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?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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?
Use the clues to colour each square.
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?
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 how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
A challenging activity focusing on finding all possible ways of stacking rods.
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....?
How many models can you find which obey these rules?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
These practical challenges are all about making a 'tray' and covering it with paper.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you find all the different ways of lining up these Cuisenaire rods?
How many different rhythms can you make by putting two drums on the wheel?
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?
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 triangles can you make on a circular pegboard that has nine pegs?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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 the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?