is math real? sure, it pops up everyday! jim rubillo national council of teachers of mathematics
TRANSCRIPT
Is Math Real?Sure, It Pops Up Everyday!
Jim RubilloNational Council of
Teachers of Mathematics
It Pops Up Everyday for Me!I’ll Show You.
Give me a FEW of your favoriteTHREE-DIGIT
WHOLE NUMBERS!
The 3-DIGIT EDUCATION Lottery
0 Community-based 0 Instructional 0 Standards
1 Child-centered 1 Academic 1 Management
2 Interdisciplinary 2 Constructivist 2 Curriculum
3 Differentiated 3 Research-based 3 Systems
4 Simulated 4 Behavioral 4 Feedback
5 Interactive 5 Technological 5 Assessment
6 Age-appropriate 6 Collaborative 6 Accountability
7 Diagnostic 7 Performance-based 7 Models
8 Prescriptive 8 Organizational 8 Mentoring
9 Coordinated 9 Portfolio 9 Monitoring
Another Approach?
Ask Adults How They Use Math
Everyday.
A Survey of Essential Mathematics
• Name OccupationOccupation• 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
How Should We AttackThis Situation?
Some Advice From
Sherlock Holmes
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!
Here are Just a Few from a Short Search
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,
Take a Ride – On a Bicycle
Rear Wheel SprocketPedal Sprocket
Gears on a Bicycle
Bike Gear Teeth in Pedal Sprocket
Teeth in Back Wheel Sprocket
Back Wheel Turns per Pedal Turn
1 39 28
2 52 28
3 39 24
4 52 24
5 39 20
6 52 207 39 17
8 52 17
9 39 14
10 52 14
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 teeth 20 + 20 + 12 = 52 teeth
Gears on a Bicycle
Bike Gear Teeth in Pedal Sprocket
Teeth in Back Wheel Sprocket
Back Wheel Turns per Pedal Turn
1 39 28 1.39
2 52 28 1.86
3 39 24 1.63
4 52 24 2.17
5 39 20 1.95
6 52 20 2.60
7 39 17 2.29
8 52 17 3.06
9 39 14 2.79
10 52 14 3.71
An Application on NCTM’s Illuminationswww.illuminations.nctm.org
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?
The Fundamentals of Medicinal Dosage
• A person takes one (1) unit of medicine every day.
• The medicine mixes quickly into the body's “fluids."
• 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?
Life Expectancy (Africa: 50 countries)
Country Years
Country Years Country Years Country Years
Algeria 70 Cote d’Ivoire 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
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
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
Life Expectancy (Disaggregated)
21 Countries 50 Countries
Life Expectancy (Disaggregated)
21 Countries 50 Countries
Median = 71Median = 50.5
Life Expectancy (North America vs. Africa)
30 40 80706050
Min=49 Q1=70 Med=71 Q3=74 Max=79
North America
Africa
Min=37 Q1=45 Med=50.5 Q3=57 Max=75
Life Expectancy (North America vs. Africa)
30 40 80706050
Min=49 Q1=70 Med=71 Q3=74 Max=79
North America
Africa
Min=37 Q1=45 Med=50.5 Q3=57 Max=75
A Change of PaceThe 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.
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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.)
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The Game of SKUNKA 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).
The Game of SKUNK (abbreviated)
S K U
Earth to Mars: What is the graph of the distance between the two?
But, let’s 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.
Earth to Mars: What is the graph of the distance between the two?
Earth to Mars: Let’s Approximate to Build a Model www.illuminations.nctm.org/
Earth to Mars: What is the graph of the distance between the two?
Why It’s a Limacon with a Loop!
http://illuminations.nctm.org/
Tax on the Innumerate?
State Lotteries
The Key ConceptEXPECTED 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)
The Key ConceptEXPECTED 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 = 999/1000Cost of Bet (amount of Loss) = -$1
The Key ConceptExpected 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
Player’s Expectation = -$500/1000 = -$0.50That is: Of every $1 played, the house” take”
is 50 cents (House Advantage 50%)
