Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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

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

Can you complete this jigsaw of the multiplication square?

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

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.

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

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

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?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

An interactive activity for one to experiment with a tricky tessellation

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.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

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?

Exchange the positions of the two sets of counters in the least possible number of moves

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

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!

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Use the interactivities to complete these Venn diagrams.

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

Find out what a "fault-free" rectangle is and try to make some of your own.

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Work out how to light up the single light. What's the rule?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Train game for an adult and child. Who will be the first to make the train?

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?

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

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

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?