Calculus · Week 25 · Integration and Accumulation of Change
The Fundamental Theorem of Calculus
The Fundamental Theorem links derivatives and integrals; seeing a classmate's reasoning from their side.
- Students will
- Students use the Fundamental Theorem of Calculus to differentiate accumulation functions, evaluate definite integrals, and describe where an accumulation function increases.
- SEL skill
- Explain why a classmate's integral error made sense before correcting it
- What it looks like
- Students practice social awareness by explaining why an imagined classmate made an FTC error before correcting it.
- Content focus
- Using the Fundamental Theorem of Calculus
- Format
- Collaborative analysis
Social awareness
Social awareness means understanding how someone else sees a situation, such as seeing why a classmate's FTC step made sense to them. 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 6.4: AP Calculus AB, Unit 6, Topic 6.4
- AB 6.5: AP Calculus AB, Unit 6, Topic 6.5
- AB 6.7: AP Calculus AB, Unit 6, Topic 6.7
- Standard for Mathematical Practice: MP3 Construct viable arguments and critique the reasoning of others
- CA Mathematics Framework (2023): Taking Wholes Apart, Putting Parts Together
- 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.
- Smooth or Sharp? Differentiability Social awarenessEstimating derivatives and seeing where a graph is smooth, cornered, or too steep, by looking from both sides.
- 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.
Previous: From Riemann Sums to the Definite Integral · Next: Antiderivatives and Indefinite Integrals
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.