## 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... make me want to kick someone. Since when does the word THERE get italicized so damn often?!I feel him.There.I groan... how can I feel thisthere?My inner goddess looks like someone snatched her ice cream.

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.

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 thediscount 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.
Hope you are enjoying your holiday, too! Thanks for the mind jogger...

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Hey Gordon! How are you? Will I see you at the Red Rock this year? Bummer that it'll be a shorter conference.

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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?

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Hi Robert. Thank you for your thoughtful comments.

multipleways 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.Reply to this

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.

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My cousins were reading

thatbook 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.)

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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.

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