﻿Hi, my name is Mrs. Barker, and I'm going to be teaching the next couple of lessons to you. I also need to introduce you to my teddy, Mr. Ted. He loves learning maths with me. I'm going to let you into a little secret. He does sometimes make mistakes, but he doesn't get bothered by them. So long as someone can explain where he's gone wrong, he can then learn from his mistakes, so that makes him happy. Now, before we get started, let's just look at the key language you're going to be using today. I know with Mr. East, you were using the words whole and part, and we're soon going to be using the words equal and unequal. If you're not sure what these words mean, you might want to pause the video right now and go away and see if you can ask a member of your family. Or if they're too busy, you could always look it up using a dictionary. Mr. East tells me that in your last lesson, you were identifying wholes and parts of whole. Let's see whether you can remember what you were up to. So if the UK is the whole, can you think of something that could be part of the whole? Let's all say it together. If the UK is the whole, then, is a part of the whole. Well done. Now, Mr. Ted just said if the UK is the whole, then Italy is the part, is a part of the whole. Do you agree with him, or do you disagree with him? Have a think about it, and maybe you could pause the video and go and chat to someone in your family about it too. So a lot of you seem to be disagreeing with Mr. Ted. But more importantly, can you explain why it is you disagree with him? All right, so Mr. Ted now thinks he understands. He said if he changes it to if Europe is the whole, then Italy is the part of the whole, would this now be correct? Lovely. Right, we're definitely ready to move on then. For this lesson, we're going to need a pair of scissors and a rectangular piece of paper or card. Now, it can be any kind of rectangle. So I've got a Christmas card here that might be useful, or this was a leaflet that came through the post or a Post-it Note. It really doesn't matter, so long as it's rectangular. If you haven't already got this, would you maybe like to pause the video now, and then you can go and get yourself ready for learning? Okay, so what I'm going to ask you to do now is we're going to cut the whole rectangle into four parts. Don't do it just yet. Let me demonstrate it first of all. So I'm going to take my rectangular card, and I'm going to do a cut here. It's a straight cut, so I've now got two parts. And then I think I'm going to do a diagonal cut there, so I can now get three parts. And then finally, hmm, let's do a curved cut here. Okay, so now I have got four parts. You can see all four parts. And the next thing you're going to do once you've done that is you're going to put the four parts back together to make the whole rectangle. That might be tricky, if you've got a plain sheet of paper and you've done some crazy cuts, but have a go. Now, do remember, you don't have to copy exactly what I have done. Any type of cut will do, so long as you end up with four parts of your rectangle. So if you'd like to pause the video now, and then you can go away. And when you've completed those two instructions, you can switch the video back on. Did you manage to put your four parts back together to form the whole? Remember, there's no right or wrong way to cut it, so long as you have four parts. Maybe yours look like one of these ones here. So now we can see that a whole is made of many parts, and many parts make one whole. Should we all do that together and say it at the same time? Are you ready? A whole is made of many parts, and many parts make one whole. Before this lesson, I looked at lots of different shapes and divided them into parts. Have a look at these. Can you spot what's the same about all of them? If you think you've worked it out, why don't you pause the video and go and tell someone in your family? Or you could always tell your teddy. That's what I'm going to do while you're talking. Did you work it out? They've all been divided into four parts. Now let's see whether or not we can name these shapes. Let's do it together. So the whole circle has been divided into four parts. The whole rhombus has been divided into four parts. The whole square has been divided into four parts. The whole triangle has been divided into four parts. The whole square has been divided into four parts. The whole rhombus has been divided into four parts. The whole triangle has been divided into four parts. And finally, the whole circle has been divided into four parts. Well done. I then decided that I would sort these shapes, and this is the way that I've sorted it them. Look closely. Can you work out why I've decided to sort them in this way? Mr. Ted thinks he's spotted it. He says that all of these whole shapes have been divided into equal parts, and these whole shapes have been divided into unequal parts. Did you spot that as well? Now, it can sometimes be quite tricky to spot whether or not parts are equal or not. I mean, certainly that rhombus is a tricky one. And one of the best ways to do that is if you can get hold of the shape and actually cut out a part, and then lie it on top of the other parts to see whether or not it fits exactly. I'll show you how we do that. Okay, so here's that rhombus. And what I've done is I've shaded one of the parts, and I've cut it out. And then what you can see is if I try it on each of the others, it fits exactly on that part. And it fits exactly over that part. And if I flip it again, it