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?

Make a mobius band and investigate its properties.

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

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

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.

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.

Surprise your friends with this magic square trick.

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!

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

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

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

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

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

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?

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

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

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

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.

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?

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

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

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

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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

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

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?

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?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

A description of how to make the five Platonic solids out of paper.

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?

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?

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

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

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 ...

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

Can you make the birds from the egg tangram?

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