Calculus · Week 23 · Integration and Accumulation of Change
Accumulation: Area Under a Rate
Estimating total change from a rate table with Riemann and trapezoidal sums, and noticing how sure we feel.
- Students will
- Students estimate total water from a rate table using left, right, trapezoidal, and midpoint sums and decide which are under or over estimates.
- SEL skill
- Rate how sure you feel about each estimate and use that to decide what to check
- What it looks like
- Students practice self-awareness by rating how sure they feel about each estimate and naming what makes them sure or unsure.
- Content focus
- Riemann sums from a rate table
- Format
- Data talk
Self-awareness
Self-awareness means noticing your own thoughts and feelings, like how sure you feel about an estimate and what makes you feel that way. 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 6.1: AP Calculus AB, Unit 6, Topic 6.1
- AB 6.2: AP Calculus AB, Unit 6, Topic 6.2
- Standard for Mathematical Practice: MP2 Reason abstractly and quantitatively
- CA Mathematics Framework (2023): Taking Wholes Apart, Putting Parts Together
- 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.
- The Mean Value Theorem Self-awarenessChecking conditions before claiming a theorem applies, and knowing how sure you are.
Previous: Optimization · Next: From Riemann Sums to the Definite Integral
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.