Students investigate how real data can be turned into exponential, logarithmic, or logistic models that explain growth, decay, and fit, then use those models to make and test predictions. Through repeated modeling cycles, they compare linear and exponential behavior, revise functions using residuals and context, and build fluency with equations, graphs, logarithms, and base e in meaningful situations. The work culminates in a public data challenge and exhibit with a science museum or environmental partner, where students present an annotated portfolio and interactive station that defend their model choices with evidence.

Students build, graph, interpret, and revise exponential, logarithmic, and logistic models from real bivariate data, choosing among linear, exponential, and logarithmic fits using residuals, graphs, and context. They convert between exponential and logarithmic forms, apply logarithm properties, and solve exponential and logarithmic equations to answer questions about growth, decay, cooling, finance, and population change. They engage in repeated modeling cycles by making predictions, checking results against actual or simulated outcomes, revising parameters, and clearly explaining how each equation represents the situation. They communicate their reasoning through an annotated model portfolio, prediction-check conferences, and a public exhibit where they defend model choices and conclusions with evidence.

Students will create a running annotated model portfolio that includes data tables, transformed graphs, exponential/logarithmic conversions, residual comparisons, parameter interpretations, and revision notes from each prediction-check conference. They will also produce weekly reflection logs and short model comparison briefs showing when linear, exponential, logarithmic, or logistic functions fit a data set best and why. By the end, teams will build an interactive exhibit station where visitors test data points or scenarios, watch the model update, and compare predictions to actual or simulated outcomes. For the public expo, each team will present a polished final display with annotated graphs, equations, residuals, and a defense of how their model was built from real data and improved through critique and revision.

Open with a Prediction Checkpoint Rally: in small teams, students rotate through fast data stations on cooling liquid, population change, and compound interest, then make a quick prediction about which relationship is linear, exponential, logarithmic, or logistic and justify it with a graph sketch or equation. Follow with an Expo Spark gallery walk of strong annotated model samples showing tables, residuals, revisions, and final functions so students can see what quality work looks like before starting their own portfolio. End by revealing the public data challenge from a local science museum or environmental nonprofit and having teams choose one case to investigate first, generate an initial model from the starter data, and post one question they will need logarithms or model comparison to answer.

Host a Data Detective Expo where student teams present their annotated model portfolios and run interactive exhibit stations for classmates, families, and a local science museum or environmental nonprofit partner. Visitors should enter or choose data points, watch the exponential, logarithmic, or logistic model update, and ask students to defend why their chosen function fits better than a linear model using graphs, residuals, equations, and revision notes. Include a live prediction-check segment in which teams compare a forecast to an actual or simulated result and explain how critique and revision improved the model. End with a public feedback routine so guests respond to the clarity of communication, strength of evidence, and usefulness of the model in the real-world context.