This work by Andrew Shauver – Ingham Intermediate School District is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

*This is a new experience for me. For the 2014-15 school year, I piloted a calculus class that I designed an updated version of the calculus class that used to be offered at our high school, but had been dormant for several years.*

*I would absolutely LOVE your feedback, especially the constructive variety. I mean that… please.*

*So, feel free to look around, take whatever you want. Anything that isn’t mine, a link will take you to the author’s site. Anything that is mine is all Creative Commons licensed. Send back any improvements. *

Also, keep in mind, that in my current assignment, I am not scheduled to teach this course in the foreseeable future. So, while I will add updates, sites, and activities that I run across, the newer ones will have my recommendation because they look awesome, not because I used it in my class and it went great.

This is ALWAYS under construction. So check back periodically. I’m sure there will have been updates.

**Calculus Units**

*These have been put together with an amazing amount of help from Sam J. Shah (@samjshah). I cannot thank him enough. Much of what you see is his material which he freely shared with me. He has given me permission to share whatever of his that you see here. All of the handouts for Unit 1 came from what he has provided me. All I did was rearrange some of the images and reformat the headers. Many thanks again.*

**Unit 0 – Welcome Back Problem Solving (The first week back… warm-up for the brains)**

The Glass is half-full… I think.

**Unit 1 – Functions and Limits**

Unit 1 Learning Goals – Student Self-Assessment

Handout 1 – Analyzing Rational Functions

Handout 2 – Sign Analysis of Rational Functions

Handout 3 – Rational Functions Backwards I

Handout 4 – Rational Functions Backwards II

Desmos Activity – Rational Functions

Handout 5 – Piecewise Functions

Handout 7 – Limits of Rational Functions I

Handout 8 – Limits of Rational Functions II

** **

**Unit 2 – The Derivative**

Handout 1 – Limit Definition of Derivative (excellent piece from Shawn Cornally)

Handout 2 – Derivatives Prequel

Handout 3 – 100m Position – 100m Velocity

Handout 4 – Position to Velocity Graphs

Handout 5 – Tangent Lines

Handout 6 – Binomial Theorem and Velocity Practice

Handout 7 – Drawing Instantaneous Velocity

Interactive Desmos Activity – Dragging Points: First, Second derivatives (designed and built by Dan Anderson)

Handout 8 – Derivative Graph Matching

Handout 9 – Intro to Derivative Functions

Handout 10 – Exploring Derivative Functions

Handout 11 – If I were in the Upper Peninsula…

** **

**Unit 3 – Introduction to Derivative Rules**

Handout 1 – Introduction to Wolfram-Alpha

Handout 2 – Discovering Derivative Rules

Handout 3 – Application of Derivative – The Soda Can Problem (Thanks University of Nottingham)

Handout 4 – Power Rule Practice

Handout 5 – Derivation of the Product Rule

Handout 6 – Product Rule Practice

Handout 7 – Derivatives Problem-Solving

Handout 8 – Trigonometry Review

Handout 9 – Right Triangle Trig Review Problems

Presentation – Trig Derivatives Proofs (Thanks James Kratky)

Handout 10 – Trig Derivatives Practice Problems

Presentation – Chain Rule Proof (Thanks James Kratky)

Handout 11 – Chain Rule Practice Problems

**Unit 4 – Advanced Differentiation**

Handout 1 – Introduction to Implicit Differentiation

Handout 2 – Implicit Differentiation Visually

Handout 3 – Introduction to Related Rates

Handout 4 – Infection!

Handout 5 – Introduction to Graph Shapes

Handout 6 – Graph Shapes, Extra Practice

Handout 7 – Absolute Max and Min

Handout 8 – Max and Min Problem-Solving

Handout 9 – Optimization Problem-Solving

Handout 10 – Draining Water Problem

Handout 11 – Ferris Wheel Problem (Spin-off of Dan Meyer #3Act – Materials referenced in handout found here)

If you have the freedom to design the sequence, I recommend against doing limits first. The derivative is exciting and connected to real world history; the limit took 150 years after that to get right. Seems to me we should give students the excitement first, and the logical tangle of a proper limit definition later. I did them between derivatives and integrals.

You make a good point and you aren’t the only person to suggest it. Shawn Cornally also starts with derivative day one. So I am considering it.

There are also come fantastic math teachers who start with limit. Our pre-Calc course doesn’t get as far a rational functions, so that was a consideration as well.

Do you feel like students need to be able analyze rational functions before they do derivatives?

Wow. That seems like a pretty basic component of pre-calc. And yet, I doubt my students remember much about rational functions.

It became clear to me last year that the limit, as a function, is a function of h (or delta x), so we’re mixing functions of x and functions of h together. No wonder it’s hard to think about precisely! It’s the issue of 0/0 that makes us need the limit, and that makes rational function concepts relevant. (Does the 0/0 gives us a vertical asymptote, or just a hole? Depends on the function.) I’m thinking I would want to review rational functions just before my careful definition of the limit, which I do later in the course. (Thanks for asking me about this – you gave me a good opportunity to think it through.)

I’m thinking that if you just say limit as h goes to 0 means that the two points get “infinitely close”, as I do at the beginning of the semester (along with saying that I might be making other mathematicians cringe!), then there’s no need yet for the rational functions. It goes before limits, but doesn’t need to go before derivatives.