﻿Hello, it's Mrs. Kingham again, how are you doing? So today, we're going to be looking at the key language today of part, whole, equal sized, times, divided, and unit fraction. I know you've seen lots of those before. So you're going to need a pencil, a ruler, and paper, so go and grab those if you can and then let's get on with today's lesson. Okay, so let's have a look at what you were looking at yesterday and the questions that Mr. Reese left you with. So, which statement was proven by this diagram? So, you had these options. Now, hopefully, you realised it that actually the answer was none of these. Because, why? Because the wholes weren't the same, so you couldn't compare. Okay, so for question two, did you draw representations, different representations, which proved that one quarter was smaller than a half? Hopefully, you could see that your wholes had to be the same. Which fraction makes it the bigger part of your whole? Absolutely, one half. On the third question, this was brilliant. You could basically do whatever you wanted. You could have picked any unit fractions. So, what I definitely knew on each side was that our numerator was one, because in a unit fraction that is always true that the numerator is one. And then really you could have a look at what the largest denominator is, the smallest denominator is. So, if I had, say, I could have one 75th and one, I don't know, 23rd, what was my rule? That the greater the denominator, the smaller the part. So therefore, I knew that one 75th was smaller than one 23rd. But you could have had any numbers in there as long as it's mathematically correct. And then here we had a, when we compare fractions, the, what was the blank? The whole has to be the same. Well done. And question four, finally, when we compare fractions, the whole has to be the same. So when we compare fractions, the whole has to be the same. Well done. Let's move on with today's lesson. Right then, here we go on the board here, you can see a red rod. You might've seen Cuisenaire rods, they're called at school. Now, they can help us to make the whole from parts. Now don't worry about the letters on the rods. They refer to the colours. So for example, on here, the r, it means it's a red rod, d is the dark green, and so on, but I'll talk you through those as we're going through the lesson. Now, do you remember the lesson when we built a whole from parts, including squares, circles, and teams of children? Well, today, we're going to build a whole using unit fractions because we know lots about those now. Now, remember, a unit fraction is any fraction with a numerator, the number on the top, that's one. One half, one third, one quarter, and one eighth they're all unit fractions. Now then, the red rod, you can see, is one third of the whole and we need to find out what does the whole look like then? Have you got any thoughts already? Now, in order to build the whole, we'll need to work out how many equal-sized parts the whole has been divided into. So if the red road is one third of the whole, like our question says here, one third of the whole, what is the whole? How many equal parts has it been divided into? That's right. The red rod is one third of the whole. So therefore, the whole must have been divided into three equal-sized parts. Can you draw that for me? Have a go. Now, your whole should have three equal parts just like this. How do you know that that's true then? Well, we know that's true because three one-thirds, one one-third, two one-third, three one-thirds make one whole. My denominator is three, therefore three equal parts make the whole. Now, let's look at the green rod. Is it longer, shorter, or the same length as one of the red rods? Of course, it's longer, but how much longer? Now, stem sentences normally help us out a lot, so I popped one at the bottom of the board here. So let's use the stem sentence on the board. The blank rod is blank times as long as the red rod. So what could we put in the blanks? What do you think? Okay. Did you say green? The green rod, so I'm going to put that in here, the green rod is one, two, three times as long as the red rod. How'd you know that's true, though? Can you explain to somebody? Hmm. Well, we know that's true because three one-thirds make one whole. One one-third, two one-thirds, three one-thirds make the whole. So the green rod, the whole, is three times as long as the red rod. Okay, let's try a different size whole this time. This time the red road is one fifth of the whole. So we need to find out what the whole is. How could we do that? Have a think. Right, so if the red rod is one fifth of the whole, how many equal-sized parts has the whole been divided into? Have a look at your denominator to help you. That's right. If the red rod is one fifth of the whole, then the whole has been divided into five equal parts. Can you draw for me what the whole will look like? Does yours look like this now? But how do we know that's true? Can you explain that to somebody? Well, we know it's true because five one-fifths make one whole. Five one-fifths. One one-fifth, two one-fifths, three one-fifths, four one-fifths, five one-fifths make the whole. Now let's look at the orange rod. Is it longer, shorter, or the same length as one of the red rods? Of course, it's longer, but how much longer? So let's have a look at our stem sentence this time. The blank rod is blank times as long as the red rod. So what would you put in the blanks? Have a go. Okay. This time, the whole is the orange rod, isn't it? The orange rod is one, two, three, four, five times as long as the red rod. How do we know that's true? Can you explain? Well, we know it's true because five one-fifths, one one-fifth, two one-fifths, three one-fifths, four one-fifths, five one-fifths make the whole, the orange. So the orange is five times as long as the red rod. Okay. So let's have a look at these two images now together. What's the same and what's different? Pause now and have a go. See if you can write some things down. Right, well one thing that's the same is that we have parts and wholes in both of the images. But are there the same number of parts? And are there the same-sized wholes in each image? No. One whole is made from three equal-sized parts and the other image is made from five equal-sized parts. But look, the red rod is the same size in each image, but is it the same unit fraction? What do you think? No. The red rod is a different unit fraction in each image, And that means that the two wholes are different sizes as well. Have a go at filling in the stem sentence for both of the sets of pictures. Now, I'm thinking of another different-sized whole. The red rod is now one half of the whole. How many equal-sized parts make my new whole? Yes. If the red rod is one half of the whole, then the whole must be made of two equal-sized parts. Are you sure? Can you explain how you know this to somebody around you? Or to yourself? That helps too. Oh, you're getting great at this. We know that it's true because two one-halves make one whole. What about the purple rod? Again, is it longer, shorter, or the same length as one of the red rods? of course, it is longer than one of the red rods. But how many times longer is the purple rod than one of the red ones? That's right. The purple rod is two times as long as the red rod. Can you justify that? Yes. The purple road is twice the length of the red rod, because two haves make one whole. Okay, now you try and use the stem sentence on the board. Can you fill it in? Did you say that the purple rod is two times as long as the red rods? How do we know it's true? Brilliant. Because two one-halves make one whole. So the purple rod is two times as long as the red rod. Well done. I think we're really getting the hang of this now. So what unit fraction could my red rod be? Hmm, one quarter? Brilliant. And in fact, it could be any unit fraction actually. What we would change, though, would be the size of the whole if it was a different unit fraction. Hopefully, you're starting to see that now. Now, I'm going to say that one red rod is now one quarter of the whole. So if one red rod is one quarter of the whole, what is the whole? Well, let's work out, how many equal-sized parts make this whole? You're right, it's four equal-sized parts. Of course, if the red rod is one quarter of the whole, then the whole must be made of four equal-sized parts. And how do we know? Well, we know because four one-quarters make one whole. Four one-quarters make one whole. This time, the four one-quarters made the same whole as the tan bar. Okay, what about the tan rod bar? How many times longer is the tan rod than of the red rods? use the stem sentence to say it aloud. We can say it together if you like. Let's go. The tan rod is four times as long as the red rod. Can you prove it? Yes. The tan rod is four times the length of the red rod because four quarters make one whole. Well done. Okay, so let's summarise our learning today with the help of this table. So first of all, the top one. Is one half is a part, then the whole is twice as much. Take two parts, put them together to make one whole. The next one. If one third is a part, then the whole is three times as much. Take three parts, put them together, and make one whole. The next one. If one quarter is a part, then the whole is four times as much. Take four parts, put them together, and make one home. How about the final row? If one fifth is a part, then the whole is, brilliant, five times as much. Take five parts, put them together, and then they will be one whole. Can you make some examples by yourself? What would it be if the unit fraction was one 10th or one 64th or 100th? What do you think? Have a go. Okay, so here's a practise activity for you to complete independently now. So this time the part is a square. And in the second column, you have to say what fraction of the whole it represents. In the third column, you write in the number of equal parts it would take to make the whole. And in the final column, you draw the whole. Now, remember this time, though, each part will be square. But you can use the stem sentence if you want it help you. If one blank is a part, then the whole is blank times as much. Take blank parts and put them together to make one whole. I'm sure you can fill in all of those blanks now. And if you want another challenge, why not choose your own parts and build your different wholes from the different unit fractions. Good luck. We can't wait to see you in the next lesson and see how you got on. Well done. Bye.

