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| </tabber> | | </tabber> |
| <restricted>
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| == Useful Resources ==
| | {{#restricted:{{8.2 Fermi Problems}}}}{{NavCard|prev=8.1 Orders of Understanding|next=9.1 Heuristics}} |
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| <tabber>
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| |-|Lecture Video=
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| <br /><center><youtube>zD-dX1lY4yY</youtube></center><br />
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| |-|Discussion Slides=
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| {{LinkCard | |
| |url=https://docs.google.com/presentation/d/1D9AqU399HJq06vzxs5Au3keVTNJWMfUCoMieWWNjnP4/
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| |title=Discussion Slides Template
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| |description=The discussion slides for this lesson.
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| }}
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| <br />
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| |-|Handouts and Activities=
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| {{LinkCardInternal
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| |url=:File:Fermi Problems Worksheet.pdf
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| |title=Fermi Problems Worksheet
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| |description=Worksheet used for all the activities in this lesson.}}
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| {{LinkCardInternal
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| |url=:File:Fermi Problem Review Practice.pdf
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| |title=Solved Fermi Practice Problems
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| |description=A PDF with solutions to some trickier Fermi problems.}}
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| <br />
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| |-|Readings and Assignments=
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| {{LinkCardInternal
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| |url=:File:How Many Licks Or, How to Estimate Damn Near Anything - Santos.pdf
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| |title=How Many Licks: Or, How to Estimate Damn Near Anything
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| |description=Aaron Santos on Fermi estimates.}}
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| <br />
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| </tabber>
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| == Recommended Outline ==
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| === Before Class ===
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| Familiarize yourself with [[:File:Fermi Problems Worksheet.pdf|the worksheet]] and print it.
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| === During Class ===
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| {| class="wikitable" style="margin-left: 0px; margin-right: auto;"
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| |5 Minutes
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| |Introduce the lesson and go over the plan for the day. Make sure people have groups, spokespeople, etc.
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| |-
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| |15 Minutes
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| |Run through the [[#American Spending on Gasoline|gasoline spending]] activity.
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| |-
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| |45 Minutes
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| |Let the students work in small groups on the [[#Government Spending|government spending]] activity.
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| |-
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| |15 Minutes
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| |Use any remaining time to work on the optional [[#Additional Problems|additional problems]]. If you don't have a separate lecture to go through the solutions to the [[#Government Spending|government spending]] problems, you should use this time to do so.
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| |}
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| == Lesson Content ==
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| === American Spending on Gasoline ===
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| In this activity, you break down an especially complex Fermi problem into its constituent parts in front of the class. This demonstrates to these problems get broken down.
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| {{BoxCaution|Students sometimes read too much into the complexity of this example. They over-complicate the problems they solve on their worksheets. Make sure to emphasize the importance of breaking down problems into the quantities that are easiest to estimate and aiming for first order causes. Going into further detail is often unnecessary and may not even improve the quality of our estimates.}}
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| ==== Instructions ====
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| {| class="wikitable" style="margin-left: 0px; margin-right: auto;"
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| |1 Minute
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| |[[#Quick Poll|Quickly poll]] the students on how much they think Americans spend on gas each year.
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| |-
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| |14 Minutes
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| |[[#Estimation Steps|Break down the actual problem]] as shown below. Explain how the units cancel out. You may draw this tree diagram step by step on a whiteboard. As you go through the thought process, have the students shout out their estimates for each of the quantities listed.
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| |}
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| ==== Quick Poll ====
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| Ask the students to quickly guess answers to the question, "How much do Americans spend on gas each year?"
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| <ol style="list-style-type:lower-alpha">
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| <li>Between zero and 10 million?</li>
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| <li>Between 10 million and 1 billion?</li>
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| <li>Between 1 billion and 100 billion?</li>
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| <li>Between 100 billion and 1 trillion?</li>
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| </ol>
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| Rather than just ''giving'' your students the answer, you demonstrate [[#Estimation Steps|how it can be solved]] with a Fermi estimate.
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| ==== Estimation Steps ====
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| [[File:Gasoline Spending Tree.png|thumb]]
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| You can break down the estimation as per the figure.
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| How close was your students' original order-of-magnitude guess to our final Fermi estimate?
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| Optionally, ask your students how would we go about calculating the plausible upper bound and lower bound estimates? For what purposes might it be useful to calculate upper and lower bounds?
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| {{BoxAnswer|Estimate an upper bound and lower bound for each estimate entering the Fermi calculation, where a rough number isn't known. Calculate it out to get a high bound and low bound.<br /><br />This might be useful if you're particularly unsure about some of your estimates.}} | |
| === Government Spending ===
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| In [[8.1 Orders of Understanding]], students simply guessed the order of government spending in three categories. In this activity, students will work in small groups, using Fermi estimation to get more concrete estimates for these quantities.
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| {{BoxCaution|These problems should ''not'' take as many steps or components as the gasoline example.}}
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| {{LinkCardInternal
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| |url=:File:Fermi Problems Worksheet.pdf
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| |title=Fermi Problems Worksheet
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| |description=Worksheet used for all the activities in this lesson.}}
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| ==== Instructions ====
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| {| class="wikitable" style="margin-left: 0px; margin-right: auto;"
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| |2 Minutes
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| |Share [[:File:Fermi Problems Worksheet.pdf|the worksheet]] with your students.
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| |-
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| |43 Minutes
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| |Let students work on the worksheet in small groups and frequently offer assistance and guidance, without giving away any answers. Feel free to move on to the optional Fermi problems below if students finish this activity early.
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| |}
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| === Additional Problems ===
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| {{BoxWarning|This activity is optional and should only be done if you don't have the time to demonstrate solutions to the [[#Government Spending|government spending]] problems in a separate lesson.}}
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| Have the students estimate in small groups any of the following quantities. Encourage them to give a lower and upper bound, as opposed to a single value. These problems were chosen as as to have a diversity of units and types of quantities being estimated.
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| # Amount of food thrown in landfills in America every year.
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| # The weight of all food an army battalion would have to bring on a 200-mile march across a rainforest.
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| # The amount of water used to irrigate all the front lawns in Los Angeles in one year.
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| # The total weight of tea (leaves) consumed by the British in one year.
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| # As a laptop keyboard engineer, how many repeated key presses would you have to rate any individual key for, so that consumers do not typically encounter the malfunctioning of any key?
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| #How much water would hotels in America save if they all went from refreshing guest towels daily to refreshing them only when left on the floor or for new guests?
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| # How much clothing gets thrown out in the United States?
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| # How many ties were bought in the U.S. in 2019?
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| # How many pieces of paper does the average American college student go through in four years?
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| # What percentage of the US GDP changes hands on an average Wednesday?
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| # How much money, in total, did Americans spend on restaurants in 2019? (these 2019 questions are because Covid mixed things up.)
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| # What percentage of total adult life hours is spent taking care of children? (Restrict to the US to make easier.)</restricted>{{NavCard|prev=8.1 Orders of Understanding|next=9.1 Heuristics}}
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| [[Category:Lesson plans]] | | [[Category:Lesson plans]] |
