Applications Based Developmental Mathematics

1. Applications Based Developmental Mathematics Pellissippi State Community College

2. ...a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity...if he challenges the curiosity of his students... and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking. George Polya, How to Solve It,1973, p. v

3. Robust Learning • Transfer • Knowledge can be applied to new tasks • Retention • Knowledge lasts beyond the test • Accelerated Future Learning • Knowledge builds on knowledge

4. What does this student know about fractions? Transcript: One half times one-fifth. Now, I have to find a multiple of 10. so half would go to five-tenths and one-fifth would go to two-tenths and multiply that and that would be one whole

5. Problem Solving

6. Problem Solving

7. The Course Design One course divided into nine modules. • Module 1: Fractions • Module 2: Decimals/Percents/Proportions • Module 3: Introduction to Algebra • Module 4: Linear Equations and Inequalities • Module 5: Graphing Linear Equations and Inequalities • Module 6: Systems of Equations • Module 7: Polynomials and Factoring • Module 8: Quadratics • Module 9: Rational Expressions and Equations

8. The Course Design • Class meets one hour per week in a regular classroom. • Class meets one hour per week in a lab classroom. • Students spend at least two hours per week in Math Center.

9. The Course Design • Students are placed into the course based on ACT/COMPASS score and in-house placement test. • Assignments include collaborative classroom activities, online assigments, learning style activities and written review assignments. • Students take written tests for each module. • Students are required to complete at least three modules in a semester. • 80% mastery required to pass a module.

10. Greatest Common Factor Stephani is organizing a class trip to Florida. She has 14 parent chaperones and 35 students. She wants to create equal sized groups of parents and students so all are in a group. 1a) What is the greatest number of groups she can make? 1b) How many students are in each group? 1c) How many parents are in each group?

11. Evaluating Expressions Joshua plans to set up a hot dog cart in the park. He pays $50 for the cart which includes the hotdogs and all supplies. He charges one dollar for each hot dog that he sells. 1. What will Joshua’s profit be after he has sold 60 hot dogs? 2. What will Joshua’s profit be after he has sold 80 hot dogs? 3. What will Joshua’s profit be after he has sold 100 hot dogs? Define a variable for the number of hot dogs Joshua has sold and use this variable to write an expression for Joshua’s profit. hotdogs dollars 60 10 80 30 100 50 h h-50

12. Applications Introduction to Solving Linear Equations Kevin loves movies. He currently owns 34 DVDs. Every week he buys one new DVD. • How many DVDs will Kevin own in 10 weeks? • In how many weeks will Kevin own fifty DVDs? • In how many weeks will Kevin own 62 DVDs? • How many DVDs will Kevin own in one year?

14. Applications Introduction to Linear Equations in Two Variables You have saved $20 to spend on video games. You plan to spend $4 each week playing them. To write an expression, define a variable for the time spent playing video games and use this variable to write a rule for your money.

15. Applications Introduction to Solving Systems of Equations We run a company that produces small paper-based products—badges, decals, etc., for events such as the Olympics. To produce each item costs us $2. We also pay an initial startup cost for production of $175, regardless of the number of items we produce. We plan to sell each item for $3.

16. Applications Introduction to Solving Systems of Equations • What is the initial cost of production? What is our initial income? • How much would the cost be to produce 50 items? What is our income if we sell 50 items? • If our income is $630, how many products did we sell? • How many products must we produce if we want our income from this product to be equal to our production cost?

17. Applications Introduction to Quadratic Functions A development company is developing a large suburban area of land into a housing community. They are dividing up the land into square tracts for each home. Because the developers want to build houses of different sizes to appeal to both small and large families, they need to consider various lot sizes. Although the plots will be different sizes, all homes will have a fifteen-foot driveway built along the front of the house. This driveway will make the length of the plot 15 feet shorter than the width.

18. Quadratic Functions • For the smallest home, the plot width is 50 feet. What will be the length and area for this plot? • For the medium sized home, the plot length is 85 feet. What will the width and area be? • If a house design requires the area of the plot to be 5950 square feet, what width and length must the developers make the plot?

19. Does this work?

20. Assessment Traditional A stockbroker bought 50 shares of stock for $11.37 each. What was the total amount of the purchase? • $568.40 • $568.60 • $568.50 • $568.61 Applications-based David is a tutor in the Math Center and is paid $9.85 an hour. Last week he worked 12.8 hours. First, estimate his pay for the week. A) $105 B) $115 C) $130 D) $145 What was his actual pay? (75%)

21. Assessment Traditional Two angles are supplementary. The larger angle measures 30 degrees more than twice the smaller angle. Find the measures of the two angles. (a) 60 °; 120° (b) 50°; 130° (c) 20°; 70° (d) 30°; 60° Applications-based Two proposals are being considered for the redevelopment of an old building. The first proposal is to turn the building into a few, large deluxe apartments. The cost of redevelopment is $500,000 and the maintenance is expected to cost $1000 per month. The second proposal is to convert the building into many small apartments. This redevelopment will be less expensive, at a cost of only $290,000, but maintenance is expected to cost $2400 per month. • For each plan, write an equation that gives the total expenses. • Use an algebraic method to determine the number of months for which the total expenses are the same. (81%)

22. Assessment Traditional Using the vertical-position equation, find the time it takes a rock to drop from a height of 100 feet to the ground neglecting wind resistance.  a.) 1 sec b.) 2.5 sec c.) 5 sec d.) 3.2 sec Applications-based You can model the motion of a pumpkin that is released by a catapult by using the vertical motion model. a) We can hurl that pumpkin 212 ft/sec from an initial height of 30 feet. Write a quadratic function that models the height of the pumpkin in terms of time. b) Identify the independent and dependent quantities and the units with which they are measured. c) How high will the pumpkin be after 3 seconds? d) When will the pumpkin first be at 690 feet high? e) When will the pumpkin last be at 690 feet high? f) Determine when the pumpkin will smash into the ground. (85%)

23. Results Traditional Elementary Algebra: 58% Intermediate Algebra: 64% Applications-based Elementary Algebra: 80% Intermediate Algebra: 80%

24. Success in the Course Developmental Mathematics

25. Success in the Course(A-C with 80% Mastery)

26. Success in College-Level MATH

27. Contact Us • Mary Monroe-Ellis • mmonroeellis@pstcc.edu • Amy Tankersley • antankersley@pstcc.edu • Suzanne Etheridge • scetheridge@pstcc.edu

28. Bibliography • How People Learn. Encouraging Robust Learning. Steve Ritter. Carnegie Learning, Inc. • Stigler, James W., Karen B. Givvin, and Belinda J. Thompson. "What Community College Developmental Mathematics Students Understand about Mathematics.“ MathAMATYC Educator 1.3 (2010): 4-16. Print