If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
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?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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.
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?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
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?
Use the clues to colour each square.
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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?
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
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 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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What happens when you try and fit the triomino pieces into these two grids?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
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.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Move just three of the circles so that the triangle faces in the opposite direction.
Make one big triangle so the numbers that touch on the small triangles add to 10.
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?
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 right angles can you make using two sticks?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
An animation that helps you understand the game of Nim.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you find all the different ways of lining up these Cuisenaire rods?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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?