Calculus · Week 5 · Limits and Continuity
Continuity and the Intermediate Value Theorem
Checking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.
- Students will
- Students classify discontinuities, check continuity with 3 conditions, and decide whether the Intermediate Value Theorem applies.
- SEL skill
- Check every condition before deciding a theorem applies
- What it looks like
- Students practice responsible decision-making by checking every condition before claiming a theorem applies.
- Content focus
- Continuity, discontinuities, and the Intermediate Value Theorem
- Format
- Collaborative analysis
Responsible decision-making
Responsible decision-making means making careful choices based on evidence, like checking every condition before you decide a theorem applies. More responsible decision-making 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 1.11: AP Calculus AB, Unit 1, Topic 1.11
- AB 1.13: AP Calculus AB, Unit 1, Topic 1.13
- AB 1.16: AP Calculus AB, Unit 1, Topic 1.16
- 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 responsible decision-making activities for Calculus
- Inverse Functions and Their Derivatives Responsible decision-makingChoosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- Choosing the Right Rule Responsible decision-makingReading how a function is built before choosing a derivative rule.
- Close Enough? Local Linear Approximation Responsible decision-makingUsing a tangent line to estimate and deciding whether to trust it.
- Finding Extreme Values Responsible decision-makingCritical points, sign charts, and choosing the right test to find local and absolute extreme values.
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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.