Towering Pizzas

TOWERING PIZZAS

Papa Joe’s Pizza prepares pizza boxes by folding them in advance for its deliveries each day and setting them on a shelf. On the one shelf, the pizza boxes are arranged as follows:

When there are two rows of pizza boxes on the shelf, the arrangement looks like this-

When there are three rows of pizza boxes on the shelf, the arrangement looks like this-

When there are four rows of pizza boxes on the shelf, the arrangement looks like this-

As more boxes are folded, the pattern continues like the boxes in the pictures above.

1. In the picture with four rows of boxes, what is the total number of pizza boxes in the first two

rows? ______

2. How does the total number ofrows of pizza boxes relate with the total number of pizza boxes?

______

3. Complete the table to represent the pizza box pattern at Papa Joe’s PizzaPalace.

Support your answer using words, numbers, and/or diagrams.

Note: “process” refers to approach student uses to determine total number of pizza boxes.

For example: 1•4=4 or 2•4=8 etc.

4. Reflect on your answer to Question 2, are you satisfied with your response when you consider the additional information in the table? Explain.

______

5. Complete the coordinate grid of data to represent the pizza box pattern at Papa Joe’s PizzaPalace.

6. What does the ordered pair (3, 12) on the coordinate grid represent about the pizza boxes?

______

7. Consider the ratio of the total number of pizza boxes to the number of rows. Compare the ratio for the total number of boxes in 3 rows to its number of rows and the total number of boxes in 6 rows to its number of rows. (Compare means to address which ratio is larger or if the ratios are equal).

Support your answer using words, numbers, and/or diagrams.

______

8. Use the ratio of the total number of pizza boxes to the total number of rows to answer the following two questions.

a. How can this ratio be used to find the total number of pizza boxes in 7 rows?

______

b. How can this ratio be used to find the number of rows if there are 44 pizza boxes?

______

9. Write a rule, using symbols, to describe the relationship between the number of pizza boxes and the number of rows.

______

10. Reflect on your responses in Questions 2 and 4 and compare them to the symbolic rule in Question 9.

______

11. Explain at least two methods a person could use for determining the total number of pizza boxes in 30 rows.

Method 1: ______

______

Method 2: ______

______

12. Write the conversation you would have with a friend why the point (23, 96) is or isn’t a point on the coordinate grid for the pattern of the pizza boxes?

______

13. Papa Joe’s PizzaPalace plans on expanding its business and will prepare three shelves that allow four boxes per row with an equal number of rows of pizza boxes on each shelf. How many rows of pizza boxes are on each shelf if the total number of pizza boxes is 288?

Support your answer using words, numbers and/or diagrams.

______

14. Write an equation that shows the relationship between the total number of boxes and number of rows of pizza boxes pictured below.

Equation: ______

SOLAR CELLS FOR SCIENCE

The United States and 15 other nations created the International Space Station, ISS, as a world-class laboratory in space. The ISS provides a gravity-free environment for about 30 experiments. Solar energy is used to run the research and maintain ISS. The power is collected from the sun with photovoltaic modules made up of two rectangular panels called arrays.

As space research increases, the demands for power increase. In the next construction phase, astronauts plan to install two more sets of solar arrays on the space station. The photovoltaic modules will then have a total surface area of 1632 square meters, which is twice the present amount. The modules will contain a total of 65,000 solar power cells, which is 32,500 solar power cells more than the present amount.

1. Complete the table. Describe any patterns you see in the sequences. ______

______

2. Make a conjecture about the proportionality of the number of solar cells to the number of array

panels. ______

______

3. Here is a graph of the number of solar cells compared to the number of array panels.

a. Write an equation of the line: ______

b. Does the graph support your conjecture? ______Why or why not?

______

4. Make a conjecture about the proportionality of the number of solar cells to the area of array

panels. ______

______

5. Here is a graph of the numberof solar cells compared to the areaof array panels.

a. Write an equation of the line: ______

b. Does the graph support your conjecture? ______Why or why not?

______

INTERNATIONAL SPACE STATION

1. The International Space Station, ISS, is more than just a laboratory in space. It represents a “city in space,” a partnership of 16 nations learning and working in a gravity-free environment. The photovoltaic modules used to store solar power are made of two rectangular panels. Each panel measures 34 meters long and 12 meters wide. Two panels provide 23 kilowatts of electricity per day.

a. Describe the patterns you see in the table. ______

b. Explain the relationship between the number of panels and the number of kilowatts.

