Purpose

The purpose of this multi-level task is to engage students in an algebraic investigation of a practical problem.

Achievement Objectives

Description of Mathematics

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

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

Task: The sides of a rectangle, in metres, are each a whole number, less than 10.

The area of the rectangle is the same value (in m^{2}) as the perimeter (in m). Is this possible?

### The arithmetic approach (show more)

- The student forms algebraic equations as a description of the steps taken in calculations. They calculate with numbers first, enabling them to focus on the steps they took as they generalise with algebra.

### The procedural algebraic approach (show more)

- The student carries out directed calculations that will lead them to form and use a quadratic equation to solve a problem.

### The conceptual algebraic approach (show more)

- The student carries out an exhaustive algebraic investigation where they to form and use algebraic equations, including quadratics, to solve a problem.

Attachments

TrickyRectangles_full.pdf538.01 KB

TrickyRectangles_arithmetic.pdf185.92 KB