towering pizzas -...

TOWERING PIZZASTEACHER EDITION

List of Activities for this Unit:

ACTIVITY STRAND DESCRIPTION

1 Pizza Boxes AS/NS

Determining patterns, Completing a table of values, graphing data, writing and comparing ratios, writing equations

2 Solar Cells for Science AS/NS

Completing a table of values; given a graph, write an equation; making predictions about proportionalilty

3 International Space Station AS/PS

Describing patterns in tables; graphing data and making predictions; Completing a table of values; writing equations

4 Populations of Washington ** See Teacher Notes ** AS/PS

Populations for Spokane, Seattle, and Walla Walla; graphing data; making predictions

5 United States Population AS Graphing data; interpreting slope and y-intercept; writing equations

Towering Pizza MC Practice Problems AS Multiple choice practice problems

Optional Activity – United States Population over age 65 years old AS

Graphing data points; interpreting slope and y-intercept; writing equations using 2 points; providing explanations for changes; finding percentage change

COE Connections Widget Factory

MATERIALSGraphing calculator (optional)RulerColored pencils/markers

Warm-Ups(in Segmented Extras Folder)

Ernie ElephantMillie’s Money MultiplesPatience’s Patience Pays OffPaydayTall Paul

Teacher: Ch 8 “Towering Pizzas” UPDATED JANUARY 2008 1

Vocabulary Mathematics & ELL:

Teacher Notes: This activity requires students to use the internet, or other resources, to find the population of these 3 cities in 1950.

Length of the Lesson: 250 minutesEssential Questions:

How do you determine a pattern? What information can be obtained once a pattern is determined? What is a ratio? How is a ratio written? What does a ratio tell us? How do we use words to write an expression or equation? What is a coordinate grid? How are points put on a coordinate grid? What is an informative title for a graph? What are the key components of a graph? What information can we learn from a graph? What is the slope of a graph? What does the slope mean within context? How can trends be identified in order to make inferences/predictions from a set of data? How accurate is data that are collected? What factors influence a trend that may not be reflected in the collected data? How does a person evaluate the accuracy of data in research?

Lesson Overview:

Before allowing the students the opportunity to start the activity: assess their prior knowledge with regards to collecting and using data. Discuss with students the most recent census tabulation. How often is the census taken in the United States? What is the process that is used to collect the census data? How is the population determined during the non-census years?

Before allowing the students the opportunity to start the activity: Establish a “set” about pizza establishments. Ask if any students work at a pizza place. How do they stack their boxes? Who prepares the boxes? Are they folded at the store or do they already arrive folded? If convenient take a picture at your neighborhood pizza of the boxes stacked on the shelf show picture in class.

Teacher: Ch 8 “Towering Pizzas” UPDATED JANUARY 2008

Area PercentageArrangement Percentage DifferenceArray PhotovoltaicCensus PredictionCompare ProportionalityConjecture RatioCoordinate Grid RelationshipEquation Relative HumidityFitted Line Rule, Symbloic RuleHeat Index SlopeKilowatts Solar CellsPatterns Y-Intercept

2

Discuss sources of data. What is the relationship between sets of data? Encourage students to let 1900 be year zero in one of the graphs and 1990 be year 0 in another graph. Use 1960 as year zero in the third and fourth graphs. How do you decode what the problem is asking you to do? Reflect on how the students make their thinking visible. How does a student support a conclusion that the student makes? This module requires internet access. Use resources from your building. May want to use graphing calculator to verify linear equations.

Performance Expectations: 5.4.A Describe and create a rule for numerical and geometric patterns and extend the patterns.5.4.B Write a rule to describe the relationship between two sets of data that are linearly related.5.4.D Graph ordered pairs in the coordinate plane for two sets of data related by a linear rule and draw

the line they determine.6.2.A Write a mathematical expression or equation with variables to represent information in a table or

given situation.6.2.B Draw a first-quadrant graph in the coordinate plane to represent information in a table or given

situation.6.2.F Solve word problems using mathematical expressions and equations and verify solutions.6.6.G Extract and organize mathematical information from symbols, diagrams, and graphs to make

inferences, draw conclusions, and justify reasoning.7.2.G Determine the unit rate in a proportional relationship and relate it to the slope of the associated

line.8.1.C Represent a linear function with a verbal description, table, graph, or symbolic expression, and

make connections among these representations.8.1.D Determine the slope and y-intercept of a linear function described by a symbolic expression,

table, or graph.8.1.E Interpret the slope and y-intercept of the graph of a linear function representing a contextual

situation.8.1.F Solve single- and multi-step word problems involving linear functions and verify the solutions.8.5.G Extract and organize mathematical information from symbols, diagrams, and graphs to make

inferences, draw conclusions, and justify reasoning.A1.1.A Select and justify functions and equations to model and solve problems.A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities.A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point

on the line, or two points on the line, and translate between forms of linear equations.A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel

and perpendicular lines.A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret

the slope and y-intercept of the line, and use the equation to make predictions.G.6.F Solve problems involving measurement conversions within and between systems, including those

involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.

