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

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

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

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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

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

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

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

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

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

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....?

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

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

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?

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?

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

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

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

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?

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

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

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?

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?

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

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

How many right angles can you make using two sticks?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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?

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

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

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

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?

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

Can you sort these triangles into three different families and explain how you did it?

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?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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

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

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

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

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

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

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?