The sky is the limit when it comes to number lines. They can be effective hands on tools, useful classroom decor options, or even a reference sheet for the student’s workspace. This episode will help you think about number lines in a new way.

**Topics Discussed**

- Open number lines
- Fraction, decimal, percent number lines
- Positive and negative integer number lines
- Double number lines
- Ratios
- Vertical number lines

**Resources**

**Grab your own copy of the FREE number line resource Ellie mentioned in this episode****:**

**See these number line examples visually in this blog post:**

https://cognitivecardiomath.com/cognitive-cardio-blog/fraction-decimal-and-percent-number-line/

You might also enjoy Episode 22 about Pi Day

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Ellie’s resources can be found on her website or on TPT.

##### Transcript

Ellie 0:20

Have you ever struggled to teach your students about number lines? If so, you're not alone. According to a recent study, 70% of elementary school teachers reported difficulties in effectively teaching this concept. But fear not. With the help of number lines, you can transform your students' understanding of numbers and improve their math skills.

Welcome to the teaching Toolbox Podcast. I'm Ellie, and I'm here with Brittany.

Brittany 0:46

Hello.

Ellie 0:48

And in this podcast, we'll explore the power of number lines in the classroom. While we can't cover all things, number lines, or we'd be here for hours, we'll look at some ways to incorporate them effectively into your curriculum. Prepare to say goodbye to the confusion and frustration and hello to confident engaged learners.

Brittany 1:08

So number lines are mathematical models or ways to see math concepts, and they can be used in so many ways. Number lines are excellent for helping students understand concepts like rounding, comparing numbers, basic operations, we can show adding, subtracting, multiplying, dividing all on the number line. When students reach middle school, they may not need number lines as much for basic operations. But for students who are still having some difficulty with things like adding and subtracting, regular use of number lines can really help them to continue to develop those concepts.

Ellie 1:55

So we can offer students different types of number lines, we can give them number lines with numbers that are already there, or we can offer open number lines which allows students to divide the number line as they need, given the context of the math problem. For example, if we're talking about addition, if the problem includes numbers that are in the 10s or hundreds, students could set up a number line that increases by five or by 10. If they deal with fractional amounts, their number line might only go from zero to one. Or they may include only specific numbers, if they're using the number line to show the addition of a problem like 17 plus 28. So maybe they would write 17 on their number line and then they would write 27, and kind of show a jump from 17 to 27, showing that they've increased by 10. And then another jump to 37, showing that another 10 has been added. And then they might go to 40, and then to 45. And kind of break that 8 from the 28 into smaller sections to get them from 17 to 45. But another student might take an open number line and start at 17 and add on the 8 first and label 25. And then they might just add 20 right away and jumped right to 45. And their number line might only show 17, 25, and 45. Some students might even show 17 plus 30. Instead of adding 28, they might add 30 on and jump right to 47. But then jump back 2 places and land at 45. And that way, they're kind of showing the compensation that they've done, of adding 2 extra and then taking them away.

So allowing students to use an open number line like this can help us as teachers see how they are thinking about the problem, and how flexible they might be in their thinking and what strategies they've got in mind as they're working with it.

The same idea applies to showing fractions on a number line. If students are adding one half plus one in three fourths, they might set up their number line to go by fourths. They could start at one half, and then jump one whole to one and a half, and then jump another three quarters to get to two and 1/4. Or they might start at one and three fourths because commutative property says we can you know start with either number first, when we're adding they could start at one to three fourths and then jump 2 fourths or half to get to the answer. Or they could start at a half, jump three fourths to get to one in the fourth and then jump one whole to get to two and a fourth. So using the number lines helps students understand that fractions are numbers, so it's important to use those number lines with fractions, and that fractions are not just shapes that are divided into pieces. They're actual numbers on the number line and and represent distance and amounts. It also helps to reinforce the concept of equivalent fractions. So there's so many ways that we can think about using these number lines, open number lines, or number lines with pre-printed numbers on them.

And yeah, and it's hard to say this without showing it, and so I'm hopeful people can kind of visualize what we're what we're saying as we're talking about it, because I really, if you could see me, I'm moving my hands like I'm moving on a number line. But because I want to be able to show that but hopefully people can, can re listen, if they didn't catch it, the first time.

