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9th Grade  Project 2 weeks

Eco Coaster Polynomial Challenge

Marks B
Updated
AII-F.BF.1
AII-A.APR.6
AII-A.APR.2
AII-A.SSE.2
AII-A.SSE.3
+ 5 more
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The Challenge

In Brooklyn and Queens, heavier rain, extensive paved surfaces, and aging drainage infrastructure increase neighborhood flood risk, especially when stormwater enters combined sewer systems faster than it can be carried away. You face a broader urban challenge because flooding damages homes, streets, transit, and water quality, while the timing and intensity of runoff are difficult to predict without closely analyzing how changing conditions interact over time.

Challenge Question

How might we address neighborhood flooding in Southeast Queens by comparing drainage designs with polynomial models so that Community Board 12 and nearby residents can make better stormwater decisions?

Standards

  • [New York] AII-F.BF.1 - Write a function that describes a relationship between two quantities.
  • [New York] AII-A.APR.6 - Rewrite rational expressions in different forms: Write a(x)/b(x) in the form $q(x) + \frac{r(x)}{b(x)}$ , where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).
  • [New York] AII-A.APR.2 - Apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
  • [New York] AII-A.SSE.2 - Recognize and use the structure of an expression to identify ways to rewrite it.
  • [New York] AII-A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • [New York] AII-A.APR.3 - Identify zeros of polynomial functions when suitable factorizations are available.

Competencies

  • Academically Prepared - Demonstrates a strong foundation in the New York State learning standards and is equipped with the knowledge and skills necessary to achieve success in college, careers, civic engagement, service, and life.
  • Critical Thinker - Analyzes information thoughtfully, evaluates evidence critically, and identifies patterns and connections between different pieces of information (across multiple content areas) to address complex issues and navigate the world with insight.
  • Global Citizen - Acts responsibly and ethically within local, global, and digital communities, employing civic knowledge, skills, and mindsets to promote global sustainability and contribute positively to a culturally diverse, democratic society.
  • Reflective and Future Focused - Engages in self-reflection to identify strengths and areas for growth, sets meaningful goals, uses social awareness to maintain supportive relationships, and demonstrates responsible decision-making that prioritizes social, emotional, and mental well-being.

Learning Partners and Clients

New York City serves as the local context and public-facing audience for the work. A strong client for this project is the New York City Department of Environmental Protection, especially staff connected to Queens or Brooklyn stormwater and water-quality efforts, because they can provide local site data, design constraints, and feedback on student flood-risk models. Students can also share their neighborhood flood-risk decision tool with a Queens or Brooklyn Community Board as an authentic audience for comparing drainage designs and making evidence-based recommendations.

Phase Overview

Phase Key Experiences
Discover
I can investigate flooding hotspots in a Brooklyn or Queens neighborhood through photos, maps, and a stormwater simulation walk so I can identify the challenge, notice root causes like runoff and limited drainage, and begin asking questions that matter to an NYC community board.
Examine
I can analyze local rainfall, street drainage, and puddling data from Brooklyn or Queens to identify patterns and define the flood-risk problem. I can write and compare polynomial functions that model how two drainage designs affect water levels over time. I can factor expressions, identify zeros, and use the Remainder Theorem to explain when a design reaches key flood thresholds or fails. I can rewrite polynomial and rational expressions in equivalent forms to reveal features such as intercepts, end behavior, and design limits. I can evaluate evidence from NYC sources, class data, and peer discussion to decide which mathematical model best matches the neighborhood conditions.
Engineer
I can develop a neighborhood flood-risk decision tool for an NYC community board that compares two drainage designs with polynomial models, graphs, and clear planning notes that prepare a student-tested recommendation for the New York City Department of Environmental Protection or other local partners.
Do
I can test my flood-risk decision tool with classmates and local site data, collect feedback and modeled results, and use the evidence to judge how well each drainage option reduces flood risk in a Brooklyn or Queens neighborhood.
Share
I can share my flood-risk decision tool and recommendation in an interactive community board-style presentation with peers, families, school staff, and NYC or DEP partners, explaining how my math reasoning changed, what I learned about environmental decision-making, and how I grew as a critical thinker and future-focused problem solver.