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

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

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

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

What is the greatest number of squares you can make by overlapping three squares?

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?

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

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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

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?

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

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

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.

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?

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

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

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?

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

Can you make the birds from the egg tangram?

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?

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

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

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

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

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

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

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

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 junk?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

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?

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

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.

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?

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 see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?