Andrew Vohland
ED 270 Final Project
6/9/2015
Grade Level
High School, most likely 11-12th graders
Content Area
Mathematics, AP Calculus
Title of Unit
Derivative Formulas
Learning Goal
By the end of the lesson, students will have a basic understanding of the
processes used to find derivatives of common formulas. These formulas
involve constants, operations applied on functions, composition of
functions, and the power rule. (Future lessons will expand on additional
methods i.e. exponential, logarithmic, and trigonometric functions.)
Technology
Standards
2. Communication and Collaboration
a. Interact, collaborate, and publish with peers, experts, or
others employing a variety of digital environments and media
3. Critical Thinking, Problem Solving, and Decision Making
a. Use multiple processes and diverse perspectives to explore
alternative solutions
4. Digital Citizenship
a. Exhibit a positive attitude toward using technology that
supports collaboration, learning, and productivity
b. Demonstrate personal responsibility for lifelong learning
5. Technology Operations and Concepts
a. Understand and use technology systems
b. Select and use applications effectively and productively
Technologies
Powerpoint – This is where the bulk of material will be presented. It seems
Integrated
to be one of the most convenient ways to sequentially distribute knowledge
without wasting resources by printing out unnecessary handouts on paper
when they can instead be kept in the digital world.
Website – This is the home base. Powerpoints will be kept here for review
in case the students need them. Until the students memorize the formulas,
they can use this to practice. I can also put up relating problems to work on
or show my methods at solving a derivative.
App – If I look into it more, I feel that I can make the app a useful tool. I
envision having a list of all the functions for quick access. It could even be
used in aspects outside of this assignment.
Resources
My notes which I will present to the students is the majority of what I would
need, besides the computer that controls the technology. Students will
probably utilize a pen and paper to copy down the notes as most students
do.
Unit Outline
What’s important to note is this style of mathematics is still of the
format of high school leveled math (meaning it’s mostly plug and chug,
instead of proofs or mathematical discoveries). Because of that, it generally
just needs a memorization of formulas. The critical skills lies in the students
being able to break down a formula by its parts and apply the appropriate
method. Therefore, much of this lesson will revolve around introducing the
formulas needed and giving problems to practice on, and subsequent
lessons will expand on why exactly these equations may work and/or
possible uses in the real world for them.
Hour 1: Explain the following formulas:
1. d/dx (c) = 0 where c is a constant value not a variable
2. d/dx [c * f(x)] = c * f’(x)
3. d/dx [f(x) + g(x)] = f’(x) + g’(x)
4. d/dx [f(x) – g(x)] = f’(x) – g’(x)
5. d/dx (x^n) = nx^(n-1)
(Power Rule)
These are the core formulas. The ideas will be presented and then followed
with a couple problems for them to solve on their own to cement the idea
down.
Hour 2: Explain the next set of formulas:
1. d/dx [f(x) * g(x)] = f(x) * g’(x) + g(x) * f’(x)
(Product Rule)
2. d/dx [f(x) / g(x)] = [g(x) * f’(x) – f(x) * g’(x)] / [g(x)]^2
(Quotient
Rule)
3. d/dx f(g(x)) = f’(g(x)) * g’(x)
(Chain Rule)
This is where the formulas become more challenging. A firm grasp of hour
1’s formulas are needed to understand this hour. When practice problems
are presented, I can mix styles of functions to get the students to try and
break down the functions into smaller pieces that require multiple formulas
to derive.