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 investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
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?
Explore the triangles that can be made with seven sticks of the same length.
I cut this square into two different shapes. What can you say about the relationship between them?
How many triangles can you make on the 3 by 3 pegboard?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
Can you find ways of joining cubes together so that 28 faces are visible?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
Have a go at this 3D extension to the Pebbles problem.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
How many different sets of numbers with at least four members can you find in the numbers in this box?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Sort the houses in my street into different groups. Can you do it in any other ways?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
What do these two triangles have in common? How are they related?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Investigate the different ways you could split up these rooms so that you have double the number.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
How many models can you find which obey these rules?
Can you create more models that follow these rules?
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.
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?
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.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
In how many ways can you stack these rods, following the rules?
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?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.