Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

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.

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?

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

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.

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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

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

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?

An environment which simulates working with Cuisenaire rods.

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?

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

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

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?

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

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

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

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?

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

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?

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?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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?

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?

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

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Number problems at primary level to work on with others.

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

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Number problems at primary level that may require resilience.

Can you complete this jigsaw of the multiplication square?

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

The clues for this Sudoku are the product of the numbers in adjacent squares.

Given the products of adjacent cells, can you complete this Sudoku?

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

"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 ...?

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