math in the real world: classroom activities that motivate students

Math in the Real World:Classroom Activities

that Motivate Students

Frank C. WilsonChandler-Gilbert Community College

Who cares if learners know how to apply math to the real world?

• Parents– Wilson (2009) showed that 97% (n = 492)

of home schooling parents agree that it is important that their learners be able to apply math in the real world

• State Governments– Modeling of real world data is one of 11

math standards included in the Common Core State Standards Initiative http://www.corestandards.org/Standards/index.htm

http://www.corestandards.org/Standards/index.htm


• Professional Organizations– AMATYC, NCTM, and MAA call on educators to teach

real world data analysis and modeling

• Students– “There seemed to be an emphasis on real world

applications of math concepts which I believe are very benificial [sic] to learning how to ‘do math' and why ‘do math'.” CGCC math student

– “I liked the fact that . . . he used real world applications thus enhancing our understanding of the material.”CGCC math student


• Employers

Bureau of Labor Statistics Employment Outlook 2006 – 2016http://www.bls.gov/opub/mlr/2007/11/art5full.pdf

Concerns

• Why use real life applications if the actual mathematics students do is the same?

• My students are not good at word problems now. Bringing in real life math models will just confuse them.

• Real life applications are great but I don’t have the time to research the data and create the activities.

Why use real life data if the actual mathematics students do is the same?

• Which question is more meaningful?– Bob is three times Mary’s age. In three years,

Bob will be twice as old as Mary. How old is Bob?– Which cell phone plan is the best value?

• Which question is more relevant?– What does x have to be in order for the average

of the six numbers to equal 90?89, 82, 88, 91, 84, x

– How many points do I have to earn on the final exam to get an A out of the class?

Which job would you prefer?Nail Pounder Tree House Builder

Pound nails into boards. Build tree houses for children.

Time Watcher Olympic Swimming Time Keeper

Stare at a clock all day and write down times periodically.

Read and report times for an Olympic swimming competition.

Number Cruncher NSA Cryptologist Perform hundreds of

mathematical computations for no apparent reason.

Use mathematics to encode and decode critical national security

information.

Student Feedback

Real life applications make the math

meaningful.

Do real life applications confuse students?

• Harrison Central High School• Chandler-Gilbert Community College

Harrison Central High School

http://www.edutopia.org/harrison-central-high-school

Chandler-Gilbert CC

Student Comments

• “Plenty of real world context. 'When would I ever use this in the real world,' is clearly and consistently and constantly answered in class.”

• “I liked the fact that . . . he used real world applications thus enhancing our understanding of the material.”

• “There seemed to be an emphasis on real world applications of math concepts which I believe are very benificial [sic] to learning how to 'do math' and why 'do math'.”

Real life applications used effectively empower

students.

I don’t have the time to research

the data and create the activities.• Watch for natural occurrences of math

and math modeling in your everyday life

• Search for textbooks that integrate real life applications into examples and exercises

• Attend presentations at conferences where others share what they have created

Real Life Uses of Math Models

• Centers for Disease Control• Business Week• Navigant Consulting

www.cdc.gov/flu/weekly

20.8cos 10 7.0

52y w

Business Week

http://www.businessweek.com/magazine/content/09_46/b4155058815908.htm

“Subway's low-cost franchising model and mainstream appeal have allowed it to add 9,500 locations in the past five years, for a total of about 32,000 outlets. At its current growth rate of 40 new stores a week, Subway is poised to surpass McDonald's in worldwide locations sometime early next year.”Boyle, M. (2009, Nov 5), The Accidental Hero, Business Week

Stores 32,000 40(weeks)

32,000 40S w w

Navigant Consulting

Brian McNamaraManaging Consultant

• B.S. in Finance from BYU• MBA from University of Texas• Works high profile litigation

cases• Uses regression analysis

daily• Shared Mr. Smith vs ABC Inc*

case with math students* Names changed

Expert Witness for Plaintiff (Mr. Smith)

$500,000

$550,000

$600,000

$650,000

$700,000

$750,000

$800,000

$850,000

$900,000 Historic/Projected ABC Royalty

Revenue

Mr. Smith Employment Termination Date

Does the model seem reasonable ?

