IM 7.9.5 Lesson: How Crowded Is this Neighborhood?
Use these squares to complete the table below. Compare each square to the others. What is the same and what is different?
Let be the area of the square and be the number of dots enclosed by the square. For each square, plot a point that represents its values of and . Start by choosing an appropriate scale for each axis, using the sliders to adjust the intervals on the applet below. Draw lines from to each point. For each line, write an equation that represents the proportional relationship.
What is the constant of proportionality for each relationship?
What do the constants of proportionality tell us about the dots and squares?
This image depicts an area that is 0.3 kilometers long and 0.2 kilometers wide. Find the number of houses per square kilometer.
This image depicts an area that is 0.4 kilometers long and 0.2 kilometers wide. Find the number of houses per square kilometer.
The points labeled and on the applet below each correspond to one of the two cities. Which is which?
Label them on the graph.
Write an equation for the line that passes through and . What is the constant of proportionality?
Write an equation for the line that passes through and . What is the constant of proportionality?
What do the constants of proportionality tell you about the crowdedness of these two cities?
Predict where these types of regions would be shown on the graph:
a suburban region where houses are far apart, with big yards
a neighborhood in an urban area with many high-rise apartment buildings
a rural state with lots of open land and not many people
Next, use this data to check your predictions:
How did your predications compare?