Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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?

There are lots of different methods to find out what the shapes are worth - how many can you find?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

What happens when you round these three-digit numbers to the nearest 100?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you find all the different triangles on these peg boards, and find their angles?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Are these statements always true, sometimes true or never true?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

This activity involves rounding four-digit numbers to the nearest thousand.

The challenge for you is to make a string of six (or more!) graded cubes.

Use the information on these cards to draw the shape that is being described.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

What can you see? What do you notice? What questions can you ask?

Are these statements always true, sometimes true or never true?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Use the isometric grid paper to find the different polygons.

Can you find pairs of differently sized windows that cost the same?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Can you compare these bars with each other and express their lengths as fractions of the black bar?

What fraction of the black bar are the other bars? Have a go at this challenging task!

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.

This problem shows that the external angles of an irregular hexagon add to a circle.

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?