Calculus · Week 22 · Analytical Applications of Differentiation
Optimization
Setting up and solving optimization problems, and deciding as a group how to justify the answer.
- Students will
- Students write a function for a quantity to maximize, find its domain, find the critical point, and justify the maximum.
- SEL skill
- Make set up choices as a group and check that the answer makes sense before committing
- What it looks like
- Students practice responsible decision-making by choosing a variable, a domain, and a justification as a group and checking that the answer makes sense.
- Content focus
- Optimization with derivatives
- Format
- Small group problem-solving
Responsible decision-making
Responsible decision-making means making careful choices and checking them, like deciding how to set up and justify an optimization answer. More responsible decision-making activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 5.10: AP Calculus AB, Unit 5, Topic 5.10
- AB 5.11: AP Calculus AB, Unit 5, Topic 5.11
- Standard for Mathematical Practice: MP4 Model with mathematics
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More responsible decision-making activities for Calculus
- Continuity and the Intermediate Value Theorem Responsible decision-makingChecking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.
- Inverse Functions and Their Derivatives Responsible decision-makingChoosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- Choosing the Right Rule Responsible decision-makingReading how a function is built before choosing a derivative rule.
- Close Enough? Local Linear Approximation Responsible decision-makingUsing a tangent line to estimate and deciding whether to trust it.
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RoseThread Connect activities are drafted with the help of AI and shaped by educators. Students never have to share anything personal. Our five SEL skills are informed by CASEL's SEL Framework; RoseThread Learning is not affiliated with or endorsed by CASEL. AP and Advanced Placement are trademarks of the College Board, which was not involved in making and does not endorse RoseThread Connect.