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 ...

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

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?

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

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

Can you make the birds from the egg tangram?

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

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

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

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

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?

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?

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

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

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

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?

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?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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 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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

For this activity which explores capacity, you will need to collect some bottles and jars.

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

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

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

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Can you put these shapes in order of size? Start with the smallest.

In this activity focusing on capacity, you will need a collection of different jars and bottles.

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

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 you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?