Why Place Value Needs To Come First

Recently, I did a video about, why we should not be teaching students subtraction strategies and instead focusing on three key concepts around subtraction that help kids develop the strategies for themselves. I received a response back that asked, “So, does this mean that we should teach place value before subtraction? And should we teach place value before addition?”.

In today’s vlog, I going to talk about why we should teach place value first before we move into helping kids understand addition and subtraction. On our quest to build our math minds so we can help build the math minds of our students.

Watch the video below OR read the transcript.

Key Takeaway #1

First, I want to talk about how without place value, kids are really just doing single digit addition and subtraction. Let’s paint the picture for a moment. There’s a child that’s just going through the motions of adding the ones column, adding the tens column, adding the hundreds column, and all they’re seeing is the digits in that column.

They aren’t really understanding what’s happening. Those are the kids who get to the end and they look at their answer, whether it’s right or wrong, and they have no clue if the answer is even reasonable because all they’ve been doing is just three different single digit addition problems or subtraction problems.

So, if we don’t do place value first, all they’re really doing is single digit addition and subtraction It’s just practice with their facts. They really aren’t learning and understanding how to add and subtract.

Key Takeaway #2

The second reason why I think we need to focus on place value first before we move into the operations is that we can end up having to teach rules. But the rules change every time we have a new set of problems to add or subtract.

For example, when kids start moving into multi-digit, we will often get kids who will line up the problems like this.

They’ll just line ’em up. Our eyes read from left to right so they want to start there. However, we teach them the rule that says, “No, no, don’t do that. You’ve got to line them up to the right.”. Everything needs to line up to the right to go column by column once you it’s lined up correctly.

Then, when they move into problems with decimals, they still try to apply those old rules. They will say, “Oh, well, before we lined it up to the right so I’m gonna line it up to the right.”

And all of a sudden, we’re like, “Whoa, whoa, hang on a second.”. It’s because they’re trying to apply that same rule they learned in order to add and subtract. However, that rule no longer applies here. So, then we have to teach them a new rule, that it’s not about lining up to the right but about lining up the decimals. It’s really not about the rules.

The reason we teach those rules is to give them a trick to help them understand what’s really happening. Unfortunately, it’s a trick because it doesn’t always work.

So, instead of saying we line them up to the right or we line up our decimals, the key understanding, whether you are adding or subtracting, is you have to add or subtract “like values”. It doesn’t matter what kind of addition or subtraction you are doing, if you put your ones with your ones, your tens with your tens, your hundreds with your hundreds, your tenths with your tenths, your hundredths with your hundredths, you can add and subtract. Even as they start working with algebra, it’s the same idea. So often, kids will try to do the ‘x2’s with the ‘x’s but they’re not the same value.

If they have the understanding that things have to be the same value, that rule applies to addition and subtraction across the board, even when you get to fractions. That’s why you can’t add fourths with halves because they’re not the same value. You have to have fourths with fourths in order to add them.

Key Takeaway #3

My last reason why I think we should be putting an emphasis on place value first, is because when they get to those more difficult problems that require regrouping, it actually makes that type of problem much easier. What I’m talking about is when we get to a subtraction problem like this (We could also do the same thing with addition).

Regrouping when it comes to subtraction is the most difficult thing to get kids to wrap their brains around. So, I wanted to go with the most difficult type of problem that kiddos are gonna encounter. When they get to this type of problem, the standard way that we teach it is to have them cross all of these out and replace it with what the regroupings are.

But when they see it like this, they’re still, again, seeing 15-7, 13-8, and 1-0. They have no concept of what they just did. What they see is a 1, a 13, and a 15. Was that even correct? They don’t know, right? Especially, when you get to subtraction across zeros, it becomes super difficult.

But, instead, if we take that same problem and we expand it out using their understanding of place value, that problem really means you have 200, you have 40, and five, 245. And you have to take away 80 and 7 out of that. There are different ways kids might set this up…this is not the only way to solve it.

Let’s take a look at what that might look like if kids are trying to do that traditional algorithm using this place value understanding.

What ends up happening is they see what’s actually going on with those numbers. It’s not just a 1, a 13, and a 15. It’s 15, it’s 130, and it’s 100.

So, one of the biggest pieces we want kids to understand when they are doing this regrouping, that’s why we call it regrouping and not borrowing now, is that you’ve really just taken that 245 and regrouped it. It is all still there. It’s just grouped differently. It now has 100, 130, and 15. That still makes 245. It’s just grouped differently. That is way different than what kids get with the traditional algorithm. It’s a totally different understanding.

So, Even as they move into adding and subtracting with decimals, this same idea holds true.

We want kids to be able to understand the value of those digits. The only way they’re gonna do that is if we focus on building their place value first, before moving into the operations. When they go to regroup, you should see that you still have 2 and.45. It’s just going to be regrouped in a different way.

I hope that this has helped you understand a little bit more as to why we need to build kid’s place value understanding instead of trying to teach them strategies. If we build their place value understanding, the strategies come from it and then all we have to do is just help them find a way to model that thinking that’s happening in their brains. So, I hope that this helped you build your math mind so you can go out there and build the math minds of your students.