In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

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

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

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.

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Here are two kinds of spirals for you to explore. What do you notice?

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

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

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

This article for teachers outlines one school's research project to explore how children, girls in particular, could be motivated in Maths through a more practical approach.

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?

Being stuck is usually thought of as being a negative state of affairs. We want our pupils to succeed, not to struggle. Or do we? This article discusses why being stuck can be fruitful.

This task requires learners to explain and help others, asking and answering questions.

Some questions and prompts to encourage discussion about what experiences you want to give your pupils to help them reach their full potential in mathematics.

In the process of working with some groups of teachers on using questions to promote mathematical thinking, the following table was developed. It provides examples of generic questions that can. . . .

In this article Liz Woodham reflects on just how much we really listen to learners’ own questions to determine the mathematical path of lessons.

Good questioning techniques have long being regarded as a fundamental tool of effective teachers. This article for teachers looks at different categories of questions that can promote mathematical. . . .