If, like me, you have both a professional and personal interest in maths education, you may be observing as I am that the time and space given to us by lockdown might be a wonderful way to help connect the two again. My clutch of primary-age grandchildren, like so many others up and down the country and throughout the world, have been doing some maths each day. I see effective home learning about mathematics to be a healthy balance (not necessarily an even division) between:
- practising skills they already know to become fluent – often this is best done with good quality online games
- using ideas they are already familiar with in a new context which demands mathematical thinking
- exposing them to something new
The second part is where I think I can really become a superhero mathematical grandmother, swooping in with some simple but very deep ideas that can powerfully alter their growing perception of mathematical structure. My cape is made of mathematical connections, my superpower is to cast great beams of fresh light on old ideas…
Using simple software with a shared whiteboard, we can play some really engaging games, which are surprisingly fun for me as well as them. I’ll take one illustrative example below, called Dotty Six (you can play and read about it on the NRICH site). The game both requires and supports fluency in basic arithmetic (because you have to do a lot of mental calculation) whilst also thinking about strategies - the enjoyable mathematical daydreaming inherent in ‘what if’.
Here is the game board - a simple 3 x 3 array.
Aim: to be the player who completes a row of boxes, each containing exactly six dots
- take turns to throw 1-6 dice
- put all the dots from that throw into one square (it may already have dots in, as long as...)
- no square can hold more than six dots
Turn A: a 3 is rolled - where to put this? If I know something about strategy for noughts and crosses, I may decide to put it in the middle or a corner.
Turn B: 4 – this can’t be put in the same square as A, as that exceeds 6. Is it best to add to a run of three boxes, or start a new one?
Can you see some of the interesting opportunities for thinking mathematically here?
Towards the end the thinking becomes more sophisticated, for example:
A’s turn: 2
If 2 is put into the 4 dot square on the top line, the danger is that B could throw a 1 on next go and can then complete that line of three boxes. Is it worth the risk?
If the 2 is put into the 4 dot square on the middle line instead, B can’t complete anything on next throw. But does it set up any other undesirable situations?
B’s turn: 6
If this is put into the left middle box, A could throw a 4 and complete that column of 3; similarly if it is put into the middle square, A could throw a six next and complete a row across. So perhaps the best place is the bottom row?
This very simple game involves multistep thinking and reasoning, plus fluency in (quite basic) calculation. It’s suitable for all ages from those with basic number sense to 10 who play by counting and without much strategy, to those for whom the arithmetic is simple but the strategy is enticing. For this reason, it truly is a ‘low threshold high ceiling’ game.
Did you try the game? What kind of thinking did it prompt? You can tweet us @CambridgeMaths or comment below.