We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
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.
What is the largest cuboid you can wrap in an A3 sheet of paper?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
Can you create more models that follow these rules?
How many models can you find which obey these rules?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Can you find ways of joining cubes together so that 28 faces are visible?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Sort the houses in my street into different groups. Can you do it in any other ways?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
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?
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?
How many faces can you see when you arrange these three cubes in different ways?
Have a go at this 3D extension to the Pebbles problem.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
How many tiles do we need to tile these patios?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
A follow-up activity to Tiles in the Garden.
It starts quite simple but great opportunities for number discoveries and patterns!
Investigate the different ways you could split up these rooms so that you have double the number.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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?
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?