Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Explore the relationship between simple linear functions and their graphs.

Explore the relationship between quadratic functions and their graphs.

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.

Consider these questions concerning inverting rational functions

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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.

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Steve has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Have a look at the ways children from Ickford Combined School and Weeke Primary sorted these cards.

The insights gained from tackling the earlier parts of this question helped many solve the final challenge.

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.