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

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

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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?

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Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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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?

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

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

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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?

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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?

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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?

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Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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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?

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Four children were sharing a set of twenty-four butterfly cards. Are there any cards they all want? Are there any that none of them want?

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

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

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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?

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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?

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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.

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How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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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?

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If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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This activity investigates how you might make squares and pentominoes from Polydron.

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Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

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Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Investigate the different ways you could split up these rooms so that you have double the number.

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When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

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George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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

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

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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?

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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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This challenge extends the Plants investigation so now four or more children are involved.

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If you had 36 cubes, what different cuboids could you make?

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Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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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?

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Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

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A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

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Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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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?

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

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The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.