case 1

Box Problem Summary, Clip 1, 2:40

In this clip the teacher is leading a discussion about the co-variation between the various quantities of the box problem.

Box Problem Summary, Clip 2, 3:08

In this clip the the teacher asks the students about the relationship between the length of the cutout and the length of the box.

Box Problem Summary, Clip 3, 5:02

In this clip the students are unsure whether the length and width of the box co-vary so she has them discuss other the relationships between quantites to help them.

Box Problem Summary, Clip 4, 2:37

In this clip the teacher is discussing the rate of change and how it is changing with a small group of students.

Box Problem Summary, Clip 5, 4:53

In this clip the teacher is discussing the rate of change of the volume with respect to the length of the cutout.

Box Problem Summary, Clip 6, 1:54

In this clip the teacher leads the class in calculating the average rate of change.

Box Problem Summary, Clip 7, 1:32

In this clip the teacher leads a discussion about whether or not there are two boxes that can have the same volume.

Box Problem Summary, Clip 6, 1:54

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  • This is an example of how the teacher helps the students recall how to calculate the average rate of change and discuss its meaning. Probably not all the students need this reminder, but it is helpful to many of the students to see this repetition if possible.
  • As you can see from this clip, the teacher connects calculating average rate of change to calculating the slope between two points, a procedure they are familiar with from their previous math courses. This will help them remember how to calculate average rate of change as the course progresses.

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