Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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. . . .
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!
Exchange the positions of the two sets of counters in the least possible number of moves
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Can you fit the tangram pieces into the outline of Little Ming?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
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?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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?
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?
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
How many different triangles can you make on a circular pegboard that has nine pegs?
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 shape. How would you describe it?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Make a cube out of straws and have a go at this practical challenge.
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?