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

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?

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

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

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

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

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

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.

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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

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

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

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

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!

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

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

Make a mobius band and investigate its properties.

Surprise your friends with this magic square trick.

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

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?

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

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?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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

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?

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?

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

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?

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

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 make the birds from the egg tangram?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

The challenge for you is to make a string of six (or more!) graded cubes.

Here is a version of the game 'Happy Families' for you to make and play.

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

These practical challenges are all about making a 'tray' and covering it with paper.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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 are some ideas to try in the classroom for using counters to investigate number patterns.