Interpreting the graph of the derivative of a function
From APEC HRDWG Wiki
The lesson “Interpreting the Graph of the Derivative of a Function” was captured on video for the APEC Education Network (EDNET) project called Classroom Innovations through Lesson Study. The lesson is an example of using the Lesson Study process of professional development in the teaching of Mathematics.
Lesson Overview
This 11th-grade lesson was conducted on October 24, 2008 as a part of the Lesson Study Institute 2008 supported by the Chicago Lesson Study Group. This lesson aims to strengthen students' understanding of the relationship between the graph of a function and the graph of its derivative by having students work backwards—determining what the shape of the function graph might be based on the graph of its derivative.
The lesson works through three problems. First, a warm-up problem provides a table stating whether the derivative is positive, zero, or negative at three values of x. Second, the main problem provides a graph of a quadratic function as the derivative. Third, an assessment problem provides a graph of a quartic function with four zeros.
[Demonstration Practice  ] (see Resource Types)
|
| Lesson Plan | Lesson Video in MPEG 4
(Video Clips and Highlights Available below. Right-click and select "Save Target As" to download the file.) |
Video Clips and Highlights from the Lesson
The video clips are selected from the full List of Episodes (above). The Full Lesson Video may be downloaded for further study.
| Description of Video Clip | Video Links |
|---|---|
| The teacher asks students to work first independently, then in groups, to determine a possible graph of a function based on a table which says that the functions derivative is negative when x=1, zero when x=2, and positive when x=3. |
1. Warm-up
|
| Groups' posters have been placed on the board. Students examine the posters and discuss them with their group. Then, the whole class discusses which posters meet, or do not meet, the given conditions, and the teacher organizes the posters into two categories. |
2. Discussion of the warm-up
|
| Students are given a graph of the derivative of a function, a parabola with two zeros. Their task is to determine the possible shape of the graph of the function. The students work independently, then in groups. |
3. Main problem
|
| Groups' posters have been placed on the board. As before, students examine the posters and discuss them with their group. This time, the teacher invites students from one group to come up and reorganize the posters into "meets" and "does not meet" categories. The class discusses the organization, and there is discussion of whether the vertical placement of the graph matters. |
4. Discussion of the main problem
|
| Students are given a graph of the derivative of a function, this time a quartic with four zeros. As before, their task is to determine the possible shape of the graph of the function. Although the instructions are to work independently at first, students immediately begin discussing the problem with each other. |
5. Assessment problem
|
| Following the same pattern as before, students discuss the posters with their group, then a student moves posters into "meets" and "doesn't meet" categories, and the teacher asks for an explanation. |
6. Discussion of the assessment problem
|
