In the video below, Matt Parker and James Grime get us thinking about the sorts of numbers that can be expressed as the difference of two squares. Use the video and our task ideas to get your students playing around with squares and constructing proofs.
Curriculum Topics Covered
Square numbers, proof – algebraic and visual, being systematic.
Can your students investigate the sorts of numbers that can be the difference of two squares, before watching the video? ‘Difference of Two Squares’ is a task we’ve made that you could use for this. See ‘Differences of Two Squares Notes’ for teacher notes on this task. Also, see this similar Nrich task: https://nrich.maths.org/742
In the video, Matt and James do not do a visual proof that all multiples of four can be written as the difference of two squares. Can your students find a way of doing this? See our proof in the document: ‘Proof Multiples of Four’.