A Parabolic Investigation


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

Achievement Objectives
NA5-7: Form and solve linear and simple quadratic equations.
NA5-9: Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.
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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Level Five