Math in the Real World: Classroom Activities that Motivate Students

1. Math in the Real World:Classroom Activities that Motivate Students Frank C. Wilson Chandler-Gilbert Community College

2. 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 Initiativehttp://www.corestandards.org/Standards/index.htm

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

4. Who cares if learners know how to apply math to the real world? • Employers Bureau of Labor Statistics Employment Outlook 2006 – 2016 http://www.bls.gov/opub/mlr/2007/11/art5full.pdf

5. 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.

6. 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?

7. Which job would you prefer?

8. Student Feedback

9. Real life applications make the math meaningful.

10. Do real life applications confuse students? • Harrison Central High School • Chandler-Gilbert Community College

11. Harrison Central High School http://www.edutopia.org/harrison-central-high-school

12. Chandler-Gilbert CC

13. 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'.”

14. Real life applications used effectively empower students.

15. 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

16. Real Life Uses of Math Models • Centers for Disease Control • Business Week • Navigant Consulting

17. www.cdc.gov/flu/weekly

18. Business Week “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 http://www.businessweek.com/magazine/content/09_46/b4155058815908.htm

19. Navigant Consulting Brian McNamara Managing 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

20. Expert Witness for Plaintiff (Mr. Smith) Mr. Smith Employment Termination Date Does the model seem reasonable ?

21. Expert Witness for Defense (ABC Inc)

22. Expert Witness for Defense (ABC Inc)

23. Expert Witness for Defense (ABC Inc)

24. Expert Witness for Defense (ABC Inc)

25. Real World Data Modeling Process • Investigate a topic of interest • Ask a question • Create a model • Use the model • Identify model limitations

26. 1st cousin, 3 times removed ME MY SIBLING CHILD CHILD 1st cousin GRAND-CHILD GRAND-CHILD 2nd cousin GREAT GRAND-CHILD GREAT GRAND-CHILD 3rd cousin GREAT GREAT GRAND-CHILD GREAT GREAT GRAND-CHILD 4th cousin http://roots.cs.byu.edu

27. 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?

28. Create a Model

29. Use the Model King James I of Scotland is my direct ancestor 21 generations back. How many direct ancestors do I have 21 generations back? I have nearly 2.1 million direct ancestors 21 generations back. King James I of Scotland 1394 - 1497

30. 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.

31. Modeling Activity • Investigate a topic of interest (influenza) • Ask a question • Create a model (graphical model given) • Use the model • Identify model limitations

32. www.cdc.gov/flu/weekly

33. 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.)

34. 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

35. Sample Exercise • Medicare Enrollees Based 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. From College Algebra: A Make It Real Approach

36. 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

37. Sample Exercises • Death Rate from Heart Disease In 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

38. Solution

39. Sample Exam Question

40. 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

41. 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

42. Questions?

43. Contact information Frank C. Wilson Chandler-Gilbert Community College frank@MakeItRealLearning.com