## More Rectangles and One Good Read

Jesus. I'd rather stick needles in my eyes than read another page of Fifty Shades. I'd heard all this buzz about it since summer, yet no one had mentioned just how awful this book is! Someone had loaned me the set, so I was looking forward to reading them over break. But sentences like

I feel him. There
I groan... how can I feel this there?
My inner goddess looks like someone snatched her ice cream.

... make me want to kick someone. Since when does the word THERE get italicized so damn often?!

I'm sorry, but I felt it was my PSA for the Holidays to mention this. However, I just started reading this book on Ramanujan, and I highly recommend it because thankfully it has restored my sanity and faith in the written word.

About them rectangles. Curmudgeon just posted this Painter's Puzzle yesterday on Christmas Day — what a nice gift for us!

A painting contractor knows that 12 painters could paint all of the school classrooms in 18 days.

They begin painting. After 6 days of work, though, 4 people were added to the team. When will the job be finished?

Students typically read this as a proportion problem: 12 painters can do it in 18 days, so 1 painter can do it in 1.5 days. Except... hmmm, no.

Edward Zaccaro uses what he calls the "Think One" strategy in his book to solve this type of problem. I guess mine is the same idea, except I draw rectangles. Shocking. :)

This is how I normally teach my kids, and what responses I hope to beat it out of get from them.

Kids are terrified of fractions already. Teaching them to solve this problem — or any of the work problems — using rational equations will only confirm how much they dread the blessed fractions. Sure, I'll get to the equations, but I just wouldn't start with them.

Another common problem — that I'll use rectangles to help my kids — goes something like this:

In a state with 10% sales tax, someone buys an article marked "50% discount.” When the price is worked out, does it matter if the tax is added first, and then the discount taken off, or if the discount is taken off, and then the tax added?

(A quick search for this type of problem yielded this "best answer" that was a total fail.)

Tax, then discount:

Discount, then tax:

Heya, I'd love to send the Ramanujan book (from Amazon) to the first person to email me at fawnpnguyen at gmail dot com. [1:49, Robin S. from PA will be receiving the book!] [3:42, Elaine W. from VT is also getting the book.]

So, there! Hope you're enjoying your break.

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• December 26, 2012 4:00 PM Gordon wrote:
Hope you are enjoying your holiday, too! Thanks for the mind jogger...
1. December 26, 2012 4:30 PM fawnnguyen wrote:
Hey Gordon! How are you? Will I see you at the Red Rock this year? Bummer that it'll be a shorter conference.
• December 26, 2012 7:41 PM Robert Kaplinsky wrote:
I like your approach but I wonder how exactly this would roll out in your class. For example, I assume you give them the problem and let them have an opportunity to solve it on their own. I also completely see how you are asking questions to help them explain the reasoning behind the rectangles. When do you transition from their solutions to your solution? Do you immediately show them your way?

For me, my usual goal is to let them come up with different ways to solve the problem and then ask questions to facilitate a conversation around how the different methods are connected.

Unfortunately more often then not, students either come up with no ways or one way to solve it. Often I have an elegant way of approaching the problem, but I find that if I introduce my way, students will often abandon their methodology for my own. Then for some students it becomes a game of, "If I wait long enough, Mr. Kaplinsky will just show me how to do it."

Thoughts?

1. December 27, 2012 1:15 AM fawnnguyen wrote:
Hi Robert. Thank you for your thoughtful comments.

"I assume you give them the problem and let them have an opportunity to solve it on their own." Absolutely. I hope this is reflected in all the teaching posts that I share.

"When do you transition from their solutions to your solution?" I hope my solution will always show up dead last, if I show it at all. Like in the most recent lesson Equilateral Triangles, I never shared with the kids any solution until after it was all over, and only to show how the different solutions compared. Last year, a 6th grader solved a puzzle in a much more elegant way than I had. I want the kids to teach me and teach each other.

"... let them come up with different ways to solve the problem and then ask questions to facilitate a conversation around how the different methods are connected." The norm for my class is: individual work, then small group work, then whole-group share. Again, I hope many of my posts show this. The structure I use for group work is similar to the "Five Practices" that I wrote about here

"Unfortunately more often then not, students either come up with no ways or one way to solve it." My algebra class does have these tendencies more than my geometry or 6th grade. When they have no way of solving a problem, I think we have to ask ourselves all these questions: 1) was the problem level appropriate and does it have multiple ways for solving it, 2) was there enough individual think/struggle time (because getting kids in small groups too early might invite social talk since no one really had anything to contribute), 3) what guiding questions can we ask to help the groups along, what is that one piece of information we could steer them toward to get the ball rolling.

Normally when only one group has something, I'll ask this group to do a quick share, just a hint, and when this group knows that they can only give a hint or ask a guiding question, they love it and try hard to craft a good question.

"Then for some students it becomes a game of..." Right, kids are very smart and will do this. But I'm way more stubborn. Funny, before break I did a problem with the geometry kids, but time was running out, so I told them we needed to move forward and I needed to give them one piece of information (NOT the answer), four kids actually stepped outside because they didn't want to hear this info yet. I really believe it's a culture that I've worked hard to develop, and this takes time. I hope the culture in my class include: "struggling is a sign of learning" and "if it's easy, it's not worth doing" and "don't bother asking Mrs. Nguyen because she ain't talking."

The rectangles should be a new strategy for all of my 6th graders and about half of my 8th graders, so I go through this process via guided questioning, then lots of practice on their own, and then some more. The toughest part for them is to figure out what size rectangle to draw, but it's a great learning process of testing and revising. When we return in January, I'll be doing this type of problem with the kids, so I'll share how it goes.

Thanks again, Robert!

• December 27, 2012 7:59 AM Robert Kaplinsky wrote:
Thank you for the very detailed response Fawn. All of these are good ideas. I hadn't seen the Five Practices post and I will have to check out that book as well.

I appreciate your insight. Some of it validates what I am already doing and some of it forces me to reflect on what I am doing and why I am doing it.

• January 2, 2013 12:57 PM Sue VanHattum wrote:
My cousins were reading that book this summer. They seemed to love it, but I had no desire to go there. (Straight erotica not being of much interest to me...) I really enjoyed the Ramanujan book too.

That is the most realistic work problem I've ever seen. (Bookmarking.)

1. January 2, 2013 8:57 PM fawnnguyen wrote:
Holy cow, I'm loving the Ramanujan book!! It's an oddly and deeply moving biography. Almost halfway through, wish I'd started it earlier during break. Thank you, Sue.