Tangents, Normals, and Rates of Change
Applying differentiation to find equations of tangents and normals to curves. Students will also solve connected rates of change problems.
About This Topic
Applying differentiation to find equations of tangents and normals to curves. Students will also solve connected rates of change problems.
Key Questions
- How do we find the equation of a tangent line?
- What is the relationship between the gradients of a tangent and a normal?
- How can differentiation model real-world rates 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 - Differentiation
Concepts and Techniques of Differentiation
Understanding the derivative as a gradient of a curve and learning the rules of differentiation. This includes the chain rule, product rule, and quotient rule.
8 methodologies
Maxima and Minima Problems
Using the first and second derivative tests to identify local maxima and minima. Students will apply these concepts to optimization problems in various contexts.
8 methodologies