The Best Way to Teach Rounding Numbers

“Five or higher and you round up.” That’s the saying I hear over and over from students but I have two questions for you. Number one, “do your students really understand that rule and know why it works?” Number two, “do they actually apply that rule correctly?” I hope you’ll stick around as we investigate the best way to teach your kids to round numbers, in our quest to build our math minds so that we can build the math minds of our students.

Watch the video or read the transcript below.

Use A Number Line

Maybe you’ve heard about rounding numbers on a number line but you’re not exactly sure what that looks like, how you do it. So, I want to show you a few examples of how to show rounding numbers on a number line. I’ve got to tell you, the hardest part is getting kids to understand what numbers to put on the number line to begin with.

Oftentimes, I will see a lot of activities about rounding on a number line but the kids already have a worksheet that already has laid out what numbers go on each side of the number line and then the kids just have to place the number on the number line.

So, I’m going to show you what it looks like and some things to really be focusing on as you’re building the ideas of rounding numbers. This is an idea I talk about inside of my Number Sense 201 course. If you’ve already done that course, you’ve probably seen this before. However, I wanted to share this little piece of the course because it’s such a powerful idea. If you’ve never done rounding on a number line, it makes a world of difference for our students and even for us as adults.

Let’s say we want to round 2635. The first question for all kids should be, “what are we rounding to?” Because there’s a lot of things that we could round here, right? We could round to the nearest 10, the nearest 100, or the nearest 1000.

Let’s start with the nearest 100. What we tend to tell kids is, “okay, look behind it, if it’s five or higher, you round up” and most kids will be just fine with that saying. I learned it that way and did just fine. but there are kids who will misapply that.

I was in my daughter’s third-grade classroom helping out one day and they were doing some rounding activities. One boy had gotten about half of the rounding sheet correct and the other half was incorrect. So, I started digging into his thinking a bit and half of the ones he got correct, he got correct for the wrong reason because of how he was looking at it. But I didn’t discover it until I dug into his thinking about the ones he got wrong. So let’s say this 2635 was being rounded to the nearest 100.  He would round this to 2700. When I questioned him about his thinking he stated, “if it’s five or higher, you round up”. I then asked, “well, what number were you looking at?” He pointed to the five. So his thinking was if there’s any number behind that number that is five or higher, you round up.

Help Kids Determine The Benchmark Numbers

As well-intentioned as that strategy is, for our kids who don’t understand, they’re just memorizing this strategy. Sometimes they’re misapplying it, sometimes they’re using it correctly but the idea really is based upon, “if it’s five or higher, it’s closer to the next benchmark number”. So, we want to help them look at what are the benchmark numbers and then look at, “is this number closer to this benchmark or this benchmark?”

So, again, the lovely number line. Just giving them an empty number line with some marks on each end and if we’re rounding to the nearest 100, what would be our benchmark numbers on each side of this? What’s the benchmark that would be higher? What’s the one that would be lower when we’re looking at hundreds? Eventually, we want kids to get to this point where they notice for example, that 2600 would be the lower benchmark and 2700 is the higher benchmark. And so we’re trying to decide between these two things. Is it closer to 2700 or is it closer to 2600?

The idea of “you look behind, if it’s five or higher, you round up”, has been based on what is in the middle. It’s really about knowing your two benchmark numbers and then what would be the middle point between these two benchmark numbers. What would be the middle point? 2650 is our middle point and then we’re looking at the number as a whole, not just looking at what’s behind it. So, now we’re looking at, “if I have 2625, where would that fall on this number line?” Well, it falls below that middle point of 2650, so now it’s closer to 2600.

So, getting kids to think about what are those two benchmark numbers on either side, what’s in the middle, and then where does our number fall on that number line, tells us which way to round it. And eventually, they’ll start noticing that if it’s the five, whether it’s at the 50 or the 500 or whatever it might be there, that we’re gonna go up to the higher amount. If it’s below that middle point, we go down to the lower amount.

Now, your benchmark numbers for 2635 will change. I’m not always going to use 2600 and 2700 because if I want to round to the nearest 10, those numbers are no longer my benchmark numbers. So, what would my benchmark numbers be if we’re rounding to the nearest 10? If we’re looking at the tens place, what are our benchmark numbers?

We want kids to get to the point where they can place the benchmark numbers here and also think about what would that middle point be and then where would our number fall in relation to that and this one would happen to fall right in the middle.

As we move into thousands, again, we’re going to have different benchmark numbers. If I want to round this to the nearest 1000, what are my two benchmark numbers gonna be? 2000 and 3000. And then what’s in the middle and then where does my number fall according to that? So, these pieces are really huge. This activity is great for helping kids understand those benchmark numbers…What are the benchmark numbers? What benchmark numbers are these closest to?

You can do the reverse of this where you give them the two benchmark numbers, where a scaffolding piece of this would be, you give the two benchmark numbers and then having them place it.  However, all too often, kids aren’t paying attention to the decision of what was the benchmark numbers. Why did we pick 2000 and 3000 when other times we might pick 2600 and 2700? What determines what our benchmark numbers are?

Doing lots of activities where you have your students determine what are those benchmark numbers is the biggest thing. Don’t jump straight into rounding and having kids place numbers onto a number line, deciding where it lies between these. First you’re going to help them understand what benchmark numbers is that number in between? Just doing lots of activities, not even talking about rounding, just talking about the benchmarks. What benchmark numbers, is that number in between? And would that change if we’re looking at our tens versus our hundreds versus our thousands?

Once they get comfortable being able to think about benchmark numbers, we can then ask them to think about, placing on a number line and thinking about what number would it round to. Which benchmark number is it closest to? Not just which benchmark numbers are on either side, but which benchmark number is it actually closest to.

Show Horizontally & Vertically

In the pictures above, I showed everything horizontally. My number line was horizontal. I’m a firm believer in showing it in a lot of different ways. So, have your number line going vertically. It doesn’t always have to be horizontal. It just worked out that way in these examples. Vertical number lines are also really powerful and we see vertical number lines a lot in our lives, for instance, the old-school thermometers that go up and down, and those fundraising posters that we make are basically vertical number lines.

So, giving kids opportunities to see it horizontally and vertically is really important, but the whole idea is, it’s not just the rule of if it’s five or higher, you round up. I want them to understand WHY. Why is it that every time it’s five or higher, we round up? What does that five really mean when I’m looking at the number as a whole and placing numbers on a number line? Doing this to help kids round, is the best way to help your kids round numbers.