How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you find all the different triangles on these peg boards, and find their angles?

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?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Hover your mouse over the counters to see which ones will be removed. Click to remove 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?

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?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

What happens when you try and fit the triomino pieces into these two grids?

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?

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?

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.

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 many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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 fill in the empty boxes in the grid with the right shape and colour?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Find all the numbers that can be made by adding the dots on two dice.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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. . . .

Here are some rods that are different colours. How could I make a yellow rod using white and red 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?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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?