2011 NYS SO Coaches 2011 NYS SO Coaches WorkshopWorkshop

Fermi QuestionsFermi Questions

Division CDivision CPresenter

Mark KramerNYS SO Fermi Event Writer

WEATHERMARK

BackgroundBackground

SpecificationsSpecifications

ScoringScoring

Answer FormatAnswer Format

Tie BreakersTie Breakers

Team WorkTeam Work

ExamplesExamples

TipsTips

33

Fermi QuestionsFermi QuestionsNamed for Nobel Prize winner Enrico FermiNamed for Nobel Prize winner Enrico Fermi

Calculated large orders of magnitude.Calculated large orders of magnitude.

Challenges SO teams to:Challenges SO teams to:

Obtain order of magnitude to Obtain order of magnitude to answer questions posed with:answer questions posed with:

Some given information, &Some given information, &

Estimated & assumed data.Estimated & assumed data.

What is a Fermi What is a Fermi question?question?Science/Math/Technology-related question

Seeks a quick, rough estimate of:

A quantity, which is either difficult, or impossible to measure directly

44

55

# of callsto & from NYC

region in July 2010?

66

All Fermi Questions are not science based:

Containers of Play-Doh purchased?2 billion (FA* = 9)

Sony Play Station 2 sold?136 million (FA = 8)

*FA = Formatted Fermi Answer

An example:An example:

How many drops of “water” caused How many drops of “water” caused

the Mississippi River flooding this the Mississippi River flooding this

spring?spring?

77

Requires an estimate of:Requires an estimate of:

Volume of a dropVolume of a drop

Volume of rain & amount of snow that Volume of rain & amount of snow that fell in the Mississippi River Basinfell in the Mississippi River Basin

Amount of runoffAmount of runoff

88

Convert unitsConvert unitsEstimate within an order of Estimate within an order of magnitudemagnitude

Answer:Answer:Power of ten (10)Power of ten (10)Only the exponentOnly the exponent

e.g.,e.g.,1,000,000 = 101,000,000 = 106 6 = 6= 60.001 = 100.001 = 10-3-3 = - 3 = - 3

99

1010

Event parametersEvent parametersNo:No: Internet accessInternet access

CalculatorsCalculatorsWatches w/calculatorsWatches w/calculatorsLaptop - ComputersLaptop - ComputersSliderulesSliderulesReference sheetsReference sheetsI-PadsI-PadsBlackberrys, etc.Blackberrys, etc.

No connection to the outside worldNo connection to the outside world

1111

Event parametersEvent parameters

Pencils &/or pensPencils &/or pens

Can leave when finishedCan leave when finished

Time or order answer sheet rec’d Time or order answer sheet rec’d

Pre-announced time - avoid Pre-announced time - avoid stampede, teams left given same stampede, teams left given same time or # time or #

Event supervisor provides detailsEvent supervisor provides details

1212

Event parametersEvent parameters

Only question/answer sheets & scrap Only question/answer sheets & scrap paperpaper

Team: 1 or 2 students

Time: up to 45 - 50 minutes

1313

Fermi team workFermi team work

Answer as many questions as possible.Answer as many questions as possible.

All teams may be quizzed together.All teams may be quizzed together.

No feedback on point counting.No feedback on point counting.

Student designated captain.Student designated captain.

Captain writes answers.Captain writes answers.

1414

Fermi answersFermi answers

Nearest integral power of 10 Nearest integral power of 10 (exponent).(exponent).

1.7 x 101.7 x 1066, record , record 66

9.5 x 109.5 x 1066, record , record 77,,

Since 9.5 x 10Since 9.5 x 1066 rounds to 10 rounds to 1077

Wrong answers: 9.5 x 10Wrong answers: 9.5 x 1066 , 10 , 1066 or 10 or 1077

Remember 0 is a valid answer !Remember 0 is a valid answer !

1515

Fermi answersFermi answers

8.8 x 108.8 x 10-3-3, , record -2record -2

8.8 x 108.8 x 10-3-3 rounds to 1 x 10 rounds to 1 x 10-2-2

0.0088 rounds to 0.010.0088 rounds to 0.01

Wrong answers: 8.8, 8.8 x 10-Wrong answers: 8.8, 8.8 x 10-33, 10-, 10-33, 10-, 10-2 2 , E-03, E-3, E-02 & E-2 , E-03, E-3, E-02 & E-2

Only the answer sheet is scoredOnly the answer sheet is scored

Not question sheet or scrap!Not question sheet or scrap!

