Let's Go To the Movies!

     If you haven't checked out the lessons and activities at Robert Kaplinsky's site, you should.  That's where we ripped off the highway sign activity, which I described here.  And don't miss his blog,  which is very thought-provoking and deserves a read.  Earlier this year Rich and I adapted his movie theater project and turned it into a week long problem solving exploration for our fifth graders.
     We started by giving the kids a folders with the following information from the local multiplex:

The first page included pricing information, movie times, ratings, and summaries, and the capacity of each theater, which Rich found out from the manager.

The second page had the rest of the movie listings.

The last page had the food prices, which Rich copied down from the theater.

We asked the kids to take a look.  They started reading each synopsis, talking excitedly about which movies they had seen and which ones they wanted to see.  They laughed about "Jackass Presents: Bad Grandpa".  They whispered about the "R" rated movies.  They debated the merits of seeing "Thor: The Dark World" in 3D.  They drooled over the snacks.  Rich and I exchanged a look.  The hook was baited, now all we had to do was reel them in.
   I decided to use the strategy I had tried last year with Shannon's fourth graders.  They would create the problems themselves, and then solve them.  We borrowed a phrase from their ILA teacher: "thin questions vs. thick questions".  We encouraged them to write some questions that were straightforward and could be solved in a relatively easy manner (thin questions) as well as more challenging, complex problems (thick questions).  They started on their own, then met in small groups to discuss and refine their questions.

Here's an example of two questions from a student notebook.

I had to include this one, which provoked a very interesting "discussion" between the question's creator and another student that I was fortunate to capture on video.  The student insisted that the problem made no sense.  No one would pay to see a movie, leave halfway through, and then go to see the second half of another movie because that would be a "waste of money".  The student who created the question tried to explain that the scenario was not supposed to be taken as anything that might realistically be expected to happen; he just thought it would be a challenging problem to solve.  The other student would have none of it, and this back and forth went on for a good 5-7 minutes.

Groups got together and put their most interesting questions on chart paper.  Rich and I looked them over and selected about 15 for the class to work on.  They varied by topic and skill level.  I encouraged Rich to post them around the room.  The kids had several days to look them over before they were asked to dig in. This time, we assigned each question a letter and asked the kids to list their top 3 choices in their notebooks.  We gave them time during class to tour the room and take a careful look at each one before they made their choices.

The following day they entered the room and saw large, blank pieces of construction paper and markers along with the questions arrayed on desks and in corners all over the room.  They were told to get working on their first choice, but that if more than three people were already working on a problem, they were to try an alternate choice and come back later.  We also provided post-its in case kids wanted to provide comments.  Some worked alone, but most solutions were the result of collaborative efforts.

This was problem C.

These kids tried to find the difference by subtracting and got the wrong answer.  This led to an interesting discussion about why adding and subtracting time is different then adding and subtracting whole numbers.

This group used a number line.  Their work was correct but the answer is wrong.  In the middle post-it the group explains that their answer was a "typo".

This group also used a number line, which they termed "useless".  One of the students who answered the question plotted it out and revised their comment on the number line to "not useless".

This was question F.  It involved calculating with decimals. 

This group was close.  When they went to find the total, they copied $87.75 as $87.00 and were off by $0.75.

This group added incorrectly and was off by $10.00.

A correct answer!

My favorite: question A.  The reason: great example of a problem with a big vertical scale.

This student added up the costs of each individual item in each meal or combo package, found the total cost, and then calculated the difference between that and the price of each package.  It took him two days.  Talk about perseverance!  He claimed that for one of the choices you'd be better off buying each item individually.

A very basic response.

Also basic, but this student has a notion that perhaps better value may be found in another option due to the relative sizes of the drinks and foods that are offered.

The student who wrote the question also provided an answer.  I'll let his work speak for itself. 

  As the experience progressed from beginning to end, Rich and I engaged in a continuing conversation about what was happening.  Our reflections:

• We felt that this was an effective model for setting up conditions where students can be engaged in both traditional and non-traditional problem-solving scenarios. 
• Motivation and engagement came from: student-designed questions that originated from a high-interest topic, and student choice regarding which problem(s) to solve.
• Mathematics arose from a need, not the other way around.
• Low barrier to entry and plenty of room to scale up.
• Tremendous amount of opportunity for communication; both verbal (in the discussions students had during the question formation phase and also during the problem-solving phase) and written (in the way students express their solutions on paper.)

We liked this "movie theater" project so much that we started contemplating another, similar experience for later in the year.  Great Adventure anyone?