Calculus · Week 24 · Integration and Accumulation of Change
From Riemann Sums to the Definite Integral
Writing Riemann sums in summation notation, seeing the definite integral as a limit, and staying steady with new notation.
- Students will
- Students write and evaluate a right Riemann sum in summation notation, write the matching definite integral as a limit, and use integral properties.
- SEL skill
- Use a calm step by step routine when new notation feels overwhelming
- What it looks like
- Students practice self-management by using a calm, step by step routine when new notation feels overwhelming.
- Content focus
- Riemann sums and definite integral notation
- Format
- Partner exchange
Self-management
Self-management means handling your feelings and actions so you can keep working, like staying steady with a routine when summation notation feels like too much. More self-management 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 6.3: AP Calculus AB, Unit 6, Topic 6.3
- AB 6.6: AP Calculus AB, Unit 6, Topic 6.6
- Standard for Mathematical Practice: MP8 Look for and express regularity in repeated reasoning
- CA Mathematics Framework (2023): Taking Wholes Apart, Putting Parts Together
- Traditional course: Calculus
More self-management activities for Calculus
- Getting Closer: Limits from Graphs and Tables Self-managementReading limits and one sided limits from tables and graphs, with a pause and check plan.
- Power Rule and Friends Self-managementFast derivative rules, with a pause and check routine that catches careless slips.
- The Chain Rule Self-managementTaking derivatives of functions inside functions, one layer at a time, without skipping steps.
- L'Hospital's Rule Self-managementPausing to check the form, then persisting when a limit first gives 0/0.
Previous: Accumulation: Area Under a Rate · Next: The Fundamental Theorem of Calculus
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