Play to 37
In this game the winner is the first to make the total 37. Is this a fair game?
Problem
This is a game for two players.
Each bag above has unlimited 1s, 3s, 5s or 7s in it.
Watch the video to see how Charlie and Liz play the game and then adapt it to set themselves new challenges. Alternatively, you can scroll down to read the rules and get started.
Aim of the game:
To be the player to add the final number to the 'running' total to make 37.
How to play:
- 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 onto Player 1's number to make a running total.
- Player 1 then has another turn and again, chooses a number from one of the bags, and adds it to the running total.
- Play continues like this with each player choosing a number and adding it onto the running total, until one player reaches the target of 37.
Play the game a few times. What do you notice?
Is this a fair game? Do both players have an equal chance of winning? Why, or why not?
Here's a slightly different version of the game...
This time, each bag above has unlimited 2s, 4s, 6s or 8s in it.
The aim is to be the player who reaches 30.
Play the game a few times. What do you notice?
Is this a fair game? Do both players have an equal chance of winning? Why, or why not?
Would having a target of 34 make any difference?
If you have bags of 2s, 4s, 6s and 8s, and you are given a target number, how will you decide whether it is better to go first or second?
Teachers' Resources
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 different versions of the game offers yet more challenge, and the chance to generalise when it is better to start the game and when it is better to go second.
Possible approach
In the video, Liz and Charlie are trying to model how you might interact with students in your class. You could watch the video and adapt what you do according to the age range you are working with.
Alternatively, you could show the video to your class, pausing when recommended to offer some thinking and playing time, and to facilitate discussion.
Key questions
Do both players have an equal chance of winning the game? Why or why not?
How do you decide whether you want to start, or go second?
Possible support
The game Nim-7 would make a good starting point.
Possible extension
The game Got It would make a good follow-up challenge.