1	Just in Time Algebra with Multimedia: Context Based, with Animation!
2	"Walter R." Walter R. Hunter whunter@mc3.edu Roseanne S. Hofmann rhofman@mc3.edu
3	Just in Time Algebra Philosophy of the the course: Applications should not only motivate, but also give concrete examples to the abstract mathematical concepts of the course. AMATYC Standards: Problems should be solved numerically, graphically, symbolically, and verbally.
4	Just in Time Algebra Statistics: Day students taught by full time faculty. p-value 0.000000121 for average grade.
5	Just in Time Algebra Statistics: Day students taught by full time faculty. p-value 0.0047 for average grade.
6	Just in Time Algebra Statistics: Intermediate Algebra Day students taught by full time faculty and passed Beginning Algebra the previous semester.
7	Benefits for Adjuncts Keep current on the “standards” Textbook provides flexible teaching modes Lecture materials Group Work Homework Exercises Multimedia matches textbook Smartboard lectures ready made
8	Time Line of Development
9	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth?
10	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth? 10 - 25 = -15
11	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth? 10 - 25 = -15 2. You loose $5 a day for the next three days, how much money will you loose?
12	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth? 10 - 25 = -15 2. You loose $5 a day for the next three days, how much money will you loose? -5 ( 3 ) = - 15
13	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth? 10 - 25 = -15 2. You loose $5 a day for the next three days, how much money will you loose? -5 ( 3 ) = - 15 3. You lost $7 for the last six days, how much more money did you have six days ago?
14	Sign Numbers 1. You have $10 and you owe the IRS $25, what is your net worth? 10 - 25 = -15 2. You loose $5 a day for the next three days, how much money will you loose? -5 ( 3 ) = - 15 3. You lost $7 for the last six days, how much more money did you have six days ago? ( - 7 )( - 6 ) = 42
15	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
16	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
17	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
18	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
19	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
20	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile.
21	Introduction to Variables A truck rental company, WE-HAUL, charges $21.95 plus 41 cents per mile. The equation relating cost and miles driven: C = .41m + 21.95
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35	"What is" What is the equation that relates weight and height? Simplify the equation. W = 5( h - 60 ) + 100 W = 5h - 300 + 100 W = 5h - 200
36	"How tall should you be..." How tall should you be if you weigh 135 lbs? Find h if W = 135 135 = 5h - 200 135 + 200 = 5h - 200 + 200 335 = 5h 335/5 = 5h/5 67 = h You should be 5 feet 7 inches tall if you weigh 135 lbs.
37	"How tall should you be..." How tall should you be if you weigh 0 lbs? Find h if W = 0 0 = 5h - 200 0 + 200 = 5h - 200 + 200 200 = 5h 200/5 = 5h/5 40 = h Does this answer makes sense?
38	"Solve for h from the..." Solve for h from the formula in part 1b. W = 5h - 200 W + 200 = 5h - 200 +200 W + 200 = 5h (W + 200)/5 = 5h/5 (W + 200)/5 = h
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40	Applications of Linear Equations - Percent
41	Applications of Inequalities Two companies offer you very similar positions. Random House will pay you $10,000 a year plus 7% commission on the dollar amount of book sales. Moore Publishing Co. will pay you $8,000 a year plus 11% commission. Random House SALES CALCULATION INCOME
42	Applications of Inequalities Two companies offer you very similar positions. Random House will pay you $10,000 a year plus 7% commission on the dollar amount of book sales. Moore Publishing Co. will pay you $8,000 a year plus 11% commission. Random House SALES CALCULATION INCOME 100,000 .07(100,000) + 10,000 17,000
43	Applications of Inequalities Two companies offer you very similar positions. Random House will pay you $10,000 a year plus 7% commission on the dollar amount of book sales. Moore Publishing Co. will pay you $8,000 a year plus 11% commission. Random House SALES CALCULATION INCOME 100,000 .07(100,000) + 10,000 17,000 S .07S + 10,000 I
44	"For what dollar amount of..." For what dollar amount of book sales does Random House pay more than Moore Publishing Co.?
