Digital Agenda

AP Calculus AB

Week of

September 21, 2015 to September 25, 2015

Unit 2: The Derivative

Check In/Do Now:Homework Corrections

Essential Question (s):
1. How is the derivative related to the interpretation of the tangent line at a point?
2. What is the relationship between differentiability and continuity?
3. What are the basic derivative rules?
Standard(s) from Instructional Guide:
4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:
4.1 Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.
4.2 Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.
4.3 Students understand the relation between differentiability and continuity.
4.4 Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions.
5.0 Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.
Student Objective (s):
2.1 Motivation for the derivative: the slope of the tangent line to approximate and instant rate if change, normal line to a curve
2.1 The definition of a derivative (finding derivatives using the definition)
2.1 Approximations of the derivative using difference quotients
2.2 The derivative as a function and as a linear operator, higher order derivatives
2.2 Differentiability and continuity
2.3 Derivatives of constants and power functions, the sum and difference rules
2.3 The product and quotient rules of derivatives
2.4 Derivatives of trigonometric functions
2.5 The Chain Rule
2.6 Implicit differentiation
6.2 Derivatives of exponential functions
6.4 ***Logarithmic functions and their derivatives
(With base e and other base also)
6.6 ***The derivatives of inverse trigonometric functions
Assessment and Student Reflection:
End of a lesson writing reflectionand exit slips

.

WHOLE GROUP
Demonstrate how to use “ask myself “ questions to understand problems
  1. What questions can you ask yourself to make sense of a problem?
  1. What can you do if you get stuck on a problem?
  1. Are there words that you don’t undersand?
  1. What is the problem talking about?
  1. What are the numbers/symbols in the problem and what do they mean?

DIRECTSTATION / COLLABORATIVE STATION / INDEPENDENT STATION
Lead a group discussion in which students
Analyze differentiable functions and continuous functions.
Students will listen and talk about their
Understanding. / Have students work on their own for several minutes before interacting with their partner. Partners should focus on explaining to each other how they arrived at the solution.
Students will explore various functions. / 1Review Limits and continuous
Functions under
AP Calculus
  1. Explore functions using a
Calculstor.