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# Arithmetic Series and Subtracting Signed Numbers

What feedback would you write on this kid’s paper? Why?

(Thanks, KN!)

## 5 replies on “Arithmetic Series and Subtracting Signed Numbers”

Not sure what feedback I’d write, but I find it interesting that s/he stuck to the notion of a difference of -12 from what I suspect was the first erroneous result (9 & -2), even though that more obviously doesn’t hold up for (-2, -13) and (-13, -24), and I bet the student knows that but didn’t bother to check or think about it. Sure, it’s easy to botch the sum or difference of signed numbers when they have opposite signs more than when they have the same sign (though subtracting signed numbers is in itself harder than adding them for many kids), but to seriously believe that there’s a difference/distance of 12 in either direction between 2 and 13, 13 and 24, etc., boggles my mind.

mpershansays:

Interesting questions!

Did you notice that list of numbers all the way at the top of the page? What are your thoughts on what they’re doing up there?

Looks like a reflection of the number line, possibly being used to avoid actual subtraction. And the kid just counted wrong or misused the tool in some other way. . . ?

They counted the number of numbers (including both the starting and ending numbers) to get the “difference” instead of counting the number of steps. So “9, 8, 7” would count as 3 to them instead of 2 spaces.

Hmm, so you’re saying that if I’m figuring the number of people waiting to be served by subtracting the number of the ticket of the first customer from the number I’m holding (assuming no one left, took more than one number, etc.), I won’t get the total number of customers? Who knew? Damn, these counting problems/strategies are treacherous little mothers. ðŸ™‚