Comments on: [Makeover] Penny Circle

By: 3 Wonderfully Awesome @Desmos Activities by @fawnpnguyen @ddmeyer @Trianglemancsd #mathchat #edchat | techieMusings

Fri, 14 Mar 2014 21:48:15 +0000

[…] Activity Activity: https://class.desmos.com/pennies Blog Post: /2013/makeover-penny-circle/ Students collect data that each person will use to estimate the answer to a problem involving […]

By: Ryan Sonognini

Ryan Sonognini — Thu, 30 Jan 2014 17:21:57 +0000

I had several students say with enthusiasm, “Can we do it again?”

Thanks for the resource. I can’t wait for more…neither can my students.

By: Marti

Marti — Tue, 19 Nov 2013 18:20:04 +0000

Beautiful activity, I went through it all as a student and I love how i could keep going back to the actual circle and find and create more data points. I was using the activity on an iPad and it worked very well, the pennies moved fairly realistically.
I truly loved how the students can see other students data for that “coopertition”! And the teacher can see the whole thing in real time on their computer…VERY WELL DONE!!

A few improvements: can you move the model sliders to the bottom of the screen? I noticed on the ipad my hand was in the way so as I was sliding i couldn’t see the graph very well. Also, could you allow teachers to add different summary questions on the last step?

CAN YOU MAKE MORE OF THESE?

By: Kevin Hall

Kevin Hall — Fri, 04 Oct 2013 17:25:43 +0000

I just worked through the activity again, and I’m pretty excited with how well the answer comes out analytically. My empirical model was approximately y = 1.3x^2, with small h and k constants.

I tried deriving this, assuming that the number of pennies is simply (Area of circle)/(Area of each penny). This gives [pi(d/2)^2]/[pi(0.75/2)^2], with 0.75 being the diameter of a penny in inches, according to the U.S. Mint. But that gave me y=1.78x^2, which was way off.

So I went back to the picture of the pennies in a circle, and decided that each penny basically takes up an area the size of the square that is circumscribed around it, because that better accounts for the empty spaces between pennies. In that case, the area taken up by the penny is just the area of the square, (0.75)^2.

I did the calculation this time, and I got approximately y=1.33x^2. It was great! So this will be my follow-up to this lesson. WHY does the empirical equation make sense. And then I do plan to move into the blog post about composition of functions, which I linked to directly above this comment.

By: Rough idea of how I want to use Penny Circle | ijkijkevin

Rough idea of how I want to use Penny Circle | ijkijkevin — Thu, 26 Sep 2013 12:34:43 +0000

[…] trying to figure out how to use Penny Circle, by Dan Meyer and Desmos.Â I think the activity is terrific, but like Luke Hodges (in the comments […]

By: anonymous

anonymous — Thu, 26 Sep 2013 12:34:22 +0000

Also beyond the scope of the problem: packing circles into circles, or spheres into spheres, is related to how much information you can fit into a radio (AM/FM/TV/WiFi/cell-phone) channel. See
http://en.wikipedia.org/wiki/Additive_white_Gaussian_noise#Channel_capacity_and_sphere_packing

By: Jim Hays

Jim Hays — Sat, 14 Sep 2013 15:15:01 +0000

This is beyond the scope of the problem, but if you have an advanced student who is intrigued by packing the pennies in as tightly as possible you might point them to the following resource:

http://www2.stetson.edu/~efriedma/cirincir/

It contains the proven ideal arrangements for 1-11, 13, and 19 pennies, and the best known arrangements for any amount of pennies up to 20.

By: George Bigham

George Bigham — Sat, 14 Sep 2013 14:47:38 +0000

I have an idea to answer the choosing contexts problem: have a brainstorming activity at the end where students think of real world contexts in which the general “circles in circles” rule might apply. Of course the teacher could have a list and get things started, but hopefully students could come up with ideas that aren’t on the list. Even if students don’t come up with ideas, if the teacher displays a long list of diverse examples, it would be more impressive than just one. It could demonstrate that a single seemingly trivial mathematical generalization applies to many concrete examples.

By: Mike Caputo

Mike Caputo — Fri, 13 Sep 2013 04:39:42 +0000

I’m using the Penny Circle project in my Algebra 2 classes this year but none of the Desmos stuff. I bought a couple of pizza screens, 10 inch and 18 inch diameter, because they keep the pennies in the circle. Students created data with their own compass drawn circles and we used the 10 inch screen for another data point.

The target is the 18 incher. Low/Just Right/High guessing first. Make the graph with the intention of future use. Then . . . wait for a couple of months to find out the real answer because we need to learn some math first to figure it out beyond just faking where you think the graph will go.

I’ll try to come back when we finish to say how it worked.

By the way, when I went to the bank to get 1000 pennies, the teller thought I meant $1000 worth of pennies and had to have a discussion with the manager in the vault before clearing up the misunderstanding.

By: Neil

Neil — Thu, 12 Sep 2013 14:33:50 +0000

Dan, very nice. I’m super excited you and desmos are teamed up.

It would be great to tie this into microbiology and cell culture populations in a petri dish. Scientists use the area of a growth circle to predict cell population. With time built in, they can determine growth rate of the culture.

Going to try this project in my precalc class today.