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2011 NYS SO Coaches Workshop

2011 NYS SO Coaches Workshop. Presenter Mark Kramer NYS SO Fermi Event Writer WeatherMark. Fermi Questions Division C. Background Specifications Scoring Answer Format Tie Breakers Team Work Examples Tips. Fermi Questions. Named for Nobel Prize winner Enrico Fermi

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2011 NYS SO Coaches Workshop

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  1. 2011 NYS SO Coaches Workshop Presenter Mark Kramer NYS SO Fermi Event Writer WeatherMark Fermi Questions Division C

  2. Background Specifications ScoringAnswer FormatTie BreakersTeam WorkExamplesTips

  3. 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.

  4. 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

  5. # of callsto & from NYC region in July 2010?

  6. 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

  7. An example: How many drops of “water” caused the Mississippi River flooding this spring?

  8. Requires an estimate of: Volume of a drop Volume of rain & amount of snow that fell in the Mississippi River Basin Amount of runoff

  9. 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

  10. Event parameters No: Internet access Calculators Watches w/calculators Laptop - Computers Sliderules Reference sheets I-Pads Blackberrys, etc. No connection to the outside world

  11. 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

  12. Event parameters Only question/answer sheets & scrap paper Team: 1 or 2 students Time: up to 45 - 50 minutes

  13. 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.

  14. 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 !

  15. 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!

  16. Scoring Answer is: Worth: Correct exponent 5 points 1 correct exponent 3 points 2 correct exponent 1 point Any other answer 0 points

  17. ScoringCorrect exponent (answer) = 7

  18. ScoringCorrect exponent (answer) = 7

  19. ScoringCorrect exponent (answer) = 7

  20. Tie breakers • 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. Tip: # correct answers more important than time

  21. Questions involve: Measurements of surroundings &/or life. Sciences from bio. to chem. to physics to earth science, etc. Everyday or infrequent occurrences.

  22. 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?

  23. “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.

  24. 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?

  25. 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?

  26. Components to answering questions An understanding of exponents Logical and critical thinking Round values BEFORE calculations Problem solving easier and faster.

  27. 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.

  28. 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

  29. 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.

  30. Possible Resources: The Lore of Large Numbers by Philip J. Davis (Paperback - July 1978)

  31. 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.

  32. 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

  33. 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

  34. 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.

  35. 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.

  36. 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?

  37. 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

  38. Even with such a bizarre calculation, Still earn 3 points! Huge flexibility

  39. Fermi questions may incorporate previous answers. How many tons would a 12-inch snowstorm weigh that covered NYS?

  40. NYS is irregular shape Assume rectangle, circle, or any basic shape. NYS = square How to calculate the area of NYS?

  41. 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.

  42. 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

  43. 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

  44. 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

  45. Tips Time is a factor 1 to 2 minutes per question Little room for discussion, debating, and deliberating No time for personality arguments

  46. 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.

  47. Don’t know FA, Guess! No answer is worth 0 points

  48. Team/Student Members Work well together – key plus Like math, numbers, etc. Think critically & quickly Make decisions Well-rounded Broad science-math background

  49. 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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