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.
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 5, 4:53
In this case she makes the move to use the graph she had drawn on the board to talk about the rate of change of the graph. Notice she brings in issues of magnitude, positive and negative and zero.
The students are not immediately convinced that there is a place where the rate of change is zero. The teacher uses an example from a previous class talking about average and instantaneous speed in order to help convince them.
The discussion then turns to calculating the average rate of change and about how choosing a smaller interval will give you a bettter estimate. Again the teacher has them recall what they did first class and then has them calculate the average rate of change.
This is an example of how the teacher took advantage of the summary to reinforce the concept of average rate of change. Since this will be a recurring concept throughout the course, it is important the students leave module 1 with a strong understanding.
