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.

Life-long learning, a teacher's impact, and pizza

My family tried a new restaurant last week. I'd been excited to visit Embers by the Lake, a pizzeria out in the country about half an hour away from our house, since they opened this summer. Although I had heard great things about the food and the atmosphere, that wasn't the only reason I wanted to visit Embers. It's run by two of my favorite middle school teachers.

Photo by Carrie Scozzaro, INLANDER

Mr. Hammons was my seventh grade math teacher. At that point, math was not my thing. I had struggled with learning my multiplication facts and felt like I would never be good at math. He was my first teacher to present math in context. I remember a project where he challenged students to design a house and calculate the cost of windows, flooring, and other materials. I had fun with the project and I willingly did calculations that I would have avoided if they were presented as bare numbers in a textbook. In fact, a discussion about compound interest in his class inspired me, a math-a-phobic middle schooler, to go home and attempt to calculate the payments on my neighbors' crazy new boat even though it wasn't an assignment for class.

I never took a class from Miss Roletto (now Mrs. Hammons), but I remember her as one of the friendliest teachers in my middle school. She was always out in the hallway between classes talking with students. She was also one of the teachers who attended our middle school's Natural Helpers retreat the same year I did. It was a great program training students and teachers to help others. Now that I'm a teacher, I really admire each teacher who gave up a weekend with family to tackle serious middle school issues through the Natural Helpers program.

Our Embers experience was terrific. My little boy was excited because it was superhero theme night there and he got to wear a cape and mask to dinner. Our server (Captain America) happened to be a former student of mine. And my former teachers kept busy as Mr. Hammons manned the wood-fired brick oven and Mrs. Hammons greeted diners and checked in with each table. The pizza was terrific - we had a sausage pizza and one with Gorgonzola cheese and mushrooms.

After we cleaned our plates, Mr. Hammons stopped by our table to ask how we enjoyed everything. I just had to ask him how he learned to make pizza. He said that he took one class, watched YouTube videos, and practiced a lot before the restaurant opened. The practice paid off, because he is making outstanding pizza. After helping so many learn during his years as a teacher and principal, his commitment to lifelong learning is on display at Embers.

Dessert at Embers is an experience as well. You make your own s'mores at the firepit out in front of the restaurant. As Mrs. Hammons started the fire for us, she commented that our waitress remembered me as a fun teacher. I told her how great it is to run into my former students and see what they are up to. She reminded me that my former teachers have enjoyed seeing me grow up and come back to teach in the school district that educated me.

It's amazing how nourishing pizza at Embers can be!

I have Googley EYES

The EXCEL foundation has awarded
over one million dollars in grant money
to Coeur d'Alene classrooms since 1986

I just found out that the EXCEL Foundation is supporting my proposal for classroom Chromebooks! I'll have one device for every three students. I figure that will give me enough technology to create a successful rotation plan for student use. I called my grant proposal "Googley EYES (Exploration Yields Extraordinary Students)". I want my students to explore their passions and take control of their learning. Here's the project summary from my proposal to give you an idea of what I have in mind.

“Self education is, I believe, the only education there is.”

-Isaac Asimov 

Great things come from exploring a passion. Imagine a classroom where students spend 20% of their time in class solving problems and investigating ideas that matter to them. When Google incorporated this 20% time into engineers’ work days, it resulted in innovations like gMail and Google News. Math students will generate questions that cannot be answered with a simple Internet search to guide their 20% time. These questions could involve a problem that could be solved by collecting and analyzing mathematical data or a student may choose to research and practice a mathematical concept of interest. Students will create a presentation, record a video, or otherwise creatively share the results of these “passion projects.” 

Students will have at least two chances during the school year to choose and complete a passion project. Although not all projects will require the use of a computing device, I want to have enough devices available in my classroom so each student can spend at least one class period each week working online to complete the project. In addition to passion projects, math students will also use the Chromebooks to research, organize data, and present solutions to real world math problems throughout the school year such as comparing the cost of the traditional “12 Days of Christmas” gifts to currently popular products.  

Reading and writing is all about communication. Authors have a conversation of sorts when their audience reads and thinks about their work. The audience for student writing has often been limited to the students’ teachers and classmates. Using Chromebooks and Google Documents will allow students to find a larger audience for their work. Students will publish a book review blog and receive and respond to comments from their readers. In addition, they will work together with digital pen pals from another school to revise and edit each others’ work using the commenting features of Google Documents.

These math and language arts activities will give students more control over their learning and equip them with the tools to be life-long learners. In addition, all of the documents they create on the Chromebooks are available on any Internet-connected device, so students can use work in class as a jumping-off point for further investigations at home. Through increased autonomy and experience in using powerful, cloud-based tools, students will be self-directed learners who are eager to learn at school and beyond!

I want to publicly thank the EXCEL foundation for all the good they do for our schools! This is the fourth project they have supported for my classroom, but my students have benefited from art, music, P.E., counseling, and other classroom projects supported by EXCEL. It's terrific to have a local foundation that will put money behind new ideas in our school district!

The order for the Chromebooks goes out on Monday and I hope to have them in my room by the end of the month. I'm excited about all the possibilities this will open up for my kids. And I'll keep you updated as I continue to experiment and refine...