In this blog, I want to share some of the great adaptations I’ve seen for maths questions. This was the theme for my session at Mathsconf10, which took place in London in June, where I tried to squeeze as many adaptations into the session as possible, like an over-enthusiastic smoothie maker!
Up front I need to say, these are things that I have had the privilege of seeing other people do. I’ve adapted some of them for my own lessons, but most of what I use has been found from other lessons, and it is in that spirit that I’m delighted to share these ideas with you.
I need to thank all the schools, trainees and teachers that have welcomed me into their lessons over the last seven years – I’ve seen some excellent questions, skilfully set up, well deployed, real head-scratchers.
I particularly like this one:
I opened with it at the maths conference, and it had most of the 100 maths teachers in the room stumped.
That’s why I like it so much!
It highlights the importance of listening to each other, and that maths is a collaborative and communicative discipline.
Interesting adaptations of classic questions
But every so often I see something that makes me go: ‘Hmm! I’ve not seen that before – that is interesting’. When I see these question adaptations, I write them down in a battered old exercise book that I carry about with me.
One that’s intrigued me recently is a question style adapted from the GCHQ codebook, which came out last year.
Here are 12 cards – arrange the cards into two mutually exclusive groups, so each group has at least three cards in it:
Easy-peasy so far. Square numbers and not square numbers. said the pupils… then they talked about the ‘squareness’ of 1 for a while, which was nice to hear.
Next, they were challenged to find as many ways of making two groups as they could in the next five minutes and record them. It prompted some great conversations too.
Here’s a variation on the theme. The task is the same, but it uses keywords instead of numbers. Can you divide these into two groups? Can you do it again? and again?
This is an interesting variant that encourages pupils to have deep conversations with each other and allows the teacher to really listen to what conceptions the pupils have.
I’ve seen this sort of exercise done in the style of the classic board game Guess Who, using shapes with younger pupils, or sometimes with formula.
Recently I have even seen the above game done with a ‘Spy Chaser’ twist. Here’s how to play. Bear with me; the setup is quite complicated the first time… but it’s worth it.
The aim of the game is for one team to catch the other team’s mathematically-named spies. The team that finds all their opponents’ spies first wins.
You need two teams of four, which are then subdivided into two pairs.
One pair are the ‘spy chasers’ and the other pair are the ‘spy masters’.
They are presented with a grid of cards showing 12 mathematical words. Each word is the name of a spy – either a purple or grey spy.
Everyone gets to see this grid, but only the spy masters get to see a second grid that shows which spies belong to the purple team and which belong to the grey team.
The spy masters will then need to give clues to the spy chasers on their team, to help them find the other team’s spies.
The purple team starts. By comparing the grid of spy names with the coloured grid, the purple team’s spy masters can tell the grey spies they need to provide clues for are: Integer, Diameter, Median, Factor, Proportion and x-axis.
The purple team’s spy masters have a minute or so to discuss their plan. They can give just two words as clues (which the whole group of eight can hear) to help the spy catchers in their team to identify the spies on the other team (the grey words on the grid). The spy chasers then need to work out which spies the spy masters are referring to.
So the purple team’s spy masters might say, “straight line” to indicate ‘x-axis’ and ‘diameter’, and “two” to indicate that there are two spies to which the clue relates.
The spy chasers of the purple team then have a few minutes to discuss and choose up to three (one more than the number provided with the clue) spy card from the table that they think match to the prompt they have been given by their spy masters.
They say the name of the spies they have chosen one at a time.
As each word is said by the spy catchers, the spy masters reveal whether it is the opponents’ spy, or one of their own team’s.
If they correctly identify one of their opponents’ spies correctly with their first guess, they can make their second. If they pick one of their own spies then their go ends. I give them counters in their team’s colour to put over chosen cards as the spies are taken out of the game.
The purple team’s spy chasers do not need to use all their guesses; they could stop after one, or two, but they can’t have more than three (one more than the number given in the clue).
Then it’s the grey team’s go.
The winning team is the first to find all the other team’s spies.
This game got quite raucous at Mathsconf, so to end with I showed some quick and easy questions that work nicely too, including the hybrid area maze and quadratic rectangles and the Venn diagram exercise from the Power-cut cookbook parts 1 and 3.
I’ll move on to assessment that makes you go ‘hmm…’ in a later blog. In the meantime, if you have any examples of interesting questions please do share them.