The Derivative Function
Students define the derivative using first principles and the limit of the difference quotient. They explore the relationship between the graph of a function and the graph of its derivative.
About This Topic
Students define the derivative using first principles and the limit of the difference quotient. They explore the relationship between the graph of a function and the graph of its derivative.
Key Questions
- How is the derivative defined using limits?
- What does the derivative function tell us about the original function?
- Where might a function fail to be differentiable?
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Planning templates for Calculus and Vectors
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.
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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.
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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.
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