Video: Representing equivalent fractions

﻿Okay, so this lesson is going to be on comparing fractions, and we're going to be able to know when two fractions represent the same part of a whole. So for this lesson, you're going to need some stuff. I'm just going to have a look on my bookshelf and see what I might use. So I've got some pegs, plastic people, I've got some marbles, I've got some coins, 20 smallest objects, it doesn't matter what they are. I've also got some sweets on my desk that I might want to use, but you also need a pencil and paper. You're not going to do lots of writing, but it's really good to be able to draw things, to help you with your thinking and your explanation. So pause the video now and go and grab yourself 20 smallest things and a pencil and paper. Did you come back? I hope so because fractions are fantastic, and we're going to learn together and we're going to really understand how we know when fractions are the same. So we need some language that's going to help us. We can get sometimes confused about language, but actually it's really helpful to be able to talk about numbers and what they represent. So what is this fraction that I've just written? You might have thought you're going to just sit here in silence. So I didn't hear you say what that fraction is, it's a half, yeah, thank you to everybody who joined in. And when I ask a question, you can say out loud, but don't disturb those people that are working if they are working in your house or if somebody is just busy and don't want to hear you doing your math, but if they're with you, then that's great, join in with you, but please join in with me. So the numerator is one, yeah, and the denominator is two, fantastic. So we're going to use that language a little bit in this lesson, so just wanted to remind you of those terms. Okay, so we're going to think about cakes. It depends what time of the day you're watching this lesson, but if you're hungry, try and concentrate 'cause it's not going to take us too long. And we've got some cakes that some people go into a shop and they're going to eat some. And there's a bit of a conversation about who eats the most. So, Sabijah, she eats one quarter of the cakes and Jess, she eats three twelfths of the cakes. And there's a bit of an argument about who actually eats the most. So this part is a bit about understanding what the numerator and the denominator is telling us. So, Sabijah, she eats one quarter of the cake. So we're going to use a sentence here that's going to help us understand what this four represents and what this one represents. So I'm going to say a sentence and then you're going to say it with me. The whole has been divided into four equal parts, so that's what this denominator is telling me. The whole has been divided into four equal parts, and one of those parts is there, has been a circled. Now, you might have in your head thought that you might've looked at a different part. It doesn't matter, as long as you were thinking of one of them. So Sabijah eats one quarter of the cakes. Okay, just have a practise using that sentence. The whole has been divided into four equal parts, fantastic. And one of those parts has been circled, great, okay. So Jess, she eats three twelfths of the cakes. Does she eat more? Does she eat fewer? Does she eat the same? So the whole has been divided this time into 12 equal parts. So on this diagram here, I'm not going to draw 12 different lines let me just count how many cakes there are all together, I'm going to skip count in threes. Three, six, nine, 12. Okay, so they're 12 cakes. So if I divide the whole into 12 equal parts, that's going to be one cake in each part. And then Jess, she eats three of them, so I need to circle three of the cakes, okay. Okay, so where's the 12, 12 equal parts, 12 cakes and three, that's the three that's been circled. Okay, so we're getting our heads around what the numerator and the denominator are explaining. Let's have a look at this slide. In order to consider, to think about whether a quarter is greater than or smaller than three twelfths, we've now done lots of things already to help us to know what symbol we can put in between these two. And they are equal, one quarter and three twelfths are equal because they represent the same part of the whole. Okay, so if I haven't convinced you, I'm going to show you another presentation. So I've got a circle that's been divided into four equal parts, and I've got a circle that's been divided into 12 equal parts. And if I've got one quarter shaded, if the whole has been divided into four equal parts, one of those is going to be shaded. And if the whole has been divided into 12 equal parts, and three of them have been shaded, then they are the same because they represent the same part of the whole, okay. We can put that equal sign in. One quarter equals three twelfths. Let's have a look at it on a number line, and I'm going to count in twelfths and you are going to count in quarters. But first of all, let's have a look about why these are in quarters. There we've got zero to one, and this part of the number line has been divided into four equal parts. And here is zero to one, and this has been divided into 12 equal parts. As I count in twelfths, I want you to be able to say the value in quarters that is the same. One twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, nine twelfths, 10 twelfths, 11 twelfths, 12 twelfths. Okay, did you say a number when I said three twelfths? Did you say a quarter? I hope so, let's try it again. One twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, nine twelfths, 10 twelfths, 11 twelfths, 12 twelfths, can I just say you had the easy job there of saying the quarters because you're getting a little bit of a tongue tie when you're saying the twelfths. And when we put those two number lines together, we can see that one quarter and three twelfths have the same position on the number line, they have the same value. One quarter equals three twelfths, they have the same position on a number line. We could also look at it with a different representation. So here we've got a quarter is shaded blue, of these circles, a quarter has been shaded blue, but we could also say this in a different way. So have a little bit of a pause of the video and have a go at writing the fractions that are the same using these three different pictures of circles that have been shaded in blue. One quarter, two eighths, three twelfths, and four sixteenths, hopefully that's what you've recorded and you've really understood that they represent the same part of the whole being shaded in blue. Okay, we're going to have a look now at a different fraction, we're going to have a look here at a fraction of a half. So a half, oh we looked at this before, didn't we? Let's just write here a half. So the whole has been divided into two equal parts, and one of those parts has been circled. And here, ooh, okay. So if I'm circling these tenths are the same. And here we've got, well, we haven't got circles this time, we've got rectangles, but this is where the whole has been divided into two equal parts, so the whole has been divided into two equal parts, and one of them has been shaded. And here, the whole has been divided into 10 equal parts and five of them have been shaded. So one half and five tenths represent the same part of the whole. And then with our number line, here we've got a half and we've got five tenths, and when we put them together, they are at the same position on the number line because they represent the same part of the whole. Okay, it's nearly time now for you to do something on your own. So you can always go back and watch this video again, if you're not quite sure, but I think you're more than ready to have a look at a third. So you are going to use your things and your pencil and paper, and you're going to show me one third, and you're going to have 15 items. I'm going to help you out here and say, do it with 15 items and write a fraction that is the same as one third. And then draw me one third of a shape, and then write a fraction that is the same as one third. And the last task is to draw me one third on a number line and write a fraction that is the same as one third on a number line. Tomorrow's lesson, we will be building on what we've learned in this lesson. So have some fun drawing some shapes and drawing things on number lines, and really have a go at using those STEM sentences. The whole has been divided into. Okay, see you tomorrow. Bye.

Lesson summary: Representing equivalent fractions

In this lesson, we develop understanding of equivalent fractions through quantity, area and numberline models.

Maths

Representing equivalent fractions

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Lesson summary: Representing equivalent fractions

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