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

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?

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

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?

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

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

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?

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?

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

Can you make the birds from the egg tangram?

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?

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?

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

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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

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

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

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

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

What shape would fit your pens and pencils best? How can you make it?

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.

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?

How many models can you find which obey these rules?

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?

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

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

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?

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