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

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

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

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?

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

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

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

Can you make the birds from the egg tangram?

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

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

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

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

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

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.

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?

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?

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. . . .

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

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?

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

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

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

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?

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

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?

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?

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?

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?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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

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

How many models can you find which obey these rules?

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?

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?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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?

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?

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?

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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?

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

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

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?

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