Friday, July 15, 2011

The order of operations isn't just face lift, brow lift then nose job. There's also multiplication and division to consider

The order of operations still gets me after all these years.  In my quest to be speedy I trip up on problems like 5-4*8.  The answer would be -27.  That's if you use the order of operations for mathematics, not the order for operations for reading from left to right.  The answer from left to right would be 8, which is wrong.  Of course there are exceptions, if the question was presented as (5-4)*8 the correct answer would be 8.  There are a few ways to arrive at this answer.  You could use the distributive property and multiply 5*8 and subtract 4*8, or you could complete the operation in the parentheses (5-4) and multiply that times 8. 1*8=8.  Same answer but a little different way to get there.

Is there a "best" way to solve the problem 5-4*8?  I would argue that yes, there is.  As students work through grades and begin solving for algebraic expressions, a problem like (5-a)*8=8 can seem a lot more complicated if students try to solve the operation in the parentheses first.  But if you break it down and say 40-8a=8, it begins to look more like the expressions they are first introduced to.

It was a relatively short week this week.  I prefer math in small bite sizes. It seems easier to understand, especially when concepts like order of operations are very compartmentalized, there isn't a lot of extra knowledge that goes in to this.  It's very straightforward and black and white, with few exceptions.  Also there's an acronym, and that's always good.

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