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Is Math Real? Sure, It Pops Up Everyday! Jim Rubillo National Council of Teachers of Mathematics.

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Presentation on theme: "Is Math Real? Sure, It Pops Up Everyday! Jim Rubillo National Council of Teachers of Mathematics."— Presentation transcript:

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2 Is Math Real? Sure, It Pops Up Everyday! Jim Rubillo National Council of Teachers of Mathematics

3 It Pops Up Everyday for Me! Ill Show You. Give me a FEW of your favorite THREE-DIGIT WHOLE NUMBERS!

4 The 3-DIGIT EDUCATION Lottery 0 Community-based0 Instructional0 Standards 1 Child-centered1 Academic1 Management 2 Interdisciplinary2 Constructivist2 Curriculum 3 Differentiated3 Research-based3 Systems 4 Simulated4 Behavioral4 Feedback 5 Interactive5 Technological5 Assessment 6 Age-appropriate6 Collaborative6 Accountability 7 Diagnostic7 Performance-based7 Models 8 Prescriptive8 Organizational8 Mentoring 9 Coordinated9 Portfolio9 Monitoring

5 Another Approach? Ask Adults How They Use Math Everyday.

6 A Survey of Essential Mathematics OccupationName Occupation Selma House Realtor Ivy Sticker Nurse Hugo First Paratrooper Walter Wall Carpet Installer G. Howie Shivers Refrigeration Specialist Phil Ovitt Politician Cindy Bag Express Line Supermarket Cashier Harry Fitabaldi Hair Club President & Client Too Howie Gettindere Locksmith Dewey, Cheatem & Howe Attorneys Sal Manella Toxic Food Expert

7 How Should We Attack This Situation? Some Advice From Sherlock Holmes

8 The Perennial Student Question: Where Is the Math in Life? Eternal Math Teacher Question: Where do I find answers? Response: Get Curious, Look Around, and Think Outside of the Math Box A few well-placed examples go a long way!

9 Here are Just a Few from a Short Search

10 What Possible Practical Use Can be Made of the Möbius Strip? Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear,

11 Take a Ride – On a Bicycle Rear Wheel SprocketPedal Sprocket

12 Gears on a Bicycle Bike GearTeeth in Pedal Sprocket Teeth in Back Wheel Sprocket Back Wheel Turns per Pedal Turn 13928 25228 33924 45224 53920 65220 73917 85217 93914 105214

13 Gears on a Bicycle Gear 6 Pedal Sprocket 52 teeth Connected by a chain to Rear Wheel Sprocket with 20 teeth One Turn of the Pedal Sprocket Teeth Engaged in the Rear Wheel Sprocket 52 teeth20 + 20 + 12 = 52 teeth

14 Gears on a Bicycle Bike GearTeeth in Pedal Sprocket Teeth in Back Wheel Sprocket Back Wheel Turns per Pedal Turn 139281.39 252281.86 339241.63 452242.17 539201.95 65220 2.60 739172.29 852173.06 939142.79 1052143.71

15 An Application on NCTMs Illuminations www. illuminations.nctm.org

16 Sampling: Do You Believe… Does a representative sample tell you as much about a population as a census (checking everyone)? Is a sip as good as a gulp? Can you believe the Gallup Poll?

17 The Fundamentals of Medicinal Dosage A person takes one (1) unit of medicine every day. The medicine mixes quickly into the body'sfluids." The body purges 25% of the medication each day. How many units of the medicine are in the body after: one day? two days? 14 days?

18 Life Expectancy (Africa: 50 countries) Country Year s Country Years Country Years Country Years Algeria 70 Cote dIvoire 54 Madagascar 55 Sierra Leone 45 Angola 38 Eygpt 63 Malawi 38 Somalia 46 Benin 50 Equator. Guinea 54 Mali 47 South Africa 51 Botswana 39 Eritrea 56 Mauritania 51 Sudan 57 Burkina Faso 47 Ethiopia 45 Mauritius 71 Swaziland 40 Burundi 46 Gabon 50 Morocco 69 Tanzania 52 Cameroon 55 Ghana 57 Mozambique 38 Togo 55 Cape Verde 69 Guinea 46 Namibia 43 Tunisia 74 Cent. Afr. Rep 44 Guinea-Bissau 49 Niger 41 Uganda 43 Chad 51 Kenya 48 Nigeria 52 Zambia 37 Comoros 60 Lesotho 51 Sao Tome 65 Zimbabwe 38 Congo, Rep. 47 Liberia 51 Senegal 62 Source: U.S. Census Bureau, International Data Base Congo, Dem Rep. 49 Libya 76 Seychelles 70

