For the last few weeks, I have visited a third grade classroom every afternoon. I love this time because I get to work with a teacher for whom I have a tremendous amount of respect. I wrote about her here.

This teacher has often told me how much she loves to teach math. She has been teaching for thirty years and she is always growing and learning. She often comments about how much her math instruction has changed over the last ten years. She has become an expert at honoring student thinking, valuing mistakes as learning opportunities, and cultivating perseverance. She told me in the beginning of the year that she was worried about math this year. She has a group of students who have so many social and emotional struggles in their lives that she is not sure how she will be able to get them to build their stamina for problem solving. She invited me into her classroom and I was honored to accept.

Admitedly, I was nervous. I am great at “talking the talk” when it comes to teaching kids how to persevere and communicate their reasoning, but “walking the walk” is really hard. This teacher “walks the walk” so well and she does it with patience and love. I knew I would be learning from her, but I was not sure that I would be bringing anything new to the table.

Awhile ago, I had read about the Hundreds Face challenge and thought, “That is so cool. I am going to try that with kids.” Then, I filed the idea with the thousands of other amazing ideas that I have seen on Twitter and WordPress in the short 6 months that I have been spiraling through the MathTwitterBlogoshpere. The beauty of the #MTBOS is that, yesterday, I found myself reading Malke Rosenfeld’s post, #HundredFace Round 2 and thinking, “Oh yeah. I remember that. That is so cool. I am going to try that TODAY with the third grade class that is struggling to persevere.”

I was still nervous. What if they didn’t get it? What if they gave up? What if they didn’t want to make faces? Should I let them build other things? If I did, what would the constraint be? I decided to ask Malke for her thoughts. Here is another beautiful thing about the #MTBOS – you can ask far away people for help. At 10:31, I posted some questions on Malke’s blog. At 11:56, Malke responded with some suggestions and a few more questions. At 12:30, I responded with my new ideas. At 1:15, I taught the lesson.

Stop for a second and think about what I just said. Now, think about this: I have never met Malke. This was the first time that we ever communicated.

When I got to third grade, I told the third grade teacher my idea. She was thrilled. “That is a great idea!” she said. Then, she took out her giant tote of Cuisinaire rods. As the kids came in and got settled, I caught her up to speed about what Malke and I had discussed. We anticipated what students would do and what we would look for to share with the whole group.

First, we took a page from Malke’s book and told the kids to explore with the rods. We smiled as we saw several kids building stairs and then noticing that they could compose rods out of other rods. They told us that 10 whites equals 1 orange. Here are some of the other equivalent compositions that they built:

Next, I told them about the challenge. Malke, the teacher, and I had all agreed that starting with 50, instead of 100, would offer scaffolding without lowering the cognitive demand of the task.

*All* of the kids started building faces. *Most* of them were thinking about how to make the face equivalent to 50 white cubes. At this point, the third grade teacher and I agreed that our priority was to encourage students to stick with the task for as long as they could. It was okay if some of the faces didn’t equal 50. We could come back to the faces next week and explore the math more deeply. Here are some of the 50 faces:

The one on the right is one of my favorites. When I first approached the student, I asked him how he knew that the face was worth 50? He wrote, “blues are 9 so I need 5 ones.” I don’t know if you can tell from his picture, but he used 4 blues to outline the face, 1 blue for the mouth, and then he tacked on a white cube to the end of the mouth.

Some of the kids were struggling with making a face that was equal to 50 and some of the kids were done and ready for more. The teacher and I conferenced and decided to offer a choice for the next challenge:

- Choice 1: Build a face that is equivalent to 100!
- Choice 2: Design your own face and tell us how much it is worth.

We weren’t sure if the second choice would offer enough of a constraint, but we think it did. The students who chose to design their own face *were* constrained by justifying the value of the face they had created. The additional constraint of defining a value was beyond their zone.

Here is a sample of two students who designed their own face and told us the value.

And here are some of the #Hundredfaces:

There are still some faces that we need to revisit next week. I love these faces, even if the math is a little off:

The best part of this lesson was at the end. We asked the students what they learned today. Here is what they said:

- “Math can be fun!”
- “Never give up! You’ll never figure your way through it and you won’t learn if you give up.”
- “We made a bunch of mistakes today so our brains must have grown.”
- “Keep going – it’s a challenge.” (This one is from the boy who looked up at me half way through the lesson and said, with a big grin on his face, “This is so much harder than I thought it would be.”

And my favorite one…

“I learned to keep trying. I was trying to make a face with only 50 and I kept getting over 50 ,and over 50, and 0ver 50. I just kept trying the 50 face. Then, I got 50. Now, I am trying to build the 100 face.”

Thanks Malke.

I absolutely loved reading this post. I’ve read it several times over and it makes my heart glad for everyone involved.

What I’m curious about is how/if you approached the recording of the faces? Did you discuss strategies as a whole class, or just give them paper & pencils, or…?

I’m also curious to hear what happens in Round 2!