1616

ScoringScoringAnswer is: Worth:

Correct exponentCorrect exponent 5 points5 points

1 correct exponent1 correct exponent 3 3 pointspoints

2 correct exponent 2 correct exponent 1 point1 point

Any other answerAny other answer 0 points0 points

1717

ScoringScoringCorrect exponent (answer) = 7

Team Answer Points Awarded7 5

1818

ScoringScoringCorrect exponent (answer) = 7

Team Answer Points Awarded7 5

6 or 8 35 or 9 1

1919

ScoringScoringCorrect exponent (answer) = 7

Team Answer Points Awarded7 5 (=)

6 or 8 3 ( + 1)5 or 9 1 ( + 2)

No answerAny other

answer0

2020

Tie breakersTie breakers1.1. Highest # of 5-point answersHighest # of 5-point answers

2.2. NYSSO: NYSSO: Same # of 5-point answers,Same # of 5-point answers,

Then # of 3-point answers, Then # of 3-point answers, Then # of 1-point answers, &Then # of 1-point answers, &

3.3. Finally time/orderFinally time/order..Tip:Tip:

# correct answers more important than # correct answers more important than timetime

2121

Questions involve:Questions involve:

Measurements of surroundings &/or Measurements of surroundings &/or life.life.

Sciences from bio. to chem. to physics Sciences from bio. to chem. to physics to earth science, etc.to earth science, etc.

Everyday or infrequent occurrences.Everyday or infrequent occurrences.

2222

How many air molecules are in this How many air molecules are in this room?room?

What is the volume of liquids of any What is the volume of liquids of any type that a person drinks in a year?type that a person drinks in a year?

How many cell phone calls are made How many cell phone calls are made world-wide on a non-holiday, world-wide on a non-holiday, workday 24-hour period?workday 24-hour period?

2323

““Disasters Offer Problem-Disasters Offer Problem-Solving”Solving”In The Schools 9/5/05 In The Schools 9/5/05 Journal NewsJournal News pg. 3Bpg. 3B

Michael Lillis, President of Lakeland Michael Lillis, President of Lakeland Federation of Teachers, asked his Federation of Teachers, asked his physics students to:physics students to:

Estimate amounts of water and food Estimate amounts of water and food

that will be needed for the victims of that will be needed for the victims of

Katrina until the area is back on its Katrina until the area is back on its

feet. feet.

2424

How many ice cubes would be How many ice cubes would be

needed to drop the water needed to drop the water

temperature in the top 12 inches of temperature in the top 12 inches of

the Gulf of Mexico back to normal?the Gulf of Mexico back to normal?(This involves physics too). Assume no mixing (This involves physics too). Assume no mixing

below 12 inches.below 12 inches.

How many gallons of water fell during How many gallons of water fell during

Hurricane/Tropical Storm Floyd?Hurricane/Tropical Storm Floyd?

2525

How many vehicles were “parked” on How many vehicles were “parked” on

the roads (not in parking spaces) the roads (not in parking spaces)

during the December 26-27 blizzard during the December 26-27 blizzard

in the NYC metropolitan area? or in the NYC metropolitan area? or

LA’s carmageddon? LA’s carmageddon?

How many steps were taken by people How many steps were taken by people

leaving the superbowl?leaving the superbowl?

2626

Components to answering Components to answering questionsquestions

An understanding of exponentsAn understanding of exponents

Logical and critical thinkingLogical and critical thinking

Round values BEFORE calculationsRound values BEFORE calculations

Problem solving easier and faster.Problem solving easier and faster.

2727

UnitExact Value

Fermi Value

Day 24 hours 25 hours

Mile 5,280 feet 5,000 feet

Pound 453.6 grams

500 grams

2828

Example (Lloyd Abrams)Example (Lloyd Abrams)

How many pounds of rice were How many pounds of rice were

consumed in the USA in the year consumed in the USA in the year

2010?2010?

With no given data, one can estimate the With no given data, one can estimate the

US population at 300 million, or 3 x 10US population at 300 million, or 3 x 1088. .

2929

Assume each person consumes 25 Assume each person consumes 25 pounds/year.pounds/year.

Student has a great amount of leeway in Student has a great amount of leeway in this estimation.this estimation.

25 lbs./person/year * 3 x 1025 lbs./person/year * 3 x 1088 people = people = 7.5 x 10 7.5 x 109 9 lbs./year = 10lbs./year = 1010 10 = = Fermi Answer (FA) =Fermi Answer (FA) = 10 10

According to the USA Rice Federation,According to the USA Rice Federation,

Answer is 6.2 x 10Answer is 6.2 x 109 9 lbs. = 10lbs. = 101010

3030

Assume:Assume: 2 - 10 lbs./person/yr., or2 - 10 lbs./person/yr., or200 - 1,000 lbs./person/yr., 200 - 1,000 lbs./person/yr.,

Team still earns 3 points.Team still earns 3 points.

