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

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 make the birds from the egg tangram?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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?

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?

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?

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

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

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?

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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?

How many models can you find which obey these rules?

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.

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.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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?

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?

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?

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

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

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?

Make a flower design using the same shape made out of different sizes of paper.

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?

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

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

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

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

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

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?

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

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?

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 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?

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

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?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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

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

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

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?

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

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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?