About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.


Personal Learning Login

Sign Up | Forgotten password?
Register with the NCETM

Mathematics Matters Lesson Accounts 45 - Angles of a Polygon

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
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 45 - Angles of a Polygon

Written by Richard Deakin
Organisation Failsworth School
Age/Ability Range Year 9 level 5/6 students

How was the session/task introduced?
Task to build on knowledge of external angles of a polygon. This came after lesson on internal angles. Teacher explained what external angle was. The main task was to create an irregular polygon with an even number of sides. with three exterior angles of 90°, 60°, 90°, and the remaining exterior angles being equal. Pupils asked (i) how many sides could the polygon have, (ii) to work out the missing angles and make sketches of what the different polygons could look like.

How was the session/task sustained?
Pupils discussed how many sides polygon had. Small groups sketched shape on plan paper. An absolute mess was created with pupils’ attempts.

How was the session/task concluded?
Successful solution was obtained by pupils and shared with other groups.

What were the critical moments?
When pupils realised that internal + external angle = 180°, so if external angle was 120°, the internal angle must be 60°. Once pupils deduced the 3 internal angles the solution became easier to obtain.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Strengthened knowledge of polygons, internal and external angles

How was that mathematics learnt?
Through deductive reasoning. The initial task helped pupils to understand external and internal angle = 180°, and external angles in polygon added to 360°, .

Other memorable outcomes
Solutions displayed on classroom walls.

RM Kaleidos maths alive http://www.learningplatform.rm.com/,
Y9 core SSM1 lesson 7 (tasks based from task in this product).


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Strategies for investigation and problem solving
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Uses rich, collaborative tasks

Browse by
Lesson Accounts
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 
21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 56, 57
Search by ... Values
V1, V2, V3, V4, V5
Search by ... Principles 
P1, P2, P3, P4, P5, P6, P7, P8

Lesson Accounts Introduction

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


Discover the 'Mathematics Matter' Project Forum







Comment on this item  
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item



06 November 2014 01:38
the lesson is interesting. I would love to teach in my class.
By heylhi1234
         Alert us about this comment  
Only registered users may comment. Log in to comment