry and examining relationships between area and perimeter. Students will draw rectangles of different areas, keeping the perimeter constant. Part two of the activity will ask students to provide non integer sided examples.

(3)(4)(5)

This activity will use all of the above skills together and will illustrate a full understanding of theses concepts if students can successfully manipulate the sides of the rectangle while keeping the perimeter constant. It is teacher led and structured in that the teacher will designate the constant for perimeter and require that students include non-integer sided examples. It is open ended in that there are many possible solutions. Students will determine their own scale for their drawings and solve the problem with their own examples within the guidelines of the activity.

(2)

Pre-Requisites/Introduction

The class will need to have an understanding of rectangles and measuring perimeter and area. A possible lead in would be a class discussion about the distinguishing characteristics of squares, rectangles, and triangles. Ask students to identify as many similarities and differences as they can.

(6)(11)(12)

Class Plans

a)Discuss ways to manipulate the sides of the rectangle to change the shape, within the perimeter restrictions. Teacher should draw examples on overhead graph.

b)Hand out graph paper and tables to be filled out with columns for rectangle number, side 1, side 2, area, and perimeter.

c)Have students work with a partner to fill out table. Ask them to create a scale for their drawings, number the rectangles they have drawn on the graph paper, and calculate data for the graph. Formulas will be unnecessary as students can count squares on the graph paper.

d)Provide a second table and ask students to repeat the steps, this time creating rectangles with non-integer sides.

(7)

Possible Student Responses

Graph Paper

(8)

After students have worked independently, have a class discussion in which the teacher asks students to give examples of patterns in their tables and to come up to the overhead and draw some of their most interesting rectangles.