Jack’s Common Core Subtraction Problem: Not So Hard After All

DISCLAIMER:  I have no children in public school nor am I a public school teacher. That said, I am no fan of Common Core (and especially not of its implementation).  I find it unfortunate, however, that people are so quick to point out how bad certain Common Core math problems are without looking at what the correct answer should actually be.  Take, for example, this math problem which has been in the news lately: common core subtraction I know this will be hard, but let’s assume for a moment that you don’t know much about subtraction and especially don’t know about things like borrowing (at least that’s what we used to call it back in the day).  While the above problem does NOT require borrowing, it’s setting us up to be able to understand how borrowing will eventually work. So what did Jack do wrong?  The goal here was to start with the first number (427), then count backwards on the number line using each place of the smaller number (316) from largest to smallest (i.e. from the hundreds place to the ones place).  Jack started by going from 427 to 327 to 227 to 127, so he expertly handled the hundreds.  Next, he needed to account for the tens place.  This is what he missed.  He should have gone from 127 to 117.  Finally, he should account for the ones place by going from 117 to 116 to 115 to 114 to 113 to 112 to 111. Why is this kind of reasoning important?  Remember, we don’t know anything about “borrowing.”  Now, instead of subtracting 316 from 427, let’s say we want to subtract 327 from 416 (416 – 327 = ?).  Using the exact same method: Go down by three hundreds – 416 to 316 to 216 to 116 Go down by two tens – 116 to 106 to 96 Go down by seven ones – 96 to 95 to 94 to 93 to 92 to 91 to 90 to 89 So without having to grasp the abstract concept of borrowing, we find that 416 – 327 = 89. Again, I’m no public school teacher, but having taught arithmetic, pre-algebra, algebra, statistics and pre-calculus at the post-secondary level, I can tell you that it’s definitely easier to get student buy-in to abstract notions like carrying and borrowing when they have demonstrated for themselves using the number line that these shortcuts do, in fact, give the correct answer. It’s OK to dislike Common Core, but you only look ignorant when you call out problems like the one above without addressing what the correct solution is and how you think the concept should be taught differently.