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Mathematics Matters Lesson Accounts 14 - Constructing a Hexagon

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 May 2008 by ncetm_administrator
Updated on 16 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 14 - Constructing a Hexagon

Written by Fiona Chapman
Organisation The Folkestone School for Girls
Age/Ability Range Year 7 mixed ability grammar school – levels ranged 4 – 6a

How was the session/task introduced?
To be able to construct a hexagon and use it to review progress and link into activities 2 and 3 (below).

The aim of the lesson was to have a rich mathematical task that would allow different ability students to achieve a variety of learning outcomes.

How was the session/task sustained?
By being broken into several smaller tasks with feedback and higher level questioning to review progress and link into next activity.

Activity one – accurate constructions - Pupils were shown how to construct a hexagon with pencil and compass. This gave a learning outcome that all pupils would be able to achieve and provided for kinaesthetic learners.

Activity two – using their sheets of circles with the vertices of hexagons marked on the circumference (photocopied examples were given to pupils who had found the first task more difficult) pupils were asked to join three points to form a triangle and to see how many different triangles they could produce. Pupils were encouraged to find logical ways of working and to explain why there were no more triangles to be found. “How can you be certain that you have found them all?” They were also asked to name the types of triangle.

Activity three – using sheets provided with further circles marked with the 6 equidistant points, pupils were then asked to repeat the exercise but have one vertex of the triangle at the centre of the circle. Pupils were asked to measure all the angles in their triangles and look for any patterns. This part was done in pairs/small groups and the pupils were encouraged to share/discuss ideas.

How was the session/task concluded?
Pairs / small groups shared their discoveries and new angle rules (circle theorems) were established.

What were the critical moments?
Pupils realising that there was a difference between thinking there were no more solutions and being able to explain why they knew that there were no more.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Constructions, use of protractors, circle theorems, logical thinking, early form of proof.

How was that mathematics learnt?
Constructions skills- knowledge passed on by teacher Use of protractor – pupils own experience with guidance Rest – Individual investigation, shared discussion of ideas.

Other memorable outcomes
Because there was not a list of ‘sums’ with right or wrong answers even the least able felt they had been successful. Lots of pupils across the ability range had ‘aha’ moments.

Least able gained construction skills and experience in logical thinking.

Most able discovered for themselves three circle theorems – angle in semicircle; angle at centre is twice angle at circumference; angles in same segment equal.

By sharing their discoveries the less able also took away knowledge beyond the normal curriculum for year 7.

Constructions taught on interactive whiteboard.

Diagrams pre-prepared on handouts for pupils struggling with constructions and to speed up discovery aspect in final activity.

All diagrams on flipcharts on interactive whiteboard for pupils to draw on in front of class when sharing discoveries and explaining their ideas.


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Fluency in recalling facts and performing skills
Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Uses higher-order questions
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’
Uses rich, collaborative tasks

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Lesson Accounts Introduction

Mathematics Matters - What constitutes the effective learning of mathematics? find out more


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