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

Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Challenge Level

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Challenge Level

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

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Challenge Level

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

Challenge Level

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Challenge Level

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Challenge Level

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

Challenge Level

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 ...

Challenge Level

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Challenge Level

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

Challenge Level

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

Challenge Level

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

Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Challenge Level

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Challenge Level

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Challenge Level

How many models can you find which obey these rules?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Surprise your friends with this magic square trick.

Challenge Level

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?

Challenge Level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Challenge Level

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Challenge Level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Challenge Level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Challenge Level

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?

Challenge Level

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Challenge Level

These pictures show squares split into halves. Can you find other ways?

Challenge Level

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Challenge Level

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?

Challenge Level

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Challenge Level

This activity investigates how you might make squares and pentominoes from Polydron.

Challenge Level

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