As you get ready to start school, here are some thoughts on the first week in AP Calculus. I looked back recently at some of the “first week of school” advice I offered in the past. Here’s a quick (actually, a bit longer than I planned) summary with some new ideas.

1. The last time I taught AP Calculus during review time a student asked if there was a list of what’s on the exam. Duh! Why didn’t I think of that? So, I made copies of the list (from the old Acorn Book) and gave it to everyone. I should have done that on Day 1. So, my first suggestion is to make a copy of the “Mathematical Practices” and the “Course at a Glance” from the 2019 AP Calculus Course and Exam Description (p. 14 and p. 20 – 23) and give them to your students. Check off the topics as you do them during the year. A “Course at a Glance” poster comes with the hard copy of the 2019 Course and Exam Description available from the College Board or at APSIs and Workshops. See here. Hang the poster in your classroom. Refer to it often throughout the year.

2. DON’T REVIEW! Yes, students have forgotten everything they ever learned in mathematics, but if you reteach it now, they will forget it again by the time they need it next week or next January. So, don’t waste the time, rather, plan to review material from kindergarten through pre-calculus when the topics come up during the year. Include short reviews in your lesson plans. For instance, when you study limits, you will need to simplify rational expressions – that’s when you review rational expressions. When you look at the graphs of the trigonometric functions, that’s when to review the graphs of the parent functions, a lot of the terminology related to graphs, discontinuities, asymptotes, and even the values of the trigonometric functions of the special angles. Months from now you’ll be looking at inverse functions, that’s when you review inverses.

3. In keeping with Unit 1 Topic 1, you may want to start with a brief introduction to calculus. Several years ago, when I first started this blog, Paul A. Foerster, was nice enough to share some preview problems. They give a taste of derivatives and integrals in the first week of school and get the kids into calculus right off the bat. Here is an updated version. Paul, who retired a few years ago after 50 (!) years of teaching, is Teacher Emeritus of Mathematics of Alamo High Heights School in San Antonio, Texas. He is the author of several textbooks including Calculus: Concepts and Applications. More information about the text and accompanying explorations can be found on the first page of the explorations. Thank you, Paul!

4. If you are not already a member, I suggest you join the AP Calculus Community. We have over 18,000 members all interested in AP Calculus. The community has an active bulletin board where you can ask and answer questions about the courses. Teachers and the College Board also post resources for you to use. College Board official announcements are also posted here. I am the moderator of the community and I hope to see you there!

5.  Here are some links to places on this blog that you may find helpful:
   1. Pacing– organizing your year.
   2. Check the Resource page from this blog.
   3. Calculator information:
      • • Calculator Use on the AP Exams The four allowed operations.
        • Good Calculator Use How to store and recall values. In several recent workshops I’ve given I found that a number of teachers did not know this way of saving time and avoiding copy errors.
        • Graphing Integrals without antiderivatives.
   4. Miscellany: These posts discuss basic ideas that I always hoped students knew about mathematics before starting calculus
      • • Stamp Out Slope-intercept Form
        • A Note on NotationIs it sin x or is it sin(x)?
        • The Opposite of NegativeThoughts on the minus sign
        • On Proof
        • On Definitions
        • On Theorems
        • For Any – For Every – For All Three important phrases that mean the same thing.
          

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