Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
How many models can you find which obey these rules?
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 thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Explore the different snakes that can be made using 5 cubes.
Take three differently coloured blocks - maybe red, yellow and
blue. Make a tower using one of each colour. How many different
towers can you make?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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.
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
If you had 36 cubes, what different cuboids could you make?
This activity is best done with a whole class or in a large group.
Can you match the cards? What happens when you add pairs of the
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?
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 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.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
Make a chair and table out of interlocking cubes, making sure that
the chair fits under the table!
Can you create more models that follow these rules?
This project challenges you to work out the number of cubes hidden
under a cloth. What questions would you like to ask?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Here are some pictures of 3D shapes made from cubes. Can you make
these shapes yourself?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
Try to picture these buildings of cubes in your head. Can you make
them to check whether you had imagined them correctly?
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
Kimie and Sebastian were making sticks from interlocking cubes and
lining them up. Can they make their lines the same length? Can they
make any other lines?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
This article takes a closer look at some of the toys and games that
can enhance a child's mathematical learning.