More Rectangles and One Good Read

I just started reading this book on Ramanujan, and I highly recommend it.

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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.

workproblemKids 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:

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Discount, then tax:

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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.]

Hope you’re enjoying your break.

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