The following is a  standard problem during our sequence and series unit.

I attempted to “3-Act” this problem using the following videos.

ACT – ONE

I showed this video first,

and then asked my students, “What is the question that comes to mind?”  The usual responses occurred, “Are these our test?”, “Why did you record your self?”,ect.   Eventually, we get to the mathematical question, “How long did it take you to grade all of the test?”

ACT – TWO

Now comes the part where I ask students what information they need.  They all ask for “How many tests?” and “How long does it take to grade one test?”  Obviously, if they had both of those pieces of information this would be a trivial problem.  I did give them the number of tests,

but I did not give student the time it takes to grade one test.  Instead, I showed this video.

I did not give students any direction on how to go about solving this problem.  I didn’t even say the word arithmetic or sequence.  From a previous problem, we had discovered the arithmetic sequence formula, but again, I did not give them the hint to use it.  I wanted to give students the freedom to solve this problem any way they like.

Side Note:  Some students thought because they knew it took 12:24 to grade 10 tests, they could simply  divide the two and that would tell them the time it  takes to grade one test.  This does not work because the clock starts before I actually start grading tests (this is the a1 in the arithmetic sequence formula).  I purposely fumbled around for a minute so students couldn’t solve this problem that way.

There were a lot of creative solutions to this problem.   However, a lot of the solutions were not entirely accurate.  Students would make assumptions when they shouldn’t have or students would make estimates about things they didn’t necessarily know.  It probably would have been worthwhile to have students look at other students solutions and find things that were wrong about them.

ACT  – THREE

If you calculate this problem correctly, it doesn’t exactly match up with the time with in the video.  This led to the discussion about whether or not this problem is arithmetic, as well as, possible reason why the amount of time it takes to grade each test would differ (i.e. an “A” test vs. a “F” test or the possibility that I would spend less time grading towards the end because I want to finish.)