List

Dice

Dice, Routes and Pathways
article

Dice, routes and pathways

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 think mathematically, especially geometrically.
Tug of War
problem

Tug of war

Age
5 to 7
Challenge level
filled star empty star empty star

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

Shut the box
problem

Shut the box

Age
5 to 7
Challenge level
filled star empty star empty star

An old game with lots of arithmetic!

Round the Two Dice
problem

Round the two dice

Age
5 to 7
Challenge level
filled star empty star empty star

This activity focuses on rounding to the nearest 10.

Five Steps to 50
problem

Five steps to 50

Age
5 to 7
Challenge level
filled star empty star empty star

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

Double or Halve?
problem

Double or halve?

Age
5 to 7
Challenge level
filled star empty star empty star

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

Shut the Box for Two
game

Shut the box for two

Age
5 to 7
Challenge level
filled star empty star empty star
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
problem

Two dice

Age
5 to 7
Challenge level
filled star empty star empty star

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

Taking a Die for a Walk
problem

Taking a die for a walk

Age
5 to 11
Challenge level
filled star filled star empty star
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.
Tug Harder!
problem

More Tug of war

Age
7 to 11
Challenge level
filled star empty star empty star

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?

Three Dice
problem

Three dice

Age
7 to 11
Challenge level
filled star empty star empty star

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

Round the Four Dice
problem

Round the four dice

Age
7 to 11
Challenge level
filled star empty star empty star

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

Round the Dice Decimals 2
problem

Round the dice decimals 2

Age
7 to 11
Challenge level
filled star empty star empty star

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

Round the Dice Decimals 1
problem

Round the dice decimals 1

Age
7 to 11
Challenge level
filled star empty star empty star

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

Game of PIG - Sixes
game

Game of PIG - sixes

Age
7 to 18
Challenge level
filled star empty star empty star

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

Tricky Track
problem

Tricky track

Age
7 to 11
Challenge level
filled star empty star empty star

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?

Odds or Sixes?
problem

Odds or sixes?

Age
7 to 11
Challenge level
filled star empty star empty star
Play this dice game yourself. How could you make it fair?
First Connect Three
problem

First connect three

Age
7 to 11
Challenge level
filled star empty star empty star

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Asteroid Blast
game

Asteroid blast

Age
7 to 11
Challenge level
filled star filled star empty star
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Six Ten Total
problem

Six ten total

Age
7 to 11
Challenge level
filled star filled star empty star

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

Dice Stairs
problem

Dice stairs

Age
7 to 11
Challenge level
filled star filled star empty star
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Roll over the dice
problem

Roll over the dice

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Roll these Dice
problem

Roll these dice

Age
7 to 11
Challenge level
filled star filled star empty star

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?

Add 3 Dice
problem

Add 3 dice

Age
7 to 11
Challenge level
filled star filled star empty star
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?
Right or Left?
problem

Right or left?

Age
7 to 11
Challenge level
filled star filled star empty star
Which of these dice are right-handed and which are left-handed?
problem

The twelve pointed star game

Age
7 to 11
Challenge level
filled star filled star empty star

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?

Dice in a Corner
problem

Dice in a corner

Age
7 to 11
Challenge level
filled star filled star filled star

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

The Dice Train
problem

The dice train

Age
7 to 11
Challenge level
filled star filled star filled star

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

A Bit of a Dicey problem
problem

A bit of a dicey problem

Age
7 to 11
Challenge level
filled star filled star filled star

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?

Scoring with Dice
problem

Scoring with dice

Age
7 to 11
Challenge level
filled star filled star filled star
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?
Troublesome Dice
problem

Troublesome dice

Age
11 to 14
Challenge level
filled star empty star empty star
When dice land edge-up, we usually roll again. But what if we didn't...?
How many dice?
problem

How many dice?

Age
11 to 14
Challenge level
filled star empty star empty star
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 there are 2 and only 2 different standard dice. Can you prove this ?
Dicing with numbers
problem

Dicing with numbers

Age
11 to 14
Challenge level
filled star empty star empty star

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?

Non-Transitive Dice
problem

Non-transitive dice

Age
11 to 14
Challenge level
filled star filled star empty star

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