2011 NYS SO Coaches Workshop
Fermi Questions
Division C
Presenter
Mark Kramer
NYS SO Fermi Event Writer
WEATHERMARK
Background
Specifications
Scoring
Answer Format
Tie Breakers
Team Work
Examples
Tips
Fermi Questions
Named for Nobel Prize winner Enrico Fermi
Calculated large orders of magnitude.
Challenges SO teams to:
Obtain order of magnitude to
answer questions posed with:
Some given information, &
Estimated & assumed data.
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What is a Fermi question?
Science/Math/Technology-related question
Seeks a quick, rough estimate of:
A quantity, which is either difficult, or
impossible to measure directly
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# of
calls
to &
from
NYC
region
in July
2010?
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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
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An example:
How many drops of “water” caused the
Mississippi River flooding this spring?
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Requires an estimate of:
Volume of a drop
Volume of rain & amount of snow that
fell in the Mississippi River Basin
Amount of runoff
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Convert units
Estimate within an order of magnitude
Answer:
Power of ten (10)
Only the exponent
e.g.,
1,000,000 = 106 = 6
0.001 = 10-3 = - 3
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Event parameters
No:
Internet access
Calculators
Watches w/calculators
Laptop - Computers
Sliderules
Reference sheets
I-Pads
Blackberrys, etc.
No connection to the outside world
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Event parameters
Pencils &/or pens
Can leave when finished
Time or order answer sheet rec’d
Pre-announced time - avoid stampede,
teams left given same time or #
Event supervisor provides details
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Event parameters
Only question/answer sheets & scrap paper
Team:
1 or 2 students
Time:
up to 45 - 50 minutes
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Fermi team work
 Answer as many questions as possible.
 All teams may be quizzed together.
 No feedback on point counting.
 Student designated captain.
 Captain writes answers.
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Fermi answers
Nearest integral power of 10 (exponent).
1.7 x 106, record 6
9.5 x 106, record 7,
Since 9.5 x 106 rounds to 107
Wrong answers: 9.5 x 106 , 106 or 107
Remember 0 is a valid answer !
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Fermi answers
8.8 x 10-3, record -2
8.8 x 10-3 rounds to 1 x 10-2
0.0088 rounds to 0.01
Wrong answers: 8.8, 8.8 x 10-3, 10-3,
10-2 , E-03, E-3, E-02 & E-2
Only the answer sheet is scored
Not question sheet or scrap!
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Scoring
Answer is:
Worth:
Correct exponent
5 points
1 correct exponent
3 points
2 correct exponent
1 point
Any other answer
0 points
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Scoring
Correct exponent (answer) = 7
Team Answer
7
Points Awarded
5
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Scoring
Correct exponent (answer) = 7
Team Answer
7
6 or 8
5 or 9
Points Awarded
5
3
1
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Scoring
Correct exponent (answer) = 7
Team Answer
7
6 or 8
5 or 9
No answer
Any other
answer
Points Awarded
5 (=)
3 ( + 1)
1 ( + 2)
0
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Tie breakers
1.
Highest # of 5-point answers
NYSSO:
Same # of 5-point answers,
Then # of 3-point answers,
Then # of 1-point answers, &
3. Finally time/order.
2.
Tip:
# correct answers more important than time
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Questions involve:
Measurements of surroundings &/or life.
Sciences from bio. to chem. to physics to
earth science, etc.
Everyday or infrequent occurrences.
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How many air molecules are in this
room?
What is the volume of liquids of any type
that a person drinks in a year?
How many cell phone calls are made
world-wide on a non-holiday, workday
24-hour period?
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“Disasters Offer Problem-Solving”
In The Schools 9/5/05 Journal News pg. 3B
Michael Lillis, President of Lakeland
Federation of Teachers, asked his physics
students to:
Estimate amounts of water and food that
will be needed for the victims of Katrina
until the area is back on its feet.
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How many ice cubes would be needed to
drop the water temperature in the top 12
inches of the Gulf of Mexico back to
normal?
(This involves physics too). Assume no mixing below 12
inches.
How many gallons of water fell during
Hurricane/Tropical Storm Floyd?
