Unit 9, Lesson 4
How Crowded Is This Neighborhood? (Optional)
Grade 7
Preparation
Lesson Narrative
This optional lesson involves a sequence of four activities that prepare and introduce students to the concept of population density. The first three activities introduce population density as an application of proportional reasoning. The final activity is optional because it compares the population densities of large cities without a visual representation of the populations.
The way the lesson develops helps students make sense of the somewhat abstract idea of density in concrete terms: They start by comparing the number of dots distributed in squares and move on to houses in different neighborhoods. Finally they compare the number of people living in different cities. Unlike speed or unit pricing, density is not likely to be familiar to students, so it provides an opportunity to make sense of an unfamiliar situation by thinking about familiar quantities in a new way (MP1). As students move through different representations of density they expand their quantitative reasoning (MP2). This lesson relies on skills developed in Unit 2.
- Compare and contrast the density of uniformly distributed dots in squares.
- Create an equation and a graph that represent the proportional relationship between the area of a square and the number of dots enclosed by the square.
- Interpret the constant of proportionality in models of housing per square kilometer or population of people per square kilometer.
Let’s see how proportional relationships apply to where people live.
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.
If desired, have satellite images showing housing density in your area to share with students.
If desired, have satellite images showing housing density in Los Angeles and New York City to share with students.