45	"For what dollar amount of..." For what dollar amount of book sales does Random House pay more than Moore Publishing Co.? Income from R.H. > Income from Moore .07S + 10000 > .11S + 8000
46	"For what dollar amount of..." For what dollar amount of book sales does Random House pay more than Moore Publishing Co.? Income from R.H. > Income from Moore .07S + 10000 > .11S + 8000 .07S + 2000 > .11S 2000 > .04S 50,000 > S Random House will pay more for sales less than $50,000.
47	"When NASA sends a rocket..." When NASA sends a rocket into space, they monitor the temperature of certain gases. Time is the independent variable and temperature is the dependent variable. Notice that negative time is used to denote time before lift off. Time Temp Time Temp -20 -20 10 80 -15 -20 15 120 -10 -10 20 90 -5 0 25 25 0 15 30 5 5 40 35 -15
48	Scatter Plots TEMP MIN What was the temperature at take off?
49	Scatter Plots TEMP MIN When was the temperature zero?
50	"An appliance repair shop charges..." An appliance repair shop charges an initial fee of $30 plus $15 per hour to fix an appliance. Complete the table to find the cost of repairing an appliance. Hours Calculation Costs 3 15(3) + 30 75 5 15(5) + 30 105 10 15(10) + 30 180 t 15t + 30 C
51	"Use the results in part..." Use the results in part a. to graph the equation in part b. Choose an appropriate scale and only graph the portion that makes sense to the problem. Label the axis.
52	"Use the results in part..." Use the results in part a. to graph the equation in part b. Choose an appropriate scale and only graph the portion that makes sense to the problem. Label the axis.
53	"Sally has a lawn-mowing business..." Sally has a lawn-mowing business for the summer. She bought a lawn mower for $200 and she charges $5 an hour. The equation that relates profit and hours worked is p = 5h - 200. How many hours does she have to work to break even? Find h, if p = 0. 0 = 5h - 200 40 = h
54	"Sally has a lawn-mowing business..." Sally has a lawn-mowing business for the summer. She bought a lawn mower for $200 and she charges $5 an hour. The equation that relates profit and hours worked is p = 5h - 200. How much money will she lose if she doesn’t work any hours? Find p, if h = 0. p = 5( 0) - 200 p = -200
55	"Graph the line p =..." Graph the line p = 5h - 200 by plotting the points obtained in parts a. and b. Choose an appropriate scale and only graph the portion that makes sense to the problem. Label the axis. Break even point (40, 0 ). Starting costs (0, -200 ).
56	Introduction to Slope
57	Introduction to Slope
58	Introduction to Slope
59	Introduction to Slope
60	Introduction to Slope
61	Introduction to Slope
62	Introduction to Slope Which grow faster: Hybrid A corn seedlings, which grew 14.6 centimeters in 15 days, or Hybrid B, which grew 11.2 centimeters in 12 days.
63	Introduction to Slope Which grow faster: Hybrid A corn seedlings, which grew 14.6 centimeters in 15 days, or Hybrid B, which grew 11.2 centimeters in 12 days. Find how fast they grow per day.
64	Introduction to Slope Which grow faster: Hybrid A corn seedlings, which grew 14.6 centimeters in 15 days, or Hybrid B, which grew 11.2 centimeters in 12 days. Find how fast they grow per day. Hybrid A: 14.6/15 =
65	Introduction to Slope Which grow faster: Hybrid A corn seedlings, which grew 14.6 centimeters in 15 days, or Hybrid B, which grew 11.2 centimeters in 12 days. Find how fast they grow per day. Hybrid A: 14.6/15 = 14.6/15 = .9733 Hybrid A grew an average of .9733 centimeters per day.
66	Applications of Graphs You are going to rent a car for a day. You have two choices, Wrecker Car company or Caddie Car Rental. Wrecker charges $20 a day and $0.75 a mile, while Caddie charges $27 a day and $0.40 a mile.
67	Applications of Graphs You are going to rent a car for a day. You have two choices, Wrecker Car company or Caddie Car Rental. Wrecker charges $20 a day and $0.75 a mile, while Caddie charges $27 a day and $0.40 a mile. Write an equation for the cost of renting a car from each company. Wrecker: C = .75m + 20 Caddie: C = .40m + 27
68	"Graph both equations on the..." Graph both equations on the same set of axis. Label each axis and choose an appropriate scale. Only graph the portion that is relevant to the problem.
