The teacher gives the students a problem that is both proportional and linear, then changes it so that it is still linear, but no longer proportional.
Comparing Proportional and Linear Situations, Clip 3, 4:25
In this example the teacher has created a third situation, now she has to get off the treadmill. Again, first they create a table of the situation, and the students are asked to create a formula and a graph of the situation.
The teacher puts the various answers on the board to allow them be discussed. Notice that she has the students discuss their answers and asks the other students what their thoughts are on the responses.
She requires justification for their answers, it is not enough to say because of the rule for transformations of functions, she requires them to justify this rule as they have not established it in this class. The teacher takes the opportunity to discuss why this would work in this situation.
