Mathemagic

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I know many mathematicians who enjoy various forms of mathematical recreation – sudoku, mathematical art, solving really hard differential equations for fun… and lots who dabble in mathematical “magic”. There is something that entrances young and old alike when a card trick is performed with verve and showmanship, but there is even more satisfaction in seeing a mathematically based card trick and figuring out how it is done.

I’m preparing for a session working with some Year 10 students in a few weeks. It’s only a short session – 45 minutes or so – and most of my favourite maths tasks take rather longer to get into than that. So a colleague suggested I did some mathematical card magic with them, and suggested the problem The Amazing Card Trick. His idea is that he’ll come in, do the trick, and then leave us to puzzle out how he did the trick – something he’s done with great success working with groups of children in the past.

I wanted to make sure I’d cemented the trick in my mind before trying it out in public with actual youngsters, so after dinner with friends (and a few glasses of wine) at the weekend, I requested a pack of cards and tried it out. My friends loved it, and had the trick figured out (complete with algebra to explain how it worked) in just a few minutes, so I’m hoping that 28 year olds are at least twice as quick as 14 year olds, and the Year 10s need a little longer to puzzle it out. Have a read of the trick as it’s explained on the NRICH site, have a go at it and see if you can figure out how it can be done. And then why not share with me your own favourite pieces of mathematical magic, just in case the Year 10s are smarter than I thought and I have 35 minutes and nothing more than a pack of cards with which to entertain them!

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3 Responses to “Mathemagic”

  1. Liz Says:

    I too think ‘magic’ tricks can be a great way of engaging children and motivating them to work on the mathematics. Yesterday I was in Glasgow with a group of Year 5 and 6 pupils and I demonstrated Counting Cards, also on NRICH: http://nrich.maths.org/1843. They loved it and worked out how to do it themselves in very efficient ways, then created their own adaptations.

    Having said all that, I can’t stress enough how important I think it is that children really do come to their own understanding that this isn’t magic at all, it’s maths. Otherwise, I’m worried some might go away with an impression that maths is even more mysterious than they already thought it was.

  2. ajk44 Says:

    You’re absolutely right of course Liz. The “magic” should be a hook to motivate children to work on the maths, but the message should be that what appears to be magic can actually be understood using the clear straightforward rules of maths. For this reason, a maths magic trick shouldn’t be performed, but instead explored.

  3. Sarah Says:

    Hello Alison,

    I’ve come across your blog via the blog of an invisible friend with a penchant for goats…

    I work for the Sussex STEMPoint (STEM Sussex) and hope you & NRICH would be happy with me asking our web bod to link to the NRICH site. I’ve recently been meeting more and more teachers who are looking for something exactly like NRICH (& the free-er the better!) to support and enhance their maths teaching.

    We also love a Maths Magician who is handily based in Sussex – Andrew Jeffrey (http://www.andrewjeffrey.co.uk/) who puts on a very informative and exciting show.

    Perhaps you could e-mail me about ways our teachers in Sussex could use NRICH? Ta đŸ™‚

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