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

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

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

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Use the tangram pieces to make our pictures, or to design some of your own!

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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?

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A game in which players take it in turns to choose a number. Can you block your opponent?

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

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

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Can you make the birds from the egg tangram?

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A game to make and play based on the number line.

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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?

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

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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?

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How many models can you find which obey these rules?

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

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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.

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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?

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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?

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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?

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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.

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. . . .

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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?

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Surprise your friends with this magic square trick.

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

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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?

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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?

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

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

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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?

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These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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

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

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Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

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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?

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

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What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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

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

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

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

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

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

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

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