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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train can continue its journey?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outline of these rabbits?
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you cut up a square in the way shown and make the pieces into a triangle?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of these convex shapes?
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of this sports car?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you fit the tangram pieces into the outline of this junk?
A huge wheel is rolling past your window. What do you see?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Can you fit the tangram pieces into the outline of the rocket?
Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
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!
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.