Average vs. Instantaneous Rate of Change
Students distinguish between average and instantaneous rates of change and calculate average rates from graphs and tables.
Key Questions
- Compare the concept of average rate of change with instantaneous rate of change.
- Explain how the slope of a secant line represents an average rate of change.
- Analyze real-world scenarios to determine when an average rate of change is appropriate versus an instantaneous rate.
Ontario Curriculum Expectations
Suggested Methodologies
Ready to teach this topic?
Generate a complete, classroom-ready active learning mission in seconds.
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 Introduction to Calculus and Rates of Change
Introduction to Limits Graphically
Students explore the concept of a limit by analyzing the behavior of functions as they approach a specific value from both sides, using graphs.
3 methodologies
Evaluating Limits Algebraically
Students use algebraic techniques (direct substitution, factoring, rationalizing) to evaluate limits.
3 methodologies
Continuity of Functions
Students define continuity, identify types of discontinuities, and apply the conditions for continuity.
3 methodologies
The Derivative as a Limit
Students define the derivative as the limit of the difference quotient and interpret it as the slope of a tangent line.
3 methodologies
Differentiation Rules: Power, Constant, Sum/Difference
Students apply basic differentiation rules to find derivatives of polynomial and simple power functions.
3 methodologies