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?

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?

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?

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?

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?

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?

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.

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

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

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

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?

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?

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?

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

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?

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?

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

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

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

Exploring and predicting folding, cutting and punching holes and making spirals.

In this activity focusing on capacity, you will need a collection of different jars and bottles.

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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

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

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

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

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?

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

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

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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

Can you make the birds from the egg tangram?

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

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

For this activity which explores capacity, you will need to collect some bottles and jars.

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

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

How can you make a curve from straight strips of paper?

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