Comments on: [3ACTS] Incredible Shrinking Dollar

By: Craig

Craig — Thu, 09 Feb 2012 20:33:02 +0000

I used this with a grade 11 precalculus class for an introduction to geometric series. They had not been given any formulas or explanations. We did an example of geometric growth previously by looking at the distances in a spider web. For the most part the students really enjoyed the challenge especially when I refused to say when or if they had the “answer”. We then took the class to the copier and did the reductions and measured to verify which had the right and wrong solutions and why. Went very well and sets up our discussion of geometric sequence formula work tomorrow. We had trouble with when the bill disappeared because we couldn’t recognize the limit of the copier but tomorrow we will look at how we can determine the limits of the copier by being able to predict the shrinking bill size at each stage. Thanks for the work. I really appreciate you posting the ideas.

By: Josh

Josh — Sat, 19 Nov 2011 07:26:33 +0000

Before giving my thoughts on why it bombed, let me say that the geometry kids ate it up in about one minute. Aside from the questioning of who this guy is who is able to copy money, they dug right in and groups finished the original problem and most finished the followup questions. Many came up to ask me how small it would have to get to be invisible. “Not sure,” I would respond. “how small do you think it should be?” which got about two of them actually thinking about the size of .00001 mm.

The algebra classes struggled more because they don’t underhand percents very well. I felt the initial hurdle was too high. I handed out the dollar outline to each student (I think one sheet to each group would have been better). I don’t want to go into too much detail, but some went right to perimeter or area, which brings up other questions.

I do think your idea of having the original and the ninth copy moght have helped as a launch point. I also think showing them either the first copy and blanking out the percent would have also been a good problem. the question could then have been, “what setting was entered?” The followup could then have been how big is the ninth copy.

Gonna try the dominos next week.

By: Josh

Josh — Fri, 18 Nov 2011 05:39:53 +0000

I am going to give the problem to my geometry classes as well. I’ll give you more complete thoughts tomorrow after they see it also.

By: Dan Meyer

Dan Meyer — Thu, 17 Nov 2011 02:54:06 +0000

Hey Josh, thanks for the feedback. It’s a lot easier to dish out positive results than the negative and I’m obliged you’d make the effort.

Presumably you didn’t blindly implement the problem. You saw it yourself and thought it’d be interesting. Do you have any sense why the problem didn’t land for your students? Any sense how I might scaffold it differently? Do you think your students would have experienced the problem any differently had I shown them the last dollar and asked, “How many times was it copied?”

By: Josh

Josh — Thu, 17 Nov 2011 00:31:43 +0000

I attempted this 3acts today in my 8th grade algebra class. I gotta say it was a bit disappointing. Potential problems: End of the day; 35 kids in the class.
Of the nine groups in the class, I think 3 were actually engaged in the problem. After they struggled with it for about five minutes, I stopped the class and we discussed how you could get started on the problem. But then I struggle with not leading them down the path of how to do it. At what point do you throw in the white flag and move on.

On a slightly positive note, one kid right off the bat, eyeballed 75% and sketched the drawings on the sheet of paper, and was within two millimeters of the answer (we projected his image over final cut from act 3)

By: Eric

Eric — Wed, 16 Nov 2011 03:56:34 +0000

@scott… pretty sure pepe was kidding. at least i hope so.

By: Karim

Karim — Thu, 10 Nov 2011 20:47:29 +0000

For what it’s worth, I think Dan’s stuff is valuable in large part because it doesn’t include the type of explicit scaffold that Mathalicious lessons do. The approach is predicated on students’ coming up with their own questions, and Dan’s gift is in crafting opportunities for them to do this (while still providing some structure, albeit subtly).

In the end, I think WCYDWT lessons and Mathalicious lessons are similar in spirit–they’re both about exploring the world–but fundamentally different at the same time. The types of topics that many Mathalicious lessons address require a more explicit scaffold; whereas students might be able to come up with “Is Wheel of Fortune rigged?” on their own, it’s unlikely that they’d transition from NikeiD.com to a discussion of paralysis by analysis without the narrative afforded by the handout.

I don’t think either one is better or worse. They’re just very different, and therefore require a different approach.

By: Dan Lemay

Dan Lemay — Thu, 10 Nov 2011 00:58:35 +0000

This looks very cool Dan. I’m going to try it with some under performing Juniors and Seniors I work with. Smart enough kids, they have just chosen to/been allowed to dumb down over the years.

I’ll let you know how it goes.

Thanks again.

By: tiredoldcliche

tiredoldcliche — Mon, 07 Nov 2011 10:48:11 +0000

apologies for combining problems here, but when i saw this video my head went to your Guggenheim thing – i really wanted to know how many *more* of these shrunken dollars it would take to create that artwork.

By: Dan Meyer

Dan Meyer — Sun, 06 Nov 2011 20:47:14 +0000

Certainly I’d like to support teachers, but “which supports?” is a huge, outstanding question and I’m not sure handouts and lesson plans are the answer.