NRICH - Doesn't Add Up

Functions and Graphs - Straight Line Graphs
Key Stage: 4 ★★

This square of area 64 is cut up and rearranged to make a rectangle of area 65. Can you explain what has happened?

This problem forces attention on what happens when we calculate area by dissection into known shapes and the care we should take in our justification. In problem solving diagrams can often be misleading, and not just diagrams we draw for oursleves. There is a need to question and check that the representation is meaningful and conveys the message accurately. This problem brings that idea to the fore.

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.