2 lbs./person/year * 3 x 102 lbs./person/year * 3 x 108 8 persons =persons =6 x 106 x 1088 lbs./year = 10 lbs./year = 1099 = = FA FA 99(within (within ± 1 of the answer)± 1 of the answer)

1,000 lbs./person/year * 3 x 101,000 lbs./person/year * 3 x 108 8 persons = 3 x 10persons = 3 x 1011 11

lbs./year = 10lbs./year = 101111 = = FA FA 1111(within (within ± 1 of the answer)± 1 of the answer)

Just fine since a team who answers and receives 3 points for every Just fine since a team who answers and receives 3 points for every question will have a good chance at winning, or coming in the top ten.question will have a good chance at winning, or coming in the top ten.

3131

Possible ResourcesPossible Resources::

The Lore of Large NumbersThe Lore of Large Numbers by Philip J. by Philip J. Davis (Davis (Paperback Paperback - July 1978)- July 1978)

3232

How many ounces does 1 cubic foot How many ounces does 1 cubic foot of of snowsnow weigh at 32 weigh at 32°°F?F?

Estimate:Estimate:

What water weighs at an assumed What water weighs at an assumed volume, &volume, &

How much water makes up 1 cu. ft. of How much water makes up 1 cu. ft. of snow.snow.

From above, calculate an estimated From above, calculate an estimated value.value.

3333

Density of water is 1 gram/cubic Density of water is 1 gram/cubic centimeter.centimeter.

Know or estimate 1 ft. is approx. 30 Know or estimate 1 ft. is approx. 30 cm.cm.

Calculate weight of 1 cubic foot of Calculate weight of 1 cubic foot of water:water:

1 g/cubic cm * (30 cm/foot)1 g/cubic cm * (30 cm/foot)3 3 * 1 cubic * 1 cubic foot foot

= 27,000 grams= 27,000 grams

3434

How much water does 1 cubic foot of snow How much water does 1 cubic foot of snow equal?equal?

Let’s make a liberal guessLet’s make a liberal guess

1 ft. of snow melts into 4 inches of water,1 ft. of snow melts into 4 inches of water,

1/3 of its original volume. 1/3 of its original volume.

1/3 of 27,000 grams = 9,000 grams1/3 of 27,000 grams = 9,000 grams

Assume 30 grams equals 1 ounce…Assume 30 grams equals 1 ounce…

9,000 grams * 1/30 gram/ounce = 3 x 109,000 grams * 1/30 gram/ounce = 3 x 102 2

ouncesounces

FA is FA is 22

3535

Actual AnswerActual AnswerDensity of water: 1 gram/cubic cm.Density of water: 1 gram/cubic cm.1 ft. = 30.48 cm1 ft. = 30.48 cm1 g/cubic cm * (30.48 cm/ft.)1 g/cubic cm * (30.48 cm/ft.)3 3 * 1 cubic ft =* 1 cubic ft =

28,316.85 grams28,316.85 grams

Snowfall at different temperatures will produce Snowfall at different temperatures will produce different water volumes. The actual amount is different water volumes. The actual amount is closer to 1/10 or 1/12 of the volume of snow.closer to 1/10 or 1/12 of the volume of snow.

3636

1/10 of 28,316.85 grams = 2,831.691/10 of 28,316.85 grams = 2,831.69

1 ounce = 28.35 grams1 ounce = 28.35 grams

2,831.69 grams * 1/28.35 gram/ounce 2,831.69 grams * 1/28.35 gram/ounce = 99.88 ounces = 1 x 10= 99.88 ounces = 1 x 1022 = = 22

Our estimated FA was correct. Our estimated FA was correct.

3737

Alternative SolutionAlternative Solution

For fun, very abstract way of thinking. For fun, very abstract way of thinking.

Imagine 1 gallon water jug = 1 cubic ft.Imagine 1 gallon water jug = 1 cubic ft.

How much does it weigh?How much does it weigh?

8 – 10 pounds?8 – 10 pounds?

3838

1 cubic foot of water = 10 pounds1 cubic foot of water = 10 pounds

Can compact 1 cubic foot of snow into a 6 Can compact 1 cubic foot of snow into a 6 inch snow cube. So I’ll assume that it melts inch snow cube. So I’ll assume that it melts to half of that in water, or ¼ of the total to half of that in water, or ¼ of the total amount of snow.amount of snow.

