Scroll down to read my latest blog post.
    Check out some of my awesome Freebies! Click on Learn more.
    Learn more
  • SHOP
    Head to my TeachersPayTeachers store for some engaging math resources that can be used in your class today! Click on Learn more.
    Learn more
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, 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.


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.

sectiontitleResource you may be interested inOther resources
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 LimitsLimits Unit 1, all inclusiveIntroduction to Limits WORKSHEET
81.1 and 1.4More on LimitsLimits from Graphs CARD SORT
91.3Finding Limits AnalyticallyProperties of Limits CIRCUIT
101.3Finding Limits AnalyticallyFinding Limits Analytically CIRCUITFinding Limits Analytically Maze
131.5ContinuityContinuity and the Intermediate Value Theorem SUM IT UP
151.6Limits Involving Infinity: vertical asymptotesVertical Asymptotes and Limits Worksheet
161.6Limits Involving Infinity: horizontal asymptotesInfinite Limits WORKSHEET
19optionalLimits of Trig FunctionsLimits of Trigonometric Functions WORKSHEET
202.1Instantaneous Rate of Change: The Derivative, Limit DefinitionDerivatives by the Limit Definition DRAG AND DROP
212.1Instantaneous Rate of Change: The Derivative, Limit Definition
222.3Basic Differentiation Rules (power rule)Derivatives Power Rule WORKSHEET
232.3Basic Differentiation Rules (sine, cosine, tangent, e^x, ln(x))Derivatives Power Rule, e^x, sine, cosine CIRCUITDerivative at a Point SUM IT UP
242.3Basic Differentiation Rules (velocity and higher order)Calculus Straight Line Motion SUM IT UP
25reviewreviewBasic Derivatives Scavenger Hunt
272.4Product and Quotient RulesDerivative Product and Quotient Rules WORKSHEET
282.4Product and Quotient Rules
292.5Chain RuleDerivatives Chain Rule WORKSHEET
302.5Chain RuleDerivatives Product Quotient Chain Rules RIDDLE WORKSHEET
31reviewreviewDerivatives and Tangent Lines CARD SORT
343.1Extreme ValuesAbsolute Extrema CIRCUIT
353.2Rolle's Theorem
363.2Mean Value TheoremRolle's Theorem and the Mean Value Theorem CIRCUIT
373.3Increasing and Decreasing FunctionsRelative Extrema Practice with QR Codes
383.3Increasing and Decreasing FunctionsFirst Derivative Test CIRCUIT
40QUIZQuiz 3.1 - 3.3
413.4Concavity and the Second DerivativeSecond Derivative Test and Concavity CIRCUIT
423.4Concavity and the Second DerivativeRelative Extrema and Inflection Points CIRCUITInflection Points and Concavity Practice with QR Codes
433.5Curve SketchingCurve Sketching CARD SORT
46reviewreview for semester examCalculus Exam Review, First SemesterCalculus Exam Review BUNDLE
47reviewreview for semester examCalculus Exam Review RAFFLE TICKET ACTIVITY | Limits and Derivatives
1precalcproperties of logs
34.3Optimization practiceCalculus Optimization CIRCUITCalculus Optimization SUM IT UP with QR Codes
42.6Implicit DifferentiationImplicit Differentiation Level 1, CIRCUIT
52.6Implicit DifferentiationImplicit Differentiation SUM IT UP
64.2Related RatesRelated Rates SUM IT UP
74.2Related Rates
105.1Antiderivatives and Indefinite IntegrationAntiderivatives and Indefinite Integrals CIRCUIT
115.1Antiderivatives and Indefinite IntegrationAntiderivatives and Indefinite Integrals CIRCUITIndefinite Integration SCAVENGER HUNT
125.3Riemann SumsRiemann Sums CIRCUIT
135.5Numerical Integration (Trapezoidal Rule)Trapezoidal Rule CIRCUIT
165.2The Definite IntegralProperties of Definite Integrals SUM IT UP with QR Codes
175.4Fundamental Theorem of CalculusFundamental Theorem of Calculus SUM IT UP
185.4Fundamental Theorem of Calculus, average valueFTC and Average Value CIRCUIT
19practiceIntegration Unit Review SCAVENGER HUNT
206.1Integration by U-SubstitutionIntegration by U-Substitution CIRCUIT
216.1Integration by U-SubstitutionDefinite Integration by u Substitution CIRCUIT
24supplementSlope Fields day 1 (optional)
25supplementSlope Fields day 2 (optional)
26supplementDifferential EquationsSeparable Differential Equations CIRCUITDifferential Equations CARD SORT
27supplementDifferential Equations day 2Differential Equations Sticky Points Review Game
287.1Area Between CurvesArea Between Curves CIRCUITArea Between Curves SCAVENGER HUNT
297.2Volumes (Disk Method)
307.2Volumes (Washer Method)Volumes of Revolution SUM IT UP
317.2Volumes (Known Cross Section)Volumes with Known Cross Sections SUM IT UPCalculus Area and Volumes DIGITAL EXIT TICKET
32projectvase projectCalculus Vase PROJECT
33projectvase project
34projectvase project
37projectHow to Adult ProjectHow to Adult Project
38projectHow to Adult Project
39projectHow to Adult Project
40projectHow to Adult Project
41Alg/Trig day 1factoring
42Alg/Trig day 2solving inequalities
43Alg/Trig day 3unit circle
44Alg/Trig day 4solving trig equations
47reviewreview for semester examCalculus Exam Review, Second SemesterCalculus Exam Review BUNDLE
48reviewreview 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.