Seizing the Opportunity for Vertical Alignment

Towards the end of the school year, I jumped at the opportunity to influence the preparation of students who enter my AP Calculus AB course.  In doing so, I helped out two fellow mathematics teachers in my department by creating a course outline and pacing calendar for a new course they were going to teach: precalculus.

The two teachers, both of whom have been in the department far longer than me, were newly selected to teach precalculus, as the prior teacher just retired after a long and successful career teaching.  They are excited for the opportunity to teach a higher level course.  Yet, then, they were a little nervous about planning out the curriculum specifics for the course.  While my effort benefited them considerably, for which they were very appreciative, it also provided me the opportunity to align our regular precalculus courses with AP Calculus AB.  These past two years, students arrived in my course lacking skill in trigonometry, algebra, and functions.  I hope to change this situation so I created the course outline and pacing calendar below.

The curriculum is based on the textbook: Precalculus, 7th ed. – Graphical, Numerical, Algebraic by Demana, Waits, Foley, and Kennedy.

Regular Precalculus Course Outline & Pacing Calendar

Precalc Curriculum

Fall Semester

Fall semester serves as a bridge for most students as they complete an algebra 2 / trigonometry course before entering precalculus.  Some students enter regular precalculus coming from an algebra 2 course that does not include trigonometry.  Students who take honors precalculus mostly took algebra 2 / trigonometry.

I strongly recommend emphasizing multiple representations  (verbal, algebraic, numeric, graphic) per topic / concept.

Precalc Sem 1

Spring Semester

Spring semester primarily focuses on completing functions followed by an introduction to limits.

Precalc Sem 2

Omitted Topics

Many of these topics are covered in an honors precalculus course.  While it is not necessary to have a regular precalculus course and honors precalculus course, per se, the adage “less is more” allows students entering an AP Calculus AB course to focus on the key prerequisites used in the course; whereas, those entering AP Calculus BC can opt for the honors course if they believe they can handle the faster pace of honors precalculus and AP Calculus BC.

Precalc Omitted

Optional Topics

The optional topics cover many of the prerequisites for precalculus.  They serve as fodder for warm-ups prior to using a prerequisite in a precalculus context.

Precalc Optional

Let me know what folks think, especially those of you teaching AP Calculus AB.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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13 Responses to Seizing the Opportunity for Vertical Alignment

  1. PLu says:

    Doesn’t your state already have a curriculum for Precalculus? As an upper level teacher this was a drawback in my mind for our state’s adopting the national common core. We already had better guidelines in place for every course including upper level. Common Core doesn’t have anything above Alg 2 and, incidentally, almost everything you have on your outline is an Alg2 topic for Common Core—check it out.


    • No, it has a set of standards for trigonometry and a separate set for math analysis, which combined equal a typical set of precalculus standards, but not a curricula per se. Yes, I am aware of the CCSSM and the considerable overlap between an algebra 2 / trig course curriculum and precalculus. However, the depth of knowledge required for calculus is beyond that which most students are capable of developing with a single year of algebra 2 / trig.

      Thanks for your thoughts!

      On Sat, Jul 13, 2013 at 1:00 AM, Reflections of a Second-career Math


  2. Your placement of trig is interesting. One on hand, it s good to get everyone on board right from the get-go. On the other, by the time they hit AB it’ll have been almost a full year since they formally covered it. I would either put it deeper in OR make sure constant review is truly built in.

    Transformation seems left out. This, to me, is essential when discussing trig. Also, I would say the financials are a non-negotiable, not only because they are interesting and practical, but also because they provide an excellent case study for that type of growth when it comes to calc.


    • Hi David. Thanks for your comments. Yes, spiraling trig throughout a must. Emphasis on transformations is noted as a footnote of sorts but perhaps not clearly enough. I will make sure that is clear. On the financials side, it pained me to make them optional, especially as I have an MBA in finance, yet I wanted to adhere to less is more. So rather than make it a must, it’s optional and ideally used as context for content.


  3. I’m not sure why you’d teach trig before functions, systems, and logs. If the precalc classes are anything like mine was this last year, the kids won’t know any algebra II.


    • It is almost six on one-hand, half a dozen on the other with respect to the sequencing of trigonometry and functions. At the same time, a fair amount of incoming students just finished an algebra 2 / trig course, so this arrangement provides a bridge. Some algebra 2 teachers even address trig at the end of the second semester, post CSTs. With the change coming with CCSSM, I am not sure how prior exposure to trig will change.


  4. says:

    I’m in a STEM program that is working on alignment from 8th grade through AP. from CollegeBoard


  5. says:

    much of this is on SAT II test; but simple ptroblems


    • Yes, precalculus is an odd lot of topics, most of which are from algebra 2 and trigonometry, which most districts teach as alg2 / trig course; I think that is a bad idea that gives short shrift to trig. At the same time, students who go on to calculus need more extensive exposure to trig, especially, and more experience with functions, specifically, transformations and inverse as well as concepts of domain and range.

      When I was in high school, there was no “precalculus” course. Students took a semester of trigonometry and a semester of analytic geometry.

      On Sat, Jul 13, 2013 at 2:25 PM, Reflections of a Second-career Math


  6. Hey! Off-topic a bit, but congratulations! You’ve been nominated by me for a Liebster Award! Enjoy?


  7. Mike Tamblyn says:

    Some topics that you ommitted, like polar and de’moives theorem, sequesnces and series, probability, I hate to not see in there, even parametrics. I feel that leaving out topics since they are not in AB is unfair. What happens when they take 2nd semester calc and they have never had an intro to parametrics or polar? Seems unfair. You certainly do not need to do a unit on limits for kids entereing AB, only BC. AB’s curriculum is so small, you can finish that by the end of march. I teach AB and teach pre-calc out of the book you mention. I do the P chapter and then 1- the end in order, but skip the matrices and the limits/derivatives at the end. Our alg 2 has so much with matrices, I feel ok skipping. My kids seem to need the P chapter. For the P chapter and maybe even ch 1, I do one section per day in a 44 min class. After that I take 2 days per section the rest of the year. hth


    • Thanks for your thoughts and sharing your approach, Mike. I took a less is more approach; somewhat like the CCSSM – less breadth, more depth. I do not believe our students would benefit from the pace required to cover the majority of topics, so I streamlined it. Honors precalc includes most of the topics you listed. They can also serve as extension topics for anyone interested.


  8. Pingback: Honored to teach Honors Precalculus | Reflections of a Second-career Math Teacher

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