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.
This problem featured in the NRICH Primary webinar in June 2022.
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.
Have another go at the game in this way, again 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 that have been recorded, 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 do learners notice? Will their noticing/s always be true? Why is this the case?
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?
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.
The problem Make 37 follows on nicely from this game and offers an excellent assessment opportunity for you.