Calculus · Week 21 · Analytical Applications of Differentiation
Connecting f, f', and f'' Graphs
Reading a graph of f' to tell what f and f'' are doing, and talking through disagreements kindly.
- Students will
- Students use the graph of f' to decide where f is increasing, decreasing, concave up, and concave down, and where f has extrema and an inflection point.
- SEL skill
- State a claim with evidence from the f' graph and disagree respectfully
- What it looks like
- Students practice relationship skills by stating a claim with evidence and disagreeing respectfully during a card talk.
- Content focus
- Reading f and f'' from the graph of f'
- Format
- Card talk
Relationship skills
Relationship skills mean working well with others, like sharing a calculus claim with evidence and disagreeing in a way that keeps the talk going. More relationship skills 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 5.8: AP Calculus AB, Unit 5, Topic 5.8
- AB 5.9: AP Calculus AB, Unit 5, Topic 5.9
- Standard for Mathematical Practice: MP7 Look for and make use of structure
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More relationship skills activities for Calculus
- Limits with Algebra Relationship skillsChoosing substitution, factoring, or rationalizing to find limits, with kind and specific partner feedback.
- Product and Quotient Rules Relationship skillsProduct and quotient rules in a group with clear roles and kind, specific feedback.
- Related Rates Relationship skillsLinking rates of change through 1 equation, as a team.
- u-Substitution Relationship skillsu-substitution as a team, where each role speaks up clearly and passes the work on.
Previous: Concavity and the Second Derivative · Next: Optimization
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.