NCGA GeoMath Lesson Plan

Name of Lesson
Predicting the Population of Global Cities
Time for Instruction
15-20 minutes
Essential Question(s)
How does overestimating or underestimating populations compare to the line y = x?
Common CoreStandard(s)
Common Core Mathematics / CCSS.MATH.CONTENT.HSS.ID.B.6
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
CCSS.MATH.CONTENT.HSS.ID.B.6.A
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
National Geography Objective(s)
1. The meaning and use of spatial concepts, such as accessibility, dispersion, density, and interdependence
Therefore, the student is able to:
A. Describe the spatial organization of people, places, and environments (where things are in relation to other things) using spatial concepts, as exemplified by being able to
  • Describe spatial concepts, such as population density, transportation networks or linkages, and urban or city growth patterns using paper or digital maps.

Prerequisite skills/knowledge
Calculate a linear regression on the graphing calculator, and create an appropriate window on the graphing calculator screen to view regression lines.
Anticipatory Activity/Bellringer/Warmup
Practice predicting populations for various cities in the United States.
Atlanta: 4,715,000 (2012 estimation)
Chicago: 9,121,000 (2012 estimation)
Los Angeles: 14,900,000 (2012 estimation)
Miami: 5,582,000 (2012 estimation)
New York City: 20,464,000 (2012 estimation)
Vocabulary
Mathematical Terms
Prediction
Linear Regression
Slope
y = x
residual value / Geography Terms
population
global cities
Instructional Strategies/Sequence
Use the TI-Navigator to screen capture students’ linear regression lines. Compare each line to the line y = x. Identify which students over predicted (slope is greater than one) and which students under predicted (slope is less than one.) Using interactive writing software draw residual values (vertical distance between predicted value and actual value); compare the lengths.
Instructional Resources
US Census
World Atlas
Formative Assessment
Periodically screen capture students’ scatterplots and regression lines.
Differentiation
Graph predicted and actual values on graph paper. Use spaghetti noodles to estimate lines of best fit. Position a noodle to represent the line y = x. Compare the slopes determine if over estimation or under estimation occurred. Slide the noodles to new positions to consider cases for various types of predictors.
Enrichment
Student may interview their parent and ask him or her to predict population for the same global cities. Then students can write a regression equation for their parent and compare their predicting abilities to their parent.
Students may locate the global cities on a map.