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'.
The game also offers the chance to focus on any of the five key ingredients that characterise successful mathematicians. The collaborative version lends itself particularly to fostering a positive attitude to mathematics as learners' resilience may be tested!
This problem featured in an NRICH Primary webinar in October 2020.
This game can be played with a 1-6 dice but ideally would be played with a decahedral 0-9 dice or a spinner (interactive versions of dice and spinners are available here).
Invite volunteers (perhaps working in teams of two) to play the game on the board and explain the rules to them and the rest of the class.
When the game is over, explain the scoring system and confirm who has won. Invite questions and encourage everyone to respond, rather than you always giving your answers. Once you feel that learners have grasped the rules, set them off on playing the game, working in pairs.
Encourage learners to justify their strategies to their partners, and draw their ideas together in a mini plenary. Some learners might question whether it is 'allowed' to put a zero in the tens column boxes and if it does not come up naturally, you may want to pose the question yourself.
Then introduce the collaborative version of the game in which you can wait until you have thrown the dice all eight times before you decide where to place each number. Either throw a dice eight times, or use the eight rolls given in the problem, and challenge learners to place the numbers so that they score as highly as possible.
After allowing time to work on this, the final plenary can be an opportunity to share thinking. Listen out for learners who are using their knowledge of place value to make decisions, and encourage everyone to construct their reasoning carefully, leaving no room for doubt.
How are you deciding where to place the numbers?
How are you trying to make sure each number sentence is true?
How could you give advice to someone else before they play if you don't know what digits they might roll?
You could challenge learners to come up with a set of eight numbers that would be easy to place in order to make the highest score, and a set of numbers that require deeper thought. What makes a set of numbers easier/harder?
Provide learners with number cards that they can move around the grid to consider different options. For the competitive version of the game, allow pairs to play against another pair, so that partners can support each other.