### 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

#### Teacher Journal CA I.2

• Updated Activity  I updated this activity to remove the experiment part. Although this was a good intro activity we found that it took too long and that the students didn't gain a great amount of understanding from the experiment.
Posted Dec 30, 2013, 2:05 AM by Mairead Greene
• Bottle Graph Activity, Part II  I spent two days on this activity this year - that was a little too long I think. It should probably have been more like 1.5 days. The first day went well - the students worked mainly independently and went through pretty much as I had planned. The second day though I spent the entire time in an interactive lecture basically on rate of change, increasing/decreasing and concave up/down. I'm not sure that it was the best thing to do - maybe if I was going to lecture I should have just gone through it more quickly or if it was going to end up being a whole class maybe there should have been more work that they could have done independently in small groups. We can see how this goes for other people and think about a change if we need to. They went home to work on the Synthesis questions and I gave them two days to work on them.
Posted Dec 30, 2013, 2:04 AM by Mairead Greene
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ConcavityCurves.nb
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Paula Shorter,
Jun 18, 2011, 12:40 PM
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FunnelCurves-1.nb
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Paula Shorter,
Jun 3, 2011, 3:45 PM
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FunnelCurves.nb
(24k)
Paula Shorter,
Jun 3, 2011, 3:45 PM