Why Number Lines Break Kids (And How to Fix Them)

Segment 5 Clips from Lockers, Rectangles, Pizzas, Oh my part 2
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Cheri: [00:00:00] Hey everybody and welcome to Tier One Interventions podcast, where we look at your core classroom and we try to maximize your gifts and help you reach every student with their math, with their writing, and with their reading skills. But we concentrate mostly on math here at Tier One Interventions podcast.

And our math leader, miss Jonily, is ready to share some gold nuggets today. Welcome to the podcast Jonily, and they are gold nuggets because these last few weeks have been a whirlwind. I'm gonna kinda take us back a little bit, and there's another community that I teach called a Math teacher Mastermind, and I'm going to launch our session today.

let me talk through this and then give me some feedback 'cause I have no idea what I'm saying right now. [00:01:00] So here's what I'm gonna do with my second graders 'cause they've done the twelves and skip counting and the 12 song. And so for my second grade, and actually this is how I would do third and fourth grade, this is how I started.

But for my second graders, I'm gonna give them 12 and two. And I'm gonna tell them what's I'm gonna ask them, what's the result of adding numbers? What's the result? So we can practice the word sum. What's the sum of 12 and two? This is very appropriate for second grade 14 when we add 'em together.

So that's good for second grade. So just the bottom part of the diamond is good for second grade. Amy, you could do the bottom part of the diamond first. Oh my gosh, I'm totally making this up right now. This is so good. Okay. For me. This is so good for me. This is all about me right now. So what I'm gonna say to my second graders next week is, remember when we were counting by twelves?

This means how much are two twelves? I don't even have to call it product. How much are two twelves? [00:02:00] Two groups of 12. Go to your one 20 chart. Let's whisper count. I already did that for you guys. My second graders can do this. I could see Amy's class doing that. Maybe not in September, but by March they would be able to do this Amy's class.

I never thought about it this way before.

Whoa. Thoughts, comments, questions, anybody? Because I am processing my own brain right now. Would you give them the one 20 chat to do that? Oh yeah. I'd have the quick thoughts. No, I'm just asking, but yes, you would. Yeah. Yep. I'm gonna give them all their resources to do that. Yeah, good question.

Oh, but later on, I would want them to do it without nothing. Okay. Eventually, right? Yeah. Good question.

I can see how [00:03:00] squares and making rectangles fits into this category. Talk about that. Because if we're talking two twelves, we're talking two twelves. We're getting out those what do you call 'em, Katy Cubes. And we are making two lines of 12 and trying to figure it out from there. I don't understand why you're saying three or third grade and above, because I could see Amy's class doing it.

You know what? Yeah. Not every first grade classroom, but Amy's for sure. Absolutely. Absolutely. Because yeah, they're just making a rectangle of two by 12. I never connected this is not the reason for rectangles here, but it is now. Now these two now, oh my gosh. I cannot believe this is happening right now.

Kirk, are you laughing hysterically? We can't see you. Not hysterically, but I am amused that John Lee didn't see all of this before. Not [00:04:00] like that, because I do dimension chart. Have I shown you guys dimension chart with the blank multiplication table? Yeah. You have? Yeah. So when we go over to 12 and then the two, and then we connect and find the connecting block, this is the array number in the connecting block.

Okay. Beth has a question in the chat, and that is, can you use the number line instead of the one 20 chart? And I wanted you to address it rather than me putting a comment in the chat. Okay. Let's let, I need to stop and I need to do something right now. I'm gonna go back because Beth, you have reminded me that people that are watching this may have no idea what I'm talking about.[00:05:00]

So you guys give some more takeaways and connections and let me find something that I need to do.

My takeaway is you just don't know how smart you are. Oh, thank you Kirk. But you should tell my family that they wouldn't listen. I know they won't, but Ryan already knows. You think so?

He wouldn't be such a laid back gentleman otherwise, I just figure he, oh, Theresa, stop buttering her up, huh?

I'm a dangerous woman.

I think this would really great engagement thing for kids because they really want to think they really do. And we kind of school that out of them in too many Amen. Classrooms. Amen. And so I think [00:06:00] even with young ones, even with or kids that we say, we lump them into a lower group.

I think if we challenge 'em and don't start with, huge numbers. Yeah. Start with little ones and they can, and I think this is a great way for fact fluency as well. Yeah.

I think that this could be added into your season, like the slides, I'm thinking. Okay, Amy, we need to meet with the dots and then the circling of the numbers and the, because that's what I was finding because Beth has never seen Beth. Beth has accelerated herself to level two and she's just jumping all in.

