Perimeter = area rectangles

Purpose

The purpose of this activity is to engage students in finding the perimeter and area of rectangles. They engage in trying to find rectangles where the number measure of the perimeter equals the number measure of the area.

Achievement Objectives
GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
NA4-7: Form and solve simple linear equations.
Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.

Activity
 

As you know, this is a special type of rectangle called a square.

If you walked the perimeter of this rectangle you would travel 4 + 4 + 4 + 4 = 16 units of length.

The area of thisrectangle is 4 x 4 = 16 square units.

The units for perimeter and area are different but both measures equal 16.

For what other rectangles are the measures for perimeter and area equal?

The procedural approach (show more)

  • The student uses trial and error approaches to find some solutions, calculating both perimeter and area correctly.

The conceptual approach (show more)

  • The student uses algebraic thinking with linear relationships by substituting values for one variable into the perimeter equals area equation.

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