Lesson on Derivatives

Established Goals:
At the end of this lesson the students should have learned how to use derivatives in order to find optimal conditions.

Understandings:
Students will understand that taking derivatives of functions is not a process “in space.”

Students will understand the applications of derivatives to real life.

Essential Questions:
How can derivatives be used outside of the classroom?

Students will know…
How derivatives are used to solve word problems as well as problems occurring in real life.

Students will be able to…
Use derivatives to optimize conditions for a given function.

Performance Tasks:
Students will be asked to create a box with maximum volume given a fixed surface area.

Other Evidence:
Students will be assessed based upon the process of creating their box.

They will also be assessed based upon their reflections papers.

Learning Activities:
Students will be given a piece of poster board, tape, and scissors.

They will be told that the class is having a competition.

The group that makes an open-topped box that holds the most pencils wins.

The prize will be the ability to drop their lowest test score.

After the competition is over, there will be a group discussion about which processes were utilized.

Students will then write a reaction paper for homework critiquing their own method and relating derivatives to the box creating activity.