Why use this resource?

This resource requires students to problem solve. It focuses on a problem of historical significance is accessible but also leads to a slightly startling observation about the relationship between the areas of two shapes.

The first two problems are accessible to all Y12 students requiring no more than GCSE knowledge. This is a useful problem for students to engage in mathematical thinking.

Possible approach

A useful approach to this problem is as a “think, pair, share” activity.

  • Think: Firstly, ask students to individually think about the problem. Some students may become stuck and you may wish to offer a hint but it is important that students should be allowed to become stuck and work through this as much as possible.
  • Pair: After a suitable length of time, ask the students to discuss the problem in pairs comparing their different methods.
  • Share: As a whole class, the students can discuss the problem.

It is possible to approach problems 1 and 2 as separate problems if you do not have time to complete the whole activity.

Key questions

  • What mathematical thinking have we done this lesson?

Possible support

Are there any shapes in this diagram whose areas we can find?

Possible extension

Extension activities are suggested in the task.

A version of this resource has been featured on the NRICH website. You might like to look at some students’ solutions that have been submitted there.