Population of the United States

POPULATION OF THE UNITED STATES

Enduring Understanding: Develop a better understanding of how to use data from a table to create a graph and make a prediction of values not included in the data set. Develop a better understanding of how to draw a reasonable line to describe the data represented by a scatter plot. Develop a better understanding of how to make a conjecture and research information to validate the conjecture.

Essential Questions:

Original Lesson / Suggestions for English Language Learners

What is an informative/meaningful title for a graph?
What are appropriate intervals for the x- and y-axes?
How is a line that fits data displayed on a scatter plot (fitted line) determined?
How is a fitted line represented as an equation?
How is a fitted line used to make a prediction?

When reading a graph, where are the x- and y-intercepts?
What is the relationship between the intercepts and the context of any problem?

What does it mean to have negative values when you are working with years?
How can trends be identified in order to make inferences/predictions from a set of data?
What factors influence a trend that may not be reflected in the collected data?
How does a person research for accurate data?

/ Vocabulary:
Interval
Fitted line
Intercept
Prediction
Context
Trend

Lesson Overview:

Original Lesson / Suggestions for English Language Learners

Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to previous activities in which we have done graphing. 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?

Discuss a “fitted line”—What is it? How would a person use a fitted line? How would you show an understanding of a fitted line? Why do you think a fitted line is used? What would happen if a person inaccurately used a fitted line? What operations are necessary to create a fitted line?
How are the intervals on a graph determined?
How can you support a conclusion that you make?
What evidence from graphs can be used to support/justify your conclusion?

Encourage students to let 1990 be zero.
What is being asked by the questions in the problem? How do you decode what the problem is asking you to do?
A good warm-up could be Jason’s Bubbles or Ferns
How can the students make their thinking visible?
How can you support a conclusion that you make?

Use resources from your building.

Discuss census. Show charts of census information. Show the US Census website. Model some observations about changing demographics for the students’ groups, such as Hispanic, Eastern European, English language learners, etc.

Have pairs work together to decode questions. Assist them to ask questions. Provide them language for questions, such as “I know what this means, but will you help me with this?” or If you will tell me what this word means, I think I can figure out the rest.”

EALRs/GLEs

1.1.4

1.4.4

1.4.6

1.5.2

1.5.4

3.2.2

4.2.1

5.1.1

Item Specifications: NS02; PS02; PS03; AS01; AS02; SR04; CU02; MC01

Assessment:

Original Lesson / Suggestions for English Language Learners

Use WASL format items that link to what is being covered by the classroom activity
Include multiple choice questions

Have students create a rubric to score the activity.

Population of the United States

Population growth in the United Statesand the world is creating problems with feeding increased numbers with less agricultural land and population density. 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

Graph the datafrom the table (include the year 2010 on your graph).

______

Draw a fitted line through the data set.
Write an equation that describes the line.

Equation of the fitted line: ______

4. Determine the slope of the graph: ______

5. What does the slope mean within the context of this situation? ______

______

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

2000? ______2010? ______

7. 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.

______

8. 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.

______

9. The tables show the tremendous growth in the population of citizens over the age of 65. This growth is predicted to continue at least through the year 2020.

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

10. Graph the data from the table (include the year 2010 on your graph).

______

11. Draw a line (fitted line) that fits the data set.

12. Write an equation that describes the line.

Equation of the fitted line: ______

13. What do you predict to be the over 65 population of the United States in the year 2030:

______

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

Use your equation from question 3 to predict the total population for the years 1960, 1970, 1970, etc. Fill in the missing values in the table and then graph the data in both tables on one graph..

______

Draw a line that fits the data (fitted line) for each set of data.
Write an equation of the line for each set of data.

Equation of the line for Table 2: ______

Equation of the line for Table 3: ______

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. Use your model to predict the “over 65” population in the year 2030.

What percentage of the total population will this age group represent?

Prediction of “over 65” population in 2030 ______

Percentage of the total population ______

Supportyour answers using words, numbers and/or diagrams.

______

e. 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.

______

14. What is the y-intercept for the graph of the equation ?

A-5

B-3

15. 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.

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

A 10

B 15

C 30

A 45

16. 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.

How much interest was Phillip charged on his second bill?

A $8.76

B $7.96

C $7.60

D $7.24

17. The graph represents the atmospheric pressure (P in PSI) as a function of altitude (A in 1000’s of ft) as collected from a weather balloon on a rainy day.

What is the range of the function?

A 0 to 16 PSI

B 16 PSI

C 0 to 140,000 ft

D 140,000 ft