﻿Hello, I'm Mr. Coward, and welcome to today's lesson about equal parts of a whole for today's lesson, all you'll need is a pen and paper or something to write on and with. If you could please take a moment to clear away distractions, including turn off any notifications, that would be great. And if you can try to find a quiet space to work where you won't be disturbed. Okay, when you're ready, let's begin. Okay, so time for the try this task. Now, I'm not going to give too much away all I'm going to tell you is that one rectangle represents one chocolate bar. Or a whole chocolate bar. So this one here, can you see how that's two fifths? Hmm, okay so what I want you to do, is I want you to pause the video and just have a go All right, so pause it. Three, two, one... Okay, welcome back, now, this is two fifths, why is it two fifths? Well because there's five equal parts and the fact that they're equal is very important. So there's two parts shaded out of five equal parts Two, our numerator, Five, our denominator. So this one, how many equal parts are there? Well there's three equal parts. So our denominator is going to be three. And how many parts are shaded? Two Okay how many equal parts are there here? There's four equal parts. How many are shaded? One Two, sorry, four equal parts. And two are shaded. And it doesn't matter where those two are, as long as two equal parts are shaded that numerator will be two. Okay, and how many equal parts is there for this one? Seven equal parts. So, how many are shaded? Four equal parts. So they should be your answers Really well done if you got them. Now, you might have also wrote this for that one. Can you see how it's a half shaded? Well, it's half of the shape, because two out of the four of them are shaded. And if you can, you can kind of picture it. That's unshaded, shaded, shaded, unshaded so an equal number of parts are shaded and an equal number of parts are unshaded So that means that half are shaded. So we are going to get a little bit more into the language of fractions. Now that top number, that is called the numerator, and that tells us how many equal parts there are. And it actually comes from a Latin word, 'numerare' probably said that wrong. Meaning to count, okay so we just count, how many parts are shaded or how many parts we want. The denominator. This tells us how many equal parts the whole is divided into. And the whole is, the idea of what is the whole, is very important and we'll look a little bit more at what exactly the whole is, throughout this lesson. Okay, and it comes from the Latin word, probably going to say this wrong again, 'denominare', meaning to name. And, so it's kind of like the name and that makes sense when you think about how was call this, or how we say this, three fifths, if it was thirds, we'd call them thirds. Two thirds, one third, two third, three thirds. If if they were, if they were... Tenths. One tenth, two tenth, three tenths, they are tenths. So that's kind of, you can see where the... Name comes from there. Okay, now this is kind of the idea of one whole that I was talking about. Can you see that first image. This one here? Well if I tell you that one of the rectangles, okay, so one of, so this rectangle here, that's equal to a whole. So how many parts are there in a whole? There is five parts in a whole. One, two, three, four, five. That there is the whole. Not both of them, just one of them, okay, so that is the whole. So what is shaded, well three parts so it's three fifths. Okay, so for this one, what is the whole? Well if I said that one circle is the whole, we have one whole two wholes, and one two three, quarters. So you can write this is two different ways. You can write it as two wholes, and three quarters, or, you can write it as four, eight, nine, ten, eleven, eleven quarters. Because that, it has to be quarters here, because it's four equal parts. Okay, this one. Six equal parts in the whole. So that is three out of six, that's one two three I shaded. So it's really important here that you remember that it is the denominator, is the total number of parts in one whole. Okay? Alright, so I want you to have a little go at this so here, this is a whole, and here, this is a whole, you have to work out what fraction is in the other diagrams. So, pause the video and have a go. Pause it, three, two, one.. Okay welcome back. Well why is this eighths? Because it's one two three four five six seven eight, eight equal parts are in a whole. And five of them are shaded so it is five eighths. Well done if you go that correct. This one over here, well how many equal parts are in a whole? One two three four... There are four equal parts in a whole. So we're going to say that that is five over four, five quarters, or, one whole one, and one quarter. Okay, well if that's the whole, what is this? Well it's two out of four equal pieces, so you can write that as two out of four. And, you could also write that as a half, Because half the shape has been shaded, and we'll get on to this more in a future lesson, but this is all to do with equivalent fractions. At the moment I will only expect you to be able to get the first part. Okay, what about this one? Well we've got two wholes, and three out of four equal parts. Or, we've got, four... Eight... nine ten eleven. Eleven out of... Eleven with four equal parts in the whole. So, eleven quarters. Okay, the first one is not a quarter, it is not Okay, the first one is not a quarter, but the second one is. Why? Well, if you imagine moving that part there, and putting it in the part next to it, you would see that they are not the same. In the first image, they are not equal parts, so that is not one out of four equal parts, so it is not a quarter. It's