Deriver’s Licenses in AP Calculus

Last year, I began using Deriver’s Licenses as a fun way to recognize students for their mastery of increasingly complex differentiation skills. I just finished creating my final Deriver’s License of the year - just in time to give the student before he takes his AP exam Monday morning!

Here’s what my Deriver’s Licenses look like:

FRONT

BACK

Right after passing the final quiz and earning their license, I take two Polaroid photos of the student holding their graphing calculator - one photo for the license and one for my Senior Wall display.

Here’s a WORD DOC (with personal information left blank) of the template I created and use.

Here’s how this process work in my class:
In order for a student to earn their Deriver’s License, they need to pass three different “5 for 5” quizzes. Each quiz has 5 questions, and here’s the important part - they need to complete a quiz with 100% accuracy in 5 minutes. These are the general topics on each quiz:

QUIZ 1: Power rule, Product rule, Quotient rule, Trigonometric derivatives

QUIZ 2: All the above, plus e^x, a^x, ln(x) rules

QUIZ 3: All the above, plus Implicit Differentiation

The students don’t like the time limit at first, but performing math successfully under pressure is a huge part of the AP exam, which is also timed. A lot of students have test anxiety, so I need them to get used to that feeling of stress and pressure in a low-stakes environment before sending them to the AP exam, a high-stakes test. Also, if you really know your derivative rules, the time limit won’t be a barrier anymore, so ‘failing’ a quiz lets students know they need to practice more and build fluency and confidence.

Students take a quiz as many times as needed until they get every question fully right. The first time they take a quiz is during class time (it’s usually the warm-up for the day). This year I gave Quiz 1 on November 1, Quiz 2 on November 15, and Quiz 3 on December 6. I have never had a student get 100% on their first try, so the next time(s) they take a quiz, they come to my room either during lunch or after school.

IMPORTANT: To prevent students from just memorizing the answers to a quiz, U have multiple versions of each of the three quizzes. They get two tries on each version, then they get a new version with different questions (similar problems with small differences).

Funny story - I have a student this year (let’s call him Student 1) who I thought got a 5 out of 5 on his first try with Quiz 1. I was super excited about it and made a big announcement about it in class, and everyone in my AP class is very close, so they were all excited for their friend too. Then, one of his friends (let’s call him Student 2) compared his quiz to Student 1’s quiz to see what he had done wrong on one of his questions. Student 2 noticed that Student 1 had gotten a question marked right while he himself got it marked wrong, even though they had the same work (big mistake on my part!) Student 2 asked me why had gotten it marked wrong (he was genuinely confused and didn’t mean to mess up Student 1’s perfect score). When I noticed my mistake, I had to take away Student 1’s 5/5 score and change it to 4/5 - we still laugh about this moment because Student 1 couldn’t believe he didn’t have the coveted “First Perfect Score Ever!” title anymore!

Here’s how I record these three quizzes in my Google Classroom. I put this ‘topic’ right at the top of the stream, since it’s typically a year-long process:

Each time they take a quiz, I leave a comment under their assignment with their score out of 5. I only submit a score and return it to them when they get a 5 out of 5:

Last year, some students didn’t come back to fully “pass” each of the three quizzes, but this year ALL of my students really got into it and took the time to earn their licenses!