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

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

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

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?

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

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

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

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.

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?

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

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

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

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 work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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.

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

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

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

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?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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?

Here is a version of the game 'Happy Families' for you to make and play.

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

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

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?

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?

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

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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?

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?

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?

Can you make the birds from the egg tangram?

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

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?

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?

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

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

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

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?

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?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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.

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

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

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

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