10 pounds * ¼ = 2.5 pounds10 pounds * ¼ = 2.5 pounds

16 ounces = 1 pound16 ounces = 1 pound

2.5 * 16 = 40 ounces, or 4 x 102.5 * 16 = 40 ounces, or 4 x 1011 = FA = FA 11

3939

Even with such a bizarre Even with such a bizarre calculation,calculation,

Still earn 3 points!Still earn 3 points!

Huge flexibilityHuge flexibility

4040

Fermi questions may incorporate Fermi questions may incorporate

previous answers.previous answers.

How many tons would a 12-inch How many tons would a 12-inch

snowstorm weigh that covered snowstorm weigh that covered

NYS?NYS?

4141

NYS is irregular shapeNYS is irregular shape

Assume rectangle, circle, or any basic Assume rectangle, circle, or any basic shape.shape.

NYS = squareNYS = square

How to calculate the area of NYS?How to calculate the area of NYS?

4242

Use U.S. to determine the area of NYS. Use U.S. to determine the area of NYS.

Estimate Estimate width of U.S.: 3,000 mileswidth of U.S.: 3,000 mileslength of U.S.: 1,500 mileslength of U.S.: 1,500 miles

Area of U.S:Area of U.S:4.5 x 104.5 x 106 6 square miles.square miles.

Assume NYS is 1/45 area of U.S. Assume NYS is 1/45 area of U.S.

Area of NYS is 1 x 10Area of NYS is 1 x 1055 square miles, square miles,

OR using 3,000 miles for the widthOR using 3,000 miles for the width

Assume 10 states across the U.S.,Assume 10 states across the U.S.,

Width of NYS is 300 miles.Width of NYS is 300 miles.

4343

Units of previous answer was ft.Units of previous answer was ft.

1 mile = Approx. 5,000 ft. 1 mile = Approx. 5,000 ft.

300 miles * 5,000 ft/miles =300 miles * 5,000 ft/miles =

1,500,000 ft. or 1.5 x 101,500,000 ft. or 1.5 x 106 6 ft.ft.

Assume NY is square…Assume NY is square…

(1.5 x 10(1.5 x 1066))22 = 2.25 x 10 = 2.25 x 101212 square feet square feet

4444

Previous FA - calculate how many tons of snow Previous FA - calculate how many tons of snow would cover NYS.would cover NYS.

1 ft of snow * 2.25 x 101 ft of snow * 2.25 x 101212 ft ft22 = 2.25 x 10 = 2.25 x 1012 12 ftft33 of of snowsnow

3 x 103 x 102 2 ounces/ftounces/ft3 3 * 2.25 x 10* 2.25 x 101212 ft ft33 = 6.75 x 10 = 6.75 x 1014 14

ouncesounces

6.75 x 106.75 x 1014 14 ounces * 1 lb/20 ounces. (really 16) * ounces * 1 lb/20 ounces. (really 16) * 1 ton/2,000 lbs. = 1.69 x 101 ton/2,000 lbs. = 1.69 x 101010 tons or FA 10 tons or FA 10

If used NYS area of 1/45 of the U.S.,If used NYS area of 1/45 of the U.S.,

Area 1.11 times larger, still FA 10 Area 1.11 times larger, still FA 10

4545

Actual AnswerActual AnswerActual area of NYS land = 47,224 square milesActual area of NYS land = 47,224 square miles 1 square mile = (5,280 ft.)1 square mile = (5,280 ft.) 2 2 = 27,878,400 ft = 27,878,400 ft22

47,224 square miles * 27,878,400 ft47,224 square miles * 27,878,400 ft22/square mile * 1 ft. of /square mile * 1 ft. of snow= 1,316,529,561,600 ftsnow= 1,316,529,561,600 ft33 of snow of snow

Actual weight of 1 cubic foot of snow = Actual weight of 1 cubic foot of snow =

100 ounces/ft100 ounces/ft33 * 1,316,529,561,600 ft * 1,316,529,561,600 ft33 = = = 1.32 x 10= 1.32 x 101414 ounces * 1 lb/16 ounces * 1 ton/2,000 lbs. ounces * 1 lb/16 ounces * 1 ton/2,000 lbs.= 4.125 x 10= 4.125 x 109 9 = FA 9= FA 9

4646

TipsTipsTime is a factorTime is a factor

1 to 2 minutes per question 1 to 2 minutes per question

Little room for discussion, debating, and Little room for discussion, debating, and deliberatingdeliberating

No time for personality arguments No time for personality arguments

4747

Quick, logical, critical thinking & Quick, logical, critical thinking & assumptionsassumptions Last example - Assume 200 by 200 miles.Last example - Assume 200 by 200 miles.

Result = correct FA instead of 1 exponent Result = correct FA instead of 1 exponent off.off.