69	Applications of Graphs Find where the two lines intersect. Label the point.
70	Applications of Graphs Find where the two lines intersect. Label the point. How far do you have drive for the two companies to charge the same?
71	Applications of Graphs Find where the two lines intersect. Label the point. How far do you have drive for the two companies to charge the same? .75M + 20 = .40M + 27
72	Applications of Graphs Find where the two lines intersect. Label the point. How far do you have drive for the two companies to charge the same? .75M + 20 = .40M + 27 .35M + 20 = 27 .35M = 7 M = 20
73	Applications of Graphs Find where the two lines intersect. Label the point. If M = 20, find C.
74	Applications of Graphs Find where the two lines intersect. Label the point. If M = 20, find C. C = .75(20) + 20
75	Applications of Graphs Find where the two lines intersect. Label the point. If M = 20, find C. C = .75(20) + 20 C = 35 The two lines intersect at (20, 35). Both companies charge $35 when you drive 20 miles.
76	"When does Wrecker charge more..." When does Wrecker charge more than Caddie?
77	"What are the cost intercepts..." What are the cost intercepts for Wrecker and Caddie? What do they mean?
78	"What does the slope of..." What does the slope of each line mean in terms of the problem?
79	Introduction to Exponents The population of Shanghai was 10,820,000 in 1974. If the population increased by 1% each year, complete the table below.
80	Introduction to Exponents The population of Shanghai was 10,820,000 in 1974. If the population increased by 1% each year, complete the table below. For 1975:
81	Introduction to Exponents The population of Shanghai was 10,820,000 in 1974. If the population increased by 1% each year, complete the table below. For 1975: 10820000 + (.01)10820000 =
82	Introduction to Exponents The population of Shanghai was 10,820,000 in 1974. If the population increased by 1% each year, complete the table below. For 1975: 10820000 + (.01)10820000 = (1.01)10820000 =
83	Introduction to Exponents The population of Shanghai was 10,820,000 in 1974. If the population increased by 1% each year, complete the table below. For 1975: 10820000 + (.01)10820000 = (1.01)10820000 = 10928200
84	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 77 78 n
85	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)10928200 77 78 n
86	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)10928200 (1.01)(1.01)10820000 77 78 n
87	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)10928200 (1.01)(1.01)10820000 (1.01)²10820000 11,037,482 77 78 n
88	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)²10820000 11,037,482 77 (1.01)³10820000 11,147,857 78 (1.01)⁴10820000 11,259,335 n
89	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)²10820000 11,037,482 77 (1.01)³10820000 11,147,857 78 (1.01)⁴10820000 11,259,335 n (1.01)ⁿ10820000 P
90	Introduction to Exponents YR CALCULATION POP 75 (1.01)10820000 10,928,200 76 (1.01)²10820000 11,037,482 77 (1.01)³10820000 11,147,857 78 (1.01)⁴10820000 11,259,335 n (1.01)ⁿ10820000 P What is the equation that relates Shanghai’s population and year? P = (1.01)ⁿ10802000, n is the number of years since 1974.
91	Introduction to Exponents Use the equation to find Shanghai’s population in 1985. P = (1.01)ⁿ10802000, n is the number of years since 1974. n = 1985 - 1974 = 11 P = (1.01)¹¹10820000 P = (1.116)(1082000) P = 12075120 The formula estimates that Shanghai’s population in 1985 was 12,075,120.
92	Negative Exponents Use the following formula to find the monthly payments of a loan. P = A i 1 - ( 1 + i )^-n P is the monthly payment A is the amount of the loan n is the number of payments i is the interest rate per month Eddie Nerder can afford a $250 car payment at 6% annual interest rate for 36 months. How expensive a car can he afford? ( Hint: I =.06 / 12 )
93	Negative Exponents 250 = A ( 0.0304 ) 8223 = A Eddie can afford an $8,223 car.
94	Introduction to Algebraic Fractions Suppose the cost of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given byc = 6800p 100 - p
95	Introduction to Algebraic Fractions c = 6800p 100 - p Find the cost for p = 75 c = 6800(75) 100 - 75 c = 510000 25 c = 20400 It would cost $20,400 to remove 75% of the particulate pollution.
