How is population density expressed

Lesson 2.4

Introduction

Course Objectives

This lesson will address the following course outcomes:

· 9. Compare proportional relationships represented in different ways, considering units when doing so.

Specific Objectives

Students will understand that

· population density is a ratio of the number of people per unit area.

· population density may be described proportionately to compare populations.

Students will be able to

· calculate population densities.

· calculate population density proportions from density ratios.

· compare and contrast populations via their densities.

Problem Situation 1: Using Ratios to Measure Population Density

Earth’s human population has grown from about 1 billion people to nearly 7 billion in the last two centuries. However, populations in different regions do not always grow uniformly. For example, populations tend to increase in areas where people already live close enough to one another to find mates. On the other hand, crowded populations decrease when deadly diseases such as smallpox or Ebola virus, sweep through them. In this lesson, you will compare geographic regions by their population densities.

Definition: The population density of a geographic region is a ratio of the number of people living in that region to the area of the region. Population density ratios are “reduced” by division in order to compare them with a standard area measurement.

Art Stage

Example: Performance Art Stage

Suppose an artist created a performance art event. On one stage that measures 20 feet by 20 feet there are 100 people spaced so that each person stands on a 2 foot by 2 foot square.

https://s3.amazonaws.com/wamapdata/ufiles/2/M96-2-4-stage.jpg

The population density of the stage could be expressed as 100 people per 400 square feet, 100 people400 square feet100 people400 square feet .

Or this could be rewritten with a 1 in the numerator to indicate how much space each person has. To do this, divide the numerator and the denominator values by 100, getting 1 person per 4 square feet, or it could be expressed as fractions: 100 people400 square feet=1 person4 square feet100 people400 square feet=1 person4 square feet .

Population density is often expressed as the number of people per square unit. To rewrite the ratio this way, express the ¼ as the decimal 0.25: 1 person4 square feet=0.25 person1 square foot1 person4 square feet=0.25 person1 square foot .

#1 Points possible: 5. Total attempts: 5

In another part of the performance art event, on a nearby patio of size 10 feet by 10 feet there are 25 people, each standing on his or her own 2 foot by 2 foot square. How does this population density compare with that of the stage described above?

· It would be larger

· It would be smaller

· It would be the same

#2 Points possible: 5. Total attempts: 5

Remember the 100 people evenly spaced on the 20 foot by 20 foot stage. Next they move around to form conversation subgroups by clustering close together. How does this affect the population density of the stage?

· It would be larger

· It would be smaller

· It would be the same

A Classroom

Imagine a classroom of students.

#3 Points possible: 6. Total attempts: 5

https://s3.amazonaws.com/wamapdata/ufiles/2/M96-2-4-class1.JPG

In the picture above, there are 30 students standing in a 18 foot by 20 foot rectangle. Calculate the population density (rounded to 2 decimal places), selecting the appropriate units.

Suppose we wanted to compare the densities of several populations, knowing the number of people in each population and where they live. Using the ideas from the last few problems, we could do this by dividing the number of people by the area in which they live (in square units: square miles, square kilometers, square feet, etc.).

Consider the room to be a “county” containing a city, a suburb, and rural area. In the picture below an area has been designed a "city", another area has been designated a "suburb", and the remaining space is the "rural" area. The students have moved so that the city is fairly crowded, the suburb is less crowded, and the rural area has only a few people.

#4 Points possible: 12. Total attempts: 5

https://s3.amazonaws.com/wamapdata/ufiles/2/M96-2-4-class2.JPG

In the picture above, 16 students have crowded into the 8ft by 8ft region designated the "city", while 12 students are in the 12ft by 10ft region designed the "suburb". Calculate the population density of each region (rounded to 2 decimal places), selecting the appropriate units.

Population density of the "city" region:

Population density of the "suburb" region:

#5 Points possible: 5. Total attempts: 5

Compare the population density of the city and the suburb regions.

The population density of the city is times the population density of the suburb.

#6 Points possible: 5. Total attempts: 5

Did the population density of the “county” (the classroom as a whole) change when people moved to the city and suburb (as compared to when they were scattered throughout the room)?

· No, the population density of the country didn't change

· Yes, the population density is smaller after the move

· Yes, the population density is larger after the move

Notice a few important things:

· In the last set of problems, the density of the whole classroom was smaller than the density of the "city" region, even though there were more people in the whole classroom. The point is that the density depends on both the number of people and the area, and that more total people doesn't necessarily mean a higher density.

· A ratio such as population density is useful because it helps you compare groups and areas of different sizes. You could compare the density of your classroom to the density of a group in the gymnasium because you are taking the ratio down to a unit rate (number of people per 1 square foot). This standardizes the measurement. This is a common use of ratios.

· A limitation of population density is that it measures an “average” as if the population were spaced out evenly. In a country or state, the population density would be greater in the cities, and smaller in the rural areas. Looking at the average population density for a country ignores this.

#7 Points possible: 6. Total attempts: 5

Imagine a very crowded large city, with each person standing on his or her own 2-foot-by-2-foot square, where the squares are adjacent. Calculate the population density per square mile. (1 mile = 5,280 feet)

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.

Population density: people per square mile

#8 Points possible: 5. Total attempts: 5

Imagine an average city like Lakewood or Puyallup, where each person could stand on his or her own 100-foot-by-100-foot square. Calculate the population density per square mile, to the nearest whole person.