## Tip 1: Invent throwing and scoring games

Inventing games is fun! And the variations children will think up make this a sure way to bring different skills into the mix. For example:

- Collect pots, jars, cups, tubs and containers. And some ping-pong balls. Ball pit balls will also do but you might need buckets instead of jars.
- Arrange the pots, jars and cups and then number them with a marker according to how many points each should be worth when you throw balls into them.
- Invent the rules, write them down together and figure out how you will keep a record of scores.

**How does this get them thinking?**

Inventing throwing and scoring games leaves endless possibilities for mathematical thinking. When first playing games, you might notice that someone wins a lot and younger siblings might be at a disadvantage. This can be sorted out in lots of ways – maybe they get to throw from a shorter distance? Or perhaps they have different balls to throw, are allowed to throw under arm, are allowed to bounce it? Or only have to hit the target?

**How does it encourage mathematical talk?**

The conversations will involve lots of talk about **fairness**. When talking about fairness, we might be talking about chance, things being **likely**, **unlikely**, **50/50 (even chance) **or **impossible**. You might also talk about your strategies of keeping score out loud. Sharing your thinking about how you work with numbers helps children develop their own strategies and notice that there are many ‘right’ ways to work with numbers.

**How can it go further?**

As the games develop, scoring can be made more advanced and not necessarily by introducing bigger numbers. It is worth trying:

- Using doubles and triples for some balls or in a way which makes sense for your invented game.
- To use subtraction in a real context, make the point target 0 and score by subtracting each time a ball is thrown into a container. Perhaps to finish the game, the player needs to end on exactly 0. This is like scoring in the game of darts.

## Tip 2: Create a height chart

This is a classic but still a good idea which can sometimes be forgotten!

- Find a wall and some long paper (a roll of lining paper works well)
- Mark on the height of your children, you, and the family pets (plants and animals included).
- Do it again after… a day, month, 6 months, a year, 10 years.

**How does this get them thinking?**

By marking height on the wall, we are using **direct comparison**. There is no need for standard units (metres and centimeters) at this point.

Later, children might want to share their record of heights with a friend or family member. If you try this out together, you might notice during your conversation that a photo doesn’t reveal enough information about the heights marked on the wall. Here, we need a standard measure which others can also work with! We introduce **standard measures** (meters and centimeters) when we need to communicate our mathematics with someone.

Once you mark meters and centimeters on your chart, then you might also draw on or mark sports stars (Serena Williams 1.75m, Lionel Messi 1.70m) or even interesting animal sizes (adult ostrich 2.7m, pet rabbit 35cm).

**How does it encourage mathematical talk?**

There is lots of mathematical language here. The conversation is one about **size**, and about **height**. Your conversation might use language like **taller, shorter, difference, fast, slow, more, less, the same.**

**How can it go further?**

When comparing height against markers you will also be thinking about time, the seasons and months. It’s interesting to ask: Who is growing the fastest? Is this the same rate all year round?

What other questions could you explore together?

## Tip 3: Play NIM

NIM is a simple but fun 2 player game which can be played in lots of different ways.

- Set up 21 objects of anything which can be easily moved (coins, pebbles, cutlery, cards etc
- Take it in turns to remove 1, 2 or 3 of these objects until all are gone.
- The winner is the last to pick up an object!

**How does it get them thinking?**

This is a simple setup of NIM with a restriction on the maximum number of objects which can be picked up. The game can be changed by:

- Changing how many objects each player can pick up! What happens if you can pick up to 5? How about 1? Is it best to go first or second?
- Changing how to win. The game can be adapted so the person who picks up the last object loses the game (this is called a misère game of NIM)
- Counting to 21 going 3 numbers at a time if you’re on the move… the winner is the person that says 21.

**How does it encourage mathematical talk?**

Here there is more thinking than talking. Nevertheless, you might use language like **first, second, possibility, chance, strategy**.

**How can it go further?**

After a while playing the simple game of NIM, you will notice a point in the game when the outcome is decided. Pause at this moment and then position the ‘winning situation’ pieces away from the others! If playing with these pieces aside, then you might notice another pattern which leads to this ‘winning situation’.

The key question is: Is there an earlier moment in the game which can lead to this point every time? Keep playing to work this out. Once you have, then apply the same logic again and you will find an even earlier moment in the game when the outcome is determined. From experience, children as young as 8 or 9 can figure this out through lots of play and physically separating out the key moments.

This is an example of *working inductively* *to prove something or find a result*. In mathematics, this is an absolutely huge idea and something all mathematicians do.

Don’t be afraid to go off-track in your explorations together or to end up at an entirely different sort of mathematical (or non-mathematical) activity. It can sometimes be better to come back to an activity on another day if your children aren’t keen the first time around.

**So get thinking, encourage mathematical talk, and go further.**

But most importantly, have fun with it!