# Striking up a mathematical conversation

- Cambridge Mathematics
- Mathematical Salad
- Striking up a mathematical conversation

## Striking up a mathematical conversation

My days have changed a little since I last blogged – then I was having one-to-one Zooms with my grandchildren, in rotation, each weekday, and offering them a little piece of maths. Now that they are partly back at school the conversations are more about the non-school stuff they have been exploring, but frequently (and delightfully) they ask me for a maths game, and I try to find something that they can then go and play with each other – not that easy when their four ages range from 5 to 11. But as I wrote in my last blog, there are loads of games that promote mathematical thinking in the players for whom the calculations involved are easy, whilst still allowing those who struggle to be able to take part – as my NRICH colleagues would say, low threshold, high ceiling. One such favourite is *Strike it Out*, and this has a very high ceiling as we shall see…

The rules are simple – take turns to write an addition or subtraction calculation for three numbers on the number line, beginning your calculation with the number that your opponent wrote last. The first two numbers of each calculation are struck out and cannot be used again. The winner is the person to take the last go.

**A’s turn:**

So, lots of choices – should I add or take away? I’ll take…

10 – 1 = 9.

**B’s turn:**

OK, so I have to start with 9 (it’s circled) because that’s the number A ended with. Has to be a take away again then…

9 – 7 = 2

**A’s turn:**

Hmm, I have to start with 2 and add as taking away isn’t possible – several choices here.

2 + 6 = 8

**B’s turn:**

I have to start with 8 – only one possibility.

8 – 5 = 3

**A’s turn:**

I can’t go, so B has won.

I wonder what questions you asked yourself as you followed this game?

Did you wonder about the numbers that were left and if those particular numbers would always be left over?

Did you consider whether it is possible to cross all the numbers off?

Did you wonder what happens to the zero?^{*}

Playing the game on the number line to 10 is over quite quickly and doesn’t offer a huge amount of excitement. Increase it to 20 however and the possibilities increase as the game becomes more complicated.

I love this game! Lots of practising basic number facts to 10 or 20 (low threshold) and more (high ceiling)^{**} questions arise –

Does it matter who goes first?

Can all the numbers be crossed off?

Is there a winning strategy?

You can read more about it and watch a video of the game being played on the NRICH site.

^{*}Of course zero can’t be used at all because a calculation would require using the same number twice, which isn’t allowed

^{**}I’d love to hear if you find a winning strategy. This question has even defeated some of my severely able mathematician friends…

**Join the conversation:** You can tweet us @CambridgeMaths or comment below.