Paging Doctor Math: Cookie Cutter Task

With Pi Day on the horizon (at the time), I decided to use a task that focused on the circle, which is a big introduction into the 7th grade curriculum. We started talking about circles about a month ago in more of a distributive practice fashion, measuring the diameter and circumference of various circles as well as a few other situations involving everyone's favorite horse Prickly Pete (apologies...low-quality video) tied to a rope (click on "problems" and yes I know it's a goat).

This task is courtesy of @mathletepearce. Here is the original situation...

https://tapintoteenminds.com/3act-math/cookie-cutter/

This task is actually also accompanied by a video of my classroom that I decided to tape as an extra bonus...

Classroom Video

Here is the information and questions I displayed for the students as they walked into the room...

http://bit.ly/1MhEopX

This task ends up being a fairly straightforward subtracting out an area situation but the circle information is so new to the students that it adds an extra layer of thinking as to what exactly needs to be subtracted out. As we went through the task, a lot of interesting student ideas or missteps occurred (in no particular order):

*Do I use the circumference or area?

*How do I find the distance or the sides of the original dough?

*What does the decimal mean at the end of the first question when I found out there were three extra cookies? This was particularly interesting because many students thought this was the leftover dough at first when it is actually how much of a cookie is left.

*Could I just ignore the twelve original cookies and not subtract them out, instead just finding how many cookies could fit into the area of the original dough?

*What's a way to find the leftover dough after the 15 cookies? Take the area left after 12 cookies and subtract off the area of 3 cookies!

*Does circumference and diameter serve any purpose other than finding the area (actually just the diameter)?

*Do the little spaces of dough in between the cookies make that much of a difference?

*If there was about 2% of the dough unused, what percentage of the dough is needed to make a cookie?

*If there is no decimal left for the dough, does that mean there isn't any dough left?

*Should I find how many of the square cookies fit into each side of the dough or figure out how much space each of those cookies are and how many would fit?

*1/4 is 25% so 1/8 would be half that much?

*Oops I figured the square cookie as a circle...

There were a lot of big x-outs on student work this time around. I was really glad we did this task when we did because I think it did force the students to think deep past just the simple circle calculations into what was actually important...and there nothing wrong with students struggling, that is just part of the process. Below are the standards, student work, and my help sheet. Happy late Pi Day!

7.G.B.4

7.G.B.6

7.RP.A.3