Expert Witness for Defense (ABC Inc)

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 $-

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

f(x) = − 90876.4978181818 x + 1208711.24R² = 0.926853618598211

ABC Royalties from Accounts from 1999-2008Data: Static Pool of 1999 Licensees Royalties

Royalty

Linear (Royalty)


$-

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

f(x) = − 90876.4978181818 x + 1208711.24R² = 0.926853618598211


Royalty

Linear (Royalty)


1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 $-

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

f(x) = 1339860.0514664 exp( − 0.128661325757676 x )R² = 0.972528358099313


Royalty


$-

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

f(x) = 1339860.0514664 exp( − 0.128661325757676 x )R² = 0.972528358099313


Royalty

Exponential (Royalty)

Real World Data Modeling Process

• Investigate a topic of interest• Ask a question• Create a model• Use the model• Identify model limitations

MEMY

SIBLING

CHILD

GRAND-CHILD

GREATGRAND-CHILD

CHILD

GRAND-CHILD

GREATGRAND-CHILD

1st cousin

2nd cousin

3rd cousin

GREATGREAT

GRAND-CHILD

GREATGREAT

GRAND-CHILD

4th cousin

1st cousin,3 times removed

http://roots.cs.byu.edu

Ask a Question

• Thomas Rogers, a pilgrim on the Mayflower, is my direct ancestor 12 generations back. (Parents, grandparents, great-grandparents, etc., are direct ancestors.)How many direct ancestors do I have n generations back?

Create a ModelGeneration

sDirect Ancestors

1 Parents (2)2 Grandparents (4)3 Great-grandparents

(8)4 165 32 direct ancestors

number of generations

( ) 2n

A

n

A n

Use the Model

King James I of Scotland1394 - 1497

King James I of Scotland is my direct ancestor 21 generations back. How many direct ancestors do I have 21 generations back?

21(21) 2

2,097,152

A

I have nearly 2.1 million direct ancestors 21 generations back.

Identify Model Limitations

• The model assumes that there was no crossover between the ancestral lines. If there was crossover (e.g. a great grandparent from one line was a sibling of a great grandparent on another line), the number of direct ancestors would be less than 2, 097, 152.

Modeling Activity

• Investigate a topic of interest (influenza)

• Ask a question• Create a model (graphical model

given)• Use the model• Identify model limitations

www.cdc.gov/flu/weekly

Search for textbooks that integrate real life applications

There is a difference between “realistic” and “real life”.• Realistic

– ACME sold 17.8 million widgets last year. Widget sales have been increasing by 4% per year for the past two years.

• Real life– The 2001 annual report of the Coca-Cola Company stated:

“Our worldwide unit case volume increased 4 percent in 2001, on top of a 4 percent increase in 2000 . . . Our business system sold 17.8 billion unit cases in 2001” (Source: Coca-Cola Company 2001 Annual Report, p. 46). (Note: A unit case is equivalent to 24 eight-ounce servings of finished beverage.)

Use textbooks that focus on real life applications

• An increasing number of textbooks are integrating real life contexts

• Chandler-Gilbert Community College is currently class testing College Algebra: A Make It Real Approach in 17 course sections

Sample Exercise

• Medicare EnrolleesBased on data from 1980 2004, the number of Medicare enrollees (in millions) may be modeled by

where t is the number of years since 1980 (Source: Modeled from Statistical Abstract of the United States, 2006, Table 132). Explain the practical meaning of the parameters of the quadratic function model.

20.00472 0.663 28.4M t t t

From College Algebra: A Make It Real Approach

Solution

• 28.4 means that the number of Medicare enrollees in 1980 was 28.4 million

• 0.663 means that the number of Medicare enrollees was increasing by 0.663 million (663,000) per year in 1980

• -0.00472 means that the rate at which the number of Medicare enrollees is increasing is itself decreasing by 0.00944 million (9440) Medicare enrollees per year each year

Sample Exercises

• Death Rate from Heart DiseaseIn 1980, the age-adjusted death rate due to heart disease was 412.1 deaths per 100,000 people. Between 1980 and 2003, the death rate decreased at a near-constant rate. In 2003, the death rate was 232.1 deaths per 100,000 people. (Source: Statistical Abstract of the United States, 2006; Table 106). Model the death rate due to heart disease as a linear function of years since 1980.

From College Algebra: A Make It Real Approach

Solution232.1 412.1

rate of change = 2003 1980

7.83 deaths per 100,000

year

7.83 412.1

years since 1980

deaths per 100,000 per year

d t t

t

d

initial value 412.1deaths per 100,000 per year

Sample Exam Question

Use what others have created

• AMATYC Right Stuff Learning Modules– 20 technology-based math projects– Includes many real life applications– Developed by Rob Kimball and a team

of educators– Available at

www.therightstuff.amatyc.org/moduleform.html

Use what others have created

10 complimentary activities for all conference attendees

• Choosing a Cell Phone Plan - Verizon: Investigating Linear Equations

• Cooking in the Kitchen: Multiplying Fractions• High School Students: Working with Rates of Change• Rolling the Dice: Using Probability• Fruit Snacks: Working with Averages• Swimming Pool Design: Working with Perimeters and

Areas• Teen Pregnancy: Investigating Cubic Functions• Shopping Center Planning: Looking at Exponential and

Linear Models• United States Population: Using Quadratic Models • Hours of Daylight - Anchorage: Working with Sinusoidal

Models

Free download at MakeItRealLearning.com/AMATYC

Questions?

Contact information

Frank C. WilsonChandler-Gilbert Community College

[email protected]

math in the real world: classroom activities that motivate students

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