Magic Vs

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It’s been a busy couple of weeks for me, so I’m going to try to round it off by blogging some of the things I’ve been doing.

Firstly, I was asked to participate in a day aimed at Gifted and Talented Year 7 pupils. Last year, I worked on the problem Odds and Evens for a similar session, which was great fun, but I didn’t feel we had time to get the most out of the task, so this year I chose to work with them on Magic Vs instead. The idea is to arrange the numbers 1-5 in a V shape so that both arms of the V add up to the same “Magic total”. I challenged the pupils to find every way they possibly could to do this, and then to come up with a convincing explanation of how they knew they’d found them all. Along the way, we had some interesting conversations about when two Vs count as the same and when they are different. I think it’s valuable to allow these discussions to emerge from the class, and for them to decide on whether two Vs are the same, rather than me deciding for them.

After they’d justified their answers and had a go with the same activity with the numbers 2-6, I asked them to suggest lines of enquiry that they might explore next. I was amazed by their inventiveness – some wanted to come up with general rules for magic Vs with consecutive numbers, some explored Vs made with all odd or all even numbers, some looked at Vs with more than 5 numbers in, and some investigated Magic Ws or Magic Xs.

We finished the session by giving pupils the chance to share anything interesting they had discovered, and the explanations they’d used to convince themselves of what they’d found. Where appropriate, I introduced a little bit of algebra to help their proofs along, but for the most part their reasoning did not rely on algebra for justification.

This is the first time I’ve used Magic Vs, but I can see that it will become a firm favourite in my repertoire of rich tasks. Even though I ran the session four times with four groups, it felt fresh and exciting each time because each new group of pupils came up with their own justifications and their own ideas to explore next. The only maths knowledge they needed in order to begin the task was an ability to add numbers, but the level of mathematical thinking they got out of it was higher than I could have hoped!

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2 Responses to “Magic Vs”

  1. Liz Says:

    I use the Magic Vs problem with primary teachers and children alike. It is one of my favourites from NRICH for all the reasons you’ve stated, Alison. I love the way that children offer conjectures, then proofs, with very little prompting from me but plenty of thinking along the way. It is a great example of a ‘low threshold high ceiling’ task.

  2. lordhutton Says:

    Great to have motivated children!

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