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How many snow people do you see?

A few weeks ago, I stopped by a friend’s class. She was putting up some student work. Super cute art project–love the faces. Then, I noticed how she had organized the kids’ work. So, I leave you with a few questions to ponder.

How many snow people do you see?

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And this question: how do you think your kids will determine the number of snow people hanging up in Mrs. Marine’s classroom?

And this one: what strategies did they actually use?

And a few more. How accurate were your predictions? Which ideas surprised you–as in a good surprise?

Which equation is correct?

On Friday, I had the opportunity to hang out in some classrooms with some awesome teachers. They were having their 7th graders work in math stations. The students were working in self-selected groups of twos or threes. They worked on one question per station. During the last round of stations, a group got stuck on this question:

Set up and solve an equation to find the value of x. Find the measurement of ∠AOB and of ∠BOC.

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Each student had worked on the question individually, and then the three kids compared answers. They each had come up with a different equation.

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My immediate thought was FABULOUS!!  The second thought was what are the teacher moves so that the outcome is the students will figure out which of the equations are correct.

The teacher joined the group, and asked the student who had written m∠AOC = 180° to explain the thinking she used to write her equation. The group all agreed that the equation was correct and it was helpful to know, but it would not help them find the value of x.

The teacher then asked the student who had written m∠BOC + 11= 180 to explain the thinking she used to write her equation. Then, the teacher asked the first student to describe how her equation connected to the equation, m∠BOC + 11= 180.

The teacher asked the student who had written 13x – 15 to explain how her equation connected to the previous equation, m∠BOC + 11= 180.

At this point, the teacher left the group to finish their work on the question.

We stepped off to the side of the room to chat about what had just happened and what the next steps might be. I pulled up Michael Fenton’s recent blog post Visual Patterns + Error Analysis on my phone, and our immediate thought was we could use his format and these 3 equations (and maybe find one more) for Monday’s class.

We decided that class will start with a list of three or four equations (per Michael Fenton) and ask the students to determine which equations are correct. As Kristen moves through the room while the students are working, she’ll take some notes to help her decide which 3 kids she wants to call on and in what order she wants them to share their thinking.

The teacher moves are super important at this point because it is about organizing classroom discussions so the kids are able to see how their ideas connect to other students’ work. We want this to happen for the kids as a result of the class conversations. We want the connections to be made as a result of student-to-student conversations not as a result of the teacher TELLING kids how ideas connect and relate. We don’t believe in teachers taking that part of the learning away from kids; we do believe in kids building the connections between ideas for themselves.

So, a huge thanks to Kristen, Brittany, and Michael for putting together such great ideas that give this week an awesome start, and for letting me join in the fun.

Resources:

1.  The teachers were using questions from Lesson 2 in module 6 of the grade 7 materials published by Eureka Math. The materials can be found on the EngageNy website.

2.  Reason and Wonder:  an awesome blog written by Michael Fenton

3.  5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein