Estimates From Limited Data

This MEI activity features a number of examples of questions that can be used to provide a simple introduction to the technique of Fermi estimation. The questions are varied, but for all of them a good estimate (to within an order of magnitude) should be achievable through common-sense assumptions and simple calculations.

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Mathematical Strand

Number and Measure

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Prior knowledge

This task should be accessible to all Core Maths students. They will need reasonable mental calculation skills, and the ability to make reasonable estimates for real-world data.

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Relevance to Core Maths Qualifications

  • AQA
  • C&G
  • Eduqas
  • Pearson / Edexcel
  • OCR

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Suggested Approaches

Use the teacher resource sheet to inform your presentation of this activity; this contains all the information needed, with thorough notes on all the questions. Students could usefully work in pairs or small groups, comparing and evaluating their estimates and calculations.

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Resources/documentation

The resources provided consist of two documents:
• Student sheet, containing the five sample questions
• Teacher notes, providing teaching guidance for each of the questions

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Relevant digital technologies

Although all of the questions can readily be solved using mental calculations (or simple written calculations), you may choose to allow access to calculators or even spreadsheets, in order to allow students to compare mental estimates to more precise calculations.

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Possible Extensions

This activity provides a starting point for Fermi estimation. The MEI activity ‘Fermi estimation’ provides numerous further examples, along with extensive teacher guidance.

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Acknowledgement

Developed by MEI, with funding from the Department for Education as part of the Critical Maths project to develop a post-16 mathematical thinking curriculum based on ideas from Professor Sir Timothy Gowers - http://www.mei.org.uk/critical-maths