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# Mathematics Matters Lesson Accounts 48 - Teaching Angles on Parallel Lines

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Created on 29 May 2008 by ncetm_administrator
Updated on 17 June 2008 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 48 - Teaching Angles on Parallel Lines

 Written by Snezana Lawrence Organisation Maths is Good for You Age/Ability Range Year 8 top set in a comprehensive school Levels 5a – 6b

There was a historical introduction to the lesson – about defining properties of geometrical elements, and introduced the students to the idea of parallel lines. We had a brief session on “imagining” where kids thought of parallel lines going into infinity.

Students were given an investigative task which concentrated on constructing an animation using Geometer’s Sketchpad on parallel lines. Angles on parallel lines were looked at, but the diagram was also extended to include a brief analysis of parallelograms, their special cases (rectangle, rhombus, square) and the areas of parallelograms.

The students had worked in groups of 4-5. They had to make the animation and come to some conclusions / generalisations. One of the students from the group was also a scribe who had to take account of all the steps they took so that if another pupil or group had their notes they would be able to a) repeat the process of making the animation. And b) understand why they came to the general statements that they did during the process.

What were the critical moments?

• Inducting students into the process of imagining parallel lines.
• Discussing (initially) the animation shown on the board but not giving too much – leaving things for students to discover and generalise.
• Students presentations to the class.
• Whole class discussion at the end.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Students worked with angles on parallel lines but they also linked that with parallelograms and were learning a skill of creating an environment (GSP) in which they can further investigate something mathematically that may not be necessarily linked to where they started from. In this case they also investigated areas of parallelograms.

How was that mathematics learnt?
Through thinking / imagining geometrical properties of lines. Through discussions, through “making” a set of parallel lines (construction). Through investigating that construction using dynamic geometry software.

Other memorable outcomes
The enjoyment of:

• Seeing something for the first time through imagining
• Seeing and making generalisations
• Ability of acquiring a technical skill - creating a construction, and acquiring a knowledge of parallel lines which encompassed all special cases
• Learning about the historical background - a quote of Bolyai (1823) when he worked on parallel lines he “discovered things so wonderful that I was astounded… out of nothing I have created a strange new world”.

Resources
Geometer’s sketchpad and laptops for the whole class.

## Values & Principles

 Fluency in recalling facts and performing skills Conceptual understanding and interpretations for representations Appreciation of the power of mathematics in society Exposes and discusses common misconceptions and other surprising phenomena Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work Uses rich, collaborative tasks Creates connections between topics both within and beyond mathematics and with the real world Uses resources, including technology, in creative and appropriate ways

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