
Rates of Change
Solve connected rates of change problems by setting up differential equations based on physical scenarios. Interpret the derivative as a rate of change in real-world contexts.
About This Topic
Solve connected rates of change problems by setting up differential equations based on physical scenarios. Interpret the derivative as a rate of change in real-world contexts.
Key Questions
- How do we link different rates of change using the chain rule?
- What are the steps to model a physical situation with derivatives?
- How do we interpret the sign of a rate of change?
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Mathematics
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 Calculus I - Differentiation
Differentiation Techniques
Review and extend differentiation rules, including chain, product, and quotient rules. Differentiate implicit and parametric equations.
8 methodologies
Applications of Differentiation
Apply differentiation to find gradients, tangents, and normals to curves. Use the first and second derivative tests to identify local maxima, minima, and points of inflection.
8 methodologies