Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

This challenge extends the Plants investigation so now four or more children are involved.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you hang weights in the right place to make the equaliser balance?

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

This task follows on from Build it Up and takes the ideas into three dimensions!

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

You have 5 darts and your target score is 44. How many different ways could you score 44?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

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?

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?