We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Can you create more models that follow these rules?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
What is the largest cuboid you can wrap in an A3 sheet of paper?
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 many faces can you see when you arrange these three cubes in different ways?
Sort the houses in my street into different groups. Can you do it in any other ways?
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.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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 cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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 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?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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.
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you find ways of joining cubes together so that 28 faces are visible?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
These pictures show squares split into halves. Can you find other ways?
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?
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.
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 challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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 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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
It starts quite simple but great opportunities for number discoveries and patterns!
Have a go at this 3D extension to the Pebbles problem.
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!
A follow-up activity to Tiles in the Garden.
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?
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
An activity making various patterns with 2 x 1 rectangular tiles.
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
In how many ways can you stack these rods, following the rules?
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?