This is one of my very favourite mathematical investigations from **I See Reasoning – UKS2**: there’s a great pattern to explore. When I was in Y6 it was one of my ‘go to’ tasks for this time of year. Here’s our first discovery:

Despite having the same sum, the numbers give different products. And the further apart the numbers get, the smaller the product. But look at this:

There’s a pattern to how the products decrease: 1 less, 4 less, 9 less, 16 less. This is a pattern of square numbers. How odd! I wonder… is this the case for this example only? Or would it work for any example where the sequence starts from a square number? So the exploration continues, and we see that the pattern is repeated (e.g. 10×10=100, 11×9=99, 12×8=96, 13×7=91).

Eventually, I would challenge the children to use this knowledge to perform calculations. For example, consider 23×17. We know 20×20=400, so it follows that 23×17=391 (9 less than 400).

A beautiful pattern to explore!

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