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

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

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?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

Explore the triangles that can be made with seven sticks of the same length.

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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.

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?

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

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

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?

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

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

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?

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?

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

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

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?

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

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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?

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?

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?

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?

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?

Can you lay out the pictures of the drinks in the way described by the clue cards?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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

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

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

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?

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?

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

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

How many models can you find which obey these rules?

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?

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

Can you make the birds from the egg tangram?

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

Surprise your friends with this magic square trick.

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?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?