**So what’s really going on in this image?**

One way to solve thirty-two minus twenty-two is to count up from 12 on your fingers, “13, 14, 15, 16, 17…” all the way up to 32. If you keep track of the count correctly, you will get an answer of 20. Let's call this the counting up by ones method.

The “new method” shows counting up by groups. Starting at 12, first you count up by ones“13, 14, 15” and write down 3. Now you can count up by fives, starting at 15, and arrive at “20.” Write down a 5. Now you can count up by tens, starting at 20 and ending at a new current value of “30.” Write down a 10 for this step. At this point, we have to go back to counting by ones, so we think “31, 32” and write down 2. Now, add up the numbers you wrote down 3 + 5 + 10 + 2 and you get 20.

The method described above could be used to check you answer after you solved the problem via the traditional vertical column subtraction method we all know so well.

We don’t have any context on the photo, so we don’t know if the student and teacher were, in fact, checking their work when they made these notes.

Everyone solves math problems in their own way. I personally think counting up by ones (counting up from 12 to 32 on your fingers) is a lot quicker than counting up by the groups 3, 5, 10, 2. My brain works that way. But if you prefer to count by groups, go for it!

What if I asked you to solve $5,000 - $4,995? You can probably do this in your head and get 5. If we wrote out how you solved the problem, it would look like 4995 + 5 = 5000. That’s the so-called “new method.” If we tried to solve this by subtracting in columns (or the “old fashioned” method), we would be required to borrow in the ones, tens, and hundreds places. For some people, that’s no problem, but many people prefer not to do subtraction with borrowing. Counting by groups makes solving this second example problem a breeze.

**What does this image have to do with Common Core?**

Common Core suggest students master certain skills (say, subtraction) by certain grade levels. It does not force math teachers to use any specific form of math instruction.

This is one of many ways of explaining subtraction to elementary school students who have just learned addition. Just go with it!

A talented tutor will adapt to the method that the student prefers to use.