Start by drawing a number line from $0$ to $20$ like this:

The first player chooses a number on the line and crosses it out.
The same player then chooses a second number and crosses that out too.
Finally, he or she circles the sum or difference of the two numbers and writes down the calculation.

For example, the first player's go could look like this:

The second player must start by crossing off the number that player $1$ has just circled.
He or she then chooses another number to cross out and then circles a third number which is the sum or difference of the two crossed-off numbers.
Player $2$ also writes down their calculation.

For example, once the second player has had a turn, the game could look like this:

Play continues in this way with each player starting with the number that has just been circled.

For example, player one could then have a turn which left the game looking like this:

The winner of the game is the player who stops their opponent from being able to go.

This powerpointpresentationalso demonstrates how to play the game. You may like to click through it.

Now it's your turn!
Try playing the game a few times to get a feel for it.
What is your strategy for winning?

This game offers an engaging context for practising addition and subtraction, but it also requires some strategic thinking. It is easily adaptable, and can be used co-operatively or competitively.

Possible approach

You could click through this powerpoint presentationone 'go' at a time, asking children to watch carefully and then to talk to a partner about what they think the rules are. After the first 'go', take some suggestions, but don't say whether they are correct or not.
Instead, click through the second 'go' and give pupils more time to talk to each other about the rules again - their initial thoughts will perhaps need adapting. Repeat this process once more and then discuss the rules so that everyone is clear.

Give children time to play several games in pairs so they get a feel for it. You could share their strategies and then ask them whether they think it might be possible to cross off all the numbers in a game. Give them time to work co-operatively with their partner on this challenge before bringing them together again to see what they have found out. Some will have realised that it is
impossible to cross off zero - encourage them to explain why this is the case.

Learners could then investigate whether it is possible to cross off all the numbers if the number line goes from $1$ to $30$ instead. Many will be able to reason that it is still not possible due to there being an even number of numbers in total. Exploring the longest possible string of calculations is interesting and the children can be asked to examine why they run out of
possibilities.

Key questions

Have you found any good ways to beat your opponent?

Can you cross out all the numbers in one game? How do you know?

What is the biggest number of numbers you can cross out?

Possible extension

Children can suggest their own 'what if ...?' questions, for example:

What if we could use multiplication/division?

What if we drew a longer number line?

What would happen if we included decimal numbers in our number line?

What if the number line extended beyond zero to negative numbers?

The possibilities are endless.

Possible support

If children are struggling with the calculations, a shorter number line may be appropriate so focusing on a number line to 10 still elicits many of the same ideas about possibilities and outcomes as well as the way in which the operations of addition and subtraction work on a limited set of numbers.