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How many vehicles were “parked” on the
roads (not in parking spaces) during the
December 26-27 blizzard in the NYC
metropolitan area? or LA’s carmageddon?
How many steps were taken by people
leaving the superbowl?
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Components to answering questions
An understanding of exponents
Logical and critical thinking
Round values BEFORE calculations
Problem solving easier and faster.
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Unit
Exact
Value
Fermi
Value
Day
24 hours
25 hours
Mile
5,280 feet
5,000 feet
Pound
453.6 grams
500 grams
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Example (Lloyd Abrams)
How many pounds of rice were consumed in
the USA in the year 2010?
With no given data, one can estimate the US
population at 300 million, or 3 x 108.
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Assume each person consumes 25 pounds/year.
Student has a great amount of leeway in this
estimation.
25 lbs./person/year * 3 x 108 people =
7.5 x 109 lbs./year = 1010 =
Fermi Answer (FA) = 10
According to the USA Rice Federation,
Answer is 6.2 x 109 lbs. = 1010
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Assume: 2 - 10 lbs./person/yr., or
200 - 1,000 lbs./person/yr.,
Team still earns 3 points.
2 lbs./person/year * 3 x 108 persons =
6 x 108 lbs./year = 109 = FA 9
(within ± 1 of the answer)
1,000 lbs./person/year * 3 x 108 persons =
3 x 1011 lbs./year = 1011 = FA 11
(within ± 1 of the answer)
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.
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Possible Resources:
The Lore of Large Numbers by Philip J. Davis
(Paperback - July 1978)
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How many ounces does 1 cubic foot of
snow weigh at 32°F?
Estimate:
What water weighs at an assumed volume, &
How much water makes up 1 cu. ft. of snow.
From above, calculate an estimated value.
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Density of water is 1 gram/cubic centimeter.
Know or estimate 1 ft. is approx. 30 cm.
Calculate weight of 1 cubic foot of water:
1 g/cubic cm * (30 cm/foot)3 * 1 cubic foot
= 27,000 grams
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How much water does 1 cubic foot of snow equal?
Let’s make a liberal guess
1 ft. of snow melts into 4 inches of water,
1/3 of its original volume.
1/3 of 27,000 grams = 9,000 grams
Assume 30 grams equals 1 ounce…
9,000 grams * 1/30 gram/ounce = 3 x 102 ounces
FA is 2
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Actual Answer
Density of water: 1 gram/cubic cm.
1 ft. = 30.48 cm
1 g/cubic cm * (30.48 cm/ft.)3 * 1 cubic ft =
28,316.85 grams
Snowfall at different temperatures will
produce different water volumes. The
actual amount is closer to 1/10 or 1/12 of
the volume of snow.
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1/10 of 28,316.85 grams = 2,831.69
1 ounce = 28.35 grams
2,831.69 grams * 1/28.35 gram/ounce =
99.88 ounces = 1 x 102 = 2
Our estimated FA was correct.
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Alternative Solution
For fun, very abstract way of thinking.
Imagine 1 gallon water jug = 1 cubic ft.
How much does it weigh?
8 – 10 pounds?
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1 cubic foot of water = 10 pounds
Can compact 1 cubic foot of snow into a 6 inch
snow cube. So I’ll assume that it melts to half of
that in water, or ¼ of the total amount of snow.
10 pounds * ¼ = 2.5 pounds
16 ounces = 1 pound
2.5 * 16 = 40 ounces, or 4 x 101 = FA 1
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Even with such a bizarre calculation,
Still earn 3 points!
Huge flexibility
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Fermi questions may incorporate
previous answers.
How many tons would a 12-inch
snowstorm weigh that covered NYS?
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NYS is irregular shape
Assume rectangle, circle, or any basic shape.
NYS = square
How to calculate the area of NYS?
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Use U.S. to determine the area of NYS.
Estimate
width of U.S.: 3,000 miles
length of U.S.: 1,500 miles
Area of U.S: 4.5 x 106 square miles.
Assume NYS is 1/45 area of U.S.
Area of NYS is 1 x 105 square miles,
OR using 3,000 miles for the width
Assume 10 states across the U.S.,
Width of NYS is 300 miles.
