This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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 cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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 each work out what shape you have part of on your card? What will the rest of it look like?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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?

Explore the triangles that can be made with seven sticks of the same length.

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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.

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Can you visualise what shape this piece of paper will make when it is folded?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Exploring and predicting folding, cutting and punching holes and making spirals.

Make a cube out of straws and have a go at this practical challenge.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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 outline of this junk?

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?

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?

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?

Here's a simple way to make a Tangram without any measuring or ruling lines.