Performance Expectations and Aligned ProblemsChapter 8 “Towering

1- Pizza Boxes

2- Solar cells for

3- International

4- Populations of Washington

5- United States

6- M/C problems


Pizzas” Subsections:

Science Space Station Population

Problems Supporting:PE 5.4.A

2, 3, 5, 7, 8, 9 2-5 1 2, 4 4-6

Problems Supporting:PE 5.4.B

9, 14 3, 5 1 6 10, 11, 22, 24

Problems Supporting:PE 5.4.D ≈ 6.2.B

5 1 1 1 18, 24

Problems Supporting:PE 6.2.A

9 3, 5 1 6 11, 22, 24

Problems Supporting:PE 6.2.F ≈ 8.1.F ≈ A1.1.B ≈ G.6.F (Linear eqns in context are conversion problems.)

2, 8, 11-13 2, 4 1 1, 4 7 3, 5, 6, 23,

24

Problems Supporting:PE 6.6.G ≈ 8.5.G

2, 13 2, 4 1 2, 4 7, 9 1, 8

Problems Supporting:PE 7.2.G (Often the slope of a linear eqn is a unit rate converter.)

7-9 3, 5 1 4-6 21, 24

Problems Supporting:PE 8.1.C

8, 9, 14 3, 5 1 1, 3-6 19-22, 24

Problems Supporting:PE 8.1.D

9, 14 3, 5 1 2-6 4, 19-21, 24

Problems Supporting:PE 8.1.E ≈ A1.4.C

3, 5 1 3-6 19-21, 24

Problems Supporting:PE A1.1.A

All of chapter 1 scaffolds the pizza problems

to linear models

3, 5 1 1-6

Problems Supporting:PE A1.4.B

9, 14 3, 5 1 2-6 18-22, 24


Problems Supporting:PE A1.6.D

9, 14 3, 5 1 2-6 18-22, 24

Assessment: Use the multiple choice and short answer items from Algebraic Sense and Number Sense that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.


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? _____________8___________________


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

______Total number of pizza boxes is 4 times the number of rows of pizza boxes OR ratio is 4:1 OR

number of rows is ¼ of the total number of pizza boxes._____________________________

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

__________Yes, they match._______________________________________________________

_________Answers will vary.______________________________________________________

______________________________________________________________________________

_______________________________________________________________________________

_________________________________________________________________________________


_________________________________________________________________________________


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

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

________Three rows of pizza boxes will hold 12 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.

___________The ratio is 4:1, box to rows._______________________________________


12:3or4:1

24:6or4:1

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?

_________Yes______________7 4 = 28 _____

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

_________44 boxes______________________

_________4:1 ratio______

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

__________p = 4r______________________________________________________________

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

_________They match – Answers will vary __________________________________________

_____________________________________________________________________________

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

Method 1: _________________Answers will vary_____________________________________

__________________________- use table - ratio of shelves to boxes _________

__________________________- graphs - equation _____________________

__________________________- ratio of boxes to shelves_______________________________

Method 2: _________ Answers will vary _______________________________________________

_________________________________________________________________________________


Define variables: p = # of pizza boxes r = # of rows

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?

__________p = 4r_______________________________________________________________

__________The number of pizza boxes needs to be a multiple of 4 and a multiple of 4 of the____

__________specified row._________________________________________________________

______________23 4 = 92 ; therefore (23, 96) is not a point on the coordinate graph for the pattern

__________of pizza boxes.__________________________________________________________

13. Papa Joe’s Pizza Palace 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.

___There will be 96 pizza boxes on each shelf. Then the 96 pizza boxes will be split equally into

rows containing 4 boxes each. Since 96 4 = 24, there will be 24 rows of 4 pizza boxes on each of

the 3 shelves.____________________________________________________________________

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

Equation: _____T = 4n + 2__________________________________________________


Define variables: T = total # of pizza boxes n = # of rows with 4 boxes

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. ___For every increase____

______of 2 array panel, the solar cell increase by 32,500. The area minus by 816 m². The ratio is 1

array panel:16,250 solar cells. 408 m²:1 array panel.______________________________________

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

panels. ______The number of solar cells increases as the number of panel increases. The number of

solar cells increase at a constant ratio of 32,500 for every 2 panels or 16,250 cells per panel._______


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: __________C = 16,25p_________________________

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

_______If the relationship is proportional, the number of panels will increase by a constant

rate. For example, the number of solar panels doubles, then the number of solar cells double.

