Number Lines

[Ritsumei]

OK. So number lines seem to be a staple of arithmetic, especially early on. Only, there doesn't seem to be any consensus as to what they're for or how they ought to be used. For instance:

 

Khan Academy leans heavily on number lines in their "addition 1" clip, with 7 individual hops on the line for +7, for example.

 

Miquan uses them, but seems to encourage drawing a single large hump to represent +7 as a lump, rather than individual hops.

 

Math Expressions barely introduces them at all in the K book that we're using, only devoting a few pages to some very limited examples.

 

My Mom teaches K, and when I talked to her she said she'd taught from books that use number lines more, and from one that uses it lots less, and she noticed that there was a lot of places for kids to make mistakes using them - after listening to her talk about it I'm wondering if it's even developmentally appropriate for most K-aged kids. She didn't think that kids at that conceptualize of numbers as a line, or even in such a lineal way for that to really work for them. (Though I've certainly seen worse ways to help a kid add!)

 

So, does anybody know what they're for, or have you see research into when kids might be developmentally ready for them, or do you just have a funny story about kids & number lines?

[boscopup]

I found the number line to be immensely helpful when my oldest was 5 and we got into a discussion about negative numbers. He completely understood it used in that manner, but he's also a more abstract thinker.

 

As far as regular use in early curriculum, MM uses it some, but doesn't dwell on it, and neither have I. It is useful for skip counting multiplication. MM use individual hops for adding, and large jumps for multiplication. That's how I remember using it as a child too.

[Amy Jo]

I think number lines should be after manipulatives. But they are nice for multiplication and for negatives. They can help show relationships between numbers too (faster to 'jump' on the number line than to compute several problems). I'm not emphasizing them with my Ker, he isn't that exact, and does better with things he can touch.

[Greenmama2]

I suspect your mother might be correct about most kids. My K age child finds arithmetic reasonably easy but I'm fairly certain she doesn't conceptualise numbers in that way. We have encountered number lines (we use quite a few different programs) and she is familiar with how to use them. I wonder if a vertical axis would make more sense to a lot of kids (Miquon has them going various directions). DD has been talking about negative numbers lately and I was thinking of drawing a vertical number line to help her play with the concept.

[3Blessings]

My husband hates the number lines because he says, "When are you going to have a number line in front of you in real life?" BUT, I have been told by math teachers that it is a tool to be used for mental math. I agree that they should be used AFTER manipulatives.

[Dana]

My husband hates the number lines because he says, "When are you going to have a number line in front of you in real life?" BUT, I have been told by math teachers that it is a tool to be used for mental math. I agree that they should be used AFTER manipulatives.

 

You'll have a number line in front of you anytime you draw one :)

 

I see them as a great tool for learning basic facts at first. My son was in a private kindergarten and when the teacher was showing them the number line, one child asked what was to the left of zero. She said not to worry about that now. My son spoke up and said, "Oh, those are the negatives: negative one, negative two, ... "

I teach math... hadn't realized he'd picked that one up at the time :)

 

I don't see number lines as essential at an early age, but familiarity with them will be useful.

 

Any real number can be represented on a number line (an important concept). The number lines are used when graphing on a coordinate plane, so getting used to plotting points on a number line is a good thing.

When solving linear inequalities, you use a number line to graph the solution set (and the graph is really useful for writing the solution set using interval notation).

[Ritsumei]

I suspect your mother might be correct about most kids. My K age child finds arithmetic reasonably easy but I'm fairly certain she doesn't conceptualise numbers in that way. We have encountered number lines (we use quite a few different programs) and she is familiar with how to use them. I wonder if a vertical axis would make more sense to a lot of kids (Miquon has them going various directions). DD has been talking about negative numbers lately and I was thinking of drawing a vertical number line to help her play with the concept.

 

I like the idea of a vertical line. I think it makes more intuitive sense to have the big numbers at the top, and the small ones lower.

 

 

 

 

You'll have a number line in front of you anytime you draw one :)

 

I see them as a great tool for learning basic facts at first. My son was in a private kindergarten and when the teacher was showing them the number line, one child asked what was to the left of zero. She said not to worry about that now. My son spoke up and said, "Oh, those are the negatives: negative one, negative two, ... "

I teach math... hadn't realized he'd picked that one up at the time :)

 

I don't see number lines as essential at an early age, but familiarity with them will be useful.

 

Any real number can be represented on a number line (an important concept). The number lines are used when graphing on a coordinate plane, so getting used to plotting points on a number line is a good thing.

When solving linear inequalities, you use a number line to graph the solution set (and the graph is really useful for writing the solution set using interval notation).

 

 

I agree, they're useful in later math (though I'd never once thought of a graph's axis as a number line! :tongue_smilie:) I'm just trying to figure out what the purpose is behind teaching them to little little kids. I think that for now, even when we're doing the Khan stuff that he associates with number lines, we're not going to worry about it. The c-rods just work better for him right now. He's only recently 5, and having the touchable manipulative is still very much a necessity much, even most, of the time. So he's probably just not ready yet.

[Kuovonne]

Miquon uses the number line a bit (after manipulatives). I think that the way Miquon uses a number line to show fractions is brilliant, especially when it comes to multiplying and dividing fractions. Miquon also uses number lines to show functions. Both topics are far beyond K level math, so it just goes to show that number lines can be used for multiple purposes.