The lesson synthesis question here is a big one, one that many adults struggle to answer!
As I look at different student answers to this question, I have three reactions:
None of these are right. Students can always add more context, nuance, and precision.
None of these are wrong! Students are answering from their current perspective. It’s honest, earnest, and accurate from their point of view.
Every student would benefit from seeing these.
One student might say, “A positive divided by a negative is always negative.” Another student might answer using turtles, saying that the bottom expression is asking how you go 6 feet when you’re traveling -3 feet per second— you’d have to go back in time two seconds.
Consider sharing those and other responses, and perhaps also giving students time to revise their thinking. In doing so, you can help students understand not just math, but also that all of us are smarter than one of us, that learning math means learning with and from people.
Dan & the Desmos Classroom Team
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