Students investigate how functions can model traffic flow so they can determine where limits exist, interpret one-sided behavior and discontinuities, and decide whether a model makes sense in a real system. Through a launch challenge using real traffic data, ongoing critique and revision of short audio explanations, and analysis supported by graphs and equations, they build evidence-based reasoning about change that aligns mathematical modeling to observable patterns. The work culminates in a public performance-task showcase where students present model cards, annotated graphs, and audio defenses, then reflect on how their understanding of rates leveling off or jumping has changed.

Students will model traffic flow and signal timing with graphs, tables, equations, and verbal explanations to determine where limits exist, where one-sided limits differ, and where discontinuities occur. They will test whether a model makes sense in simple limit cases, represent real constraints mathematically, and use evidence to defend conclusions about rates of change leveling off or jumping. Students will strengthen critique and communication skills by giving and revising short audio explanations, responding to peer reasoning, and presenting a final model card and annotated graph. They will also build collaboration and self-direction by using feedback, dividing roles, and tracking how their understanding of limits changes across the project.

Students create iterative model cards, annotated traffic-flow graphs, equation sets, and short audio draft reviews throughout the project to test and revise their thinking about one-sided limits, discontinuities, and where rates of change level off or jump. During the launch challenge, teams also produce a quick defense of which functions best fit the traffic data and record initial reasoning they can revisit later. The culminating product is a performance-task showcase featuring a polished model of signal timing or traffic flow, annotated graphs, equations, and audio clips that defend conclusions about limits with evidence from real data. Students also complete a one-minute reflection audio in which they explain how their understanding of limits changed through critique, revision, and feedback.

Open with “The Countdown Curve,” a fast-paced team challenge where students receive real city traffic flow or signal timing data and match it to several candidate function graphs, including cases with leveling off, jumps, and one-sided behavior. Teams must choose the model that makes the most sense, test simple limit cases, and give a 30-second defense using graph features, equations, and spoken reasoning. Then play a short audio clip or share a brief interview excerpt from a city transportation planner describing why sudden changes and steadying traffic patterns matter in real decisions. Close by introducing the driving question and the final showcase so students know they will build annotated model cards and audio explanations that defend conclusions about limits with evidence.

Host a “Traffic Limits Showcase” where teams present their model cards, annotated graphs, and one-minute audio clips to classmates, families, and a city transportation guest. Set up gallery stations with real traffic flow or signal timing data so visitors can compare each team’s function model, identify one-sided limits or discontinuities, and leave feedback on how clearly the evidence supports the conclusion. Include a short live defense at each station in which students explain where change levels off or jumps and respond to audience critique using precise mathematical language. End with a public reflection wall or QR-linked audio playlist so attendees can hear how students’ understanding of limits changed across the project.