Project Teachers' Notes

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.

 

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

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?

When will two quadratic functions intersect?

Can I tell from a quadratic function where its graph has a turning point?

 

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.

Key questions

What do you think these function machines do?

What will happen if we input 5? 13? 100? 0.7? ...

What other questions could we ask?

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

What's the same? What is different?

Can you explain?