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,
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Estimation 180 update & RSS

Head over to Estimation 180 and throw the blog in your RSS feed. I usually update the site once every week or two and the RSS feed will alert you of those updates. Don't worry, they're not daily and it's definitely not s-p-a-m, as I despise s-p-a-m.

Huge update of estimates today starting at Day 78 and going through Day 91 (over halfway done). Home Depot was just so fun.

*Can you spot something suspicious on Day 86?

Enjoy!
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Bottomless Mug

I found this glorious sign a few weeks back at Bruegger's Bagels and ended this post with saying I'll work it into a 3 Act.

As promised, here is the 3 Act lesson.

Act 1: My question: How much money could you actually save?
Other popular questions can be found at 101qs.com. I like getting to that initial question because many of the others will be answered along the way.

Act 2 info would look like this for my area, but the cost of a medium sized cup of Bruegger's coffee might be different in your area (for a limited time, of course). Check their website.

Now you know the cost of the mug, but I find the 3 days, 5 days, and 7 days per week (the rate where you live next door) very intriguing. In solving this one, my natural tendency was to round that cup to $1.90. Be careful, that difference could buy you a bagel or two. Anyway, have fun with this one. My wife and I just celebrated the birth of our daughter on New Year's Eve day. I don't drink coffee, but I do enjoy iced tea and this Bottomless Mug Club is starting to look rather appealing now.

Personally, I like the sequel tasks more than the original task. Sequel tasks include:

• On what day in 2013 would you break even if you get coffee 3 days/week, 5 days/week, everyday?
• When would be the last day to buy the mug and still save at least $1.89?
• What could be the prorated price of the mug if bought in January? February? March?... 

Have a sequel to add? Toss it in the comments.

Happy 2013,
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