How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Make a cube out of straws and have a go at this practical challenge.
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Can you visualise what shape this piece of paper will make when it is folded?
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?
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.
Reasoning about the number of matches needed to build squares that share their sides.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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?
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?
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?
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?
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?
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.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you cut up a square in the way shown and make the pieces into a triangle?
How many triangles can you make on the 3 by 3 pegboard?
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 can you put five cereal packets together to make different shapes if you must put them face-to-face?
An activity making various patterns with 2 x 1 rectangular tiles.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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.
Here's a simple way to make a Tangram without any measuring or ruling lines.
How many models can you find which obey these rules?
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 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?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of the telescope and microscope?
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 the workmen?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 the candle and sundial?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?