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Hey there!
I've been teaching high school math for over 20 years. I write about my experiences here and also share activities that I have done with my classes that have been successful (and some that have been not so successful).

What to Teach in Non-AP Calculus

I have taught IB Math and I have taught non-AP Calculus. I love Calculus. I love it because it is challenging and I am always looking for ways to improve how I teach it. I also love teaching it because the class is generally filled with 11th and 12th graders; I prefer the older students because they view their teachers as humans; not as "grown-ups-who-are-always-telling-me-what-to-do" like their parents.

Read more about me here.

Here's how we handle the non-AP calculus class at the (independent) school where I teach:

In addition to this non-AP calculus class, our school also offers AP Calculus AB, AP Calculus BC, AP Statistics, and a post-AP class.  All of these classes last for the full year.

Because we offer those advanced classes, I make the non-AP calculus course like a survey course. We don't do super difficult problems. (For example, we do not cover derivatives or integrals of a^x or log(x). We do not cover derivatives of inverse functions.). I want my students to be exposed to differential and integral calculus, but I doubt many of them will study any calculus after they graduate high school (the class is usually 95% seniors, 5% juniors). If they *do* study calculus in college, it will likely be a Business Calculus class - in which case they will be at an advantage because they've already been exposed to calculus.

You might also be interested in what I teach in Algebra 2 or what I teach in Precalculus (on-level and honors).

Starting the Year

We start the year with a few days of Algebra topics (we end the year with some, too). We started this in 2019 because I was constantly going back and reminding them about point-slope form, the laws of exponents, and rational expressions as we were doing the calculus topics. Covering these topics at the beginning was successful; it prevented me from having to do it later and it also gives the students a few days to adapt to being back in the classroom after the summer.


The textbook we use is open-source (and therefore FREE!): http://www.apexcalculus.com/

Pacing Guide

Below is my pacing guide for my non-AP Calculus class. Note: our classes meet for 65 minutes and we are on a 7-period rotating schedule. Sometimes a class meets 3 times a week, sometimes 4; it depends on the week.

The links will take you to resources that I have available in my TeachersPayTeachers store. You can buy all of my current and future calculus products here: hoffmath.info/calculusbundle.

If you want a FREE Google Sheets version of this pacing guide, scroll down to the bottom of this page.

1day 0 orientation day
2supplementAlgebra topic: Writing Linear Equations
3supplementAlgebra topic: Laws of Exponents
4supplementAlgebra topic: Simplifying Rational Expressions
5reviewreview of algebra
6QUIZQUIZ on algebra topics
71.1 and 1.4An Intro to Limits
81.1 and 1.4More on Limits
91.3Finding Limits Analytically
101.3Finding Limits Analytically
151.6Limits Involving Infinity: vertical asymptotes
161.6Limits Involving Infinity: horizontal asymptotes
192.1Instantaneous Rate of Change: The Derivative, Limit Definition
202.1Instantaneous Rate of Change: The Derivative
212.3Basic Differentiation Rules (power rule)
222.3Basic Differentiation Rules (sine, cosine, tangent, e^x, ln(x))
232.3Basic Differentiation Rules (velocity, displacement)
242.3Basic Differentiation Rules (higher-order; acceleration)
272.4Product and Quotient Rules
282.4Product and Quotient Rules
292.5Chain Rule
302.5Chain Rule
33TESTTest 2.1 - 2.5
343.1Extreme Values
353.2Rolle's Theorem
363.2Mean Value Theorem
373.3Increasing and Decreasing Functions
383.3Increasing and Decreasing Functions
40QUIZQuiz 3.1 - 3.3
413.4Concavity and the Second Derivative
423.4Concavity and the Second Derivative
433.5Curve Sketching
I *could* cover more in the first semester, but I like to save 4 or 5 days as flex days (think: teacher is absent, majority of the students are absent, or the students need more practice because they're struggling). Every year we find a way to use those flex days we build into the schedule. We are always slowing down; rarely speeding up.

Review for Semester 1 Exam
1precalcproperties of logs
34.3Optimization practice
42.6Implicit Differentiation
52.6Implicit Differentiation
64.2Related Rates
74.2Related Rates
105.1Antiderivatives and Indefinite Integration
115.1Antiderivatives and Indefinite Integration
125.3Riemann Sums
135.5Numerical Integration (Trapezoidal Rule)
165.2The Definite Integral
175.4Fundamental Theorem of Calculus
185.4Fundamental Theorem of Calculus, average value
196.1Integration by U-Substitution
206.1Integration by U-Substitution
23supplementSlope Fields day 1 (optional, not covered in 2021)
24supplementSlope Fields day 2 (optional, not covered in 2021)
25supplementDifferential Equations
26supplementDifferential Equations day 2
277.1Area Between Curves
287.2Volumes (Disk Method)
297.2Volumes (Washer Method)
307.2Volumes (Known Cross Section)
31projectvase project
32projectvase project
33projectvase project
36projectHow to Adult Project
37projectHow to Adult Project
38projectHow to Adult Project
39projectHow to Adult Project
40Alg/Trig day 1factoring
41Alg/Trig day 2solving inequalities
42Alg/Trig day 3unit circle
43Alg/Trig day 4solving trig equations



Review for Semester 2 Exam

If you want a FREE Google Sheets version of this pacing guide, scroll down to the bottom of this page.

Ending the year

I *could* end the year with a project, but I don't like the last week of the year to be a project. During the last few weeks of the school year, the senioritis is bad, the weather is nice, and the students are not focused or interested in being in class. That's why I like to have one final unit where we cover a bit more algebra and trig topics that we think they might see on a college math placement test. 

It's also beneficial to end the school year (right before exams) with a test because students that have an 85% or higher can exempt the exam. I like to have a major grade at the end of the semester in order to keep their attention.

The structure of the class

Because we move so slowly, my lectures do not typically take the entire 65 minutes. I try to either give them time to work on their homework or I will do activities: Board Problems, Scavenger Hunts, Gimkit.com, Sticky Points review game, Raffle Ticket Review Activity, etc.

This is by far my favorite class to teach. I have a lot of autonomy; I don't have a deadline by which I have to cover all of the material. I don't have an outside entity (i.e. College Board) that dictates *what* material I have to cover; there's no class that follows this in the sequence and there's no external exam! What more could you ask for?!

Let's continue the conversation. Join me in my Facebook group.