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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

I don't currently use a textbook. If you feel you need one as a reference, I suggest this open-source (and therefore FREE!) textbook: 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 calculus resources here: bit.ly/calcbundle.


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

LessonTitleUnitHomework AssignmentOther resources
1day 0 orientation day0: prerequisites
2Algebra topic: Writing Linear Equations0: prerequisites
3Algebra topic: Laws of Exponents0: prerequisites
4Algebra topic: Simplifying Rational Expressions0: prerequisites
5review of algebra0: prerequisites
6QUIZ on algebra topics0: prerequisites
Buy Unit 1 hereBuy the Full Curriculum here
71.1Introduction to Limits. Finding limits graphically1: Limits and Continuity1.1 Introduction to Limits WORKSHEET (included)Limits from Graphs CARD SORT
81.2More About Limits1: Limits and Continuity1.2 More About Limits WORKSHEET
91.3Properties of Limits. Finding Limits Algebraically1: Limits and Continuity1.3 Properties of Limits CIRCUIT (included)
101.4Finding Limits Analytically1: Limits and Continuity1.4 Finding Limits Analytically CIRCUIT (included)Finding Limits Analytically Maze
11reviewreview1: Limits and Continuity
12QUIZQUIZ1: Limits and Continuity
131.5Continuity1: Limits and Continuity
141.6Intermediate Value Theorem1: Limits and Continuity1.6 Continuity and the IVT SUM IT UP (included)
151.7Infinite Limits1: Limits and Continuity1.7 Vertical Asymptotes and Limits Worksheet (included)
161.8Limits at Infinity1: Limits and Continuity1.8 Infinite Limits WORKSHEET (included)
17reviewreview1: Limits and Continuity
18TESTTEST1: Limits and Continuity
optionalLimits of Trig Functions1: Limits and Continuity1.9 Limits of Trigonometric Functions WORKSHEET
Buy Unit 2 hereBuy the Full Curriculum here
192.1Instantaneous Rates of Change2: DifferentiationDerivatives by the Limit Definition DRAG AND DROP
202.2Differentiation2: Differentiation
212.3The Power Rule2: DifferentiationDerivatives Power Rule WORKSHEET
222.4Derivative of Sine, Cosine, Tangent, e^x, and Natural Log2: Differentiation2.4 Power Rule, e^x, sine, cosine CIRCUIT (included)Derivative at a Point SUM IT UP
23reviewreview2: DifferentiationBasic Derivatives Scavenger Hunt
24QUIZQUIZ2: Differentiation
252.5Higher Order Derivatives & Straight Line Motion2: DifferentiationCalculus Straight Line Motion SUM IT UP
262.6Product and Quotient Rules2: Differentiation
272.7Product and Quotient Rules with Trig, e^x and Natural Log2: Differentiation2.7 Product and Quotient Rules WORKSHEET (included)
282.8Chain Rule2: Differentiation2.8 Chain Rule WORKSHEET (included)Product Quotient Chain Rules RIDDLE WORKSHEET
292.8 day 2Chain Rule Day 22: DifferentiationDerivatives and Tangent Lines CARD SORT
30reviewreview2: Differentiation
31TESTTEST2: Differentiation
Buy Unit 3 hereBuy the Full Curriculum here
323.1Extreme Values3: Graphical Behavior of Functions3.1 Absolute Extrema CIRCUIT (included)
333.2Rolle's Theorem3: Graphical Behavior of Functions
343.3Mean Value Theorem3: Graphical Behavior of Functions3.3 Rolle's Thm and the MVT CIRCUIT (included)
353.4First Derivative Test Day 13: Graphical Behavior of Functions3.4 Relative Extrema Practice with QR Codes (included)
363.4First Derivative Test Day 23: Graphical Behavior of Functions3.4 First Derivative Test CIRCUIT (included)
37reviewreview3: Graphical Behavior of Functions
38QUIZQUIZ3: Graphical Behavior of Functions
393.5Concavity and the Second Derivative Day 13: Graphical Behavior of Functions3.5 Inflection Points and Concavity Practice (included)
403.5Concavity and the Second Derivative Day 23: Graphical Behavior of Functions3.5 Second Derivative Test and Concavity CIRCUIT (included)
413.6Curve Sketching3: Graphical Behavior of FunctionsRelative Extrema and Inflection Points CIRCUIT
42reviewreview3: Graphical Behavior of FunctionsCurve Sketching CARD SORT
