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?

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.

An environment which simulates working with Cuisenaire rods.

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

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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?

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

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?

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?

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

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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?

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?

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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

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

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?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

"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 ...?

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?

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?

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

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

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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 find any perfect numbers? Read this article to find out more...

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Can you find a way to identify times tables after they have been shifted up?

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?

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

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?

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?

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

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?

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.

56 406 is the product of two consecutive numbers. What are these two numbers?

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

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?

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.