How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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?
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?
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?
A game for two players. You'll need some counters.
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?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
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. . . .
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?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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 many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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 smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?
Move just three of the circles so that the triangle faces in the opposite direction.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
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 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?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
A variant on the game Alquerque
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Here's a simple way to make a Tangram without any measuring or ruling lines.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Here are shadows of some 3D shapes. What shapes could have made them?
Which of these dice are right-handed and which are left-handed?