43TESTTEST3: Graphical Behavior of Functions
44reviewreview for semester examExam Review, First Semester (not included)Exam Review BUNDLE
45reviewreview for semester examExam Review RAFFLE TICKET ACTIVITY (not included)--
46Examsemester examFinal Exam, First Semester (not included)Final Exam, Both Semesters
Buy Unit 4 hereBuy the Full Curriculum here
474.1Optimization4: Applications of the Derivative4.1a Optimization SUM IT UP with QR Codes (included)
484.1practice optimization4: Applications of the Derivative4.1b Optimization CIRCUIT (included)
494.2Implicit Differentiation4: Applications of the Derivative4.2a Implicit Differentiation Level 1, CIRCUIT (included)
504.2Implicit Differentiation with trig and natural log functions4: Applications of the Derivative4.2b Implicit Differentiation SUM IT UP (included)
514.3Related Rates4: Applications of the Derivative
524.3practice Related Rates4: Applications of the Derivative4.3 Related Rates SUM IT UP (included)
53reviewreview4: Applications of the Derivative
54TESTTEST4: Applications of the Derivative
55Optimization Project4: Applications of the DerivativeOptimization Project
56Optimization Project4: Applications of the Derivative--
57Optimization Project4: Applications of the Derivative--
Buy Unit 5 hereBuy the Full Curriculum here
585.1Antidifferentiation and Properties of Integrals5: IntegrationAntiderivatives Power Rule CIRCUIT (included)
595.1Antidifferentiation, day 25: IntegrationAntiderivatives and Indefinite Integrals CIRCUIT (included)Indefinite Integration SCAVENGER HUNT
605.2The Definite Integral5: IntegrationProperties of Definite Integrals SUM IT UP (included)
615.3Riemann Sums5: IntegrationRiemann Sums CIRCUIT (included)
62reviewreview5: Integration
63QUIZQUIZ5: Integration
645.4Trapezoidal Rule5: IntegrationTrapezoidal Rule CIRCUIT (included)
655.5Fundamental Theorem of Calculus5: IntegrationFundamental Theorem of Calculus SUM IT UP (included)
665.5Fundamental Theorem of Calculus, day 25: IntegrationFTC and Average Value CIRCUIT (included)
675.5practice5: IntegrationIntegration Unit Review SCAVENGER HUNT (included)
68reviewreview5: Integration
69TESTTEST5: Integration
Buy Unit 6 hereBuy the Full Curriculum here
706.1Integration by U-Substitution6: Integration Part 2Integration by U-Substitution CIRCUIT (included)
716.1Integration by U-Substitution Day 26: Integration Part 2Definite Integration by u Substitution CIRCUIT (included)
726.2Differential Equations6: Integration Part 2Separable Differential Equations CIRCUIT (included)
736.2Differential Equations day 26: Integration Part 2Differential Equations CARD SORT (included)Differential Equations Sticky Points Review Game
74reviewreview6: Integration Part 2
75quizquiz6: Integration Part 2
Buy Unit 7 hereBuy the Full Curriculum here
767.1Area Between Curves7: Applications of IntegrationArea Between Curves CIRCUIT (included)Area Between Curves SCAVENGER HUNT
777.2Volumes (Disk Method)7: Applications of IntegrationVolumes of Revolution The Disk Method CIRCUIT (included)
787.3Volumes (Washer Method)7: Applications of IntegrationVolumes of Revolution SUM IT UP (included)
797.4Volumes (Known Cross Section)7: Applications of IntegrationVolumes with Known Cross Sections SUM IT UP (included)Calculus Area and Volumes DIGITAL EXIT TICKET
80vase project7: Applications of IntegrationVase PROJECT (included)
81vase project7: Applications of Integration--
82vase project7: Applications of Integration--
83review7: Applications of Integration--
84TEST7: Applications of Integration--
85reviewreview for semester examExam Review, Second Semester (not included)Exam Review BUNDLE
86reviewreview for semester exam
87Examsemester examFinal Exam, Second Semester (not included)Final Exam, Both Semesters


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; no class follows this in the sequence, and there's no external exam! What more could you ask for?!

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