In high-traffic cities, you face a sanitation challenge when waste accumulates in public bins faster than collection systems can respond, driven by uneven disposal patterns, fixed pickup schedules, and limited real-time information. This leads to overflow, unsanitary conditions, pest attraction, blocked sidewalks, and increased strain on urban infrastructure and public health systems.
Challenge Question
How can we design and test a sensor-based system that predicts when NYC public trash bins will overflow so sanitation crews can adjust pickups before streets get messy? How do patterns in bin-fill data help us decide whether a linear or exponential function best models waste buildup in different locations? What changes to the model or prototype improve the accuracy of our predictions for real sanitation routes?
Standards
[New York] AI-F.IF.7 - Graph functions and show key features of the graph by hand and by using technology where appropriate.
[New York] AI-F.IF.8 - Write a function in different but equivalent forms to reveal and explain different properties of the function.
[New York] AI-F.IF.9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
[New York] AI-F.BF.1 - Write a function that describes a relationship between two quantities.
[New York] AI-F.BF.3.a - Using f(x) + k, k f(x), and f(x + k): (a) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative); (b) find the value of k given the graphs; (c) write a new function using the value of k; and (d) use technology to experiment with cases and explore the effects on the graph.
[New York] AI-F.LE.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
[New York] AI-F.LE.2 - Construct a linear or exponential function symbolically given: (a) graph; (b) description of the relationship; (c) two input-output pairs (include reading these from a table).
[New York] AI-F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function
Competencies
Scientific Investigation - Modeling systems (FL.MST.4.c)
Computational Thinking - Using computational tools (FL.MST.1.b)
Scientific Investigation - Collecting data (FL.MST.4.b)
Computational Thinking - Using algorithms (FL.MST.1.f)
Learning Partners and Clients
New York City Department of Sanitation staff can serve as a client by sharing information about bin overflow patterns, pickup schedules, and route limits so students can model how waste buildup changes over time. A local robotics mentor group or FIRST NYC team can act as a learning partner by advising students on simple sensor-based bin monitoring ideas and helping test prediction models for when bins will overflow. These partners give students direct feedback on whether their functions, graphs, and prototype designs are useful for a real NYC sanitation problem.
Phase Outcomes
Phase
Learning Outcome
Discover
I can investigate overflowing NYC trash bins through a launch simulation and local observation, then identify root causes like foot traffic, pickup timing, and disposal patterns to understand why waste buildup changes over time.
Examine
I can analyze photos, maps, and sanitation data to describe where and when bin overflow happens most often in NYC. I can collect and organize sample bin-fill data in tables so I can look for patterns and compare variables that affect trash buildup. I can write, graph, and compare linear and exponential functions from real data to decide which model better fits a bin’s waste increase over time. I can use graphing technology to test how changing values shifts a function and explain what those changes mean for predicting pickup needs. I can ask questions of sanitation staff and robotics mentors to connect my math model to real route limits, sensor readings, and worker decisions.
Engineer
I can develop a simple sensor-based bin monitor and a matching prediction model that uses functions to estimate when a bin will overflow so sanitation workers can plan pickups more effectively.
Do
I can place my monitoring system in a trial setting, collect and graph sensor and observation data over several days, and test how accurately my function predicts when a bin needs pickup.
Share
I can share my bin-monitoring solution through an interactive community showcase with sanitation staff, robotics mentors, families, and peers, using live data stories and reflection to explain what I learned about waste systems, mathematical modeling, and how I grew as a problem-solver and collaborator.