In Calculus we are currently doing rates problems. If you are familiar with AP Calculus, then you should be pretty intimate with the famous Amusement Park problem and all of its children.

My calculus book only has 2-3 simple problems on this topic so I have created about 10 of my own multiple part questions over the years for practice on this topic.

This is the 3rd year that I have had students create there own problems. Here’s the break down of what we did.

1st week – Students worked on my problems and we discussed them in class.

2nd week – Students created problems and we took a quiz.

**Day 1** – Practice set of 2 problems students made last year + Sandy Beach AP problem.

** Day 2** – Check answers from day 1 and in groups or 2-3 students write their own scenarios with equations and questions. Create your own rates Scenario

**Day 3** – Students review another groups question and help them to adjust the problem. Then they wrote their scenario in a google doc and put it in our class folder. Rates Problem Review Sheet

**Day 3 (Evening)** – I looked through all the student problems and picked one from each class. I ended up picking 2 from one class, so 4 total problems. I did a little editing myself and combined the 4 problems into the quiz for this topic.

**Day 4** – Students took the quiz they created in class. Rates Quiz

If you don’t look at their problems, at least check out the titles:

**The Great Cat-Tastrophe**

** Wang’s Wontons on wheels**

** Havana’s Hats**

** Save the Fishies!**

** Day 5** – The half-day before spring break, so… you know… Something Awesome!

This was one of the most enjoyable times teaching this topic. The buy-in was huge with students creating the assessment.

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What a great idea. I like the student samples. Would you say that the groups who invented only one rate (vs. two rates, as the Catastrophe group did) didn’t completely understand the assignment?

Not necessarily. I didn’t require them to use two rates. However, I think I may expand the assignment next year so that each group writes 2 problems: One with 1 equation and one with 2 equations. Or maybe I’ll just require them to use two equations… Something to think about. Thanks!