Archive for July, 2010

A great way to spend a day

July 14, 2010

Yesterday I attended a day of mathematical fun to celebrate the retirement of Jenny Piggott, who stepped down as NRICH director earlier this year. In the morning, we worked on problems which had been suggested by people who had worked with Jenny over the course of her career. These were varied – we talked about Pythagorean triples, methods of buttoning up one’s shirt, and what happens when you drop elephants into a lake! Some of these problems will no doubt be developed into tasks on the NRICH site in the next few months.

The Pythagorean triples task reminded me of something else I’ve tackled recently, as I ended up with the same set of equations to solve as I had done when working on another problem. Unfortunately I can’t find such a problem in my notes, and I can’t remember what it was I was working on – maybe it was all a very vivid dream! We were seeking triples (sets of three whole numbers that could be sides of a right-angled triangle, so satisfying Pythagoras’s theorem a^2+b^2=c^2) where two of the numbers differed by 1. Having worked on Pythagorean Triple problems before, I quickly found examples where the longer two sides differed by 1. It wasn’t immediately obvious whether it was possible for the perpendicular sides to differ by 1 though – I won’t post my further musings on this just yet in case people want to investigate it for themselves.

In the afternoon, we did some lovely mathematical origami. Alas, no camera with me today but my model ended up very like this. Read more about making them here. Then while tea was served, Bubblz entertained both young and old with mathematical bubbles which took me back to vague memories of an undergraduate course on calculus of variations that I attended ten years ago! It’s days like this that enthuse and energise us as maths educators to remember why we love our subject so much, and help us to pass on our passion to those we work with.


Magic Vs

July 6, 2010

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!