Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping 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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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 find all the different ways of lining up these Cuisenaire rods?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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 different rhythms can you make by putting two drums on the wheel?
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?
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?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
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.
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Explore the different snakes that can be made using 5 cubes.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
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?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
Can you fill in the empty boxes in the grid with the right shape and colour?
Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
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 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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
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?