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Play to 37

Age 7 to 11
Challenge Level

Play to 37

This is a game for two players.

Decide who is going first.
Player 1 chooses one of the numbers from the bags above (1, 3, 5 or 7).
Player 2 then chooses a number from one of the bags and adds this number onto player 1's number.
Player 1 then has another turn and adds that number onto the total.
Play continues like this with each player choosing a number and adding it onto the running total. 
The winner is the player who reaches the target number of 37.

Have a go at the game with a friend.
How many numbers did you use altogether?
Have another go.  How many numbers did you use this time?

What is the largest number of numbers that could be used to reach 37?
What is the smallest number of numbers that could be used to reach 37?

Can you use all the different number of numbers in between to reach 37?

What do you notice?
Can you explain this?

Why play this game?

At a basic level, this game provides an opportunity for children to become more fluent in addition.  In order to try to win, learners will need to think ahead and this element of strategy demands higher-order thinking.  Stepping back to analyse the number of numbers used offers yet more challenge and the chance to generalise in terms of addition of odd numbers.

Possible approach

Show the picture of the bags of numbers on the interactive whiteboard and explain the rules of the game.  You could suggest that you play against the class, or two children could play, or you could split the class in half to play in two teams.  Either way, use the board to record the numbers chosen and the running total.  Play again in this way, once more recording the numbers selected and the totals.

Give learners time to play in pairs several times and to record their games as they go along.  Then, bring everyone together and ask each pair how many numbers they chose in each game.  Record these on the board.  Referring to the largest number of numbers and the smallest number of numbers, ask the children whether these are the largest and smallest possible.  Set them off on this challenge and at a suitable point, open it out into trying to find all the number of numbers in between.

In a plenary, you can record the number of numbers made on the board, all the way from seven (7+7+7+7+7+1+1) up to thirty-seven (thirty seven ones).  What does the group notice?  Why is this the case?

Key questions

How do you know that you can't use more numbers to make 37?
How do you know you can't use fewer numbers to make 37?
What do the numbers 1, 3, 5 and 7 have in common?

Possible extension

The problem Make 37 follows on nicely from this game and offers an excellent assessment opportunity for you.

Possible support

Encourage children to use apparatus to help them with the addition if that is where they are struggling.  A calculator could be useful if you want them to focus on the analysis rather than the calculations.  Learners might like to play Totality before trying this game.