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.
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.
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
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
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?!