Overview

Today’s activity is a high-energy and meaningful review that generates student-to-student discussions about the meaning of different derivative expressions and the labeling associated with each derivative. The activity, “Crack the Code,” is an exciting competition between groups trying to determine the secret, winning 4-digit code!

Four multi-step problems (two graphical analysis, two with context interpretation) require students to label several statements as “True” or “False.” The number of “True” statements in Problem 1 becomes the first digit in the code. The number of “True” statements in Problems 2 – 4 then become the 2nd, 3rd, and 4thdigits in the secret code.

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Teaching Tips

All students were given a copy of Problem 1 and groups worked until they determined the first digit. At that point, the next problem was distributed. We wanted to avoid the situation where each student in the group was working simultaneously on a different problem.

Scoring the activity can be accomplished by several methods: you may choose to have groups bring each digit to you as it’s discovered and confirm (or not) their work, or you may have groups write their complete code on the board or on a slip of paper. Award prizes, points, or congratulations as you see best!

Any remaining time can be used to reinforce concepts, model correct vocabulary and justifications, review homework assignments, or to resolve student misconceptions from Topics 4.1 – 4.3. Emphasize that each successive derivative in a problem (or any problem with context) adds a layer to the derivative label, and that the additional layer comes from the units on the independent variable (the units on the x-context, for example). Review our lessons for Topics 4.1 – 4.3 for more information on this.

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Exam Insights

Particle motion and rate in/rate out questions are predictable components of the AP Calculus Test, appearing on both the AB and BC forms. Interpreting a derivative value as well as approximating derivative values are common items on the FRQ section.

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Student Misconceptions

Quiz 4.1 – 4.3 reminder for students: Correct notation is imperative. Students should be disallowed from writing only the derivative expression without naming which derivative they are writing. For example, writing “cos(x) + 2x” is unacceptable, but the form “f “(x) = cos(x) + 2x” is a complete statement.