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This month's NRICH site has been inspired by the way teachers at Kingsfield School in Bristol work with their students. Following an introduction to a potentially rich starting point, a considerable proportion of the lesson time at Kingsfield is dedicated to working on questions, ideas and conjectures generated by students.

Working on this project will encourage students to work together, discuss ideas, develop conjectures, suggest new lines of enquiry, solve problems and generally experience how a mathematical community functions.

Charlie's Mapping is one of several starting points. Here are the sort of questions that might emerge:

When are lines parallel?

When are they perpendicular?

What affects the direction and steepness of a graph?

Can I tell from a function where its graph will cross the axes?

Which functions give straight lines, and which give curves?

The interactivity could be used as a starting point to encourage students to make conjectures about functions and graphs, in a similar way to how students at Kingsfield School are introduced to the topic.

Read the article Kingsfield School - Building on Rich Starting Points, which has links to a description of a Kingsfield teacher's first lesson on functions and graphs, and a video showing how these ideas are put into practice in the classroom.

For teachers who want to create their own alternatives to Charlie's Mapping for use in the classroom, here is an introductory video explaining how to build, load and save your own examples.

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To read more about the Number Plumber, visit Grumplet's blog where you can comment on how you have used the number plumber and share links to files you have created. We are continuing to develop this resource so your feedback and ideas will be very useful.

What do you think this function machine does?

Can you predict an output, and test it?

What possible questions could we ask?

Can you make any predictions about what might happen when we change the function machine?

What's the same? What is different?

Can you explain?

Alison's Mapping provides a starting point based on quadratic functions.

Become Maths Detectives encourages exploration of numerical patterns.