Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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?
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?
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
These pictures show squares split into halves. Can you find other ways?
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.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
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?
Explore one of these five pictures.
A follow-up activity to Tiles in the Garden.
What do these two triangles have in common? How are they related?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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.
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
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?
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
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?
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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!
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Sort the houses in my street into different groups. Can you do it in any other ways?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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.
Investigate the different ways you could split up these rooms so that you have double the number.
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?
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?
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?
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?
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 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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many models can you find which obey these rules?
Can you create more models that follow these rules?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.