Tricky rectangles


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

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.




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 m2) 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.

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