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Double or Halve?

Age 5 to 7
Challenge Level

Double or Halve?

This is a game for two players.

You will need a dice or you could use our interactive dice.

How to play:
  • Decide on a target number.  This is the total that both players are trying to make.
  • Player 1 throws the dice.  S/he can choose whether to double the number shown or halve the number shown.
  • Player 2 throws the dice.  In the same way, s/he can choose whether to double the number shown or halve the number shown.  Player 2 adds his/her number onto Player 1's number to make a running total.
  • Play continues like this with each player rolling the dice, halving or doubling the number and adding the result onto the running total.
  • The winner is the player who reaches the agreed target exactly.
Here are some questions to think about:

Must each player always take a turn?
Does it matter if you go first or second?
Are there any particularly good numbers to choose as your target? 

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.

Possible approach
At the start of the lesson, model the game on the whiteboard. Either the teacher can play as both players, or two children who are confident with doubling and halving can play against each other. At this point, do not tell the rest of the class the rules of the game.

Then ask the class what they think the rules are. Recap on doubling and halving on the board, and play this game against the class. When it is the class’ turn, choose a child to roll the dice and then the pupils can make the number out of multilink cubes. They can then work on whiteboards to double and half that number.

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. Show the class an odd number made up of multilink cubes, and talk about how we cannot break this exactly in half unless we cut one of the cubes in half. Talk about how in this game, they will not be allowed to cut one of the cubes in half, so they will only be able to half their number when it is even.

After pupils have had some hands-on practice with doubling and halving numbers, they can play the game in pairs, writing down their target number and running total on a whiteboard 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.

Key questions
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?

Possible extensions
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. Then allow pupils to play the game where they always have the option to double or halve the number, even if the answer is not a whole number.

Possible support
Numicon, multilink cubes or similar may help children to calculate the halves and doubles.