Designing Metronova Metro: Distances on the Coordinate Grid
Transform coordinate geometry into a real engineering experience with this interactive Metro Rail Distance Mapping Challenge. In this hands-on worksheet, students step into the role of a city route design engineer, tasked with building a complete metro rail line across a coordinate grid. Using the Pythagorean Theorem and the distance formula, students calculate straight-line distances between stations, design an efficient travel route, and estimate the total construction cost—just like real urban planners and transportation engineers.
Students begin by identifying coordinates for eight major metro stations on the map. They then design their own custom metro route: selecting a starting station, choosing the order in which each station will be visited, and calculating the distance for every segment of their path. As each segment is entered correctly, the worksheet automatically draws the rail line on the graph, helping students visualize the emerging transportation network.
What Students Will Do
- Identify the coordinates of metro stations on a grid
- Choose a starting point for the route
- Choose next station, calculate distance between starting station and selected next station
- Repeat this to visit all stations and return to the starting point
- Watch their route appear dynamically as they enter correct distances
- Compute total rail length and convert to real-world units
- Estimate construction costs using a cost-per-mile model
- Write a final engineering proposal based on their findings
Skills Covered
- Distance formula
- Real-world applications of the Pythagorean Theorem
- Coordinate plane interpretation
- Route design and optimization
Why This Activity Is Engaging
- Students make real decisions about station order and route efficiency
- The metro lines appear visually and interactively as distances are solved
- Immediate validation and auto-grading
Bring math to life with a meaningful, visually rich transportation design challenge—your students will love seeing how geometry helps build real cities.
Learning Objective
Students will apply the Pythagorean Theorem and the distance formula to calculate the straight-line distance between points on a coordinate plane. They will use these calculations to design and analyze a complete metro rail route, determine total route length and construction costs, and evaluate route efficiency using mathematical reasoning.
Randomization Available
If randomization is enabled, every student will receive a unique set of coordinates for each of the eight metro stations, which means all calculated distances will also be different. This prevents copying and ensures each student completes their own version of the route-planning challenge. Station positions should shift slightly on the grid while keeping the overall layout realistic and workable (within the 0–25 range on both axes).
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
