## Reflection: High Quality Task Density & The Earth - Section 3: Density "Proof"

This was an idea derived from a Japanese "lesson study" reading that I conducted, in which the math teacher slowly piece-mewled information that allowed students to solve a complex mathematics problem. In a sense, there are two things working here: students need to figuratively (and sometimes literally) put their heads together to solve the task, but they also need to actively select the information they need to do so. This ultimately pushes the cognitive load more onto the students in that they select the tools, procedures, and steps necessary to solve the problem.

Another element in what I wanted to do here was to have my students struggle with a problem. In thinking about how this went, I think it was interesting to let students struggle with this. I feel at times that class time was "wasted" in letting them grapple with a problem, and some students in particular groups seemed to reach frustration level quicker than I thought. I think a potential work around here would be to do this as a summative/post-lesson group assignment. We did it after an exceedingly brief introduction - something to the effect of "let's remind ourselves what density is - here's the formula, and here's what I was thinking..." and then launching into the problem noted in the video - how can an aircraft carrier float despite its massive weight? Can we prove its density? If I moved this until after students had "re-familiarized" themselves with the content and process, they might have built up a bit more intrinsic perseverance. Even so, I'm excited to try this again and continue to take a few instructional risks in my classroom.

Density Proof
High Quality Task: Density Proof

# Density & The Earth

Unit 2: The Dynamic Earth
Lesson 3 of 16

## Big Idea: Students try to solve a unique challenge problem showing how an aircraft carrier can float in water.

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60 minutes

### Kane Koller

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