We’ve discussed the learning paradigm of “

*Watch it, Do it, Teach it*”. It is one thing to watch someone do something; still another to do it yourself; but quite another to teach it to someone else. Real learning comes from teaching. Learning also does not occur in a vacuum. We learn through our interactions with others and with our environment. Collaboration is an important life-skill for the 21st century global citizen.

The goal of this final project is to work together to teach a calculus concept

and by doing so learn at the same time.

Nowhere is it more evident that calculus is the mathematics of change than in related rates problems. When two quantities change over time, the rates of their change are often related to each other. That’s one of the differences between algebra and calculus. In algebra we study the relationship between quantities. In calculus we study the rates of change of those quantities. In this respect, an algebraic equation is a static snapshot of two quantities frozen in time, while a differential equation of calculus represents a dynamic video of those quantities set in motion.

Within each group, the final project consists of three

**tasks**:

**PRESENT**a related rates problem. Select a scenario from the pool of classic related rates problems or create an original situation with similar parameters. Act out the scenario either by video or by stitching together a storyline of still photos. Be creative! Use toys, props, or other inventive ways to illustrate your scenario (puppets, claymation, etc.). Here are some examples to spark your imagination.

Filling a cylinder

Baseball runner

Moving sea creatures

Stone thrown in lake

Flying pig

Reeling in the big fish

Your related rates problem should be presented clearly and concisely; i.e. in a way that it could be used as a homework or test problem. Make sure that it is fully-specified, but not redundant (that is, there can’t be too little or too much information to solve the problem). Your problem should not be ridiculously difficult, nor should it be so simple that it is practically trivial. It must require calculus to solve.

**SOLVE**your related rates problem. The solution will include a written description of the problem. All variables used to model the scenario will be clearly defined. The solution will contain a graphic to illustrate a “snapshot” of the scenario; and each step of the solution will be properly annotated.

**REFLECT**on your work on this project.

Each member of the group will describe his/her contribution to the project.

Each member of the group will write a reflection on what he/she learned from working on the final project. This may include the use of a new Web 2.0 tool or computer skill, thoughts on collaborative group work, or insight into related rates problems.

The presentation of your problem will be posted to our blog. It will begin with an introduction which includes a statement of purpose, the

*nom de plume*of each group member, and a brief description of the project scenario. After the presentation, provide a hyperlink to our wiki where you will post the solution and reflection portions of the project. Here is the rubric for the project.

The finished project is due by 3:00 pm on Friday, March 5. This final project will be a reflection of your learning, group effort, and commitment to excellence. I hope that you have fun teaching the concept of related rates to others who will benefit from your knowledge.

Cheers, Bru

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