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?

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?

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

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?

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

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

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

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

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.

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

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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 arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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 practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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

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

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?

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?

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

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

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

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

Can you make the birds from the egg tangram?

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

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

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

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

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?

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

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

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

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

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

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

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

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?

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?

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?

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

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?

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

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