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Mathematics Matters Lesson Accounts 38 - Handshakes Investigation

This page has been archived. The content was correct at the time of original publication, but is no longer updated.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 38 - Handshakes Investigation

Written by Pamela Wyllie
Organisation Consultant
Age/Ability Range The lesson described was an INSET session for teachers in key stage 2. The teachers were of mixed ages, had been taught in different ways and had different mathematical strengths.

How was the session/task introduced?
Spoken introduction by the session leader was brief and the challenge was – Can you find a way to predict the number of handshakes for any number of people if they all shake hands with each other.

Teachers were asked to:

  • work on the ideas yourself until you have something to share;
  • find a partner who is ready and share each person’s ideas;
  • get together as whole group and talk about what we’ve done.

How was the session/task sustained?
There was time to engage with the mathematical situation and ‘play’ with ideas, before needing to work with partner.

How was the session/task concluded?
People shared different ways of modelling the situation, different ways of expressing the general rule; session leader prompted people to make connections between the different models and rules.

What were the critical moments?
Being ready to share ideas; finding a partner who was also ready at that time; being an active listener as well as speaker; respecting other people’s approaches.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
That there are different ways of modelling a situation and sometimes a simple diagram can be much more powerful than more ‘algebraic’ expressions at illuminating the structure of a situation – but having both is great. Some algebraic manipulation.

How was that mathematics learnt?
Through articulating it to someone else; hearing other learners’ explanations of why their rules worked, seeking commonalities.

Other memorable outcomes
Feeling able to adopt different approach.

Pencil and paper


Downloadable PDF

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Values & Principles

Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Builds on the knowledge learners already have
Encourages reasoning rather than ‘answer getting’

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Lesson Accounts Introduction

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


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