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 1, 3:42
In this example the teacher starts off with definition of proportionality and it takes a while to get a response from class. Notice the teacher makes sure there is meaning behind everything they say, always requiring them to justify their answers.
She also has them recall the wheatgrass problem they worked on. Techniques like this can help students recall old strategies they have employed on previous problems that may help them with the current problem.
She goes on to create a table of the situation. They give the graph and equation, but in the next clip the teacher will alter the problem to make the situation linear, this is one way of bridging between proportionality and linearity.
