What to Teach in Non-AP Calculus

I have taught IB Math, AP Calculus, and non-AP Calculus (which we call "On-Level 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 entire 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. Still, I doubt many of them will study calculus after graduating 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 gave the students a few days to adapt to being back in the classroom after the summer.

Textbook

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 I have available in my TeachersPayTeachers store. You can buy all my current and future calculus products here: bit.ly/calcbundle.

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

	section	title	Resource you may be interested in	Other resources
1		day 0 orientation day
2	supplement	Algebra topic: Writing Linear Equations
3	supplement	Algebra topic: Laws of Exponents
4	supplement	Algebra topic: Simplifying Rational Expressions
5	review	review of algebra
6	QUIZ	QUIZ on algebra topics
7	1.1 and 1.4	An Intro to Limits	Limits Unit 1, all inclusive	Introduction to Limits WORKSHEET
8	1.1 and 1.4	More on Limits	Limits from Graphs CARD SORT
9	1.3	Finding Limits Analytically	Properties of Limits CIRCUIT
10	1.3	Finding Limits Analytically	Finding Limits Analytically CIRCUIT	Finding Limits Analytically Maze
11	review	review
12	QUIZ	QUIZ
13	1.5	Continuity	Continuity and the Intermediate Value Theorem SUM IT UP
14	1.5	Continuity
15	1.6	Limits Involving Infinity: vertical asymptotes
16	1.6	Limits Involving Infinity: horizontal asymptotes	Infinite Limits WORKSHEET
17	review	review
18	TEST	TEST
19	optional	Limits of Trig Functions	Limits of Trigonometric Functions WORKSHEET
20	2.1	Instantaneous Rate of Change: The Derivative, Limit Definition	Derivatives by the Limit Definition DRAG AND DROP
21	2.1	Instantaneous Rate of Change: The Derivative, Limit Definition
22	2.3	Basic Differentiation Rules (power rule)	Derivatives Power Rule WORKSHEET
23	2.3	Basic Differentiation Rules (sine, cosine, tangent, e^x, ln(x))	Derivatives Power Rule, e^x, sine, cosine CIRCUIT	Derivative at a Point SUM IT UP
24	2.3	Basic Differentiation Rules (velocity and higher order)	Calculus Straight Line Motion SUM IT UP
25	review	review	Basic Derivatives Review
26	QUIZ	QUIZ
27	2.4	Product and Quotient Rules	Derivative Product and Quotient Rules WORKSHEET
28	2.4	Product and Quotient Rules
29	2.5	Chain Rule	Derivatives Chain Rule WORKSHEET
30	2.5	Chain Rule	Derivatives Product Quotient Chain Rules RIDDLE WORKSHEET
31	review	review	Derivatives and Tangent Lines CARD SORT
32	review	review
33	TEST	Test
34	3.1	Extreme Values	Absolute Extrema CIRCUIT
35	3.2	Rolle's Theorem
36	3.2	Mean Value Theorem	Rolle's Theorem and the Mean Value Theorem CIRCUIT
37	3.3	Increasing and Decreasing Functions	Relative Extrema Practice with QR Codes
38	3.3	Increasing and Decreasing Functions	First Derivative Test CIRCUIT
39	review	review
40	QUIZ	Quiz 3.1 - 3.3
41	3.4	Concavity and the Second Derivative	Second Derivative Test and Concavity CIRCUIT
42	3.4	Concavity and the Second Derivative	Relative Extrema and Inflection Points CIRCUIT	Inflection Points and Concavity Practice with QR Codes
43	3.5	Curve Sketching	Curve Sketching CARD SORT
44	review	review
45	TEST	TEST
46	review	review for semester exam	Calculus Exam Review, First Semester	Calculus Exam Review BUNDLE
47	review	review for semester exam	Calculus Exam Review RAFFLE TICKET ACTIVITY | Limits and Derivatives
		SEMESTER 2
1	precalc	properties of logs
2	4.3	Optimization
3	4.3	Optimization practice	Calculus Optimization CIRCUIT	Calculus Optimization SUM IT UP with QR Codes
4	2.6	Implicit Differentiation
5	2.6	Implicit Differentiation	Implicit Differentiation SUM IT UP
6	4.2	Related Rates	Related Rates SUM IT UP
7	4.2	Related Rates
8	review	review
9	TEST	TEST
10	5.1	Antiderivatives and Indefinite Integration	Antiderivatives and Indefinite Integrals CIRCUIT
11	5.1	Antiderivatives and Indefinite Integration	Indefinite Integration SCAVENGER HUNT
12	5.3	Riemann Sums	Riemann Sums CIRCUIT
13	5.5	Numerical Integration (Trapezoidal Rule)	Trapezoidal Rule CIRCUIT
14	review	review
15	QUIZ	QUIZ
16	5.2	The Definite Integral	Properties of Definite Integrals SUM IT UP with QR Codes
17	5.4	Fundamental Theorem of Calculus	Fundamental Theorem of Calculus SUM IT UP
18	5.4	Fundamental Theorem of Calculus, average value
19		practice	Integration Unit Review SCAVENGER HUNT
20	6.1	Integration by U-Substitution	Integration by U-Substitution CIRCUIT
21	6.1	Integration by U-Substitution	Definite Integration by u Substitution CIRCUIT
22	review	review
23	TEST	TEST
24	supplement	Slope Fields day 1 (optional)
25	supplement	Slope Fields day 2 (optional)
26	supplement	Differential Equations	Differential Equations CARD SORT
27	supplement	Differential Equations day 2	Differential Equations Sticky Points Review Game
28	7.1	Area Between Curves	Area Between Curves CIRCUIT	Area Between Curves SCAVENGER HUNT
29	7.2	Volumes (Disk Method)
30	7.2	Volumes (Washer Method)	Volumes of Revolution SUM IT UP
31	7.2	Volumes (Known Cross Section)	Volumes with Known Cross Sections SUM IT UP	Calculus Area and Volumes DIGITAL EXIT TICKET
32	project	vase project	Calculus Vase PROJECT
33	project	vase project
34	project	vase project
35	review	review
36	TEST	TEST
37	project	How to Adult Project	How to Adult Project
38	project	How to Adult Project
39	project	How to Adult Project
40	project	How to Adult Project
41	Alg/Trig day 1	factoring
42	Alg/Trig day 2	solving inequalities
43	Alg/Trig day 3	unit circle
44	Alg/Trig day 4	solving trig equations
45	review	review
46	TEST	TEST
47	review	review for semester exam	Calculus Exam Review, Second Semester	Calculus Exam Review BUNDLE
48	review	review for semester 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 terrible, 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 with an 85% or higher can exempt the exam. I like to have a major grade at the end of the semester 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 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.

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