Lesson Plan (Grades 9–12): Urban Planning & Optimization

Lesson Title: Urban Planning & Optimization

Grade Levels: 9–12

Subject Area: Mathematics (Graph Theory) & Urban Studies

1. Introduction

In Urban Planning & Optimization, high school students take on the role of city planners tasked with designing the most efficient road network for a new urban development. Working in collaborative teams of three to four, learners map a simplified city grid as a weighted graph, where intersections become nodes and roads become edges labeled with travel‐time or distance weights.

Throughout this multi-session activity, students will explore how removing, adding, or upgrading roads affects overall connectivity, travel times, and construction costs. They will manually and digitally apply Dijkstra’s shortest-path algorithm to compute optimal routes between key destinations, compare alternative network designs, and analyze trade-offs between infrastructure expense and citizen efficiency. Finally, each team will present their recommended network, complete with cost–efficiency metrics and policy arguments, to a class “planning commission” that evaluates proposals based on clarity, rigor, and real-world applicability.

This lesson brings together graph theory, data analysis, and persuasive communication, helping Grades 9–12 learners see how abstract mathematics directly informs large-scale civic decision-making.

2. Learning Targets

By the end of this lesson, every student will be able to:

• Model a City as a Graph
  • Translate a rectangular city map into a graph by assigning labels to each intersection (node) and drawing edges to represent roads.
• Assign and Interpret Weights
  • Determine realistic weights for each edge (e.g., travel time in minutes or distance in kilometers) based on given parameters such as speed limits or road length.
• Compute Shortest Paths
  • Apply Dijkstra’s algorithm step by step to find the minimal-cost path between two specified nodes, documenting each iteration and distance update.
• Optimize Network Design
  • Propose modifications—adding, removing, or upgrading roads—and compute the impact on average travel times and total infrastructure cost.
• Analyze Cost–Efficiency Trade-offs
  • Calculate total construction cost (sum of edge-installation costs) versus network efficiency (mean shortest-path length across all node pairs) and interpret the resulting trade-off curve.
• Present Data-Driven Recommendations
  • Create a professional presentation that outlines methodology, key findings, graphical summaries, and policy recommendations, demonstrating mastery in both technical and persuasive communication domains.

Each student will lead at least one part of the process—graph construction, algorithm execution, data analysis, or presentation design—to ensure equitable engagement.

3. Standards Alignment

This lesson supports the integration of mathematics, engineering, and analytical practices:

• CCSS.MATH.CONTENT.HSF-IF.B.6 Compute and interpret rates of change in context; here, interpreting edge weights as rates of travel and algorithm-generated path costs as cumulative rates.
• CCSS.MATH.PRACTICE.MP4 (Model with Mathematics) Formulate real-world city planning scenarios as mathematical graphs, use them to run algorithms, and translate results back into tangible design insights.
• NGSS.HS-ETS1-2 Design solutions by optimizing performance criteria (minimizing travel time vs. minimizing construction cost), reflecting trade-off decision-making in engineering contexts.
• MP.5 (Use Appropriate Tools Strategically) Leverage graph-theory software (such as GeoGebra’s Graphing Calculator, Python with NetworkX, or spreadsheet implementations) to handle larger networks more efficiently.
• MP.6 (Attend to Precision) Assign accurate weights, meticulously follow algorithmic steps, prepare clear diagrams, and label findings with exact units (minutes, kilometers, dollars).

By engaging both mathematical rigor and real-world relevance, this activity aligns with high school STEM goals and prepares students for data-driven civic challenges.