The “Common Core” Subtraction Technique Caleb Bonham Criticizes is Actually Useful

I’m a fan of Caleb Bonham’s work. However, in his recent video on Common Core, he gets a little off-track. The subject is a technique for subtracting one number from another. Bonham claims the technique in question was imposed by a Common Core curriculum and that it is overly complicated. In fact, the technique is very old and very useful. The fact that a Common Core program happens to use it is no cause to damn it.

As Bonham explains, the traditional solution to the problem, thirty-two minus twelve, is to first subtract “two minus two” in the “ones” column, then subtract “three minus one” in the “tens” column, for the correct answer of twenty.

The approach used by Common Core, by contrast, asks a student to see the following:

32 – 12 = ?
12 + 3 = 15
15 + 5 = 20
20 + 10 = 30
30 + 2 = 32
The sum of the 3, 5, 10, and 2 is 20.

Bonham thinks this approach is overly complicated, and, in some situations, he’s right. But the approach indicated is, in fact, how I often do subtraction problems in my head (except that in this case I’d jump straight from twelve to twenty, and so get eight plus ten plus two), and it’s a perfectly legitimate approach. It is also an approach that helps students reach a conceptual-level understanding of addition and subtraction, rather than merely learn rules of subtraction by rote.

Of course, in this case, because we’re dealing with two, two-digit numbers that end in the same digit, adults and more-advanced students can easily see that the difference between the numbers is some increment of ten (in this case twenty). But what to do in other cases?

To illustrate the advantage of the approach given, consider the problem thirty-one minus twelve. In this case, the rule-based approach requires that a student “borrow” from the three. It’s much easier to solve the problem in your head by saying, “eight plus ten plus one equals nineteen.”

Or consider the problem seventy-three minus twenty-eight. A good way to do this problem in your head is to think, “To go from twenty-eight to thirty I need to add two; to go from thirty to seventy I need to add forty; to go from seventy to seventy-three I need to add three. The total is forty-five.” There are other good ways to find the answer, of course, but, for me, the way I described is the easiest way to do it in your head.

The broader lesson here is that, just because something is associated with Common Core, doesn’t mean its bad.

Update: I’ve also written about a vague, nonsensical problem from a Common Core-approved test.