The scatterplot of the data lies on a line through the origin. When a proportional relationship

is graphed, the line goes through the origin. _______________________________________

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

panels. _____The number of solar cells increase proportionally to the area of the panels at the rate of

39.83 solar cells to 1 m²._____________________________________________________________


Define variables:

where, C = number of solar cellsp = number of array panels

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

a. Write an equation of the line: ______C = 39.83a_____________________________

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

____The scatterplot of the data line on a line through the origin. When a proportional

relationship is graphed, the line goes through the origin. There is a constant rate of change.__


Define variables:

when C = number of solar cellsa = area of panels

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. ____As the number of panels increases by 2, the

area increases by 816 m² and the kilowatts increases by 23.____________________

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

_______The ratio of kilowatts to one array panel is 11.5:1_________________________

c. Graph the relationship.

d. Predict the number of kilowatts if there had been 16 array panels. _____184 kilowatts___

11516 = 184


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. _______K = 11.5a___________________________________


Define variable:

K = number of kilowattsa = number of array panels

POPULATION OF WASHINGTON

Population Data for Selected Cities in Washington State 1900-1990

Year Spokane Seattle Walla Walla1900 36,000 81,000 10,0001920 104,000 315,000 16,0001940 122,000 368,000 18,0001960 182,000 557,000 25,0001980 171,000 494,000 26,0001990 177,000 516,000 29,0002000Data 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.

from graph from equations

Walla Walla Spokane Seattle

________________________________________________________________________________

________________________________________________________________________________

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?

Actual 1950 populations

Walla Walla = 24,102 peopleSpokane = 161,721 peopleSeattle = 467,591 people

_________________________________________________________________________________

_________________________________________________________________________________

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.

Year 2000 predictions Year 2000 Actual

Walla Walla peopleSpokane 196,143 peopleSeattle 563,375 people


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 POPULATION1990 249,949,0001991 252,636,0001992 255,382,0001993 258,089,0001994 260,602,0001995 263,039,0001996 265,453,0001997 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.

Population Estimates for the United States 1990-1997


Population in Millions

2. What is the population indicated by the fitted line for year 0? ____249,949,000____________

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

_________________________________________________________________________________

4. What is the slope of the line? ___ Hand: 2,563,400 or Calculator: 2,562,297.62 ______


Year of estimate (where 1990 =0, 1991 = 1 etc.)

2 4 6 8 10 12 14 16 18 20

300

290

280

270

260

250

5. In the context of this problem what does the slope mean? _____ The slope in the context of this

situation means the increase in the United States population each year.________________________

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

Equation of the line:

(1,252,636,000) & (265,453,000) 252,636,000 = 2,563,400(1) + b

b = 250,073,000

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.

Census 2000 total population for US was 281.4 million.


The answer can be arrived by dividing the difference by 281,400,000 or divide the student’s projected

population by 281,400,000 then subtracting the answer from 100% or 1 – (dependent on the number

of student uses).___________________________________________________________________

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 ______-- accuracy in plotting points on the graph____________________________

_____________-- accuracy of fitted line__________________________________________

_____________-- accuracy in reading exactly where a point lies on the graph_____________

_____________-- growth isn’t necessarily perfectly linear____________________________

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.

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 the percent of the training ride Tanisha completed?

A. 14%

B. 75%

C. 86%

D. 116%

Teacher: Ch 8 “Towering Pizzas” UPDATED JANUARY 2008

STATE No. of Hospitals

Average Length of

StayAL 119 7.0AK 16 5.7AX 61 5.5AR 88 7.0CA 440 6.0CO 71 6.8CT 35 7.4DE 8 6.8FL 227 7.0GA 162 7.2

25

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 Overview High 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 203015

million20

million28

million31

million33

million38

million41

million56

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? ____15 million_____________________________

20. What does this intercept mean in the context of the population data? ____The population is 15

million in 1960.__________________________________________________________________


21. What is the slope of the line? (0,15); (40,38)

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 made in problem #17. Give two explanations on why the predictions could be different.

Explanation 1: _______ Calculator: 57.19 Million; Graph: 55 Million; Hand: 55.25 Million _____

_________________________________________________________________________________

_________________________________________________________________________________

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 203012.4 12.5

a. The percentage of population changes at 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.

b. Determine the y-intercept. _______________________________________________

c. Write an equation that describes the line.

(25, 12) & (40, 13.8)

Hand: y = 0.12x + 9

Calculator: using 15.7% 0.1056x + 9.2375using 15.6% 0.10476x + 9.2556using 16.2% 0.10976x + 9.1472


d. 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 __Hand: 352,609,000 Calculator: 352,655,238

Percentage of the total population ___16.2% or 15.6% or 15.7%______________Support your answers using words, numbers and/or diagrams.

e. 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: _______________________________________________________________________


______________________________________________________________________________


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