Continuity and the Intermediate Value Theorem
This topic defines continuity at a point and over an interval. Students apply the Intermediate Value Theorem to guarantee the existence of roots.
About This Topic
This topic defines continuity at a point and over an interval. Students apply the Intermediate Value Theorem to guarantee the existence of roots.
Key Questions
- What makes a function continuous?
- How are limits related to continuity?
- How does the IVT guarantee a root?
Planning templates for Calculus
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Limits and Continuity
Evaluating Limits
Students explore the concept of a limit graphically, numerically, and algebraically. They learn to evaluate limits of various functions as they approach specific values.
2 methodologies
Infinite Limits and Asymptotes
Students investigate the behavior of functions as they approach infinity or vertical asymptotes. They connect these limits to the graphical representation of rational functions.
2 methodologies