Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

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

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

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

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

Can you put these shapes in order of size? Start with the smallest.

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

What is the greatest number of squares you can make by overlapping three squares?

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?

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

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

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

Can you find all the different ways of lining up these Cuisenaire rods?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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

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?

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.

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

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 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?

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

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

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

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?

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....?

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

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?

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

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!

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

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

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

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?

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

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

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.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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

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?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?