# 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