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# Mathematics Matters Lesson Accounts 43 - Graph Plotting with Software

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Created on 29 May 2008 by ncetm_administrator
Updated on 23 July 2009 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 43 - Graph Plotting with Software

 Written by Peter Lacey Organisation ECARDA Ltd Age/Ability Range High set Y11 and then into sixth form

Graph plotting programme – plot y = x² – can you translate left/right; up/down. Students investigated transformations in groups of 3 in front of computer.

The task grabbed student’s interest. Proved challenging and good fun.

With an unanswered question from students*.(see below)

What were the critical moments?
In ‘moving’ the curve up with y = x² + a students in one group described the transformation as “a new curve parallel to the original”. Other members of the group suggested it wasn’t parallel “because the lines got closer at the top”. The teacher used this episode to generate a whole class discussion. Teacher worried about using the word parallel in non-linear contexts; students not worried and talked about railway lines which went round bends had to be the same distance apart. With prompting from the teacher – using the model of railway sleepers – agreed distance apart had to be measured at right-angles to the rail.

*Discussion led to the question ‘what do we do to y = x² to make a ‘parallel curve’? Lesson ended at this point with students saying they would manually plot the curve. Same teacher took the question to a group of sixth formers (y13) saying that y11s had posed the question but got stuck. Over two sessions the teacher used the question to introduce parametric equations. Back with the Y11s the manual plots revealed that ‘parallel’ lines, if that’s what they were, could include ‘kinks’ on the ‘inside track’ where the bend was particularly acute. Perhaps this was analogous to wheels on an axle turning in opposite directions in order to make a tight turn. A display of this work was made.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
By Y13 – understanding of nature of parametric equations.
By Y11 – ambiguity of use of word parallel and need for clear language / definitions. The existence of more complex transformations. Maths can throw up questions as much as provide answers

How was that mathematics learnt?
Engagement / discussion

Other memorable outcomes
A question thrown up by one group of learners may be picked up by another. Even young learners can probe the subtlety of the meaning of mathematical words & ideas.

Resources
A graph plotting programme

## Values & Principles

 Conceptual understanding and interpretations for representations Strategies for investigation and problem solving Uses resources, including technology, in creative and appropriate ways

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