Calculus · Week 1 · Limits and Continuity
What Changes, and How Fast?
Average rate of change on smaller and smaller intervals, and noticing how confident each step feels.
- Students will
- Students compute average rates of change from a distance function on shrinking intervals and use limit notation to name the value they approach.
- SEL skill
- Rate confidence on each step and name a strength and a shaky spot
- What it looks like
- Students practice self-awareness by rating their confidence on each step and naming which step feels strong or shaky.
- Content focus
- Average rate of change and the idea of a limit
- Format
- Think write pair share
Self-awareness
Self-awareness means noticing what you are thinking and feeling, including which math steps feel strong and which feel shaky. 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 1.1: AP Calculus AB, Unit 1, Topic 1.1
- AB 1.2: AP Calculus AB, Unit 1, Topic 1.2
- 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
- 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.
- Accumulation: Area Under a Rate Self-awarenessEstimating total change from a rate table with Riemann and trapezoidal sums, and noticing how sure we feel.
Next: Getting Closer: Limits from Graphs and Tables
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.