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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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 trapeziums, of various sizes, are hidden in this picture?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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?

An activity making various patterns with 2 x 1 rectangular tiles.

These practical challenges are all about making a 'tray' and covering it with paper.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

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

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

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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?

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.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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?

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

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

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....?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Can you draw a square in which the perimeter is numerically equal to the area?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?