Introduction to Derivatives: Definition and Basic Rules
Understanding the formal definition of the derivative and applying power, constant, and sum rules.
Key Questions
- Explain the relationship between the limit definition of the derivative and the slope of a tangent line.
- Differentiate between the power rule and the constant multiple rule in practice.
- Construct the derivative of a polynomial function using basic differentiation rules.
Common Core State Standards
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 The Language of Functions and Continuity
Introduction to Functions and Their Representations
Reviewing definitions of functions, domain, range, and various representations (graphical, algebraic, tabular).
2 methodologies
Function Transformations: Shifts and Reflections
Investigating how adding or subtracting constants and multiplying by negative values transform parent functions.
2 methodologies
Function Transformations: Stretches and Compressions
Analyzing the impact of multiplying by constants on the vertical and horizontal scaling of functions.
2 methodologies
Function Composition and Inversion
Analyzing how nested functions interact and the conditions required for a function to be reversible.
2 methodologies
Introduction to Limits: Graphical and Numerical
Investigating the intuitive concept of a limit by observing function behavior from graphs and tables.
2 methodologies