Every maths teacher has lessons that should have worked better than they did. Lessons where the planning was faultless, the theme had hooks and catches, and all things concrete, abstract or pictorial were spot on. The sort of lesson where you “would have gotten away with if it hadn’t been for those meddling kids”.
And then there are activities that are unexpectedly successful, and you end up using them, or variants of them, again and again. My ‘What’s wrong with this picture’ tasks, for example.
I have started to collect these activities together and, like any good mathematician, I’ve kept an eye out for like terms and patterns. I call this collection my ‘Power cut cook book’ because the first few ‘recipes’ were added when I was working a school where there was frequently no power and I had to resort to using old-school resources in lessons.
This exercise is based on the Numberwang game from That Mitchell and Webb Look (and I still call it Numberwang in my head, but the cultural reference goes over the heads of my current year 10).
To play, give the students a large piece of paper, and get them to draw a nice big line in the middle, with numbers from –10 to 1000 in a logarithmic style.
The students then spend some time in groups adding any number that they know that is special in some way to the number line. It is interesting to see them race and stall as they access different parts of their knowledge. In the example below, you’ll spot all sorts of numbers from absolute zero, to the boiling point of water, to the number of degrees in a right angle.
It’s really interesting to overhear the discussions they have in their groups too. For example, adding the numbers relating to circle theorem to the line led to an interesting – and spontaneous – discussion about the ‘prime-ness’ of 1.
I’ve also tried NumberLine with groups of younger students or students who are currently under-attaining. I found that some groups needed a little more prompting, as they didn’t really have the staying power to keep going when they ran out of ideas, so I made a set of image cards to help them out when they got stuck. Here’s a few examples below:
I adopted this from a Craig Barton exercise after seeing him at MathsConference.
The idea is that you assign a criteria to each circle (for example: even, prime and multiple of 3) and students have to fill the different regions with numbers that meet those criteria. If they think a certain reason is impossible to fill, they have to explain why.
This is a really useful exercise for a number of reasons:
- students can always start somewhere
- different regions vary
- you can set really challenging extensions – and so can the students
- it helps students make links. For example, highest common factor/lowest common multiple is very neat on a Venn if the students set up each set as ‘times tables’/’multiples of 3, 4, 5’.
This exercise went so well that I now have a set of pre-printed blank three-, two- and four-set Venns, ready to use in class.
In this example, the student was asked to find a scenario where there was nothing in the middle intersection and only one number in at least one other intersection:
If you have any technology free or low-tech activities that you would like to add to the Power cut cook book then please share them with me via Twitter.