CA I.2 Bottle Graph Exploration, Part II
Purpose: To define rate of change and develop some language to describe non-linear relationships.
Classroom Procedure: We use the class discussion questions as an opportunity to define rate of change and concave up/concave down. We also relate what how concave up and down and increasing/decreasing relate to the rate of change. Finally students should work on the last question independently to see if they have made sense of those ideas during the class discussion.
Ideas this Activity Builds On: The work from MI CA1 where students did similar work on cylinders. This also builds on students prior knowledge of graphs and descriptions of graphs.
Introduction/Motivation of the Activity: This activity can be motivated by asking how the graphs would have been different in M1 CA1 if we had a martini glass instead of the cylindrical glasses. Then telling students that we are going to continue with this train of thought and work on more complicated shapes today.
Need to Establish by the End of Activity/Wrap-Up: A definition of rate of change, increasing, decreasing, concave up, concave down and how all of these are related to each other.
Additional Notes: This is a neat link to look at after working on the funnel question on the synthesis activity: http://www.learner.org/courses/learningmath/algebra/session1/solutions_c9b.html