But she just joined us literally two months ago. So here's what I wanna do right now and I found it. Okay. This is good for all of us, but this is gonna be really good for Beth. [00:07:00] Okay. And Amy, it's so funny that you just said that because that's what I was trying to find was this, so that I can make a better connection with all of us.

Let me back up for just a minute because all of you have access to this. You all have access to this. So if I back way up, what you're gonna see is all of these things are in levels, and I even level my diamond problems. And I'm gonna show you, I keep saying, I'm gonna show you an example of that. I am.

But I level all of the tasks as well, but many of the levels are exactly the same. There actually could be three levels, but I made more because people are uncomfortable with only three levels because they're always saying their kids are lower than any level I create. But I'm like, yeah, but you're foc you're not teaching it, right?

So anyway, these are the levels that you have access to. Each level has a color. When you go into the levels, what you're gonna notice is there's a first 15 day [00:08:00] now for level three, this is applicable all the way up through the other levels. Kathy mentioned this too. I can use this with sixth graders, even though it's level three.

So don't let the level and grade level scare you away for level three. Beyond the first 15 days. We actually have monthly weeks that continue to bring back first 15 day items. So I pooled one of these weeks 'cause I knew it would be in, in one of these. So one of the days that I, one of the lessons I might do would be this.

It's on a slide deck and you all have access to this. And this is actually what I did with my second graders when I was explaining that to you earlier today. I just didn't give you the visual, which I should have. That's my bad. Okay, tell me about this. Tell me about this. These are the rectangles I'm talking about with chunks of 12.

And I reiterate with my kids, okay? We can use a strategy to find lots of twelves by using whisper counting, and then the loud number gets marked on the one 20 chart. So if you wanna use this [00:09:00] with your kids, these slide decks are there in level three. You'll see this in the title level three week C. So if you wanna go back to pink level three week C, even if you're a seventh grade teacher, go get this and use this with your students.

So for a one 20 chart, I like a one 20 chart rather than a number line. The number line is the most abstract symbol that kids can exercise with in school. If kids don't understand number line, that doesn't tell me L much because even my top students don't understand number line. We use number line as a tool, but the number line is actually one of the worst tools that we can use to teach the concept.

I wanna use the number line to assess the concept because my ultimate goal is to get kids good at number line. [00:10:00] But number line to teach the concept, it's like teaching facts and skip counting with money. When kids don't understand money, I want kids to understand money and I wanna use money to teach the math, but if they don't understand money to begin with, using money as the tool to teach the math is a double whammy.

So using number line oftentimes, now this is not always true, but using number line is not my first go-to tool for actually facilitating the instruction when they're in the learning phase. I will use number line after they've had lots of experience with one 20 chart, because the number line is much more abstract, but they can connect it to the one 20 chart.

A very concrete, sensory based application of the number line is to take [00:11:00] a one 20 chart, make a big one on a piece of paper. And this is in tier one interventions. I'm not sure exactly where, because Sherry has adapted number one 20 charts where for kids that have trouble with fine motor and scissors, there are thicker lines.

We have all these AP adaptations of one 20 charts in level one. But the reason is, the reason we make thicker lines is we print a big one 20 chart and each kid. And just follow my cursor here. Cuts on this first row line. So we make one bar of one through 10. So we cut off the one through 10, then we cut off the 11 through 20 and then we cut off the 21 through 30.

I actually have fi fids kids physically cut the rows. Then what happens is we take this second row and we move it over here beside. So one of the exercises I do with kids is transforming the one 20 [00:12:00] chart into the number line, physically tactilely and sensory based. So they start to connect. When they see a horizontal or a vertical number line, they have physically multiple times cut the one 20 chart to show the number line.

Now the one 20 chart to show the number line, and I'm gonna show this here, the one 20 chart to show the number line. So if I have one through 10 here and then I have 11 through 20 here on the number line or on the one 20 chart, 'cause the kids are cutting and putting them side by side, this still is not as abstract as a nu a number line.

Kids are not gonna relate this to a number line because guess what? These bars are two dimensional. These are two dimensional and they have spaces and not tick marks. So kids are still not gonna make, I have to explicitly say, and a lot of times I'll [00:13:00] write it with dry erase. I have to explicitly say, and actually one of the systems we use for dividing into 10 parts is I can go exactly in the middle.

