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

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?

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

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.

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 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?

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?

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

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?

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

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

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

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

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

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

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

Use the number weights to find different ways of balancing the equaliser.

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?

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

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

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?

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?

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 shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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

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?

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

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....?

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

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

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?

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.

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

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

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

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