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

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

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

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!

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

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?

Make one big triangle so the numbers that touch on the small triangles add to 10.

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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?

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?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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?

Can you complete this jigsaw of the multiplication square?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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 that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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.

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

Twenty four games for the run-up to Christmas.

Work out the fractions to match the cards with the same amount of money.

How many right angles can you make using two sticks?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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 work out how to balance this equaliser? You can put more than one weight on a hook.

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Complete the squares - but be warned some are trickier than they look!

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.