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 greatest number of squares you can make by overlapping three squares?

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

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.

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

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?

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

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

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?

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

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

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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?

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

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?

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

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

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?

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

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

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?

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

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 outlines of the lobster, yacht and cyclist?

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

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

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

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 candle and sundial?

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 these people?

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

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

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?

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 this telephone?

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

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

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

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

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

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

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

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

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?