# Recreational Mathematics

### by Livia Mitson (April 2020)

One of the problems with maths being a subject that everyone has to study is that lots of people get fed up with it.  Some get fed up with it at primary school; others just don’t get on with algebra.

But there is a massive difference between school maths and maths.

I was appalling at art in school.  To the extent that in year 9, before I could finally heave a sigh of relief and drop it completely, we sat a final art exam where we had to draw a flower.  I knew I wouldn’t be able to even attempt anything realistic so I drew a picture that didn’t look anything like the flower, but had various shapes and colours from the flower.

And yet, I still enjoy looking at paintings.  I still enjoy creating pictures (even if they don’t much look like the thing they are supposed to be).  I enjoy taking photographs.  Art is part of me as a person, even though I failed school art.

Equally, for centuries, maths was enjoyed by many people who had never come across school maths.  (In some cases this was because there weren’t schools they could go to.)

I dropped school maths age 16.  (I’m now a maths teacher, so I did pick it up again later, and I got the bug as far as getting a maths degree).  But while I wasn’t doing school maths, I did do some maths.

My favourite bit of maths that I do all the time with my family is “I’m thinking of a number”.  There are lots of variations on this game, but my favourite one is the “Clues” variation.

Here we go:  I’m thinking of a number.

Here’s a clue – it’s smaller than 10!

(This is normally the point at which my children when small would start yelling out numbers).

Here’s another clue – it’s even!

By this point, as I was thinking of the number 6, someone has guessed it.

A more difficult variation is the Twenty Questions variation.  If you haven’t heard of it, Twenty Questions is a great game that you can play anywhere as you don’t need anything for it.  Particularly good for long car journeys and boring Sunday afternoons.

You need at least two people to play it.  Person A thinks of something.  (For example, in our house, that might be our dining room table).  The other person (person B) then can ask only twenty questions to work out what it is.  BUT – the sting in the tail is that person A can only answer yes or no.

So it might go:

Q:  Is it alive?

A: No

Q: Is it in England?

A: yes

And so on.  There’s a real skill in developing good questions for this game.

However, this is a great game for maths. I might think of a number.  Here the questions are going to be a bit different.

Q:  Is it bigger than 10?

A: no

Q: is it a fraction?

A: yes

Q: has it got a one in it?

A: no

Q: has it got a two in it?

A: yes

Q:  has it got a three in it?

A: yes

And you can see that this person is using a series of questions that are going to get to twenty pretty quickly without working out what fraction it is.

Maybe you could come up with some better questions?

One of the things that I spend a lot of time thinking about is how to bring in the creativity and playfulness that you get with recreational maths into school maths.  It’s quite hard to do, and it’s even harder to do with on-line learning.

But I thought I’d share with you a task that I’ve created that builds on the idea of using twenty questions to find a number.  As is traditional in mathematics, once you get an idea you tend to run away with it…. After coming up with clues for one number, I thought – what about giving clues for two numbers…..

When (and it will be when, not if) you get stuck with these, see if you can create some of your own puzzles like this.  I’d love you to send them to me.

These questions form part of our new Online Learning resources.  Do explore these resources (for primary and for secondary).

Here is a direct link to the task referred to in this blog.

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