If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Make one big triangle so the numbers that touch on the small triangles add to 10.
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Move just three of the circles so that the triangle faces in the opposite direction.
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.
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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 the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
What is the greatest number of squares you can make by overlapping three squares?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different triangles can you make on a circular pegboard that has nine pegs?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
Sort the houses in my street into different groups. Can you do it in any other ways?
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
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 dark green rod using yellow and white rods?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
Find out what a "fault-free" rectangle is and try to make some of your own.
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you find all the different ways of lining up these Cuisenaire rods?
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 10 in the circles so that each number is the difference between the two numbers just below it.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
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?