fits exactly over that part. So I can then prove to myself that all of those parts are equal. Remember my rectangle that I cut up at the beginning? I wonder which of these groups that would fit into. So here we go. These two parts, they actually are equal. But remember that part and that part? So my rectangle would fit into the unequal parts group. What about your rectangle? Which group would yours fit into? I wonder, is there more than one way a shape can be divided into equal parts? What do you think? Let's have a look at a square and see if we can work it out. Okay, here's a square, and it's been divided into parts. Are these parts equal or unequal? Yes, they are. So let's say it together. The square has been divided into equal parts. Now let's have a look at this square. Are the parts equal or unequal? The square has been divided into equal parts. And what about this one? Oh, this is a bit trickier. Remember, this is one way you need to imagine this shape, and you need to imagine it flipping and seeing whether it fit. Ooh, yes, it does. So are they equal or unequal? So all together, the square has been divided into equal parts. Now, all of those squares are equal-size squares, and yet you can divide them into equal parts in different ways. Is that going to be true of a triangle as well? Is it possible to divide a triangle into four equal parts? What do you think? Oh, remind me, how many sides in a triangle? Lovely. Let's have a look then. So here's a triangle. Ooh, what kind of triangle is this? It's an equilateral triangle. You're right. And can we see how many parts it's been divided into? Let's count together. One, two, three, four. It's been divided into four parts. And are they equal or unequal? So let's say it all together. The whole has been divided into four equal parts. Well done. So what about these shapes? Has the whole shape been divided into equal or unequal parts? Let's do it together, and let's use a sentence. So first of all, the circle, the whole has been divided into four unequal parts. And now let's do the triangle. The whole has been divided into four unequal parts. The rhombus, the whole has been divided into four unequal parts. And finally, the square, ooh, this one's got wavy lines on it for the first time. The whole has been divided into four unequal parts. Well done. Now, are you ready for a challenge? Mr. Ted thinks it's only possible to divide a whole into equal parts using straight lines. Do you agree with him, or do you disagree with him? Hmm, you might want to pause again and have a little discussion with someone in your family. And it might help you if I show you these pictures. Maybe this will help. Have a look closely at these because these shapes have not been divided using straight lines. And are the parts equal or unequal? Now, remember the trick that I showed you before. If we want to check whether parts are equal, we can always cut out a part and see if it fits on the other. So do you think that would be a good idea on this one? Let's give it a go. Okay, so here's this one with the wavy lines, and I've shaded in one of the parts and cut it out. And then you can see, oh, it fits on that one, it fits exactly on that one, and it fits exactly on that one. So I'm afraid Mr. Ted is not correct. It is possible to divide a whole into equal parts, not just using straight lines but also using curved lines and zigzag lines. Wow. So we've come to the end of our learning for today. Well done for your hard work. Before we meet again, I'd really like it if you can have a go at this practise activity, and you're going to need some more paper rectangles for this. Can you find a way to divide the whole rectangle into two equal parts, three equal parts, four equal parts, five equal parts? You could go on forever, but I wouldn't recommend it. What you can do if you really want to challenge yourself is once you've found one way, can you find a different way to divide your shape into equal parts? Ooh, one final thing. In order that you're ready to learn for our next lesson, can you please make sure that you prepare beforehand three strips of paper? They just need to be rectangular strips. The length doesn't matter too much, and they don't have to all be the same length. But if you could bring three along to the next lesson, then you'll be ready to learn. Thanks. Bye.

In this lesson, we will explore the concept of 'equal' and 'unequal' parts demonstrated through a rectangle separated into parts.

In this lesson, we will explore the concept of 'equal' and 'unequal' parts demonstrated through a rectangle separated into parts. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y3 Maths

Key Stage 2

Year 3

Explore the Concept of 'Equal' and 'Unequal' Parts

Fractions: parts and wholes

UNIT

Explore the whole and part relationship in familiar contexts, using area, linear and quality models

Explore the whole and part relationship and generalise that a part is always smaller than the whole

Embed the concept of equal parts and unequal parts

Develop understanding that equal sized parts do not have to look the same

Compare the size of parts when the whole is defined using familiar contexts

Explore that size of part is relative to the size of the whole using familiar contexts

Consider part whole relationships within the context of quantity models

Build a whole when a part is known

Explore different contexts for building a whole when a part is known

Lesson overview:Explore the Concept of 'Equal' and 'Unequal' Parts

Core Content

Fractions: parts and wholes: