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Mathematics Matters Lesson Accounts 28 - Chair Problem

This page has been archived. The content was correct at the time of original publication, but is no longer updated.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 28 - Chair Problem

Written by Lee Northern
Organisation Cornwall Education Development Service
Age/Ability Range Year 9 Low-ish to middle ability (ie level 5 some 6) Post-SATs

How was the session/task introduced?

B B B   G G G
□ □ □ □ □ □ □

The teacher arranged 7 chairs at the front of the room as illustrated above. Three boys were sat at the left hand end, 3 girls at right. They were told that they must swap places. Can only move one way, and do a jump or a slide. Ref: ATM Points of Departure.

“Kangaroos” (Known as ‘frogs’ to many I’m sure!) must exchange places (eg X, O are different types of kangaroo) XX_OO …. They were asked to consider the number of moves it takes – gave deliberately difficult task to start with. Jump and slide only possible moves.

How was the session/task sustained?
The pupils sustained it themselves with my prompting…”what if” questions. The challenge was to understand the problem and devise strategies. They were motivated by wanting to know why. What was interesting was the engagement of pupils on a task with little utilitarian purpose (to them).

How was the session/task concluded?
Pupils were satisfied they had understood the problem, though a full solution had not been achieved.

What were the critical moments?
Pupils being able to get up move around and physically act out the movements. Asking own questions – “what if” and “let’s try this…” moments. Freedom to share ideas, to experiment, to talk, argue, discuss.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Strict content minimal: huge amount of other learning: recording, representation, pattern spotting, rule forming and checking, sequencing, discussion and communication, explaining and justifying.

How was that mathematics learnt?
By experience and experimentation. The key learning for me was that, as a teacher, you must take risks.

Other memorable outcomes
Practically all the ECM agendas!
Enjoyment, intellectual satisfaction.
That maths is a lot more than the SATs!!

Some chairs.


Downloadable PDF

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Values & Principles

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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