Top 5 Ways To Use Number Lines In Math

Number lines are an essential mathematical model. However, if you are anything like me, you didn’t grow up doing math using number lines. So, if we didn’t use it or learn that way, it becomes hard for us to teach it to our students. Today we’re going to take a look at my top 5 ways to use number lines in the math classroom. I’m going to give you the quick overview of the top 5 and I’m going to show some slides that show you what it looks like using a number line for these 5 concepts.

My top 5 are rounding, addition & subtraction, and multiplication & division on a number line. We’re also going to talk about how number lines build spatial relationships for our students. Then the last thing I want to talk about is using number lines to help kids understand percents and finding the percent of type questions.

Watch the video or read the transcript below.

Rounding

Let’s dig into number one, rounding. I’m not going to go to in-depth on rounding because you can watch my video all about rounding on a number line that will give you more explanation.  The whole idea is, getting kids to place the number we’re trying to round, on the number line, based upon the benchmark numbers that we’re trying to think about “does it round up to this amount or down to this amount”. If they can place it on a number line, that visual helps them to see which amount it’s closest to. This is a better way to start out than the way that I learned, which was, “if it’s five or higher, you round up”. So if you want more details, head back to the vlog post all about using number lines to round.

Addition & Subtraction

The second one is adding & subtracting. There are lots of different strategies that kids will use when they’re adding and subtracting. Way different than when I grew up or even when I first started teaching. It was still about just learning the traditional algorithm. Now the traditional algorithm is part of it, but part of what we’re trying to do is let kids solve addition and subtraction, multiplication and division, anyway that they can. As long as it’s efficient and accurate and based on their understanding, it’s an okay way to solve the problem.

I want to show you some of those strategies that kids might come up with (this is not all of them, but just some of them) and how the number line can really help kids to visualize it. Not just the kids who are doing it, because they’re seeing how all of these numbers work, but the number line can help the other kids understand what that kid was doing.

I’m going to start off with fractions because fractions are not friendly sometimes. One of the things that’s helpful is that kids will want to make the fraction friendly.

So if I’m adding 2 ¾ and I’ve got to add 3 ¾, and 2/4 onto that, one of the things that kids will do is say, “if I just added a ¼, I could get to 3”. Then once they’re at 3, that’s one of those kind of benchmark friendly numbers, it becomes easier for them to just add the remaining piece of the 3 ¼ to get to their answer.

As I’m talking about these strategies, these are not things you have to teach to kids, it’s things that kids will naturally do if they understand numbers and how numbers work. The number line is a great way for them to take what they’re doing in their head and have a way to show it on paper. The number line is a notation, it’s a model. The number line itself is not a strategy. There’s nothing that tells me what to do on the number line. Kids will use them in different ways.

Let’s take a look at an example of subtraction. Often times, kids will want to round one of those numbers to a friendly number. If one of the numbers is near a friendly number, they will want to round. The hard part with subtraction is that once they get here, they know that the answer to that is “47”, but the hard part is they don’t know what to do next. They knew that they changed the problem, but they aren’t quite sure how to undo what they did. They will say to themselves, “well I added 11 to get to the 300 so I should subtract 11” because they feel like it needs to balance out.

However, when we show it on a number line, and we use that notation to show their strategy and we show how they started at 347 and they jumped back 300, a lot of times kids are like “wait, I jumped back too far. I went farther than I was supposed to so I actually need to add the 11 back in”. So when kids are struggling and they’ve got a strategy part of the way, like they’ve got this idea, but it’s not quite working right, having a visual model of that strategy can really help them understand it better. So a number line is always, just seems to be a great strategy, a great notation to help them visualize the strategy.

Spatial Relationships

Spatial relationships is a really huge piece for kids and their understanding of how numbers relate to each other. Spatial relationships gives kids a visual but also talking about how those visuals relate. With small amounts, it’s nice to just have visual pictures of 7 and 5 for instance, and talking about what’s the same and what’s different.

