This investigation is great for getting pupils to “spot” square number patterns – it’s particularly useful as a little starter a couple of weeks after completing the topic to remind them of the sequence of square numbers. Pupils could also make the patterns from multi-link cubes and then demonstrate how the top and bottom patterns can be turned into squares.
I’ve also used this as a time-filler activity with half a class of Year 10s and asked them to come up with the nth term rule for the top and bottom patterns (n² and (n – 1)² respectively), then combine this to get the nth term rule for the complete pattern (gives 2n² – 2n + 1 when expanded and simplified). They then used this to predict and check the next pattern in the sequence.
