When working with students, we have to use specific math terms. Referring to a number as the one on the top doesn’t serve them well into the future. Let’s talk all about the official terms for fractions like numerator, denominator, and what they mean including tricks to remembering those root parts of these math terms.
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Hey, it’s Adrianne from Math for Middles. So excited to be with you today. So today we’re gonna talk a little bit about the language of fractions. It might sound important to you. Spend time in this activity with our students because when you have a child who struggles with math, typically it’s due to a couple of different things.
They may have issues with directionality, remembering procedural steps, and remembering words for certain things and because often has a whole lot of no meaning to them, these words like fraction, numerator and denominator and so it’s difficult to keep them straight, which one’s what? A lot of teachers make the mistake of just, what’s the number on the top? What’s the number on the bottom? We have to be really specific in our language when we’re talking to students about fractions for it to be a really successful experience.
So I thought I would just explain some of these language pieces to you and what we do here at Math for Middle school students when we’re talking about these things when we’re introducing this idea of fractions.
So the first word here is the word fraction itself. What does it mean? Well, it means to break, right? You’ve had a fractured bone before, you broke it. Fraction, to break. In a lot of students, it doesn’t really make a whole lot of sense until they actually break something. One of the activities that we do when we’re working on place value is when we’re working within the one’s column, we actually have physical craft sticks that we have and we break them to make our first half and they very quickly learn, “Oh, I broke it into two equal parts,” that’s really important to say, equal parts, there was two of them, that’s one half and one half, and two halves is the same as one so that’s a really important concept.
The other thing that’s really interesting that we need to make sure we’re doing is that we’re tying this idea of fractions to division because that’s what it is. We’re dividing that craft stick that we had originally into two equal parts. So improper fractions, well, that’s actually just division if I had 15 over 3, that’s the same as saying division, right? That’s 15 divided by 3. We do not teach these things isolated to our students but rather we teach them together. So that’s a really important piece for our students, for them to understand. We practice moving between the three types of division and what they look like.
Let me show you really quick with just a pen here. We have just the regular division symbol, we have our long division, and then we have a fraction bar which also means division. So going back to our 15 divided by 3, we need students to understand that this is the same as this. 15 divided by 3 and also here. This part, this is so tricky for our students when they see 3 on the outside and 15 underneath, it doesn’t follow the pattern, it doesn’t seem to go with it. So this is something that we explicitly practice with our students and they understand at this point, “Okay, fractions are division.” So it’s really important thing to talk about. Let me erase those real quick. So that’s the first word we covered, it’s fraction. What is it? It means to break.
The next thing we talk about is actually not numerator, I talk about denominator next. Denominators are an interesting word because we have D plus nominer is where it came from and that means to name, we’re naming it. It tells us the total parts of the fraction. So looking at my three examples here, they’re all the same quantity, what’s different about them is how they’re broken up, what their total parts are.
So here we have six total parts, that’s our denominator. Here we have four, total parts that’s our denominator. Here we have 10 and that’s our denominator. So it’s really important for us to talk about that. The denominator, he’s the boss, he calls all the shots, he tells us how much, how many total parts we have. That phrase, “How many,” can get really confusing too if we use it in the context of the numerator so I prefer to just say, “It tells us the total parts.” The total equal parts that we’ve broken this up into, which is really important.
I try to tie it to something rememberable …. rememberable, memorable as well, such as the terminator, right? Most of my students are middle schoolers and they’ve probably seen the movie The Terminator and so we talk about Terminator, he’s such a cool guy, he calls all the shots, you know? He dictates how the movie’s going and the denominator is the same way, he’s calling all the shots, he’s telling us the total equal parts that this whole has been broken up into. So they know the denominator goes at the bottom and that it’s telling us that really specific information and that it means to name.
The next word we tackle is numerator. Now the numerator, it means to count or to number and so it’s telling us how many parts we have, the shaded area. What’s going on here? What’s telling us the rest of the story? How many parts are shaded? How many are we working with? So these are really important concepts and a lot of my students are really good at big picture things but if you’re giving them just procedural ways to tackle fractions, a lot of this stuff becomes meaningless to them and they’re not going to be able to keep track of it because procedures and attention to detail, that’s really hard for them. But, if you explain the big picture, why, why these words are such that they are and how they work, students grasp onto that and they remember.
It’s actually something that we explicitly teach them but practice over a time too. We practice labeling and identifying, what the numerator was? What the denominator was? What would it be like if I wrote it as a division sentence or in a long division? Those kinds of things because they’re helpful skills for in the future. So I know there’s a lot of parents out there that feel resistant to this idea of just doing things all with models but it’s really important for those kids that are not good with the detail.
So if you’ve got a kid that struggles with remembering a list of chores that you give them, there’s a good chance that this modeling and this talking about the language here is a really important key for them to understand what’s going on. So I thought it would be helpful just to talk about the big picture, why we spend time on language here in multisensory math, the visual piece of it, and connecting those two together so that the child can understand the bigger picture of how it really works and I hope that’s helpful to you.
If you have questions about that, let me know, I would love to talk more about this. We work with students all online, does not matter where you live, your child can have access to multisensory math. If you are curious about working with us, head over to mathformiddles.com to learn more and we’ll talk to you again soon.
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