Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
You'll need a collection of cups for this activity.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
What shapes can you make by folding an A4 piece of paper?
For this activity which explores capacity, you will need to collect some bottles and jars.
In this activity focusing on capacity, you will need a collection of different jars and bottles.
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Can you create more models that follow these rules?
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
Can you visualise what shape this piece of paper will make when it is folded?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
Explore the triangles that can be made with seven sticks of the same length.
Can you fit the tangram pieces into the outlines of the chairs?
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?
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Here's a simple way to make a Tangram without any measuring or ruling lines.
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
Can you make the birds from the egg tangram?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of the child walking home from school?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 outline of this junk?
Can you fit the tangram pieces into the outlines of these people?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Can you fit the tangram pieces into the outlines of these clocks?
Make a flower design using the same shape made out of different sizes of paper.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.