BIG things in math - Part 3

Read part one and part two to see how my fifth grade students began using Jorge Rodriguez-Gerada's "Out of Many, One" in math class.

After figuring out the square footage and weight of the materials used for "Out of Many, One," I wanted to give my students the opportunity to create something large. My original plan was to go outside and measure our school's field, make a scale drawing of the field, figure out an image that would fit the shape, and then use string to mark a portion of the artwork in a little-used corner of the field. A week of very rainy days made that plan impossible, so we figured out a suitable indoor alternative.

My fifth grade math students separated into two teams to design large posters for one of our school's hallways. I showed my kids the wall spaces available for posters before giving them a selection of different size graph paper and the requirement to include a quote or slogan that represented a growth mindset, but otherwise I left them alone to come up with something. 

Our spaces had obstacles including a fire extinguisher

The first day of work on the project consisted mostly of measuring the space for the poster. Both groups recorded a number of measurements, but had a difficult time translating those to a scale drawing. Seeing that my students needed some more experience with scale drawings, we spent part of the next class period looking at diagrams, blueprints, and other scale drawings and discussing how large objects were represented accurately in smaller drawings. We also looked at our second activity with "Out of Many, One" in an attempt to see how we previously worked with scale.

It didn't take long from there for students to complete their scale drawings. When they presented them to me for approval, I asked how much butcher paper they needed and how large the writing and other features would be on the poster to double-check their scale drawings.

Next, students divided up the work on their posters. It was interesting to see how one group put assigned members certain squares from the graph paper while the other group chose one person to work on text and others to complete specific drawings on their poster.

This group used 1/2 inch graph paper

Both groups ran into trouble with teamwork along the way. I did my best to let them solve their issues, but I had to step in a couple times to help. One group had a very difficult time drawing objects on the big poster to the correct scale based on their scale drawing. I frequently checked in and had them look back at the scale drawing to confirm that their poster matched the plan.

Turning the scale drawings into large murals
took a lot of careful measuring

In the end, my students created some nice art for a bare spot in the hallway, got some practice measuring & multiplying, and learned a bit about scale drawings. It definitely took longer than I planned. We spent three full math periods working on the project and used the last ten to fifteen minutes of class frequently for about two weeks. Still, the students really enjoyed the project and it gave them a chance to demonstrate their budding understanding of scale. If I do this with next year's fifth graders, I would want to give them some more opportunities to work with scale drawings before getting to this project and I would want to speed up the process of creating the final posters. Still, it was a fun project and it makes me excited to find more extended problem solving opportunities for all of my math groups. And I'll keep you updated as I continue to experiment and refine...  

BIG things in math - part 2

Read part one to see how my fifth grade students began using Jorge Rodriguez-Gerada's "Out of Many, One" in math class.

This satellite image was captured by DigitalGlobe's GeoEye-1 satellite
on Oct. 6, 2014. Image from the National Portrait Gallery's website.

After figuring out how much dirt was used in the creation of "Out of Many, One," my kids tried to figure out just how big this colossal artwork is. We looked at a number of photos of the work, but decided that the one to the right gave us the easiest picture to measure. It didn't take long for students to realize that they needed more information to figure out the scale.

I pulled up a map of the National Mall on Google Maps to give us some context of the area. After a little discussion, we decided that we should figure out the length of another feature in the picture. We chose the road to the west of the DC War Memorial. Although the road had a small curve around the memorial, it was the easiest to clearly identify in the picture and on the map. The road measured 400 feet long. Students used that measurement to come up with a scale for the map and estimate the square footage of "Out of Many, One." If I were to do this project again, I would find measurements for other landmarks, such as the width of the reflecting pool, to see if we come up with similar estimates when basing our scale on other known distances.

Image from Google Maps

We weren't done exploring big things just yet. My students went from using scale to estimate the size of this artwork to creating their own scale drawings for a giant artwork. They're still working hard on that project, and I promise to let you know how it goes.

You can see my students' final project in part three.

BIG things in math

Watch this video. What mathematical questions come to mind?

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.