Can you cover the camel with these pieces?
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?
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?
What happens when you try and fit the triomino pieces into these two grids?
Use the clues to colour each square.
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?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different rhythms can you make by putting two drums on the wheel?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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. . . .
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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 activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
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 find out in which order the children are standing in this line?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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.
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.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you find all the different ways of lining up these Cuisenaire rods?
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 work out how to balance this equaliser? You can put more than one weight on a hook.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.