A Parabolic Investigation


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

Description of Mathematics

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

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


Task: a rectangular sheet of card, with perimeter = 80 cm is made into an open-topped box, by folding in 2 cm x 2 cm squares from each corner. Investigate the relationship between x, the length of one side of the card and C, the capacity of the box.



The arithmetic approach (show more)

  • The student makes and measures concrete examples to lead them to solve the problem.
  • The student links the practical task to a generalised model

The procedural algebraic approach (show more)

  • The student carries out directed calculations that will lead them to find a quadratic relationship.

The conceptual algebraic approach (show more)

  • The student carries out an algebraic investigation that allows them to describe a quadratic relationship.

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