8.2 Fermi Problems: Difference between revisions
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After this lesson, students should | After this lesson, students should | ||
# | # Be confident in their ability to make a reasonable magnitude estimate of quantities for which one has no intuitive guess or direct knowledge. | ||
# Identify quantities that would and would not be appropriate to estimate with a Fermi calculation. | |||
# Provide rough estimates for real-world quantities using “back-of-the-envelope” (Fermi) approximations. | |||
# Evaluate the credibility of quantitative statements using “back-of-the-envelope” approximations. | |||
# Use Fermi estimates to identify first, second, third order causes for example problems, and estimate their effect sizes. | |||
=== Definitions === | === Definitions === | ||
* ''' | * '''Fermi Estimates''' | ||
*: | *: A systematic estimate of a quantity based on what you know. The typical goal is to get within an order of magnitude of the right answer. (This often proves possible even for topics about which you know very little.) The steps to do this are the following: | ||
*:* Decompose the problem into multiple components that you can estimate. (Break down unfamiliar components into familiar components). | |||
*:* Estimate components using approximations. | |||
*:* Combine estimated components to calculate Fermi estimate. | |||
*:* Compute upper and lower bounds (maximum and minimum quantities above/below between which you are fairly confident the correct estimate should be). | |||
* '''Order of Magnitude''' | |||
*: A factor of ten. | |||
=== Examples === | === Examples === | ||
Revision as of 09:57, 4 November 2021
Learning Goals
[Link to PlayPosit]
[Link to instructional video]
More details: [link to topic on SSS website]
After this lesson, students should
- Be confident in their ability to make a reasonable magnitude estimate of quantities for which one has no intuitive guess or direct knowledge.
- Identify quantities that would and would not be appropriate to estimate with a Fermi calculation.
- Provide rough estimates for real-world quantities using “back-of-the-envelope” (Fermi) approximations.
- Evaluate the credibility of quantitative statements using “back-of-the-envelope” approximations.
- Use Fermi estimates to identify first, second, third order causes for example problems, and estimate their effect sizes.
Definitions
- Fermi Estimates
- A systematic estimate of a quantity based on what you know. The typical goal is to get within an order of magnitude of the right answer. (This often proves possible even for topics about which you know very little.) The steps to do this are the following:
- Decompose the problem into multiple components that you can estimate. (Break down unfamiliar components into familiar components).
- Estimate components using approximations.
- Combine estimated components to calculate Fermi estimate.
- Compute upper and lower bounds (maximum and minimum quantities above/below between which you are fairly confident the correct estimate should be).
- A systematic estimate of a quantity based on what you know. The typical goal is to get within an order of magnitude of the right answer. (This often proves possible even for topics about which you know very little.) The steps to do this are the following:
- Order of Magnitude
- A factor of ten.
Examples
- [item 1]
Common Misconceptions
- Mistaken quote
- Explanation.
Context
[Explanation of how the current topic into the larger context of the course by explaining how the previous topic(s) relate to the current topic and leaving cliffhangers for future topics where relevant throughout the lesson]
Before
- X.X Lesson Name
- Explanation.
- Itemized explanation.
After
- X.X Lesson Name
- Explanation.
- Itemized explanation.
Recommended Outline
Before Class
- [Any essential logistical things that need to be done for this class]
- Prepare a seating chart.
- Review PlayPosit and discussion questions and ask faculty, Gabriel, or Emlen any questions you have.
- (Optional) Prepare a presentation.
During Class
- (5 min) Come up with some fun way to assign the roles of spokesperson and notetaker (e.g. earliest birthday in the year, lives furthest from campus). Remind them of the responsibilities of these roles.
- ([#] min) [Description of some module from #Lesson Content]
- (5 min) Collect questions for plenary.
After Class
- [Any essential logistical things that need to be done as followup for this class]
- Collect answers from notetakers for the forum / plenary.
Lesson Content
Clicker Question
- Question
- Option 1
- Options 2
Activity 1: Name
[Brief description of and motivation for the activity]
| Common misconceptions and any useful tricks, tips, guidelines, or other background |
Instructions
Discussion Questions
- Question 1
- Subquestion a
| Intended answer to the above question. |
| Possible misconception that may need to be corrected and clarified. |
- Subquestion b
Collect Questions for Plenary
(5 min) Collect remaining questions from the students for faculty in plenary (can be questions for clarification, extension, discussion, etc.), and add [ here].