Franklin College: High School Math Day 2016
Professional Development Workshop
Sample Activities for an AP Calculus Class
All of the files and links given below are posted on the Franklin College
High School Math Day webpage (http://mathematics.franklincollege.edu/mathday.cfm)
1. Desmos Interactive Activities:
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A variety of interactive math activities are available at https://teacher.desmos.com. You can
either use one of the activities contributed by someone else, or create your own. In addition to
calculus activities, there are many activities related to algebra, precalculus, and other courses.
For each activity, you can generate a class code that can be used to monitor your students’
progress in real-time. For most activities, students can also be shown the responses of several
other students.
Limits and Continuity:
o https://teacher.desmos.com/activitybuilder/custom/574de5cdab71b5085a2aad42#
o This activity does a good job helping students visualize one-sided limits and notions
related to continuity.
Card Sort: Derivative Match
o https://teacher.desmos.com/activitybuilder/custom/57b342ce867e43be309e0451#
o Students are given “cards” containing the graphs of many functions. They have to pair
each function’s graph with the graph of its derivative and answer other questions
related to the relationship between a function and its derivative.
2. Tangent Lines Activity: Angry Birds Simulator
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In the video game Angry Birds, the yellow bird, Chuck, travels along a parabolic path until you
tap on the screen, at which point he begins to move along a line tangent to the parabola. In this
activity, students create a simulator of a particular Angry Birds level to determine where you
should tap on the screen to make sure that Chuck hits his target.
Related Files:
o AngryBirdsInstructions.docx: Instructions provided to the students to guide them
through the creation of an Angry Birds simulator.
o AngryBirdsDataFile.xlsx: A sample Excel document creating the simulator.
 I only provided the students with the original data points, which are highlighted
in green. Everything highlighted in yellow was created by the students as they
worked through the instructions provided above.
 You could give your students as much or as little of this file already completed
as you wanted to. In particular, if your students are not comfortable with Excel,
you could work through how to find the equation for the path of the yellow bird
by hand (as outlined in the instructions above), and then provide them with the
simulator to test their results.
3. Graph Sketching Activity:
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Students break up into pairs to try to graph the function being described by the other student
based only on verbal descriptions of the important features of the graph.
Related File:
o DrawMyFunction.pdf: Handouts provided to each group
4. Optimization Activity: Are the Girl Scouts maximizing their profits from cookie sales?
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Students may be dissatisfied with traditional optimization problems that often seem contrived
or unrealistic. In this activity, students each complete a survey to determine how many boxes
of Girl Scout cookies their class would buy at various prices. This information is then used to
determine what the optimal price is for the Girl Scouts to charge to maximize their profits on
cookie sales to their class.
Related Files:
o GirlScoutCookieDataCollection.xlsx: Initial survey given to the students:
o GirlScoutCookieInstructions.docx: Instructions given to students to guide them in using
Excel to find the price at which profit is maximized.
 If your students are not comfortable with Excel, you could use Excel to find the
equation of the appropriate trendline together as a class, and then do all of the
remaining steps entirely by hand.
o GirlScoutCookieSurveyResults.xlsx: A sample Excel document showing all of the steps
of this project.
 I only provided the students with the original survey results, which are
highlighted in green. Everything highlighted in yellow was created by the
students as they worked through the instructions provided above.
 You could give your students as much or as little of this file already completed
as you wanted to.
5. Riemann Sums and Gum:
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This tactile activity helps some students remember how to draw left, right, and midpoint
rectangles when computing a Riemann sum. Each student is given a curve on a piece of paper
and a 5-pack of gum. They slide the sticks of gum up from the bottom until the correct portion
hits the curve to draw in their rectangles.
Related File:
o RiemannSumsAndGum.docx: Contains a sample curve for the students to estimate the
area under.
6. Real-Life Speed vs Distance Comparisons
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When learning about the area under a curve, a common application provided is that the
area under a velocity curve gives the total displacement of the moving object. However,
some students may struggle to accept that this is actually true, especially when they create
their estimates using Riemann sums based on limited data. In this activity, the students are
given the actual speedometer readings from their professor’s recent trip, and they use a
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Riemann sum to estimate how far their professor travelled. When they compare this to the
distance travelled as measured by the professor’s odometer, they see that they really do get
a close estimate. In a variation to this project, students could collect their own data by
taking measurements on a track using a FitBit or some other device that can measure
speeds.
Related Files:
o SpeedVersusDistanceInstructions.docx: The instructions provided to the students
for how to complete this activity
o Speeds.xlsx: The data file provided to the students to help simplify computations.
The computations necessary for this activity can be done with a calculator instead of
Excel as long as this data table is provided to the students.
o SpeedsLabSolution.xlsx: A sample Excel file containing the computations necessary
to determine how far Prof. Hoehn travelled using her speeds. The cells highlighted
in green are what I provide the students, while the cells highlighted in yellow are
created by the students as they work through the instructions provided above.
7. Review Activities:
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Sudoku Puzzles: End-of-the-semester review games where students answer calculus questions
to fill in numbers on a Sudoku puzzle
o Sudoku1.docx
o Sudoku2.docx
o The puzzles given above are modifications of puzzles obtained from
http://www.pleacher.com/mp/puzzles/apsudo.html. This website contains many more
sample puzzles on precalculus review, limits, derivatives, integrals, applications, and AP
Exam Review.
Jeopardy.pdf: A jeopardy-style review game for the end of a semester (or year) spent covering
limits, derivatives, and integrals (up through u-substitution).