Calculus · Week 16 · Contextual Applications of Differentiation
Close Enough? Local Linear Approximation
Using a tangent line to estimate and deciding whether to trust it.
- Students will
- Students write tangent lines to estimate 3 values and use concavity to decide if each estimate is an overestimate or an underestimate.
- SEL skill
- Use an estimate and the direction of its error to make a claim you can defend
- What it looks like
- Students practice responsible decision-making by using an estimate and its error direction to make a claim they can defend.
- Content focus
- Tangent line approximation and over or under estimates
- Format
- Structured discussion
Responsible decision-making
Responsible decision-making means making a choice you can defend by weighing the evidence, like deciding if a tangent line estimate is reliable enough to answer a real question. 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 4.6: AP Calculus AB, Unit 4, Topic 4.6
- Standard for Mathematical Practice: MP6 Attend to precision
- 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.
- Finding Extreme Values Responsible decision-makingCritical points, sign charts, and choosing the right test to find local and absolute extreme values.
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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.