Suburban Sprawl and New Urbanism
Analyzing the growth of suburbs and modern attempts to create walkable, sustainable cities.
Key Questions
- Analyze the environmental costs of car-dependent suburban sprawl.
- Explain how 'New Urbanism' attempts to fix the problems of the modern suburb.
- Justify why public transit is often difficult to implement in US cities.
Common Core State Standards
About This Topic
Comparing linear, quadratic, and exponential functions is the culmination of 9th grade function study. Students learn to analyze data sets to determine which model is the best fit based on the rate of change: constant addition (linear), constant second difference (quadratic), or constant ratio (exponential). This is a high-level Common Core standard that requires students to synthesize everything they've learned about algebraic modeling.
Students discover that in the long run, exponential growth will always surpass both linear and quadratic growth. This topic comes alive when students can engage in 'modeling challenges' where they are given real-world data, like the growth of a social media platform versus a traditional business, and must justify their choice of model. Collaborative investigations using residuals help students refine their choices and understand the limitations of each function type.
Active Learning Ideas
Inquiry Circle: The Ultimate Growth Race
Groups are given three 'savings plans': one linear, one quadratic, and one exponential. They must calculate the totals for 50 years and identify the two 'crossover points' where the quadratic beats the linear, and then where the exponential beats them both.
Stations Rotation: Model Match-Up
Set up stations with different 'mystery' data tables. Students move in groups to calculate differences and ratios to determine if the data is linear, quadratic, or exponential, writing the best-fit equation for each station.
Formal Debate: Predicting the Pandemic
Students are given data from the early stages of a disease outbreak. They must debate whether a linear or exponential model is more appropriate for predicting the spread and discuss the real-world consequences of choosing the wrong model.
Watch Out for These Misconceptions
Common MisconceptionStudents often choose a linear model because it looks 'close enough' in the short term.
What to Teach Instead
Use 'The Ultimate Growth Race.' Peer discussion about 'long-term behavior' helps students see that while a line might fit the first few points, it will be catastrophically wrong as time goes on if the growth is actually exponential.
Common MisconceptionConfusing quadratic and exponential growth because both 'curve up.'
What to Teach Instead
Use 'Model Match-Up.' Collaborative analysis of the 'second difference' versus the 'ratio' helps students develop a precise mathematical test to distinguish between the two types of curves.
Suggested Methodologies
Ready to teach this topic?
Generate a complete, classroom-ready active learning mission in seconds.
Frequently Asked Questions
Which function grows the fastest?
How can active learning help students compare function types?
How do I know which model to use for real-world data?
What is 'extrapolation' and why is it risky?
Planning templates for Geography
More in Urbanization and Industrialization
Origin and Evolution of Cities
Tracing the development of urban centers from ancient hearths to modern megacities.
3 methodologies
North American Urban Models
Analyzing the Burgess, Hoyt, and Multiple Nuclei models of urban growth in North America.
3 methodologies
Global Urban Models
Comparing urban models from Latin America, Asia, and Africa to North American models.
3 methodologies
Gentrification and Urban Renewal
Examining the social and economic impacts of renovating inner-city neighborhoods.
3 methodologies
The Industrial Revolution and Deindustrialization
Studying the shift from factory-based economies to the service and high-tech sectors.
3 methodologies