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

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!

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?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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

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.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

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 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?

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

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?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

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.

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

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?

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

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

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

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?

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

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?

This challenge is about finding the difference between numbers which have the same tens digit.

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!

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

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?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

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.

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?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Here is a chance to play a version of the classic Countdown Game.

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?