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Mathematics Matters Lesson Accounts 17 - Completing the Square

This page has been archived. The content was correct at the time of original publication, but is no longer updated.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 17 - Completing the Square

Written by James Knightbridge
Organisation The Blandford School
Age/Ability Range Year 12 – 4 weeks into the C1 course

How was the session/task introduced?
Revision of the skills that were learnt from the previous lesson on how to complete the square, students were reminded of the activities that helped them understand during the previous lesson.

How was the session/task sustained?
Pace – the lesson appeared to go off at a tangent – the whole class discussed translations of linear and quadratic equations – The students used a print out of x² and an acetate sheet to test/confirm their ideas, opportunity for individual and/or small group work.

How was the session/task concluded?
The students were given a quadratic and told to sketch it. What techniques could they use? Some completed the square.

What were the critical moments?
The Eureka moment – the link between completing the square and the graph transform.

The realisation by the students that they already had the skills to solve a new type of problem.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
There are a range of techniques that we can use to sketch a quadratic curve – some may be easier to use than others.

How was that mathematics learnt?
Building on previous knowledge and providing continuity between lessons – reminding students of the skills they have which in turn builds their confidence – when the students are in their comfort zone we can then dare them to take risks.

Other memorable outcomes
There were opportunities for individual, small group and whole class learning.

Outcomes informed my planning for the following lesson (to sketch quadratics where the coefficient of x was not equal to one.

Graph drawing software Acetate sheets and pens
Quadratic print out.


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Conceptual understanding and interpretations for representations
Builds on the knowledge learners already have
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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