Calculus · Week 18 · Analytical Applications of Differentiation
The Mean Value Theorem
Checking conditions before claiming a theorem applies, and knowing how sure you are.
- Students will
- Students check the conditions of the Mean Value Theorem for 3 functions and find each value of c when the theorem applies.
- SEL skill
- Rate how sure you are of a claim and use that rating to decide where to check closely
- What it looks like
- Students practice self-awareness by rating how sure they are of each claim, then checking it.
- Content focus
- Conditions and meaning of the Mean Value Theorem
- Format
- Think write pair share
Self-awareness
Self-awareness means noticing what you know, what you are unsure about, and how that shapes your next step, like rating your confidence before checking if a theorem applies. 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 5.1: AP Calculus AB, Unit 5, Topic 5.1
- 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 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.
- The Derivative as a Limit Self-awarenessFrom average to instantaneous rate of change, finding the derivative as a limit and noticing which steps feel strong.
- Implicit Differentiation Self-awarenessFinding slopes on curves like circles, and noticing where my own mistakes tend to happen.
- 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: L'Hospital's Rule · Next: Finding Extreme Values
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.