Casio TEAMS Grant

Systemic Initiative Teaching Environment

Algebra (SITE-A)

Workshop Materials

Graphing, Tracing, and Zooming

Lessons

1.  Ten students prepared for a quiz and kept track of the time that each spent studying. Each reported the number of hours on the quiz and the teacher recorded the quiz grade of each student.
Is there a relationship between the number of hours spent preparing for the quiz and the quiz grade?

2. Framers believe that there is a linear relationship between the average amount of rainfall during the growing season of carrots and the average weight of a carrot produced.
Is there a linear relationship between the average amount of rainfall and the average weight?

3)  The cost of operating the Internal Revenue Service (IRS) increased steadily from 1980 to 1990.
Is there a linear growth pattern in the data supplied?

4) In 1980, 3.5% of the doctorates in engineering were awarded to women. By 1990, 8.5% were being earned by women.
Can you find the average rate of change in the percentage of engineering doctorates earned by women from 1980 to 1990?

5) The percentage of female law enforcement officers in the United States rose from 9.4% in 1983 to 13.8% in 1990.
Can you find the average rate of change in the percentage of female law enforcement officers in the United States from 1983 to 1990?

6) In 1970, 130 African-American women held elected Federal Offices in the United States. By 1990, the number had increased to 1950. In 1973, Barbara Jordan became the first African-American woman from a Southern state to serve in the United States Congress.
Can you find the average rate of change in the number of African-American women holding elected Federal Offices in the United States?

7) Gratuity on service at a restaurant is usually 15% of the cost of the meal before the tax is added to the bill.
Can you develop a table that displays what the amount of gratuity should be for meals costing between $20 and $200 with dollar increments of 10?

8) A certain culture of bacteria doubles every hour. This type of growth is commonly called exponential growth and it is quite rapid.
Can you develop a table that displays what the bacteria count is every hour given an initial bacteria count of 100 and allowing the growth to take place over the next 10 hours?

9) The hourly wage at a fast food restaurant starts at $4.75 per hour with $0.25 increments after each subsequent year of working experience at the restaurant. Hourly employees can work only 37.5 hours per week, do not get paid vacations, and work 52 weeks per year.
Can you develop a table that shows at each stage of a nine year employment period what an employee earns each week and each year?

10) Use the CASIO fx7400G to draw the graph of the inequality 2 x + 3 y > 2 y + 1

11) Use the CASIO fx7400G to draw the graph of the inequality y + 2 < x2 (squared)

12) Use the CASIO fx7400G to draw the graph of the inequality y x2 (squared) > 1

13) Use the CASIO fx7400G to draw the graph of the inequality y > x2 (squared)  + 6 x + 16

14) Use the CASIO fx7400G to draw the graph of the inequality
y > lesson14a.gif (1800 bytes)

15) Use the CASIO fx7400G to draw the graph of the inequality
y <  lesson15a.gif (1746 bytes)

16)  Use the CASIO fx7400G to draw the feasibility region of the system of inequalities given below and
find the integer values of the vertices:
  y < 4, y < -2 x + 12, y > -2/3 x + 4

17)  Use the CASIO fx7400G to draw the feasibility region of the system of inequalities given below and
find the integer values of the vertices:
  y < - 2 x + 20, y > - 10 x + 36, y > - 2/5 x + 36/5

18) Use the CASIO fx7400G to draw the feasibility region of the system of inequalities given below and
find the integer values of the vertices:

image18.gif (2009 bytes)

19)  All three of these activities are closely related and can be accomplished graphically using the CASIO fx7400G.
1.Find the roots of y = x2
(squared) + 4 x + 5
2.Solve for x: x2
(squared) + 4 x + 5 = 0
3.Factor x2
(squared) + 4 x + 5

20)  All three of these activities are closely related and can be accomplished graphically using the CASIO fx7400G.
1.Find the roots of y = x3
(cubed) - 4 x2(squared) + 7 x - 6
2.Solve for x: x3
(cubed)  - 4 x2(squared) + 7 x - 6 = 0
3.Factor x3
(cubed)  - 4 x2(squared) + 7 x - 6

21) Solving an equation of quadratic form can be accomplished graphically using the CASIO fx7400G.
Solve for x: x4 - 13 x2 + 36 = 0

22) An experiment was performed which measured the number of hours a certain brand of battery allowed a toy rabbit to operate. Twenty-four randomly selected batteries of that particular brand were tested. Below are the number of hours each battery lasted.
Hours 34 37 29 31 32 33 31 29 28 35 36 30 36 30 29 34 22 33 35 32 30 32 34 28
Use the CASIO fx7400G to draw a boxplot for these data and give the five-number summary (Min, Q1, Median, Q3, Max) of the hours.

23) In a large urban public school district, a random sample of the percent of students in Algebra who pass are given
below:
Percent 80 78 82 83 78 80 75 79 82 89 81 79 80 79 81 82 76 73 80 79 81 78 80 77
Use the CASIO fx7400G to draw a boxplot for these data and give the five-number summary (Min, Q1, Median, Q3, Max) of the hours.

24) Below are the percents of the popular vote won by the successful candidate in each of the presidential elections from 1948 to 1988.

Year      

1948

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

Percent

49.6

55.1

57.4

49.7

61.1

43.4

60.7

50.1

50.7

58.8

53.9

Use the CASIO fx7400G to draw a boxplot for these data and give the five-number summary (Min, Q1, Median,
Q3, Max) of the hours.

25) A fisheries researcher compiled the following data on lengths of randomly selected 6-year-old white female
crappies (in millimeters):
217 219 231 225 223 235 230 217 222 214 225 251 220 225 220 221 253 210 218
221 228 222 233 220 218 225 234 222 227 213 235 223 222 223 234 224 231 220
Use the CASIO fx7400G to draw a histogram for these data.

26) A fisheries researcher compiled the following data on lengths of randomly selected spawning female speckled trout (in millimeters):
310 298 323 316 308 311 323 317 301 322 309 313 294 318 307 295 320 304 317
321 301 320 313 316 321 306 324 317 303 322 311 309 302 310 296 323 316 308
Use the CASIO fx7400G to draw a histogram for these data.

27) A teacher uses a ten point grading scale to measure student performance. The following data were the final course averages for a class of 23 students:
56, 61, 79, 91, 91, 74, 70, 93, 55, 54, 93, 55, 65, 92, 64, 46, 97, 56, 79, 70, 60, 61, 68
Use the CASIO fx7400G to draw a histogram for these data.

28) Consider the following data:

X

0.2

0.4

0.6

0.8

1.1

1.3

1.4

1.7

1.9

2.2

2.3

2.6

2.7

3.0

3.2

Y

2.6

2.3

2.1

2.0

2.1

2.1

2.2

2.5

2.8

3.3

3.8

4.4

5.1

5.9

6.8

Use the CASIO fx7400G to a quadratic regression for these data.

29) Consider the following data:

X

0

5

10

15

20

25

30

35

40

45

50

Y

600

4215

7030

9045

10260

10675

10290

9150

7120

4335

750

Use the CASIO fx7400G to a quadratic regression for these data.

30) Consider the following data:

X

50000

100000

200000

250000

350000

450000

500000

550000

600000

Y

3.8258

4.2923

4.8491

5.0426

5.3439

5.5751

5.6733

5.7527

5.8448

Use the CASIO fx7400G to a logarithmic regression for these data.