This was a precal class but I think would be an awesome activity with Middle Schoolers.
I got to teach one of my favorite lessons in a Precalculus class this week, which I developed several years ago from a paper by Thomas Osler, Fun with 0.999…
We started with a Quick Poll. Students could select as many or as few choices as they wanted.
I shared their responses separated
and grouped together.
In the first class, one student selected all three choices.
In the second class, 5 students selected all three choices.
I set the timer for a few minutes and asked students to think individually about how they could argue their selection(s).
Then I asked them to talk together about their ideas.
I walked around and listened. These are the conversations I heard:
A: 1/3 is 0.3 repeating. 2/3 is 0.6 repeating. If we add 1/3 and 2/3, we get 1. If we add 0.3 repeating and 0.6 repeating, we get 0.9 repeating.
B: 1/9…
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Use More CAS 