Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

An investigation that gives you the opportunity to make and justify predictions.

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you work out some different ways to balance this equation?

Can you make square numbers by adding two prime numbers together?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Have a go at balancing this equation. Can you find different ways of doing it?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

If you have only four weights, where could you place them in order to balance this equaliser?

Can you find different ways of creating paths using these paving slabs?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

How many different sets of numbers with at least four members can you find in the numbers in this box?

Number problems at primary level to work on with others.

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Number problems at primary level that may require resilience.

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Are these statements always true, sometimes true or never true?

Can you explain the strategy for winning this game with any target?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Got It game for an adult and child. How can you play so that you know you will always win?

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.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

An environment which simulates working with Cuisenaire rods.