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

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?

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Follow these instructions to make a five-pointed snowflake from a square of paper.

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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.

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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

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

Make a flower design using the same shape made out of different sizes of paper.

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

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

What is the greatest number of squares you can make by overlapping three squares?

This activity investigates how you might make squares and pentominoes from Polydron.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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?

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

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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?

What do these two triangles have in common? How are they related?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

An activity making various patterns with 2 x 1 rectangular tiles.

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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?

Can you make the birds from the egg tangram?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Can you deduce the pattern that has been used to lay out these bottle tops?

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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

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?

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

Follow these instructions to make a three-piece and/or seven-piece tangram.