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# Mathematics Matters Lesson Accounts 4 - Using Knowledge of Parallel Lines and Transversals to Prove Angle Sum of a Triangle

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Created on 27 May 2008 by ncetm_administrator
Updated on 25 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 4 - Using Knowledge of Parallel Lines and Transversals to Prove Angle Sum of a Triangle

 Written by Andrea Kite Organisation Archers Court Mathematics and Computing College Age/Ability Range Year 8 Working at level 5c – 6b

Starter task: using knowledge of parallel lines and transversals to prove angle sum of a triangle.(See additional lesson plan proforma)

Students were divided into groups, each with its own learning objectives. Groups 1 and 2 – discovering necessary conditions for side lengths of triangles (i.e. the sum of 2 shorter sides>the length of the longest side). Group 3 – solving word problems relating to angles of a triangle.

Students worked in twos and threes within their groups given equipment and a task.

Group 1 – Geostrips in 3 sizes. Task was to find as many different triangles that could be made ( and also ones that could not be made).

Group 2 – How many different triangles of sides with integer lengths and perimeter 36 could be made. Which combinations were not possible?

Group 3 – Mathematical team games (Tarquin Publications) Students had clues to decipher and would create a series of triangles. By finding unknown angles they would then use the letters of the angles to find a phrase.

As pupils worked in their small groups, I questioned them – How were they working systematically? What previous knowledge / skills did they draw upon?

Group 1 – Students needed to consider how they knew they had tried all possibilities.

Group 2
– Use previous work on constructing triangles.

Group 3
- Knowledge of angles in a triangle, but also understanding and using the clues from the team games book.

Groups 1 and 2 were also encouraged to consider the conditions for the lengths of sides of triangles, particularly necessary conditions for the sum of the 2 shorter sides.

Students were asked to write sentences to explain their learning.

What were the critical moments?
One group during the starter realised how they could use alternate angles to discover the proof of the angle sum of a triangle.

In Group 1 discovering the conditions of shorter lengths of triangle sides.

Group 2 realising that using previous knowledge / skills of constructing triangles could help.

Group 3 Realising that drawing diagrams will help.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?

How was that mathematics learnt?
Through pupils’ independent learning, trial and error/improvement.

Other memorable outcomes

## Values & Principles

 Conceptual understanding and interpretations for representations Strategies for investigation and problem solving Builds on the knowledge learners already have Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work Encourages reasoning rather than ‘answer getting’

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