## Wednesday, February 03, 2016

### Math Systems: Geometry, Base Ten, and Real Number Exploration

Today in one class we extended a previous solid figure lesson to learn more about volume, 3D figures, and surface area. We looked at the relationship between folding paper and making nets. Our first rectangular prisms didn't come out exactly as we planned, and in our error we learned more. Later students designed their own prism nets and began making their solid figures. It was a great exploration, one that we'll continue tomorrow.

In the other two classes we talked a lot about math systems with a specific focus on comparing the Base Ten Place Value system and the Real Number System. As we begin to move into fraction models, discussion, and study, I wanted to revisit both of those systems since there was some confusion about the models with respect to the role of zero and the role of the decimal point.

As we talked about the systems, we talked about systems in general. I said that most learning profits from system think and we then discussed the actions and elements related to systems study. I used the example of hip hop. I said that I didn't know much about hip hop and when I tried to participate in a Twitter #hiphoped chat, I had a hard time following the language. As I spoke, a few hip hop experts in the class helped me out. They clarified language, discussed the structure, and emphasized important elements of hip hop. One boy said, "When we write a rap, we're indebted to it." and proceeded to explain what he meant.

We're studying math through the lens of the invented system that it is. We're looking deeply at how some systems are embedded into other systems similar to Russian nesting dolls. We're thinking about the language, parts, behavior, and connections between and amongst systems. And we're learning through lots of making and talking.

Moving forward students will complete their 3D nets and figures. We'll make those rulers we planned to make today. We'll celebrate Team Week by making more nets and boxes as well as personalized coordinate grid designs for our "secret" teammates--the ones we'll do special things for all week.

I love that fact that math teaching and learning is becoming so much more full and beautiful as we access the topic with a blended perspective and approach. Today as a boy left the class, he said, "This was a great math class." That's the kind of results I'm looking for. Onward.