What happens when you try and fit the triomino pieces into these two grids?
Use the clues to colour each square.
Can you cover the camel with these pieces?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
How many different rhythms can you make by putting two drums on the wheel?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
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 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 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 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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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....?
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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. . . .
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing 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?
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each 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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
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 many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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.