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 34 - Using Pythagoras' Theorem

This page has been archived. The content was correct at the time of original publication, but is no longer updated.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 34 - Using Pythagoras' Theorem

Written by Murphy
Organisation Unknown
Age/Ability Range Unknown

(a) What was the mathematical task(s)?
Context – Medium-high ability Y8, two lessons after being introduced to, use and proved, Pythagoras’ Theorem.

Given approximately 15 diagrams, each containing 2 sizes of circles, asked to find radius of larger, given radius of smaller = 1. Tackle in any order.
For example:

(b) What learning culture was created? How was this achieved?
Initially competitive. When individual problems solved, student demonstrated to class (if they wanted to listen). Occasional applause for some. I saw others applying techniques they’d seen others use. Debate over one or two – presenter had made assumptions which weren’t true, for example, about symmetry. Impressive creative thinking (eg adding lines to the diagram). Real sense of students appreciating each others ideas

(c) How could you tell that the task(s) achieved the intended purposes? Do you have any evidence?
All students were building on the work of others. Those who said it was ‘hard’ also said they followed others’ work and had a sense of awe: “How did he think to do that?” Genuine joy in other students’ ideas

(d) Is this example available to see/read about?
No - but the 15 diagrams are taken from a ‘Mathematics in School’ Article January 1999

(e) Can you say why you chose this example? What criteria were in your mind?
First and foremost the appreciation students showed for each others work; a sense of achievement and desire to prove; enjoyment of running with one idea (Pythagoras) and creative thinking.


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Strategies for investigation and problem solving
Encourages reasoning rather than ‘answer getting’

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



There are no comments for this item yet...
Only registered users may comment. Log in to comment