Not sure how many feet there are in a mileNot sure how many feet there are in a mile

An educated guess of 3,000 ft.An educated guess of 3,000 ft.

Less costly than deliberation for 20 seconds Less costly than deliberation for 20 seconds on the accurate conversion.on the accurate conversion.

4848

Don’t know FA, Don’t know FA, GuessGuess! !

No answer is worth 0 No answer is worth 0 pointspoints

Team/Student MembersTeam/Student Members

Work well together – key plusWork well together – key plus

Like math, numbers, etc. Like math, numbers, etc.

Think critically & quicklyThink critically & quickly

Make decisionsMake decisions

Well-roundedWell-rounded

Broad science-math backgroundBroad science-math background4949

5050

From 5 years ago:From 5 years ago:1.1. What is the total number of foot-long What is the total number of foot-long hot hot dogs that are equivalent in length to dogs that are equivalent in length to the the perimeter of the 48 contiguous states perimeter of the 48 contiguous states (excluding islands)?(excluding islands)?

12,108 miles x 5,280 ft./mile = 6.4 x 1012,108 miles x 5,280 ft./mile = 6.4 x 1077 = 8 = 8

2,000 +2,000+3,000 +3,000 = 10,000 miles 2,000 +2,000+3,000 +3,000 = 10,000 miles x 5,280 ft/mi = 5 x 10x 5,280 ft/mi = 5 x 1077

FA = 8FA = 8

5151

Another question from 5 years agoAnother question from 5 years ago

Teenager drives nonstop across country from Teenager drives nonstop across country from NYC to LA at 60 mph. Another teenager NYC to LA at 60 mph. Another teenager speeds nonstop at 80 mph, how many speeds nonstop at 80 mph, how many nanoseconds sooner does the speeder arrive nanoseconds sooner does the speeder arrive in LA?in LA?

3000 miles (NYC to LA is about 2790 miles)3000 miles (NYC to LA is about 2790 miles)

50 - 37.5 = 12.5 hrs. faster50 - 37.5 = 12.5 hrs. faster

12.5 hrs x 60 min/hr x 60 sec/min x 1012.5 hrs x 60 min/hr x 60 sec/min x 1099 ns/sec ns/sec ==

4.5 x 104.5 x 101313 = FA = 13 = FA = 13

5252

2007 State Competition2007 State Competition

How many revolutions does a 15-inch How many revolutions does a 15-inch diameter wheel make on I-88 in NY diameter wheel make on I-88 in NY from its beginning to end from its beginning to end (approximately Binghamton to (approximately Binghamton to Albany)?Albany)?

FA = 5FA = 5

(1/3)(1/3)3333 FA = -16 FA = -16

5353

A View From the Back of the Envelope

Fermi Questions - A Louisiana Lessons Web Activity

Fermi Questions Library - Collection of Fermi Questions

5454

Rules: coaches & student manuals

Rules amended: clarification page

Old websites may not comply with rules

Fermi revived from 2008

5555

No penalties for wrong answersNo penalties for wrong answers

FA (exponents): positive, negative or 0FA (exponents): positive, negative or 0

Check work!Check work!

Time is rarely the deciding factorTime is rarely the deciding factor150 top score, 1 extra point may move 150 top score, 1 extra point may move

team up multiple positions, whereasteam up multiple positions, whereas

Time will only break a tie! Time will only break a tie!

Wrap-Up

5656

Wrap Up - Take it with Wrap Up - Take it with youyouEstimate, guess, do something!Estimate, guess, do something!

Don’t leave an answer blankDon’t leave an answer blank

Don’t skip a questionDon’t skip a question

Questions may rely on previous FAQuestions may rely on previous FA

Alternates & a well-practiced teamAlternates & a well-practiced team

5757

Wrap Up - Take it with Wrap Up - Take it with youyouTeam make up & answer questionsTeam make up & answer questions

Use internet examplesUse internet examples

Timed event – practiceTimed event – practice

Bring extra pencils/pensBring extra pencils/pens

Students connect & work well Students connect & work well togethertogether

No time for arguments = captainNo time for arguments = captainDon’t let 1 question upset the Don’t let 1 question upset the

moment (guess/mark & come back)moment (guess/mark & come back)

5858

Now It’s Your TurnNow It’s Your Turn

Let’s write awesome Fermi Questions.Let’s write awesome Fermi Questions.

Remember, bias should not enter the Remember, bias should not enter the question, such as how many bagels are question, such as how many bagels are eaten in New York City per year?eaten in New York City per year?

A student/team from upstate may not A student/team from upstate may not appreciate how popular bagels are appreciate how popular bagels are downstate. downstate.