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?

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

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

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?

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

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

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

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

Surprise your friends with this magic square trick.

Make a mobius band and investigate its properties.

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

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

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

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 ...

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?

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

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

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

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

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

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

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?

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.

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

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

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

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

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

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

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?

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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?

How can you make a curve from straight strips of paper?

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?

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?

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

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

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?

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

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

Can you make the birds from the egg tangram?