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.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Sort the houses in my street into different groups. Can you do it in any other ways?

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

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

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?

What is the largest cuboid you can wrap in an A3 sheet of paper?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

An investigation that gives you the opportunity to make and justify predictions.

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

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

Why does the tower look a different size in each of these pictures?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

How many models can you find which obey these rules?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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

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?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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?

Can you find ways of joining cubes together so that 28 faces are visible?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

How many faces can you see when you arrange these three cubes in different ways?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.