is math real? sure, it pops up everyday! jim rubillo national council of teachers of mathematics

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%)

If you would like a copy of the PowerPoint, send an e-mail to:

JRubillo@nctm.org