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Mathematics Matters Lesson Accounts 16 - Revising/Reviewing Skills Involving Representing 3D Shapes in 2-D

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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 16 - Revising / Reviewing Skills Involving Representing 3D Shapes in 2-D

Written by Hannah Pomroy
Organisation Skipton Girls’ High School
Age/Ability Range Y10 set 1 of 2 – Selective grammar school (working at NC level 8/9)

How was the session/task introduced?
Revising / reviewing skills involving representing 3D shapes in 2D (introductory lesson to unit of work on area, volume and scale factors, establishing students prior knowledge and understanding).

To promote visualisation skills, team work, co-operation, listening skills, recognition of interconnectedness of skills between topics in mathematics lessons and between different curriculum areas.

On arrival students had a puzzle on their desk. The puzzle asked them in pairs to identify the different views of a) a tea-table (with cup, saucer, jug, teapot and sugar bowl on) and b) a park (with tower, tree and hut), views from different directions (elevations). There was an overall picture (plan view) and then different side elevations to choose from.

After reviewing this exercise we discussed what skills they had been using (generic as well as mathematical) and I explained the aims for the lesson along with the possible outcomes, and the real-life applications (this was discussed and agreed collectively).

How was the session/task sustained?
We then wrote down all the different ways they could think of to display / represent 3D objects in a 2D way.

What students did/gained: For the most part they listened and contributed suggestions although some wrote brief notes on the ideas collectively generated. (I encourage them always to write down as much or as little as they wish. If there are key facts to be learnt I often provide a suggested format, but prefer them to use their own What I might have changed: This part of the lesson was very effective as I was able to get a grip on past experience and to assess the level at which many pupils were working at. They contributed freely to ideas and some showed future career aspirations therefore I would not change anything here.

On a PowerPoint I had a series of 3-d views on isometric paper and a series of plan/side/front elevations. With mini white boards they were asked to note which was correct for each shape. What students did / gained: This is a strategy I use often and the pupils are well trained in what is expected. They were required to think for themselves and are a little competitive but on the whole they are very supportive of one another. I was able to fully assess individual’s ability / understanding. The students further practised visualisation and where also required to do this quite quickly.

The pupils were then paired again. Each pair was given 20 multi-link cubes. One pupil from each pair came to the front and looked at a drawing on isometric paper of a 3D shape. They then had to return to their partner and describe it. When complete the partner brought the shape to me to assess it. If correct the partner then had a go and so on.

What pupils gained: Again visualisation, clarity of description, teamwork and co-operation.

How was the session/task concluded?
To complete the lesson I wished to practice nets in order to establish full understanding in preparation for surface are calculations, and for completeness. I knew that all pupils would have met this before and that making nets again would be unnecessary repetition. To start with all pupils took part together in a web-site activity identifying correct nets for cubes- teamwork, cooperation, visualisation etc.

Then they made nets that had strings attached to pull them up into the 3-d solid. They really enjoyed this and also were inspired sufficiently to go on and generate their own from more computer shapes.

What were the critical moments?
I think the lesson was successful largely because the pace and variety of activity engaged the students, and they learnt and rehearsed visualisation skills through mathematical activities that crossed curricula boundaries.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Interconnectedness of different mathematical ideas – they were able to use the visualisation practised in this lesson to advance their understanding of surface area calculations in the next lesson; they practised construction skills when making nets; they worked hard as teams to communicate precisely and concisely – a key mathematical skill.

How was that mathematics learnt?
Through a lot of different activities stimulating and motivating them in different ways.

Other memorable outcomes
At the end of term more pupils put one of the activities from this lesson on their term review sheet, than any other.

Power Point
Views worksheet
Multi-link cubes and isometric drawings
Card and string for nets activity and worksheet of instructions.


Values & Principles

Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Uses rich, collaborative tasks

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