In this clip the teacher asks the students to come up with their own definition of what it means for two quantities to be proportional.
Definition of Proportionality, Clip 3, 5:29
In this case, the teacher has asked the students to create their own definitions and uses this activity as an opportunity to visit with individual groups. This can give her insight into what students are and are not understanding about proportionality.
As she goes to the groups they do mention covariation and while covariation is useful in understanding proportionality, it is not sufficient. The teacher does a nice job with her questioning and notice she does NOT give the definition to the students, but rather helps them negotiate what makes sense.
As the video shows, the students can talk about the process of solving the problem, but not why it works. It is important as a teacher to encourage justification in terms o the quantities involved in the problem. In this case the teacher uses the juice problem to remind the students about the fact that they need a constant ratio.
