Fuel Sense Making & Black Box Defrost

Sparking Curiosity:

I put this video on infinite loop while the students filed into the class. I let it play and said “here is your warm up today”

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I said nothing else. I was letting the curiosity build. After it looped and looped students started to work. Without saying a word about it students were trying to find how long it will take to defrost an item that weighed 3.5 pounds.

Igniting MY Moves:

Since I routinely let students struggle to solve problems instead of showing them immediately a “how to”, I have to be ready to give feedback on what they try on the fly. I want to help push them in not only a direction that solves the problem but prepares them to see solutions that are not their own and solutions that attempt to address our learning goal for that day. That takes careful planning which is not an easy thing. 
Plan with Precision so you can proceed with great flexibility” – Tom Schimmer.
When I first started teaching so much of my planning was solely focused on answering questions like, What topic? What examples?, and How long do I spend on it? Now my planning time is mostly spent trying to answer: How will the students solve this problem? How can I use what they will do to shape the lesson? What do their attempted solutions tell me about what they have learned so far? So my planning process has gone from examples like this where I was so concerned with WHAT….
to spending most of my time thinking about HOW. HOW will the students respond to the task? What does that look like? That takes a ton of anticipation. Anticipating their solutions and strategies puts me in a better position to understand their thinking and help shape that thinking. For each possible attempt I need to be ready to provide feedback to help them achieve our goals.
For the Defrost Black Box problem from above the learning goal I am hoping to pull out is “Relations can be represented in various ways” and “Problems can be solved in a variety of ways” I anticipated that some of my students would attempt to solve it with a unit rate.
Possibly some of my students may solve it with a table of values and linear relation.
Some may set up a proportion.

The book 5 Practices for Orchestrating Productive Mathematics Discussions has been an invaluable guide to help me re-design my planning time.

Fuel Sense Making

Since my goal is for students to see “Relations can be represented in various ways” and “Problems can be solved in a variety of ways”
I need to be ready to fuel their sense making by linking the different student strategies together.
Here are some of what the students tried.

I did not anticipate students using seconds.

I also did not anticipate students using additive thinking with the unit rate.

We learn so much from our students by allowing them to show their thinking. Imagine all the missed conversations with my students from 2005 – 2013. Imagine how many of my students felt like they were failures because their brains didn’t tell them to solve those problems the same way the I did. When in reality they had so many good insights that just needed to be tailored.
Selected students presented their strategies to the class. Now it was time to show how their strategies connect together.
We showed how the unit rates that many of them found and used showed up the table solution.
We moved from there to show how this would be represented on our number lines. 
Yes the planning that comes from Igniting My Moves and Fuel Sense Making takes time and it is not easy. But I can tell you that it is worth it.
On a side note: Help me settle a problem. A teacher said, “Students might find a real microwave more engaging than the fake one you have shown.”
Is version 2 of the Black Box Defrost more engaging or worth doing more because it is real? What are your thoughts?
Version 2: The More Real version

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Thanks for reading!

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