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. . . .

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

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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

This activity involves rounding four-digit numbers to the nearest thousand.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Find all the numbers that can be made by adding the dots on two dice.

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

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?

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.

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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

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

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?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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. . . .

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 possible answers?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these numbers to the nearest whole number?

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

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?

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?

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?

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.

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

This article takes a closer look at some of the toys and games that can enhance a child's mathematical learning.