As we moved through the calculus unit on related rates I searched for a way to bring more meaning to the topic and to make it more exciting. Some students were struggling and I wanted a solid review day before the quiz. I came up with this “Develop and Sell it” Activity. Essentially I gave students 4 related rates problems that were as “real world” as I could find. I had students work in groups of two to four and told them that they could only work with their group. They were told that they worked for a firm that worked out related rates problems for companies. Their task was to “develop” the solution and “sell” their reasoning and solution to the company.

Once they had found solutions that each group member agreed to, I assigned each student in the room a number 1-4. Students who received a number 1, for example, then congregated and compared solutions and methods to that problem. This then allowed students to see different perspectives on the same problem and “argue” about whose answer was right. It was a tremendously engaging activity that the students enjoyed and it relied on one important piece: I couldn’t help at all. I didn’t tell them if their answer was right, if their method was correct, or “what I would do in their situation.” They had to rely on their reasoning and justification. Taking myself out of the equation *forced* students to analyze each other’s work and critique each other’s reasoning. That was the best part of the activity!

In the future I would love to get actual questions from companies and industry. I’ve also considered video questions and other ways to make the problems more authentic.

As usual, any feedback you can give me would greatly appreciated!

(Here is the Pages Version of the Activity)

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It’s great to see you providing opportunities for your students to develop “soft skills” that will make a tremendous difference in their lives, regardless of their career path. I like to use inventory management for related rates, as this is universal business issue is addressed by calculus.

Thanks for the feedback! I should incorporate more business examples as I know many students would benefit from that.