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?
Sort the houses in my street into different groups. Can you do it in any other ways?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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.
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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!
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?
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 investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you find all the different triangles on these peg boards, and find their angles?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Use the clues to colour each square.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you sort these triangles into three different families and explain how you did 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.
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 try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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.
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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?