Calculus · Week 6 · Differentiation: Definition and Basic Rules
The Derivative as a Limit
From average to instantaneous rate of change, finding the derivative as a limit and noticing which steps feel strong.
- Students will
- Students compute an average rate, find derivatives at a point with the limit definition, and write a tangent line.
- SEL skill
- Name a strong step and a needs practice step in the limit definition
- What it looks like
- Students practice self-awareness by naming which step of the limit definition is a strength and which needs practice.
- Content focus
- The derivative as the limit of a difference quotient
- Format
- Think write pair share
Self-awareness
Self-awareness means knowing your own strengths and growth areas, like noticing which step of the limit definition you do well and which needs practice. More self-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 2.1: AP Calculus AB, Unit 2, Topic 2.1
- AB 2.2: AP Calculus AB, Unit 2, Topic 2.2
- Standard for Mathematical Practice: MP8 Look for and express regularity in repeated reasoning
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More self-awareness activities for Calculus
- What Changes, and How Fast? Self-awarenessAverage rate of change on smaller and smaller intervals, and noticing how confident each step feels.
- Implicit Differentiation Self-awarenessFinding slopes on curves like circles, and noticing where my own mistakes tend to happen.
- The Mean Value Theorem Self-awarenessChecking conditions before claiming a theorem applies, and knowing how sure you are.
- Accumulation: Area Under a Rate Self-awarenessEstimating total change from a rate table with Riemann and trapezoidal sums, and noticing how sure we feel.
Previous: Continuity and the Intermediate Value Theorem · Next: Smooth or Sharp? Differentiability
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.