How many models can you find which obey these rules?
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.
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.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Can you create more models that follow these rules?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
How many triangles can you make on the 3 by 3 pegboard?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This activity investigates how you might make squares and pentominoes from Polydron.
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
These practical challenges are all about making a 'tray' and covering it with paper.
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.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outlines of the chairs?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outlines of these clocks?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of the telescope and microscope?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?