really important that when we are dealing with fractions, that we remember that it's equal parts out of a whole. Okay, so now, I need you to decide which of the following are true. So I'd like you to pause the video and have a go, and just on that last one, we'll consider one of that rectangle to be a whole, okay? So pause in three, two, one... Okay, welcome back, so the first one. One quarter is shaded. Is that correct? Well, they're equal parts, but there's five equal parts so it is not a quarter, it is one fifth. One half is shaded, well there's two parts but they are not equal so that is not a half. Here? Yes we do, we have four equal parts and one of those parts is shaded so it is quarter. And what about this one? One, two, three. There are three equal parts in the whole, not six, so it would be four thirds, okay, Massive well done if you've got them correct, if you found them a bit tricky, don't worry, because these are the examples that people always trip up on. But if you did get it right, that is absolutely amazing. And hopefully, you've learnt something from it if you didn't Okay, just going to have a little look now about placing these fractions on a number line. So here, the hexagon is a whole. So we've got one whole, and we've got two wholes What is this? In comparison to this? Well this trapezium here is half of a hexagon. So, it would go here. So that one, would go...I'm going to try and squeeze... There we are. That one would go there. Okay, what about this one? Well imagine splitting it up. Splitting the hexagon up, like this, and I'm going to remove the writing as well so it will make it a bit easier. So here we've got six triangles, so, and those are equal parts. So now you can kind of see how that's one part missing, so it's one, two, three triangles, and then two down the bottom. So that's two parts and that's three parts, so its' five out of six parts. So that will go, roughly, somewhere about there. Five out of six equal parts. Because it you imagine splitting the number line up into one part, well that was about half, something... Like there So I've split my number line up into one part, two part, three parts, four parts, five parts, six equal parts. So my five equal parts on my number line would be here, okay? Five equal parts of a whole there. And what about this one? Well we've got one, and one sixth. One out of... one little triangle. So that would be, the same distance from that on that side, and on that side, because they are both one sixth away from a whole. This is one sixth less. This one is one sixth more. So that one would go over here. Okay, so hopefully you could follow that, and now I want you to use the shape. Now, there's some blanks that need to be filled in, and you need to try and match each picture here to the fraction. And on each fraction we have a mixed number, that's like a whole number and then a fraction part. And we have an improper fraction. So let me just write those words down for you here. So this is the improper fraction. And it's improper, when the numerator is bigger, so the numerator is bigger, than the denominator. And it's a mixed number when there's a whole number, here, and then a fraction part there. Okay, so pause the video and have a go. Pause in three, two, one... Okay, so hopefully you managed to have a go. And hopefully you got that this, went with this one. It was one and a half, a whole one and a half of one, which is also the same as three halves. Now can you see this one? This one's in thirds, and there's two, in two thirds, or there are one two three four five six seven eight, eight thirds and this one, there's ten out of six equal parts or there's a whole one and four out of six equal parts, okay? Really well done if you got that. If not hopefully you've learned from my explanation there. Okay, so now it's time for the independent task, so I'd like you to pause the video, and have a go, and resume once you've finished. Okay, welcome back. Here are my answers. You may need to pause the video to mark your work. Okay so hopefully that was all okay for you, and now it is just time for the explore task. So, what we've got is we've got three different representations of a fraction. We've got a fraction as we would normally write it. We have a number line representation. We have a worded representation, and we have a bar model representation. Now I would like you to for this explore task, match them up. So, pause the video to complete your task, resume once you've finished. Okay, and here are my answers. So, mark your work, see how you've done. And that is all for today's lesson. Thank you very much for all your hard work, and hopefully you enjoyed the lesson, and hopefully you learned something, and I will see you next time.

The hexagon drawn below represents 1. What fraction does A show?

The hexagon drawn below represents 1. What fraction does B show?

The hexagon drawn below represents 1. What fraction does C show?

The hexagon drawn below represents 1. What fraction does D show?

The hexagon drawn below represents 1. What fraction does E show?

Equal parts of a whole

In this lesson, we will look at fractions by exploring equal parts of a whole and express fractions greater than one as a mixed number and as a single fraction.

Maths

Y7 Maths

Key Stage 3

Year 7

Conceptualising and comparing fractions

Number

THEME

UNIT

Fractions and units of measure

Fair shares

Equivalent fractions

Comparing fractions (Part 1)

Comparing fractions (Part 2)

Ordering decimal fractions

Mixed Comparisons

The rectangles below represent 3 chocolate bars. How much would each child get if they were shared between 5 children?

Lesson overview:Equal parts of a whole

Core Content

Conceptualising and comparing fractions: