## Thursday, January 17, 2013

### Best Halves [Square]

A few months ago Dan Meyer reached out to Timon Piccini, Chris Robinson, Nathan Kraft and me to participate in what would eventually become his Best Midpoint, Best Square, Best Triangle, and Best Circle series of 3 Act lessons. I was honored to be part of a stellar group and great lesson. I love the potential of these lessons and can't wait to use them with my geometry kiddos later this year. Currently Dan and Dave Major have kicked it up a notch with some great interactive play/learning for better best squares, also providing us with an interactive teacher's guide. Check it out: I nearly cried tears of joy upon reading their two posts: Dan and Dave.

Recently, I've had conversations with Fawn Nguyen about fractions and although fractions aren't the spotlight of my Algebra and Geometry curriculum, I'm still fascinated by them and in turn want to help students build their number sense or spatial reasoning. I had an idea to extend Dan's Best series into the realm of fractions and emailed him for his blessing, hoping I'd do it justice. Here's what I came up with so far:

You might notice
it closely resembles Dan's format with very few stylistic differences. "If it ain't broke, don't fix it." That's my motto here. I called on Dan and a few other comrades to make an appearance and compete in this first installment of Best Fractions. This first installment: "Who drew the best half?"

Thanks to Dan, Fawn, Sadie Estrella, and Shauna Hedgepeth for taking the time to contribute. They were great sports! I still don't know who drew the best half yet.

I see a lot of geometry potential here: area, perimeter, midpoints, distance, coordinates, polygons, etc. I'd love to target primary grades with this activity as well (not just secondary), finding an entry level that elementary kids are capable of exploring. I'm not too sure calculating the area of trapezoids would be appropriate for a 4th and 5th grade classroom, but I might be wrong.

I'm not pretending to nail this 3 Act lesson and I'd love some feedback on how you would apply this in your class or make it better. I'm still working on the Act 2 information and will gradually chip away at it over time.  I gathered enough information from the contestants to keep me busy for the next year. I plan to release other installments of Best Fractions, specifically the best half, third, fourth, and fifth of both a square and circle. Just imagine the fun with circles: area, sector area, arc length, degrees, percentages, and more. Stay tuned!

Test it out on your students in the meantime and give me some feedback. Click here for directions and handouts to use with your students.

Best,
420

1. I think it will get significantly more difficult with your thirds and on. Definitely lots of other ways to apply this sort of clip. Great work and thanks for sharing.

1. Agreed. I'm curious to see how it evolves. I like the half as a low-entry point for all.

2. Love it! Going to do this with my 9's next semester. First as an introductory activity, then again later on. Instead of using your video, I am thinking I will probably have 4 contenders from class draw on the smartboard/board (haven't figured out if I am in a room with a smartboard yet), and then PDF a paper version for them to work on for the next day (after some bets and guesses first). Also instead of 1/2 of a square, I'll probably begin with 1/3 of a square first.

1. 'd love to hear how it goes. I plan to do a competition as well in class with my students. I'm curious to see how these evolve to thirds, fourths, and fifths, but having half creates a low entry point.

3. See a great potential for scaffolding here also. I would guess every kid will measure "best half" by some subtraction method (subtracting the actual distance/area from 1/2. This becomes (potentially) more complicated when defining "closest thirds" if people are asked to draw both thirds.

1. Yes, the evolution to smaler equal parts will be interesting.

4. Looks great! Only thing I saw was that it might be easier for you and for those watching the video if the squares started off larger. That would magnify any small differences in the halves.

1. Great point. The halves are definitely similar looking. Just wait until you see thirds, fourths, and fifths: plenty of small differences.

5. I've been working on something almost identical (but on paper) for the past few weeks with 4th-6th graders. We've been having some fascinating conversations. I'll send you the handout with related comments if you like.

Cindy (love2learn2day.blogspot.com)
email: love 2 teach 2 day at gmail dot com

1. I'd love that. I'm working with a 4th and 5th grade teacher this year and they'd be appreciative too. Thanks!

2. Thanks! Send you the pdf.