I don't have to share the middle. Then I need five and five. So I have to share the middle, and then two extra lines and I have to share the middle and do two extra lines. That's a strategy to get mostly equal parts in. In a bar model. I call this a bar model, but how does the bar model start? The bar model starts with paper strips and paper folding.

See, this is how all the reference tasks connect. So now what I can do is after the kids cut out the one 20 chart, I'll be like, Hey look that's one of our paper strips. And the paper strip would go from zero to 10. So sometimes our paper strip goes from zero to one, sometimes from zero to 60, sometimes from zero to 12, if we're gonna make the circle with time.

But sometimes this one is gonna go from zero to [00:14:00] 10. So this paper strip and actually, john Lee, be better than this. Be better. You're better than this. Actually, for this, I would use a blue paper strip because how do we fold the blue paper strip? So for paper folding. The blue paper strip has to make, you guys can't see.

I'm sharing my screen and you're seeing me small probably. So sorry. Okay sorry. The blue paper strip is always associated with five parts explicitly to make five parts. I'm gonna show you. I don't, I'm not, I don't want you to do it. Okay. You touch the edges together, you open it up, you have three equal parts.

So to do five parts, I explicitly teach students touch the edges. You have three equal parts. You make a crease. Okay? You have three equal parts, but two of them have layers. So you have two, two and one. That's five parts. So wherever this edge is, I have to make a [00:15:00] crease there. Okay? So I would actually use this.

Now, how would I get 10? If I have five, how do I get 10? Ah, Theresa held up two fingers because she knows that if I fold on these creases and then do my iterations from the white paper strip, which is doubling the parts or folding in half, I'm gonna fold every part in half and that's gonna create 10 pieces.

That is what the blue paper strip does. So literally now I can go from zero to 10 and each spot is one. So if I wanna connect paper folding to this, I can do this here. You guys, I'm teaching this on the fly. This was not a part of today, but I'm, we're just, sorry, not sorry. Okay. So Beth, so what happened?

Go ahead. So Beth, don't stress yourself out. You only can learn so much at one time and [00:16:00] I'm not sure that you have access to that slide deck that she was showing you. So I'll have to get that to you. Okay. And this is actually, this is for Beth, but it's actually for all of us. So if I extend those lines from the 120 chart, the first row, and cut that what I do on the dry erase board, and this is how I make the connection for the kids.

We have the bar model and then we extend the space lines 'cause they know what those mean. And then I say to my kids, okay, so now if I erase the bar, if I erase the bar, what can you tell me? Tell me about this like partial bar. What do you see? What do you notice? And this is what I do with the kids to connect to number line.

'cause now I have just a single line with these tick marks and I'll ask the kids, what is the length of this [00:17:00] line? My, my algebra one ninth graders mess this up because they count the tick marks. They count the inside tick. No, we have to count the spaces. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The length of this is 10 units, 10 units.

That's the top of the one 20 chart. See how important this one 20 chart is and then how important the bar model is. 'cause we take the one 20 chart, kids physically make bar models that are each 10. They put 'em side by side. That still doesn't get us to number line. We have to then create this and have it, have them watch it transform right in front of their eyes.

So some people then say to me, that's great John Lee, but they have to take state test and they're just gonna see number line. I know. Okay. So on a state test, when they see number line and we wanna look at, let's say fifths from [00:18:00] zero to one. Okay. Now kids, at least in our state, they're allowed to use like tracing paper and stuff during the test.

Or they can draw this on their own or whatever. Like they, they can do this. I teach my kids that if they see a number line, they're struggling with number line just to make this a bar with all the spaces. So that's one of the best interventions we can do to help kids transition to understanding number line and the kids can do the intervention and adaptation on their own.

Because I teach kids how to do this, I teach them how to. Take the number line and make the bar. Now, for a lot of kids they're like oh, I got it, got. For other kids, they're like, so then we have to take it to the other point where we have to bring the physical back out again. But we start from the physical to the two dimensional, to the bar model, to the number line.[00:19:00]

But then always we're doing that cycle forward and in reverse given the number line to the bar, to the paper. So we're always using that cycle forward and backwards.

Cedric:  “And that’s where we’ll pause for today. We unpacked skip-counting, twelves, rectangles, and how to scaffold iteration up and down grade levels. Next week is our grand finale—where everything comes together: reference tasks, number lines, paper strips, algebra tiles, and the entire connected ecosystem behind Mastery Math Method. It’s the episode that ties the bow.

And hey—if you’re loving this and want to get the full workshop where we go step-by-step into the Mastery Math Method, you can sign up to experience one workshop for just $47. The link is waiting for you.”