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Mathematics Matters Lesson Accounts 42 - Geometry on A4 Paper

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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 42 - Geometry on A4 Paper

Written by Peter Hough
Organisation NCETM
Age/Ability Range Year 8 but can be used at most levels

How was the session/task introduced?
Hold up a sheet of A4 paper ask students to describe what they know about it. Learners worked in groups of 3-4. All responses shared with whole group until exhausted. Then instructions for folding A4 sheet into a kite were given verbally. Learners encouraged to help each other. Each created kite. See folding pattern.

How was the session/task sustained?
At each of the 2 folds the same question was asked “What are the properties of this shape?” Once folded to form kite – unfold to create shape with fold lines. Emphasise with pencil. Pose questions. “What are the angles formed by these lines?” “Can you give explanations?”

How was the session/task concluded?
Learners compared results and reached a consensus on each table. Then each table formed a tiling design by combining their congruent kites. Learners discussed the properties of the tiling.

What were the critical moments?

  • The way learners were happy to be helped and to help other learners with folding.
  • When learners realised they had to draw on their prior knowledge. Some produced list of what they already knew e.g. angle sum of a triangle

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?

  • A range of properties of shapes and angles depending on their prior knowledge.
  • How and why shapes fill 2D space.
  • How to give mathematical explanations.
  • Angle properties learned and consolidated.
  • Using prior knowledge to solve problems in an unfamiliar context. How was that mathematics learnt?
  • Through collaborative sharing/pooling of prior knowledge (whole class and in groups)
  • Using group discussion to analyse unfamiliar problems.

Other memorable outcomes
My realisation that this is almost a generic activity. Same process can be applied to any folded shape. Can be extended to challenge “A” level students.


Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Fluency in recalling facts and performing skills
Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Builds on the knowledge learners already have
Exposes and discusses common misconceptions and other surprising phenomena
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
Creates connections between topics both within and beyond mathematics and with the real world
Uses resources, including technology, in creative and appropriate ways

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Lesson Accounts Introduction

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


Discover the 'Mathematics Matter' Project Forum







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