How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of these clocks?
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 outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outline of this plaque design?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you fit the tangram pieces into the outline of Mai Ling?
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?
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 Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outline of this telephone?
Can you visualise what shape this piece of paper will make when it is folded?
What shape is made when you fold using this crease pattern? Can you make a ring design?
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?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
How many models can you find which obey these rules?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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 Wai Ping, Wah Ming and Chi Wing?
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?
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Here's a simple way to make a Tangram without any measuring or ruling lines.
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 fit the tangram pieces into the outline of these convex shapes?
Can you fit the tangram pieces into the outline of this sports car?
Can you cut up a square in the way shown and make the pieces into a triangle?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Can you fit the tangram pieces into the outline of Granma T?
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.
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?