______

c. Graph the relationship.

d. Predict the number of kilowatts if there had been 16 array panels. ______

e. Use the table to determine the number of array panels if there are 276 kilowatts being produced.

f. Write an equation that describes the relationship between the number of kilowatts to the

number of array panels.______

POPULATION OF WASHINGTON

Population Data for Selected Cities in WashingtonState 1900-1990

Year / Spokane / Seattle / Walla Walla
1900 / 36,000 / 81,000 / 10,000
1920 / 104,000 / 315,000 / 16,000
1940 / 122,000 / 368,000 / 18,000
1960 / 182,000 / 557,000 / 25,000
1980 / 171,000 / 494,000 / 26,000
1990 / 177,000 / 516,000 / 29,000
2000

Data from “Population of Cities, Towns, & Counties”, Office of Financial Management, State of Washington

1. On the same graph, place the data points for each city. Use a different color for each city. Remember to write an informative title, label your axes and use correct intervals.

2. For the year 1950, determine a population conjecture for each city. Explain how you determined your conjecture.

______

3. INTERNET ACCESS NEEDED FOR THIS: Research the population for each city for the year 1950. How does each of your conjectures compare to the actual population? What reasons can you identify if your conjectures differ from the actual population?

______

4. Predict the population for each city in the year 2000 and fill in your predictions in the table. Research the population reported by the census bureau for each city in 2000.

Support your answer using words, numbers and/or diagrams.

UNITED STATES POPULATION

1. Population growth in the United States and the world has been a topic of conversation for years as the concern grows regarding over-crowding, feeding the increased population with less agricultural land and population density among many avenues for discussion. Listed in the table are the estimated population statistics for years 1990-1997 as published by the U.S. Census Bureau in June 1997.

Population Estimates for the United States 1990-1997 (Table 1)

YEAR / POPULATION
1990 / 249,949,000
1991 / 252,636,000
1992 / 255,382,000
1993 / 258,089,000
1994 / 260,602,000
1995 / 263,039,000
1996 / 265,453,000
1997 / 267,901,000

The graphed line approximates the data from the U. S. Census Bureau data. Provide a title and axis labels for the graph.

2. What is the population indicated by the fitted line for year 0? ______

3. What does this “y-intercept” mean in the context of this population data? ______

______

4. What is the slope of the line? ______

5. In the context of this problem what does the slope mean? ______

______

6. Write a symbolic equation whose point solutions would lie on the line:

Equation of the line:

7. What do you predict to be the population of the United States in the year:

2000? ______2010? ______

8. Research what the actual census total was for the year 2000. How close were you? What was the percentage difference?

Support your answer using words, numbers and/or diagrams.

______

9. Identify two (2) factors that could have influenced why your prediction matched or did not match what the Census Bureau reported for the population in 2000.

Factor 1______

______

Factor 2 ______

______

TOWERING PIZZA MULTIPLE CHOICE PRACTICE PROBLEMS

1. The table represents how the air temperature combines with the humidity to form the heat index.

Which statement is correct?

 A. As the humidity and temperature decrease, the heat index increases.

 B. As the humidity and temperature increase, the heat index decreases.

 C. As the humidity increases and the temperature decreases, the heat index increases.

 D. As the humidity decreases and temperature increases, the heat index increases.

2. The chart shows 10 states and the average length of patient stay in days in each of their

hospitals.

STATE / No. of Hospitals / Average Length of Stay
AL / 119 / 7.0
AK / 16 / 5.7
AX / 61 / 5.5
AR / 88 / 7.0
CA / 440 / 6.0
CO / 71 / 6.8
CT / 35 / 7.4
DE / 8 / 6.8
FL / 227 / 7.0
GA / 162 / 7.2

Which statement is true?

 A. Five of the states had an average length of stay of at least 7 days.

 B. Five of the states had an average length of stay of less than 6 days.

 C. The state with the most hospitals had the largest average length of stay.

 D. The state with the fewest hospitals had the shortest average length of stay.

3. Tanisha and some friends from her bicycle club went on a training ride from West Palm Beach to Miami. They planned to ride 45 miles from West Palm Beach to Fort Lauderdale, another 10 miles to Hollywood, and finally 15 miles to Miami. Tanisha’s bicycle got a flat tire north of Miami, and she was unable to complete the training ride. Her odometer showed she had traveled 60 miles.

Which closest represents thepercent of the training ride Tanisha completed?

 A. 14%

 B. 75%

 C. 86%

 D. 116%

4. Which is the y-intercept for the graph of the equation ?

 A. -5

 B. -3

 C. 3

 D. 5

5. This year, 75% of the graduating class of OverviewHigh School had taken at least 8 math courses. Of the remaining class members, 60% had taken 6 or 7 math courses.