19 Life Expectancy (North America: 21 countries) Country Years Country Years Antigua 71 Haiti 49 Bahamas 71 Honduras 70 Barbados 73 Jamaica 75 Belize 71 Mexico 72 Canada 79 Nicaragua 69 Costa Rica 76 Saint Kitts 71 Cuba 76 Saint Lucia 72 Dominica 73 Trinidad & Tobago 68 Dominican Republic 73 United States 77 El Salvador 70 Grenada 65 Source: U.S. Census Bureau, International Data Base Guatemala 66

20 Life Expectancy ( 71 countries ) Stem and Leaf Plots Data Is Preserved Distribution is Visible Easy to Find Median Suggestions Use Graph Paper (Why) Make Sure Data is Sorted

21 Life Expectancy ( Disaggregated ) 21 Countries50 Countries

22 Life Expectancy ( Disaggregated ) 21 Countries50 Countries Median = 71 Median = 50.5

23 Life Expectancy (North America vs. Africa) 304080706050 Min=49 Q 1 =70 Med=71 Q 3 =74 Max=79 North America Africa Min=37 Q 1 =45 Med=50.5 Q 3 =57 Max=75

24 Life Expectancy (North America vs. Africa) 304080706050 Min=49 Q 1 =70 Med=71 Q 3 =74 Max=79 North America Africa Min=37 Q 1 =45 Med=50.5 Q 3 =57 Max=75

25 A Change of Pace The Game of SKUNK http://illuminations.nctm.org/LessonDetail.aspx?ID=L248 This lesson allows students to explore the difference between choice and chance in a game context. It is based on the article Choice and Chance in Life: The Game of SKUNK, which appeared in the April 1994 issue of Mathematics Teaching in the Middle School. Brutlag, D. (1994). Choice and chance in life: The game of SKUNK, Mathematics Teaching in the Middle School, 1(1), 28-33.

26 26 The Game of SKUNK The object of SKUNK is to accumulate the greatest possible point total over five rounds. The rules for play are the same for each of the five rounds. At the beginning of each round, every player stands. Then, a pair of dice is rolled. (Everyone playing uses that roll of the dice; unlike other games, players do not roll the dice for just themselves.)

27 27 The Game of SKUNK A player gets the total of the dice and records it in his or her column, unless a "one" comes up. If a "one" comes up, play is over for that round and all the player's points in that column are wiped out. If "double ones" come up, all points accumulated in prior columns are wiped out as well. If a "one" doesn't occur, the player may choose either to try for more points on the next roll (by continuing to stand) or to stop and keep what he or she has accumulated (by sitting down).

28 The Game of SKUNK (abbreviated) S K U

29 Earth to Mars: What is the graph of the distance between the two? But, lets assume the Earth is at origin of a polar coordinate system and we will measure and plot the distance from Earth to Mars as they both revolve about the Sun.

30 Earth to Mars: What is the graph of the distance between the two?

31 Earth to Mars: Lets Approximate to Build a Model www.illuminations.nctm.org/

32 Earth to Mars: What is the graph of the distance between the two?

33 Why Its a Limacon with a Loop! http://illuminations.nctm.org/

34 Tax on the Innumerate? State Lotteries

35 The Key Concept EXPECTED VALUE Example: The Daily Number A three-digit number from 000 through 999 is selected at random. BET $1, IF YOU WIN, Get back $500 (including your $1)

36 The Key Concept EXPECTED VALUE Example: The Daily Number A three-digit number from 000 through 999 is selected at random. Probability of Winning = 1/1000 Payoff = $499 Probability of Losing = 999/1000 Cost of Bet (amount of Loss) = -$1

37 The Key Concept Expected Value for the Daily Number Probability Amount of Winning times Won 1/1000 x $499 = $499/1000 Plus Probability Amount of Losing times Lost 999/1000 x -$1 = -$999/1000 Players Expectation = -$500/1000 = -$0.50 That is: Of every $1 played, the house take is 50 cents (House Advantage 50%)

38 If you would like a copy of the PowerPoint, send an e-mail to: JRubillo@nctm.org

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