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.