You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

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

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

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

This article for students gives some instructions about how to make some different braids.

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

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

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

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

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

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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

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?

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

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

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

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 ...

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?

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

Learn about Pen Up and Pen Down in Logo

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

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

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

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?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

More Logo for beginners. Now learn more about the REPEAT command.

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

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?

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

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

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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 does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

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?

How many models can you find which obey these rules?

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?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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.