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I loved writing this post and being a part of this lesson. It was fun and I learned so much! We didn’t scaffold the recording at all. We just asked the students to record their justification to us. Many of them sketched the figure. Some were using numbers and equations. Interestingly, if their sketch proved to be “off” by a few, they adapted the sketch, but forgot to adapt the actual rods. Some of them have sketches that equal 100, but the pictures I took of the rods actually equal 101 or 105. I would like to use this discrepancy in a lesson next week – maybe a notice/wonder type activity. I am a little nervous about sharing their mistakes. This group is pretty fragile when it comes to risk taking and confidence. I would hate to have it turn negative. I would love any suggestions about this.

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Okay, I have some thoughts! It seems like they were working individually? Does everyone have some kind of record of their face from yesterday? If not, I bet it was a memorable day and they’ll be able to remember how they made their face and the counting strategies they used.

Instead of a close analysis of individual work, I wonder if what might be most supportive for this class would be to focus on the different strategies everyone used to build & record their face in the first round. If they worked individually they could pair up and share with each other and then you could create a group record of all the strategies.

After that, challenge them to build a new face (different from last time) with a focus on their recording strategy. I liked the two choices you and the teacher gave them and think they’d work well for Round 2 and maybe offer a third option?

I just had the thought that a Hundred Face challenge is like a puzzle a kid builds for themselves!! I also wonder if the art teacher has a self-portrait unit where they can extend the face making to focus on the natural symmetry of the face. There’s a lot to notice there that can be connected to magnitude of the rods…but that’s just me thinking out loud…

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Yes! Each student has a recording of at least one of the faces they created. I love your idea about focussing on the strategies next week. I think if we hand them back their work from this week, they will be able to articulate which strategy they used. As I am thinking about it now, I am wondering if there are actually two different strategies – one for building and one for recording- maybe? I want to ask them how they got started – I am curious about whether they chose their blocks first or used trial and error and made adjustments as they went? Maybe I will just ask “How did you build your 50 face?” I really like your idea of building more than 1 face. I am trying to figure out if we need to lower the number for this task – take it down to 20? Actually, as I try it myself, I think 20 might be too few. I would like for them to build at least one more face that they can prove is 50. I am still a little worried about the few kids that didn’t do a 50 face. They ended up making their own faces and telling us how much they were worth. What if I asked them to build a second face that was worth the same amount, but looked different? I also agree with you about integrating more partner talk and justification next week. We could start with a turn and talk about how you built your face (referring to their pictures).

By the way, as I was trying to build my own 50 face this morning, I started thinking about integers when I was trading pieces. I am wondering about trying this with a 7th grade class because I wonder if any of them will go there – they are halfway through an integer unit. Our middle school art teacher is wonderful – maybe I can run with this. Any thoughts on that?

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First of all, this article just came to mind. Not sure why, but it’s one of my favorite examples of merging visual arts with number sense and making. 🙂 http://mason.gmu.edu/~jsuh4/math%20masterpiece.pdf

“How did you build your 50 face?” is a great question! I think you’ll get a lot of interesting answers that will help move everyone forward.

I agree the baseline should be 50. From there 100 seems like a natural (and not-too-threatening-to burgeoning-perseverance) next step.

Also, what were the values of the faces made kids who built first and then tallied their worth? Were they in the ball park of 50? I ask because I’m curious about your overall goal. Perseverance is one of your goals, but it sounds like you’re also focusing on something else too. Does this something else hinge on having “50” or “100”? Is it okay if they don’t have the target number but are able to create a convincing justification?

I don’t have a whole lot of experience with integers but if you’re noticing that it’s part of your math & making process I’d encourage you to explore that a little more!

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I am glad you asked about our other goal. It prompted me to reflect. I think, now that the kids are engaged with the push/pull of this task, I would like them to be able to think more deeply about the equivalence piece. But, first, they probably need to be able to justify their thinking. I would like for them to be able to compare/contrast their justifications. Some are counting, others are adding. One of the questions that I have is: Are some students choosing the blocks based on how easy it is to justify the total. For instance, several students stuck with the ten rods or the 9 rods plus one. I am wondering if they will be able to see their own numbers in each other’s work. For example, one student used four 10 rods, one 9 rod, and 1 unit cube to make 50. Another student used four ten rods and 5 two rods to make 50. The first student labeled the rods and wrote an equation. The second student labeled his rods. I am wondering what they will say if I ask them what is the same? what is different? Would it lead to a conversation about 9 + 1 = 2 + 2 + 2 +2 +2? Recently, I have become very sensitive to how I represent student thinking when we are discussing numbers. I have found myself thinking really carefully and listening very closely when K-3 students are sharing their thinking and I am trying to record it for them. In fact, more and more, I have been handing off the marker to them because I am so nervous about losing something in the translation. So…. As we watch them build new 50 faces, I think I will look for pairs of students that will prompt discussions of equivalence. Then ,ask them to compare and contrast with each other and try to listen very closely. Wish me luck. I will let you know how it goes next Wednesday. Thanks again Malke. What a wonderful gift to be able to process with you.

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