But as we move forward, we want to help kids use the number line as one of those visuals. So that if they were to place 7 on this number line, where would it go? How do you know it goes there? What does it tell you about how it relates to 10? Where would 5 go? Where would 12 go? All of those kinds of things because it’s a nice visual but again, number lines are pretty abstract. So you want to first start with actual things where they can see 7 things in comparison to 10 things.

However, as kids start moving up into larger amounts, we don’t want them to have to draw 70 things in order to see how it compares to 100 things. So the number line gives us a model that is extendable. We can use it for all kinds of numbers that we are working with kids about. So we want to start with physical things, move to visual images, but then the number line can be a great visual to help us see relationships between amounts.

Even when it comes to fractions, this becomes a huge visual for our kids. Number lines are a great visual for fractions and understanding how fractions relate to each other. If I wanted to place ¾, where would I put it on that number line? And kids might partition, but then things like if I wanted to place 13/16, where would I put that on the number line? Or even 15/16? I may not be asking the kids to partition it into 16ths, I want them to know that 15/16 is darn close to a whole. The idea is that they can place things on this number line that gives them a visual to then talk about how numbers relate to each other.

Percents

The last one I’m going to talk about is percents because oftentimes kids struggle with percents. Well not just kids, but adults as well. I was the adult who was a math teacher and when it came time to figure out the percent of tip that I needed to leave for a waiter or waitress, I was pulling out my cell phone to figure it out because I didn’t have any visuals, I didn’t have any strategies for figuring out percentages. A number line is a great way to do that and what it essentially becomes is a double number line.

So we start out with this idea of zero to 100, but that 100 is really 100% or the whole amount we’re working with. So if my bill was $24 I could figure out lots of things on here. But not even just in that scenario of a bill. What if I just wanted to know 50%? Would being able to place this on a number line help me out? 50% should be half, right? And so what’s half of the 24?

Now, most of the time, they know that fairly quickly, but then we can use that visual to help us with other things like 25%, or 1/4, right. We want kids to be able to visualize where that would fall on the number line and use that to help them out.

We start with friendly amounts, but then you can move to things that maybe aren’t as friendly, and show them on the number line. Now here’s a typical problem that we do with percents. “Ms. Thompson has 12 Labradors. This is 20% of all her show dogs. How many show dogs does she have?”

When I was in school, we were taught to set this up as an equation and figure out what goes on each side of the equal sign and figure out what the unknown is. Once I learned that I could show this on a number line, it changed everything for me. It helped me so much in understanding “percents of” questions.

In this story, I know that 12 Labradors is 20% of what she has for show dogs. And that’s what I’ve modeled on the number line. From there, the goal is to figure out what’s 100%. How many show dogs does she have? Well the cool part about once it’s here, the kids will figure it out in a lot of different ways. And in ways that build their number sense. They aren’t just computing. Remember, it’s about building math minds, not just creating calculators. I could plug this into a calculator and get the answer but I want to encourage my kids to be thinkers, not just calculators. Yes, I want them to get the answer. Yes, I want them to calculate it. But I want them to build their math mind while they do that.

So you might see kids from here say “well, if 20% is 12, 40% would be double that, and then if I doubled that, that would get me 80%, and then when I get 80%, all I have to do is add that 20% on to figure out what the 100% would be.”

You might have some kids who don’t see it that way and they say, “I can just halve that 20%, that would give me 10%. And once I know 10%, that could tell me what 100% is.” They’re using their number sense, but the number line is helping them visualize this idea, right, to build their understanding while they’re also computing and figuring out the answer.

Remember, this is not a complete list. If you have a favorite way that you love to use number lines that I did not talk about, let us know down in the comments. Or if you have a favorite activity, leave the link to it down in the comments. Help all of us build our math minds because this is not the only way to use number lines in the classroom.

If you want a short little summary of each of these in a PDF download, there’s a link below this video and at the bottom of the vlog, where you can request a download. It will give you these top 5 ways and show some visuals along with it. I hope this helped you build your math mind so you can build the math minds of your students.