NRICH - Fence It

Area and Perimeter
Key Stage: 3 ★

If you have 40 one-metre sections of fencing, what is the largest rectangular area you could fence off? What if there was a wall to help you?

This problem challenges students to work systematically while applying their knowledge of areas of rectangles. It offers opportunities for higher level mathematical thinking (optimising and graphing) in a context that doesn't require sophisticated mathematical content. This problem could be revisited when students are able to use algebraic techniques (e.g. maximising by completing the square).

This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.


The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.