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

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

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

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?

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?

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

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

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?

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

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

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

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

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.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

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

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?

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?

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?

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?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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

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

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?

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.

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?

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?

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?

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?

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

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

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?

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

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.