Why do this activity?
This activity provides a context for doubling and halving, as well as adding to keep a running total. The children will also be thinking about strategies they could use to win the game.
This problem featured in an NRICH Primary webinar in June 2021.
At the start of the lesson, model the first few turns of the game on the whiteboard. If you have another adult in your classroom, the two of you could play against each other. Alternatively, you might play against two children who will need to be briefed beforehand! At this point, do not tell the rest of the class the rules of the game, instead invite them to watch the game being played
and consider what the rules might be.
Ask chldren to share their noticings and their suggestions about the rules, and use the ensuing discussion to clarify how to play.
Once the rules have been established, play again, this time involving the whole class either against you, or in two teams. Ideally, all children will have access to practical equipment that they could use to help them double/halve. Each time the dice is rolled, allow time for learners to double and halve that number, perhaps recording on a mini whiteboard, before asking what number
they will add to the running total.
This will provide a good opportunity for discussing what happens when an odd number is rolled, as halving this will not give a whole number answer. Invite children to suggest what might be done in these cases. Is halving still 'allowed' in this game if you roll an odd number?
Once the pupils have had this experience of playing the game altogether, they can play in pairs, writing down their target number and running total on a whiteboard or in their books for each game.
Stop the class halfway through the session to discuss what strategies they are using. When do children think it is better to halve rather than double their number? Talk about whether pupils need to think harder at the beginning or near the end of a game, and encourage pupils to think about what strategies they need to use at the end of the game in order to win. Are they allowing a player to 'pass'? If not, what happens if a player goes over the total?
What is double the number you rolled?
If we halve the number you rolled, will the answer be a whole number? How do you know?
Why did you choose to double/halve that number?
What will happen if you choose a different target?
Extension 1: Pupils could use a 0-9 dice rather than a 1-6 dice, which will lead to them doubling and halving slightly bigger numbers. They could also be encouraged to choose a larger target number.
Extension 2: If pupils are very confident with the concept of halving, introduce them to what happens when an odd number is halved. Encourage them to find their own ways of recording this - they might like to draw a simple shape and shade half of it, or write 'two and a half' in words.
Numicon, multilink cubes or similar may help children to calculate the halves and doubles.