CA III.3 Related Rates

Purpose: To introduce students to related rates problems building on their understanding of the chain rule.

Classroom Procedure: Students should be given time to work on the multiple choice portion of the first question in small groups and then this should be discussed in detail with the whole class. This is the place where students are making the connection between the chain rule that they have learned in Module II and the fact that this gives us a relationship between different rates of change that can be helpful in answering other questions. After this discussion class time should alternate between students working on the remaining problems in small groups and whole class discussions on these problems when it seems appropriate given the misconceptions or struggles that are happening in those small groups. This activity will either require some significant work on the students part outside of class or two days of class time.

Ideas this Activity Builds On: This activity mainly builds on the students understanding of the chain rule that was developed in Module II. This activity also builds on the work we have already done on translating from narrative representation into symbolic representation. There is no need of implicit differentiation here.

Introduction/Motivation of the Activity: To use our understanding of the chain rule to help take advantage of our knowledge about one rate of change to find another rate of change.

Need to Establish by the End of Activity/Wrap-Up: How to identify a relationship between two changing quantities, write down that relationship symbolically and move from that relationship to a relationship between the rate at which those quantities are changing.

Additional Notes: There are no synthesis questions for this activity. In many ways the next activity serves as the synthesis for this activity as we move to related rates questions that require implicit differentiation. Implicit differentiation will be introduced within that activity.

Teacher Journal CA III.3

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    Students often struggle with focusing on what the method is for these questions instead of focusing on applying their understanding of the concepts for each question. As far as method goes, I do encourage them to first assign each changing quantity a variable name, then write down all the relationships and values that they can identify from the narrative given in terms of those variables. Then identify what they are looking for and see how the relationships that they have can help them find this unknown quantity. This however in my mind is as far as you can come to identifying a method for this type of question and this usually falls far short of what students are looking for. I often talk to students about the fact that the skills we have been building in class so far (reading independently, moving between representations, reasoning from concepts) should all help them in these questions that do not have a clear method attached.
    Posted Jun 13, 2012, 5:47 PM by Mairead Greene
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Mairead Greene,
Nov 19, 2013, 7:54 AM
Mairead Greene,
Nov 19, 2013, 7:55 AM