Brittany 5:43

It is so cool. Another way you can use number lines is to have them as part of the decor in your classroom, Ellie kept a fraction decimal percent number line above the whiteboard in the front of her classroom, with the most common fractions, decimals, and percent equivalences up there. This really helped her students to learn those common equivalences. It was almost a daily reference for them since these numbers popped up so frequently. I know in my class, we always had the five eighths and point 675, I believe it is always showing up in our math book that always was a big one for our students. And she actually made a smaller version of this number line for students to keep in their notebooks. It is a free PDF download in her TPT shop cognitive cardio math, if you want to use it with your students, and we will put the link in the show notes.

Ellie 6:54

Yes, students love those number lines, we used to make them figure out their grades. So if they had a quiz, and they got a four out of five on the quiz, they could easily look up at the number line and go, ooh, four fifths, four out of five, that's 80%. You know, and they could use that as a quick reference for small things like that. And then if they wanted to see if they got two out of three, correct, you know, that was one of the repeating decimals. So we had the repeating decimals, and the terminating decimals up there. So they could kind of see which one was greater than the other, it was just so useful. So many, so many things we could talk about there. So but I'll I'll keep going.

I also had a positive and negative integers number line at the top of another one of the walls in my room. So when we started thinking about negative numbers, we all had this huge visual that we could look at and talk about when we're moving in the positive or negative direction when we're combining numbers. So when we started with the very basics, you know, negative one plus four, we could look up there and use a pointer to reach up there and show jumping on that number line. This one was also very helpful when we started working on absolute value, it was very easy to see that both negative three and three were the same distance from zero, and therefore they had the same absolute value.

Brittany 8:08

Great idea! Double number lines is another way you can use number lines when you're looking at the relationship between amounts, like when finding the percent of a number or when working with ratios. With percents, the number you're finding a percent of on 1 number line and 1 - 100% on another so if you're dealing with say 80 for example, we'd mark 40 at the 50% line, 20 at the 25% line, and 60 at the 75% line. Or we could break the percentages into increments of 10 percent.

Ellie 8:09

Yeah, so then if you're saying I would like to know what 25% of 80 is, and you've got them lined up in that way, then it's very easy to see how those numbers are broken up equally, the 100% and the 80 in the same way we could use that with ratios. So if we know that a basic ratio is five to four, one number line will go by fives, and the other will go by fours. And we will kind of line up those increments on the number lines, line them up with each other. So we can then determine if we have six sets of five we would be at 30 on the number line. And then the six sets of four would bring us to 24 on the fours number line. So we could see that the ratio equivalence would be 30 to 24. And we could also see the other equivalences of five to 4, 10 to 8, 15 to 12, 20 to 16, and 25 to 20. So lots of ways we could use number lines. And as we said, we can't go into all of them today because we would be here forever.

Brittany:Another way we can use number lines is by using vertical number lines, which is a lot like using thermometers or teaching about thermometers. So you can visualize the pattern of increasing 10s, and ones with two digit numbers, students can easily see the sequence and repetition of the digits that way, students more easily understand the value of numbers, they're able to see the numbers increasing or decreasing in value. So they can easily see that like 53 is lower or less than 55. Because it's under the 55. Whereas 67 is higher or more than 63. Because it's above the 63. Students understand that counting up and counting down when adding or subtracting. It's evident that sums increase because they go up the number line, while, differences decrease, they go down the number line. And then lastly, kids make a connection between the terms rounding up or rounding down to the nearest 10. When they look at vertical number lines,

Ellie:And thinking about rounding, I feel like even in middle school, students still have some some difficulty with rounding and understanding those concepts. So getting it on the number line and making it visual like that is really, really helpful for them.

Brittany:Yeah, quite a few kids still have challenges with rounding.

Ellie:So if you aren't using number lines already, think about a way that you could start incorporating them into your classroom, maybe one or two of the ideas that you heard today. There's something that you could quickly incorporate. Remember, if you want to you can grab that free fraction decimal percent number line that would quickly help you get started with number lines in the classroom by giving that as a reference for students on a regular basis.

Brittany:So we encourage you to incorporate number lines in your next math lesson, and then share the results with us by writing a review for the podcast on Apple, Spotify or Google.

Ellie:Yeah, we would love to hear what you do.

Brittany:We hope this has provided a new tool for your teaching toolbox. And we will catch you next week for a new episode.

Ellie:Bye.

Brittany:Have a great day.