Teacher Guide, Middle School Activity 1

TEKS covered by this activity: 6.8A, 6.10D, and 6.12A

This Pre-AP* activity introduces the calculus topic rate of change. It was conducted in a Pre-AP grade 6 classroom. Students began drawing graphs from data collected by pouring rice into containers and then moved to a more abstract level by drawing graphs from pictures of containers. The purpose of this activity was to have students think about the rate at which the height of rice in various containers changed depending upon the shape of the containers. Students were divided into groups of three to four people. Each group used three different shaped containers and took measurements of the heights of rice in their containers.

The students in each group accomplished the following activities:

1. Measured fixed quantities of rice using a coffee or laundry detergent scoop (The students poured the rice into the container and then measured, recorded, and graphed the resulting height of the rice after each scoop. This process was repeated for two other shaped containers.)
2. Displayed their three graphs on the wall for student discussion
3. Discussed the different slopes in each of their graphs and how the slopes relate to the rate of change of the height
4. Selected three different containers and drew individual graphs* based on the data displayed on the wall
5. Used worksheets* to continue their study of graphing and rates of change
6. Summarized their work* by answering the following questions:
   1. Which of the containers has the slowest rate of change of rice height with respect to volume?
   2. What general statement can you make about the relationship between the shape of the container and the rate at which the rice changes with respect to volume?

Reflections on the activity: In thinking back over the activity, the instructions should stress that the students explain, in complete sentences, the reasoning behind their graphs or why they matched a graph to a particular container. All axes should have been labeled and have appropriate scales.

*See student samples of work associated with this activity.