0.9 Repeating

This was a precal class but I think would be an awesome activity with Middle Schoolers.

Easing the Hurry Syndrome

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.

1 Screen Shot 2015-05-01 at 6.22.27 PM

I shared their responses separated

2 Screen Shot 2015-04-27 at 11.36.55 AM

and grouped together.

3 Screen Shot 2015-04-27 at 11.37.22 AM

3_1 Screen Shot 2015-04-27 at 11.37.28 AM

In the first class, one student selected all three choices.

In the second class, 5 students selected all three choices.

4 Screen Shot 2015-04-27 at 2.48.04 PM

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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