# Bridges (no tricks)

Posted on July 15, 2015

I’ve had several more students in today than most days this summer, including one  going through a test review, and working through some pie pieces on ALEKS.   She pretty much had things down, except that -10 + 2x – 8 led to “two negatives make a positive, right?”   (She’d done fine with 2x – 7x … because she’s memorized the rules…)  So I gave her both the “you lose ten pounds one week and 8 pounds the next, and you’ve gained weight?”   … but also that when it comes to adding, “Two wrongs don’t make a right!”   She settled on “if they’re both negative, you add them,” which unfortunately, translates more often than not into changing it to a positive number… I refrained from singing “same sign, add and keep” (“row, row, row…”)  …

So on my little bike ride ’round campus (four laps because it’s not the sauna it was yesterday!) it occurred to me that most students see subtraction of integers as totally separate rules.   (SHe didn’t get to the subtracting part while she was here, so I don’t know how she’s faring there.)

We teach them that “adding a negative number is the same as subtracting,” and almost everybody does reasonably well with that… but half of them crash and burn when subtraction is thrown in (and sometimes *then* stop being able to add negative numbers), so I’m thinking of including practicing the converse — seeing that 8 + -3 is 5… but also rewriting 9 – 5 as 9 + -4.