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?

Sort the houses in my street into different groups. Can you do it in any other ways?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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?

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?

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.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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

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?

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

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

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?

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

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....?

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

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

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?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

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

Can you find all the different triangles on these peg boards, and find their angles?

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

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?

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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.

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

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

Practise your number bonds whilst improving your memory in this matching pairs game.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?