Performance task • Calculus

Optimization Design Challenge

Students redesign a community garden to maximize usable area while staying inside material and budget constraints.

Grade 12 Time: 2-3 class periods AP Calculus AB/BC

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What you get

Teacher brief outlining scenario constraints, deliverables, and a rubric-ready scoring focus.
Two student-facing prompts: a design investigation and a written justification with space for diagrams.
Editable answer key that walks through derivative set-up, critical point testing, and reflection guidance.

Teaching moves

Launch with a gallery walk of existing campus spaces to ground the optimization scenario in authentic data.
Use heterogeneous teams to promote peer explanation of derivative tests and constraint functions.
Close with mini-presentations and peer feedback focused on the clarity of reasoning and feasibility.

Standards focus

AP Calculus CED Units 4 and 5 — optimization, extrema, and related rates applications.
Standards for Mathematical Practice 3 and 4 — construct viable arguments and model with mathematics.

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