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Mathematics Matters Lesson Accounts 44 - Paper Helicopters

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
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 44 - Paper Helicopters

Written by Pratt
Organisation Unknown
Age/Ability Range Unknown

(a) What was the mathematical task(s)?
What makes the best design for a paper "helicopter"?

  1. Make a spinner and try it out. 
  2. Compare 2 spinners.
  3. Why did you like that one?
  4. What variables affect the flight (usually time of flight)
  5. In groups, explore the variable (e.g. length of wings) comparing it to the dependent variable (time).
  6. Perhaps use Active Graphing:
    (a) Enter a few ordinate points into a spreadsheet
    (b) Generate a scatter-graph
    (c) Decide what to do next in the experiment
    (d) Go to (a)

(b) What learning culture was created? How was this achieved?
No one task generates a culture. Indeed a task can create discipline problems of culture clashes with expectations of behaviour in task. Aiming for a culture in which mathematics is used to explore an interesting problem, resulting in the learning of new mathematics. Students need to work in small groups and work together, sharing roles in task. The mathematics should be seen as powerful.

(c) How could you tell that the task(s) achieved the intended purposes? Do you have any evidence?

  • used graphs to make decision about where to take the experiment.
  • used data analysis methods to increase accuracy of experiment.
  • worked productively together.
  • could describe relationship between independent and dependent variables in question

(d) Is this example available to see/read about?
Ainley, Pratt and Nardi: article in Educational Studies in Mathematics (ESM) Ainley: article in Micromath. Ainley, Pratt and Hansen: article in British Educational Research Journal (BERJ)

(e) Can you say why you chose this example?
What criteria were in your mind? Engaging students (purpose); Engagement leading to focus (utility); Problem solving; Awareness of the power of mathematics (graphing as an analytical tool; average for smoothing errors. I have used the example many times and at many levels. It seems to provide an opportunity for thinking of graphs as analytical tools, rather than as presentational tools. Chosen out of frustration at narrow use of graphing in schools.


Downloadable PDF

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Values & Principles

Appreciation of the power of mathematics in society
Uses rich, collaborative tasks
Uses resources, including technology, in creative and appropriate ways

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