Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these two grids?
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?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
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?
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....?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
How many different rhythms can you make by putting two drums on the wheel?
These practical challenges are all about making a 'tray' and covering it with paper.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
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?
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.
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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 work out how to balance this equaliser? You can put more than one weight on a hook.
How many triangles can you make on the 3 by 3 pegboard?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Try this matching game which will help you recognise different ways of saying the same time interval.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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. . . .
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
How many different triangles can you make on a circular pegboard that has nine pegs?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
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?