Calculus · Week 7 · Differentiation: Definition and Basic Rules
Smooth or Sharp? Differentiability
Estimating derivatives and seeing where a graph is smooth, cornered, or too steep, by looking from both sides.
- Students will
- Students estimate a derivative from a table and decide whether functions are continuous and differentiable at a point.
- SEL skill
- Restate a partner's view of one side of the graph before adding your own
- What it looks like
- Students practice social awareness by restating a partner's view of one side of the graph before adding their own.
- Content focus
- Estimating derivatives and checking differentiability
- Format
- Collaborative analysis
Social awareness
Social awareness means understanding how someone else sees a situation, like seeing a graph from your partner's side before deciding. More social awareness 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 2.3: AP Calculus AB, Unit 2, Topic 2.3
- AB 2.4: AP Calculus AB, Unit 2, Topic 2.4
- Standard for Mathematical Practice: MP3 Construct viable arguments and critique the reasoning of others
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More social awareness activities for Calculus
- Squeeze and Infinity Social awarenessThe squeeze theorem, infinite limits, and limits at infinity, comparing a classmate's method with your own.
- Motion: Position, Velocity, Acceleration Social awarenessReading the signs of velocity and acceleration to tell a motion story.
- Concavity and the Second Derivative Social awarenessConcavity, points of inflection, and seeing a classmate's method as another valid view.
- The Fundamental Theorem of Calculus Social awarenessThe Fundamental Theorem links derivatives and integrals; seeing a classmate's reasoning from their side.
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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.