Welcome to Clip from Spiral logo

Interactive video lesson plan for: Derivatives Unit 3

Activity overview:

The student will investigate derivatives presented in graphic, numerical, and analytic
contexts and the relationship between continuity and differentiability. The derivative will
be defined as the limit of the difference quotient and interpreted as an instantaneous rate
of change.
Mathematics Standards of Learning
APC.6 The student will investigate the derivative at a point on a curve. This will include
a) finding the slope of a curve at a point, including points at which the tangent is vertical
and points at which there are no tangents;
b) using local linear approximation to find the slope of a tangent line to a curve at the
c) defining instantaneous rate of change as the limit of average rate of change; and
d) approximating rate of change from graphs and tables of values.
APC.7 The student will analyze the derivative of a function as a function in itself. This will
a) comparing corresponding characteristics of the graphs of f, f ', and f ";
b) defining the relationship between the increasing and decreasing behavior of f and the
sign of f ';
c) translating verbal descriptions into equations involving derivatives and vice versa;
d) analyzing the geometric consequences of the Mean Value Theorem;
e) defining the relationship between the concavity of f and the sign of f "; and
f) identifying points of inflection as places where concavity changes and finding points
of inflection.
APC.8 The student will apply the derivative to solve problems. This will include
a) analysis of curves and the ideas of concavity and monotonicity;
b) optimization involving global and local extrema;
c) modeling of rates of change and related rates;
d) use of implicit differentiation to find the derivative of an inverse function;
e) interpretation of the derivative as a rate of change in applied contexts, including
velocity, speed, and acceleration; and
f) differentiation of nonlogarithmic functions, using the technique of logarithmic
differentiation. *
* AP Calculus BC will also apply the derivative to solve problems. This will include
a) analysis of planar curves given in parametric form, polar form, and vector form,
including velocity and acceleration vectors;
b) numerical solution of differential equations, using Euler's method;
c) l'Hopital's Rule to test the convergence of improper integrals and series; and
d) geometric interpretation of differential equations via slope fields and the relationship
between slope fields and the solution curves for the differential equations.
APC.9 The student will apply formulas to find derivatives. This will include
a) derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse
trigonometric functions;
b) derivations of sums, products, quotients, inverses, and composites (chain rule) of
elementary functions;
c) derivatives of implicitly defined functions; and
d) higher order derivatives of algebraic, trigonometric, exponential, and logarithmic,
functions. *
* AP Calculus BC will also include finding derivatives of parametric, polar, and vector

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Derivatives Unit 3 on Google+ Share Derivatives Unit 3 on Twitter Share Derivatives Unit 3 on Facebook Pin Derivatives Unit 3 Email Derivatives Unit 3

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.


Carry out a quickfire formative assessment to see what the whole class is thinking


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome