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?

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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?

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 make square numbers by adding two prime numbers together?

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

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?

This package will help introduce children to, and encourage a deep exploration of, multiples.

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.

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?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

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?

Can you complete this jigsaw of the multiplication square?

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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

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

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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!

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

"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 ...?

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

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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

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?

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?

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

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.

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

An environment which simulates working with Cuisenaire rods.