Use these four dominoes to make a square that has the same number of dots on each side.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

This challenge is about finding the difference between numbers which have the same tens digit.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Find a great variety of ways of asking questions which make 8.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Investigate the different distances of these car journeys and find out how long they take.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?