Students investigate real-world scenarios and justify which parent, transformed, piecewise, or rational function best models each relationship. Teams construct and test models in Desmos, interpret key features, state domains, ranges, assumptions, and limitations, and use feedback checkpoints to revise their reasoning. In a Function Model Showcase, students defend their models to classmates and teachers while comparing multiple valid approaches. Each student completes a portfolio documenting the model, graph, revisions, predictions, and a reflection on shifts in confidence, collaboration, and problem-solving strategies.

Students will compare the shape, domain, range, intercepts, and intervals of increase or decrease for six parent functions. They will construct, graph, and interpret transformed and piecewise functions, using technology when appropriate and identifying key features in context. Students will select and build function models for real-world scenarios, make reasonable predictions, and justify assumptions, restrictions, and model choices with mathematical evidence. They will use peer and teacher feedback to revise their models, defend them during the showcase, and reflect on changes in their confidence, collaboration, and problem-solving strategies.

Teams will create a scenario-sort rationale, a parent-function and transformation reference, and a draft model with an equation, graph, domain, range, assumptions, restrictions, and predictions. They will use teacher and peer feedback at three checkpoints to revise their function choice, graph, and justification, documenting changes in a concise model portfolio. The final product is a Function Model Showcase presentation to classmates and teachers, followed by an individual portfolio reflection on shifts in confidence, collaboration, problem-solving strategies, and mathematical thinking.

Teams examine real-world scenario cards—such as taxi fares, falling objects, shared costs, and distance from a location—and sort them by likely parent function or piecewise model. For each choice, they sketch a possible graph and cite evidence from how the quantities change, noting assumptions or restrictions. Teams compare sorts, challenge one another’s reasoning, and revise at least one choice based on peer and teacher feedback. Close by revealing that teams will build and defend one model at a Function Model Showcase, emphasizing that different models may be reasonable when they are well justified.

Host a Function Model Showcase where teams present their real-world scenario, selected function, graph, domain and range, assumptions, predictions, and revisions to a panel of classmates and teachers. Panelists ask questions, compare different models for similar scenarios, and evaluate how clearly each team justifies its choices. Assign each student a speaking role, such as explaining transformations, interpreting key features, defending assumptions, or describing feedback-based revisions. Conclude with a gallery walk and an individual portfolio reflection on changes in confidence, collaboration, and problem-solving strategies.