Digital Unit Plan Template
Unit Title:
Name:
Introduction to Derivatives
Dulce Fonseca
Content Area: Calculus
Grade Level: 12
CA Content Standard(s)/Common Core Standard(s):
4.0 Students demonstrate an understanding of the formal definition of a derivative of a function and
the notation
4.1 Students demonstrate of an understandingof the derivative of a function as the slope of the tangent
line to the graph
4.2 Students demonstrate an understanding of the interpretation of the derivative as instantaneous
rate of change. Students can solve a variety of problems from physics, economics, chemistry, 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.
7.0 Students compute derivatives of higher orders.
Big Ideas:
 What is a derivative? How can it be described in non-mathematical language and how can it be
described graphically?
 How is a derivative computed and how can we recognize what derivative rules to use?
 What are some applications of derivatives?
Unit Goals and Objectives:
Goals: The purpose of this unit is to expose students and teach students about the basics of derivatives.
 Students will learn what a derivative is in simple mathematical terms.
Students will be able to explain differentiability.
 Students will learn the different ways to compute derivatives.
 Students will learn the rules of derivatives, as well the derivatives of trigonometric functions.
 Students will know how derivatives are applied to moving objects.
Objectives:
 Students will be exposed to the idea of the derivative as the slope of a tangent line to a graph.
 Students will learn to use the limit definition of a derivative.
 Students will know if a function is differentiable based on its graph.
 Students will be able to recognize and use the product rule, quotient rule, and chain rule.
 Students will continue their introduction on proof writing, particularly with the rules of
derivatives.
 Students will memorize and be able to compute the derivatives of trigonometric, inverse
trigonometric, exponential, etc. functions.
 Students will compute higher ordered derivatives.
 Using derivatives, students will learn to find and analyze velocity and acceleration of moving
objects.
Unit Summary:
The digital unit plan is on the introduction to derivatives. There will be online activities to complete,
from gathering information and interacting with digital tool. We will begin by learning the definition of
the derivative and what a derivative actually is. We will learn how continuity deals with
differentiability. This will give us the tools necessary to learn the “shortcuts,” or the rules, of
derivatives. This will lead to the applications of derivatives. How are they used? Why are they
important?
Assessment Plan:
Entry-Level:
Formative:
Summative:
 Review continuity.
 Review what a limit is.
 Non graded quiz on the use
of the unit circle, composite
functions and basic physics
properties.





Corners
Student Teacher Letters
Graphic Organizer
Peer quizzing
Traditional quizzes
 Student led conferences
 Exam covering all the
material of the unit
Lesson 1
Student Learning
Objective:
All but one of the
objectives are
addressed in
lesson one:
Students will
memorize and be
able to compute
the derivatives of
trigonometric,
inverse
trigonometric,
exponential, etc.
functions
Acceptable
Evidence:
-Evaluate using
derivative
definition
-Evaluate using
rules of
derivatives.
-Given a graph,
graph the
derivative at
indicated
points, if
differentiable.
-Solve physics
problems using
derivatives.
-Successful
completion of
Guided Notes
Instructional
Strategies:
☐ Communication
☐ Collection
☐ Collaboration
☐ Presentation
☐ Organization
☐ Interaction
Lesson Activities:
-Review continuity.
-Review what a limit is.
Teacher Lecture and Guided Notes will
cover the following:
-Students will review derivative as the slope
of a tangent line to a function and as the
rate of change.
-Students will be given different types of
functions, polynomials, quadratics,
trigonometric, etc. and will find the
derivatives by using power rules
-Given graphs as visual representations,
determine if a graph is differentiable at a
given point.
-Solving physics problems using
derivatives.
Lesson 2
Student Learning
Objective:
Acceptable
Evidence:
-Demonstrate
-Studentswill be
ability to not
exposed to the
only USE the
idea of the
product,
derivative as the quotient and
slope of a tangent chain rule, but
line to a graph.
to recognize
WHEN these
-Students will
should be used.
know if a
function is
-Given a
differentiable
function, be able
based on its
to take the
graph.
higher ordered
derivatives.
- Students will be
able to recognize -Successful
and use the
completion of
power, product,
Werbcise.
quotient, and
chain rule.
-Students will
memorize and be
Instructional
Strategies:
☐ Communication
☐ Collection
☐ Collaboration
☐ Presentation
☐ Organization
☐ Interaction
Lesson Activities:
-Review the derivative as the slope of a
tangent line to a graph: video
-Continue writing proofs.
-Use the rules of derivatives to compute
including the chain rule.
-Use the “must know” derivative functions.
-Continue learning how to write proofs.
-Review on continuity and its relationship
to differentiability.
able to use
derivatives of
trigonometric
functions.
- Students will
compute higher
ordered
derivatives.
-Students will
continue their
introduction on
proof writing,
particularly with
the rules of
derivatives.
Lesson 3
Student Learning
Objective:
Acceptable
Evidence:
- Students will be
able to recognize
and use the
product rule,
quotient rule,
and chain rule
-Students are
able to organize
their thoughts
into coherent
sentences and
examples.
-Students will
memorize and be
able to compute
the derivatives of
trigonometric,
inverse
trigonometric,
exponential, etc.
functions.
-Successful
completion of
Graphic
Organizer.
Instructional
Strategies:
☐ Communication
☐ Collection
☐ Collaboration
☐ Presentation
☐ Organization
☐ Interaction
Lesson Activities:
- Students state all the rules of derivatives
in mathematical and symbolic form.
-Students give examples of each of the rules
of derivatives.
-Students do more in depth computations of
derivatives using the chain rule.
-Graphic organizer: gives students the
chance to present problems the way they
wish the teacher presented.
Unit Resources:
Match Multiple Derivatives Graph:http://www.geogebratube.org/student/m17726
Try to Graph the Derivative Function:http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_try_to_graph.html
The Intuitive Notion of the Chain
Rule:http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_intuitive_chain_rule.html
Derivative of e^x Proof:http://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/e_to_the_x
Derivative of sin(x) Proof:http://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx
Derivatives Using the Limit Definition:https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/defderdirectory/DefDer.html
Tips for Derivatives:http://www.math.brown.edu/UTRA/derivtips.html
What is Acceleration: http://www.edinformatics.com/math_science/acceleration.htm
Position, Velocity, and Acceleration in one Dimension:
http://www.sparknotes.com/physics/kinematics/1dmotion/section2.rhtml
Velocity and Acceleration: http://home.windstream.net/okrebs/page205.html
Useful Websites:
Calculus Derivatives 1:http://www.youtube.com/watch?v=rAof9Ld5sOg
Derivative Tracer: http://www.geogebratube.org/student/m127
Differentiability vs Continuity: http://oregonstate.edu/instruct/mth251/cq/Stage5/Lesson/diffVsCont.html
Higher Ordered Derivatives Practice Problems: http://oregonstate.edu/instruct/mth251/cq/Stage5/Lesson/diffVsCont.html
Simple Derivative Examples: http://www.youtube.com/watch?v=jj2dnXbNO3E&feature=youtu.be
Millionaire Calculus Game:http://www.intmath.com/integration/millionaire-calculus-game.php
Introduction to Derivatives: http://www.education.com/study-help/article/calculus-help-foundations-derivative/