This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

When dice land edge-up, we usually roll again. But what if we didn't...?

In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Which of these dice are right-handed and which are left-handed?

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Use the interactivity or play this dice game yourself. How could you make it fair?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

This dice train has been made using specific rules. How many different trains can you make?

A tool for generating random integers.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

This challenge combines addition, multiplication, perseverance and even proof.

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?