In this lesson, we will take unit fractions of shapes and build the original whole from them. We will use mathematical sentences to describe how many of each fraction makes up the whole.

In this lesson, we will take unit fractions of shapes and build the original whole from them. We will use mathematical sentences to describe how many of each fraction makes up the whole. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y4 Maths

Key Stage 2

Year 4

Construct a whole from a part and identify the fraction it represents

Working with fractions

UNIT

Divide and describe the same whole when divided into differing numbers of equal parts

Understand fraction notation to represent a relationship between part and whole

Begin to use and understand the terms 'Numerator' and 'Denominator'

Name unit fractions and match them with the fraction notation and a representation

Embed previous fraction work using a linear model

Assign unit fraction names and notation to 3D representations

Assign unit fraction names and notation to equal parts of quantities

Recognise and reason about unit fractions in a variety of contexts

Understand that Equal Parts Can Look Different - Area

Understand that Equal Parts Can Look Different - Volume and Area Contexts

Compare unit fractions using a fraction wall

Reason about comparing unit fractions

Compare unit fractions in a measure's context

Can we compare unit fractions of different wholes?

Build and compare different wholes from the same unit fractions that represent the same length

Build and compare different wholes from the same unit fractions that represent different lengths

Build and compare different wholes from different unit fractions that represent the same quantity

Build and compare different wholes from different unit fractions that represent different quantities

Build and compare wholes when different unit fractions represent different amounts

Lesson overview:Construct a whole from a part and identify the fraction it represents

Core Content

Working with fractions: