Challenge Level

Find a partner and a 0-9 dice. The interactivity here can be used to simulate throwing different dice.

Each of you draw some cells that look like the picture below. (You don't have to make the cells on the left a different colour, but we will refer to those cells later.) Alternatively, you could print off this sheet of cells.

**Version 1**

Take turns to throw the dice. After each throw of the dice, you each decide which of your cells to put that number in.

Throw the dice eight times until all the cells are full and you have created four two-digit numbers.

If both of your number sentences are correct, you score a total of the two numbers written in the four blue boxes.

If only the first number sentence is correct, then you score points equal to the number in the top two blue boxes. If only the second number sentence is correct, you score points equal to the number in the bottom two blue boxes.

The winner is the person with the greatest number of points.

Play the game several times so you get a good feel for it.

What do you notice?

Do you have any good strategies for winning?

How could you give advice to someone else before they play if you don't know what digits they might roll?

**Version 2**

Now, work *with* your partner, rather than against them.

If the eight numbers thrown are 5, 2, 8, 4, 1, 5, 1 and 9, and you are allowed to put them in the cells once all eight are known, where would you place them in order to get the highest possible score? How do you know this will give the highest score?

We would love to hear about your 'noticings' and strategies for playing the competitive game, as well as your solutions for the final part. Please do share your thinking!