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Units of previous answer was ft.
1 mile = Approx. 5,000 ft.
300 miles * 5,000 ft/miles =
1,500,000 ft. or 1.5 x 106 ft.
Assume NY is square…
(1.5 x 106)2 = 2.25 x 1012 square feet
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Previous FA - calculate how many tons of snow would
cover NYS.
1 ft of snow * 2.25 x 1012 ft2 = 2.25 x 1012 ft3 of snow
3 x 102 ounces/ft3 * 2.25 x 1012 ft3 = 6.75 x 1014
ounces
6.75 x 1014 ounces * 1 lb/20 ounces. (really 16) * 1
ton/2,000 lbs. = 1.69 x 1010 tons or FA 10
If used NYS area of 1/45 of the U.S.,
Area 1.11 times larger, still FA 10
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Actual Answer
Actual area of NYS land = 47,224 square miles
1 square mile = (5,280 ft.) 2 = 27,878,400 ft2
47,224 square miles * 27,878,400 ft2/square mile * 1 ft. of
snow= 1,316,529,561,600 ft3 of snow
Actual weight of 1 cubic foot of snow =
100 ounces/ft3 * 1,316,529,561,600 ft3 =
= 1.32 x 1014 ounces * 1 lb/16 ounces * 1 ton/2,000 lbs.
= 4.125 x 109 = FA 9
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Tips
Time is a factor
1 to 2 minutes per question
Little room for discussion, debating, and
deliberating
No time for personality arguments
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Quick, logical, critical thinking & assumptions
Last example - Assume 200 by 200 miles.
Result = correct FA instead of 1 exponent off.
Not sure how many feet there are in a mile
An educated guess of 3,000 ft.
Less costly than deliberation for 20 seconds on the
accurate conversion.
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Don’t know FA, Guess!
No answer is worth 0 points
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Team/Student Members
Work well together – key plus
Like math, numbers, etc.
Think critically & quickly
Make decisions
Well-rounded
Broad science-math background
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From 5 years ago:
1.
What is the total number of foot-long hot
dogs that are equivalent in length to the
perimeter of the 48 contiguous states
(excluding islands)?
12,108 miles x 5,280 ft./mile = 6.4 x 107 = 8
2,000 +2,000+3,000 +3,000 = 10,000 miles
x 5,280 ft/mi = 5 x 107
FA = 8
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Another question from 5 years ago
Teenager drives nonstop across country from NYC
to LA at 60 mph. Another teenager speeds
nonstop at 80 mph, how many nanoseconds
sooner does the speeder arrive in LA?
3000 miles (NYC to LA is about 2790 miles)
50 - 37.5 = 12.5 hrs. faster
12.5 hrs x 60 min/hr x 60 sec/min x 109 ns/sec =
4.5 x 1013 = FA = 13
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2007 State Competition
How many revolutions does a 15-inch
diameter wheel make on I-88 in NY from its
beginning to end (approximately
Binghamton to Albany)?
FA = 5
(1/3)33
FA = -16
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A View From the Back of the Envelope
Fermi Questions - A Louisiana Lessons
Web Activity
Fermi Questions Library - Collection of
Fermi Questions
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Rules: coaches & student manuals
Rules amended: clarification page
Old websites may not comply with rules
Fermi revived from 2008
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Wrap-Up
No penalties for wrong answers
FA (exponents): positive, negative or 0
Check work!
 Time is rarely the deciding factor
150 top score, 1 extra point may move
team up multiple positions, whereas
Time will only break a tie!
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Wrap Up - Take it with you
Estimate, guess, do something!
 Don’t leave an answer blank
 Don’t skip a question
Questions may rely on previous FA
Alternates & a well-practiced team
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Wrap Up - Take it with you
Team make up & answer questions
Use internet examples
Timed event – practice
Bring extra pencils/pens
Students connect & work well together
No time for arguments = captain
Don’t let 1 question upset the moment
(guess/mark & come back)
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Now It’s Your Turn
Let’s write awesome Fermi Questions.
Remember, bias should not enter the
question, such as how many bagels are
eaten in New York City per year?
A student/team from upstate may not
appreciate how popular bagels are
downstate.
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