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

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

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

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

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?

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

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?

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?

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?

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

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

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?

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

Can you make five differently sized squares from the tangram pieces?

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

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?

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

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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?

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?

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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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

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

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?

Can you fit the tangram pieces into the outline of this telephone?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the workmen?

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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?

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