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 multilink cubes and then demonstrate how the top and bottom patterns can be turned into squares. I’ve also used this as a timefiller 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. 
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