After two viewings, my fifth graders wondered how many pounds of dirt it took to create Jorge Rodriguez-Gerada's "Out of Many, One" portrait on the National Mall. Through the first viewing, most just wondered what the heck was happening until their jaws dropped at the final reveal.
One of my goals for this school year is to frequently engage my math students in extended problem solving. About once a month, I want to give my students a challenge that takes a week or more worth of math switch classes in order to find a solution. I've scoured all of my books and countless websites for resources, but I'm most excited for the projects that pop into my mind when I hear a great story on NPR, read about something unbelievable from mental_floss, or watch an especially interesting video shared by a friend.
My first attempt at creating an extended problem came together after learning about Dan Meyer's Three-Act Tasks at a recent district collaboration. Later that same day, I saw a video about the "Out of Many, One" project and realized it would make a great first act and a Three-Act Task would be a great kick-off for an extended problem. The first act of a Three-Act Task presents students with a chance to generate mathematical questions and estimate an answer. After coming up with their question, I asked my fifth graders to make a high and low estimate.
For act two, students generate more questions to pull out the information they need to solve the problem. Some of their questions didn't lead to helpful information, but we discussed them all. Eventually, many of my students asked how many truckloads of dirt were delivered to the site. Luckily I had a video for that, too.
The kids still didn't have enough information. They figured out they needed to ask how much dirt a dump truck holds. I had already reverse engineered the problem, so I was able to tell them that the trucks for this project carried between six and seven tons of dirt each.
I encourage a lot of teamwork in my math classes, so students worked together to make the unit conversions and figure out just how to use the information they had to find the answer they sought. Some found an answer right away and began trying to figure out how much sand was there, too.
Finally it was time for act three: the big reveal. We visited the National Portrait Gallery's page about the work to find out some more information and check our answers. Most of the class had been successful in finding an answer close to 1,600,000 pounds of dirt. The best part of act three was comparing that figure to students' initial estimates. The largest act one estimate was 600,000 pounds. One student commented that she didn't even know it was possible to have a million pounds of dirt in one place.
We read some more about the artwork and had a short non-mathematical discussion about the artist's choice to assemble features from many real people into a portrait. It was a great experience for my math students. We weren't done though, that was just our first day and a half, and I wanted my students involved in a problem for a week (or a little more). I'll post later this week about where we went next.
Be sure to read part 2 and part 3.
Be sure to read part 2 and part 3.
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