Sum Difference Game

To play the game you need two dice of one colour and one of another, or a 1-to-6 spinner. Here two dice are GOLD and one is WHITE. Roll the dice, add up the numbers on the two GOLD dice and then subtract the number on the WHITE. If you use a spinner then spin 3 times, add the first two scores and subtract the third, for example, if the numbers on the gold dice are 6 and 1, and the number on the white is 4, the result is 3.

Play a game against a friend. In the Zero-Six game you win if the final score is zero and she wins if the score is 6. Do this many times and score a point each time you win a round. Is this a fair game? How do you know?

Try it out. Play the game many times and see what numbers you make each time by doing the addition and subtraction.

Work in pairs and talk about what to do and how to record your results when you throw the dice. After experimenting, try to predict totals that will NOT be possible and those that will. Check these predictions. Can you decide whether the game is fair or not?

What about the Even-Odd game where you win if the final score is odd and your friend wins if it is even?

For an even more challenging game, decide on two operations then allow players, on their turn, to choose which to apply to the gold dice and which to the white.

Simple DICEY OPERATIONS Game with 2 dice. There are 4 versions of this game for 2 players or 2 teams. At the start players agree whether to use addition, subtraction, multiplication or division, and how many rounds to play. The player with the highest sum, difference, product or quotient in each round wins a point. Take turns to roll 2 dice and either add, subtract, multiply or divide one number by another. After the agreed number of rounds the player with the highest number of points wins the game.

Make up your own games with different rules and decide whether your game is fair or not.

Click here to download the SUM DIFFERENCE GAMES worksheet

Click here to download the SUM DIFFERENCE GAMES Inclusion and Home Learning Guide

Click here to download the SUM DIFFERENCE GAMES Note for Teachers

Click here to download the SUM DIFFERENCE GAMES poster

Notes for Teachers, Worksheet and inclusion Guide will be added soon. Watch this space for this, and for more mathematical games to follow.

This activity is adapted from the NRICH task Roll These Dice with permission of the University of Cambridge. All rights reserved.