Magic Squares 4 – Polo Squares

A while ago I pointed out that while I’ve never found creating a simple 3×3 magic square very useful in the classroom there are plenty of spinoff activities that really do work well.  I devised Polo Squares when I was giving a session for 300 children at the Royal Institution in the middle of London.  The children were from a dozen or more schools and I wanted to offer something that was easily accessible and could be instantly usable no matter how big the groups were or whether they arrived early or with just five minutes to spare.

Every child had a set of ten digit cards, from 0 to 9.  I asked them to make a hollow square using eight of the cards, so the cards on each side of the square add up to the same total.  I provided lots of blank record sheets; clearly a lot of work was done at home after the session, because the postman was delivering solutions for weeks afterwards.

Polo Purple

I’ve no idea how many different Polo Squares there are, but I know it’s several dozen, so no-one’s going to say “I’m finished, what do I do next?”  Each solution uses eight of the ten cards, so there’s an element of Trial and Improvement.

And there are plenty of challenges – “What’s the highest / lowest Polo total?”, “Can you make all totals in between?”, “Which totals have the highest number of solutions?”, …..

Polo Squares offer a nice challenge – even wider than I’d realised; George was just five, and the younger brother of someone who’d attended the session.

Polo George

Using digit cards helps the activity and also makes it feel like fun.  The cards invite the use of some problem-solving skills (look at L & A’s) , and give some meaty mental arithmetic practice.

Polo L&A

And in just the same way I could use them with children waiting for my session to start, teachers can have some digit cards and answer blanks available on parents’ evenings!

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