Which percent of the graduating class had taken fewer than 6 math courses?

 A. 10

 B. 15

 C. 30

 A. 45

6. Phillip charged $400 worth of goods on his credit card. On his first bill, he was not charged any interest, and he made a payment of $20. He then charged another $18 worth of goods. On his second bill a month later, he was charged 2% interest on his entire unpaid balance.

Which is the amount of interest Phillip was charged on his second bill?

 A. $8.76

 B. $7.96

 C. $7.60

 D. $7.24

7. A geneticist studying twins read that fraternal twins occur in 1 out of every 80 births. The scientist uses a random sample of 560 mothers-to-be.

Which represents the number of would be mothers expected to give birth to fraternal twins?

 A. 7

 B. 70

 C. 8

 D. 80

8. In 1977, there were 12,168,450 U.S. households with cable television. In 1997, there were 65,929,420 U.S. households with cable television.

Which represents the average rate of change per year in households with cable television during that time period?

 A. 2,688,048.5 households/year

 B. 5,376,097.0 households/year

 C. 53,760970.0 households/year

 D. 65,320,997.5 households/year

9. A rabbit population grew in the following pattern: 2, 4, 8, 16…. All the rabbits are expected to live while the pattern continues.

Which is the number of rabbits there will be in the 8th generation?

 A. 32

 B. 128

 C. 256

 D. 512

10. Frank plans to set up a fruit juice stand at the state fair. He will purchase 500 cans of juice for $135, and he will charge $2 for each can he sells. In addition to the cost of the juice, Frank will need to pay $20 to set up the stand.

Which expression could Frank use to find out how much money he could make, after expenses, for selling j cans of juice?

 A.

 B.

 C.

 D.

11. Every year in the Chinese calendar is named for an animal. Each year in the table below has been designated as a “Year of the Ox.”

The variable n represents any “Year of the Ox.”

Which expression represents the previous “Year of the Ox”?

 A.

 B.

 C.

 D.

OPTIONAL ACTIVITY – UNITED STATES POPULATION OVER AGE 65 YEARS OLD

17. The tables depict the tremendous growth in the population of citizens over the age of 65 rounded to nearest millionth. This growth is predicted to continue at least through the year 2020. If the rate of growth were to continue to 3020, predict the population for 2030.

The Actual and Predicted Over 65 Population in the United States 1960-2030 (Table 2)

1960 / 1970 / 1980 / 1990 / 1995 / 2000 / 2010 / 2020 / 2030
15 million / 20 million / 28 million / 31 million / 33 million / 38 million / 41 million / 56 million

18. Label axes, title graph, determine and write scales for both axis based on drawn line that approximates population data.

19. What is the y-intercept for the line? ______

20. What does this intercept mean in the context of the population data? ______

______

21. What is the slope of the line?

Explain how you determined the slope.

______

22. What is the equation of the line? ______

23. Use the equation in # 13 to find a population prediction for 2030. Compare this prediction to the prediction you madein problem #17. Give two explanations on why the predictions could be different.

Explanation 1: ______

______

Explanation 2: ______

______

24. The Percentage of the Total Population that is Over 65 in the United States 1960-2030

(Table 3)

1960 / 1970 / 1980 / 1990 / 1995 / 2000 / 2010 / 2020 / 2030
12.4 / 12.5

The percentage of population changesat the same rate as the rate indicated in the data presented in the table,fill in the missing values in the table and then draw a line related to the data. Be sure to title graph, label axes, and write scales.

Determine the y-intercept. ______

Write an equation that describes the line.

In the years 2020-2030, most of you will be in your early- to mid-forties, earning a fairly decent yearly salary and potentially supporting a family. According to our model, there will be a rather large segment of the population over 65 years of age. What percentage of the total population will this age group represent?

Percentage of the total population ______

Support your answers using words, numbers and/or diagrams.

Prediction of “over 65” population in 2030 ______

Percentage of the total population ______

Support your answers using words, numbers and/or diagrams.

In #24 you predicted the “over 65” population in the year 2030. In part d above you predicted the percentage of the population that was over 65 in 2030. Use your two predictions to predict the total U.S. population in 2030. Support your answers using words, numbers and/or diagrams

f. What will be the ratio of those over 65 to those under 65 in 2030?

Support your answers using words, numbers and/or diagrams.

h. Describe three issues for you and society if such a large part of the population of the United States over 65 years of age. Use information from the graphs and tables to support your conclusions.

Issue 1: ______

______

Issue 2: ______

______

Issue 3: ______

______

Student: Ch 8 “Towering Pizzas”UPDATED JANUARY 2008