This game is thought-provoking and very engaging. It encourages discussion of place value, alongside valuable strategic mathematical thinking and it helps learners become more familiar with the mathematical symbols for 'greater than' and 'less than'.
Setting up the game with students working collaboratively with a partner offers the chance for them to focus on all five key ingredients that characterise successful mathematicians.
This problem featured in an NRICH Primary webinar in October 2020. It also featured in an NRICH Primary and Secondary webinar in November 2022.
This game can be played with a 1-6 dice or a decahedral 0-9 dice (interactive versions of dice and spinners are available here).
Invite volunteers (working in two teams of two) to play Version 1 of the game on the board. Explain that the aim is to fill the cells so that the statements are correct.
When the game is over, explain the scoring system and confirm who has won. Invite the whole class to work out the maximum score that would have been possible with the eight numbers that were rolled. Once you feel that learners have grasped the rules, set them off on playing the game, working in teams of two. Encourage learners to justify their strategies to their partners.
After each game, challenge teams to find the highest possible score they could have achieved, if they had known all eight rolled numbers in advance. Add these scores to their running totals and keep playing rounds of the game until one team has reached 500 (or 1000) points.
In the final plenary, challenge students to consider Version 2 of the problem (using the numbers 1-8). Encourage learners to use their knowledge of place value to make decisions, and challenge everyone to justify their reasoning, leaving no room for doubt.
How are you trying to make sure each number sentence is true, while still managing to get a high score?
How are you deciding which cells to fill in first?
An interesting follow-up to this game is More Less is More, which again challenges learners to create correct statements, but this time after carrying out some simple calculations.
Learners could try a single-digit version of the game initially, rolling the dice four times.
Learners could be provided with number cards that they can move around the grid to consider different options.