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 recreate this Indian screen pattern? Can you make up similar patterns of your own?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
Follow these instructions to make a five-pointed snowflake from a square of paper.
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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?
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?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Explore the triangles that can be made with seven sticks of the same length.
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?
A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?
What shapes can you make by folding an A4 piece of paper?
In this activity focusing on capacity, you will need a collection of different jars and bottles.
For this activity which explores capacity, you will need to collect some bottles and jars.
You'll need a collection of cups for this activity.
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
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.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you make the birds from the egg tangram?
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
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?
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 fit the tangram pieces into the outline of this junk?
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 Little Fung at the table?
Can you fit the tangram pieces into the outlines of these people?
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 outline of the child walking home from school?
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 this telephone?
Can you fit the tangram pieces into the outlines of the chairs?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
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?