Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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....?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different triangles on these peg boards, and find their angles?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
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?
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?
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.
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?
How many triangles can you make on the 3 by 3 pegboard?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
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?
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.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you draw a square in which the perimeter is numerically equal to the area?
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
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?