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?

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?

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

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

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?

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.

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

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?

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

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

Make a mobius band and investigate its properties.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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

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

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

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

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

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

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

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?

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

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

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.

Surprise your friends with this magic square trick.

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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

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?

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

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.

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

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

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.

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

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

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

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 ...

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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