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 your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Sort the houses in my street into different groups. Can you do it in any other ways?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Explore the triangles that can be made with seven sticks of the same length.
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?
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?
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.
These pictures show squares split into halves. Can you find other ways?
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Can you create more models that follow these rules?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Can you find ways of joining cubes together so that 28 faces are visible?
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.
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 triangles can you make on the 3 by 3 pegboard?
An activity making various patterns with 2 x 1 rectangular tiles.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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!
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.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Have a go at this 3D extension to the Pebbles problem.
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?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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.
How many models can you find which obey these rules?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?