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

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

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

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 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 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?

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.

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?

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?

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

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

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

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

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?

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?

A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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

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?

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

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

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

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

An interactive activity for one to experiment with a tricky tessellation

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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.

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.

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

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

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

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

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?

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