96	Introduction to Algebraic Fractions c = 6800p 100 - p Find the cost for p = 100 c = 6800(100) 100 - 100 c = 680000 0 c = undefined The formula cannot compute the cost of removing all of the pollution.
97	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t.
98	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t Find the height of the arrow for t = 2. h = -16(2²) + 160(2) h = -16(4) + 160(2) h = -64 + 320 h = 256
99	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t Compute the height for: t = 2, h = 256 t = 5, h = 400 t = 8, h = 256 t = 10, h = 0
100	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t According to the calculations above, when will the arrow reach its maximum height? t = 5 The arrow reaches the maximum height in 5 seconds. The maximum height is 400 feet.
101	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t According to the calculations above, when will the arrow hit the ground? When the arrow hits the ground the height, h, is zero. t = 10 The arrow reaches the ground in 10 sec.
102	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t Graph the points obtained in a through d.
103	Introduction to Quadratics William Tell shoots an arrow straight up with an initial velocity of 160 feet per second. The height of the arrow is given by the equation h = -16t² + 160t Graph the points obtained in a through d. The points are: ( 2, 256) ( 5, 400) ( 8, 256) (10, 0)
104	Introduction to Quadratics h vertex intercept t
105	Quadratic Graphs and Quadratics Earl Black makes tea bags. The cost and revenue of making and selling x million tea bags per month is C = x²- 38x + 400 R = -x²+ 78x. C and R are in thousands of dollars.Find the equation for profit.
106	Quadratic Graphs and Quadratics Earl Black makes tea bags. The cost and revenue of making and selling x million tea bags per month is C = x²- 38x + 400 R = -x²+ 78x. C and R are in thousands of dollars.Find the equation for profit. P = R - C P = (-x²+ 78x) - (x²- 38x + 400) P = -x²+ 78x - x²+ 38x - 400 P = -2x² + 116x - 400
107	Quadratic Graphs and Quadratics Graph the profit equation. Explain what the vertex, x and p intercepts mean in terms of making tea bags. Make sure you label the axis and use an appropriate scale.
108	Quadratic Graphs and Quadratics
109	Quadratic Graphs and Quadratics P = -2x² + 116x - 400 1. The Vertex, (29, 1282), means; If Earl Black sells 29 million tea bags they will get a maximum profit of 1.282 million dollars. 2. The x-intercepts, (3.675, 0) (54.33, 0), mean; If Earl Black sells 3.675 million or 54.33 million tea bags they will break even. 3. The P-intercept, (0, -400), means; The company’s start up costs.
110	Quadratic Graphs and Quadratics Suppose Earl Black needs to make $500,000 in profit (P = 500). Graph this line on the graph above and find out where the line intersects the graph. Explain what the answers mean.
111	Quadratic Graphs and Quadratics
112	Quadratic Graphs and Quadratics Suppose Earl Black needs to make $500,000 in profit (P = 500). Graph this line on the graph above and find out where the line intersects the graph. Explain what the answers mean. Find x, if P = 500. 500 = -2x² + 116x - 400 0 = -2x² + 116x - 900 a = -2, b = 116, c = -900 x =9.228, 48.77
113	Quadratic Graphs and Quadratics x = 9.228, 48.77 The line intersects the graph at (9.228, 500) and (48.77, 500). If Earl Black needs to make $500,000 in Profit then they need to sell 9,228,000 or 48,770,000 tea bags.
114	Quadratic Graphs and Quadratics
115	Quadratic Graphs and Quadratics When does Earl Black make more than $500,000 in profit?
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120	Changes in Teaching Focus
121	Visualization in the broadest sense has always been important in mathematics
122	Purpose of Multimedia Modules Expectations by students To present visualizations of concepts To present animations To require interactive participation of learner
123	Materials Web Page ToolBook PowerPoint Excel Flash Merlot ScreenWatch
124	Web Page Resource
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147	Learning Objects small bits of reusable materials learning modules
148	Merlot - Learning Objects http://www.merlot.org/Home.po
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153	Next Semester? Ongoing project Living book Flash
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