Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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?
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?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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?
Use the clues to colour each square.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
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 many different rhythms can you make by putting two drums on the wheel?
Can you cover the camel with these pieces?
These practical challenges are all about making a 'tray' and covering it with paper.
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
What happens when you try and fit the triomino pieces into these two grids?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Use the clues about the symmetrical properties of these letters to place them on the grid.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
How many trapeziums, of various sizes, are hidden in this picture?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
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?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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....?
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 to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?