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Implicit Differentiation continued (Topic 3.2)

Unit 3 - Day 6

​Learning Objectives​
  • Calculate derivatives of implicitly defined functions.

​Success Criteria
  • I can fluently calculate the derivative of an implicit function.

Quick Lesson Plan
Activity: Castle Attack


Additional Materials:

  • 30 implicitly defined functions

  • answer key with derivative expressions

  • method for public scorekeeping which students can edit during the game


Lesson Handout

Answer Key


Students will review the techniques and notation of implicit differentiation as they compete in teams to correctly write the most derivative expressions.

Teaching Tips

Form teams of 3 or 4 students and allow each team to create a unique name or logo for public scorekeeping. We give students 60 seconds to draw a castle on the board for their team. During the course of the game teams will easily be able to change their own score and manipulate the score of their competition.

Before the game begins, give each team a score of 3 marks (stars, checkmarks, smile emoticons, etc.) and place 30 equations face down on a table. To start the competition, a representative of each team runs to the front table, chooses one equation, and goes back to their team to construct the derivative.

When completed, the team representative then shows the derivative expression to the teacher.

If the derivative is accurate and correct, the representative removes one mark from their team’s score and adds one mark to another team’s score. The representative returns the original equation to the table and chooses a new equation.

If the derivative expression is not correct, the representative returns to the team and they continue working. (After sustained effort, you might consider allowing a team to select a different problem…)

The competition ends when one team has no marks remaining --- a score of 0 wins!

Note: To hasten the end of the game, certain problems can be worth TWO marks (perhaps the prime-numbered problems?) or even THREE marks (the perfect squares?). You may deem some problems more difficult than others and randomly award extra points for correct answers. The teacher controls the scoring in this game depending on the time available for play.

Student Misconceptions

This is a high-strategy game as students rush to complete derivatives but also try to choose which team receives additional marks. Have fun!

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