Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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

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?

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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....?

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

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

What happens when you try and fit the triomino pieces into these two grids?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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

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

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

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?

Try out the lottery that is played in a far-away land. What is the chance of winning?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

A train building game for two players. Can you be the one to complete the train?

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.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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?

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?

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

An interactive activity for one to experiment with a tricky tessellation

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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.

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.

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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

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