Video: Embed the concept of equal parts and unequal parts

﻿Hi, it's Mrs. Barker again. In our last lesson, we were using the language part, whole, equal, and unequal, and we're going to be using those words again today. If you remember, I also asked you to bring along three strips of paper, which I hope you've got ready, and also if you've got a pen or pencil and ideally a ruler too, that would be really useful. So if you haven't got those things, would you like to pause the video now and go away and see if you can find them and then come back to me. Let's just recap what we were doing in the last lesson. Remember, we were looking at shapes and deciding whether they've been divided into equal or unequal parts and using this sentence to help us. So let's have a go together. Have a look at this shape. How many parts has it been divided into, and are they equal, unequal? What you think? They are unequal. So let's say it together. The whole has been divided into four unequal parts. Great. Let's have a go at this one, have a look at the parts. Are they equal or unequal, and how many of them are? That's right, they're equal. So let's say it together. The whole has been divided into four equal parts. And one more shape. Remember this one. So let's have a look carefully at this. How many parts are there? Are they equal or unequal? Correct, they're equal, aren't they? So can you say this one on your own? Well done. We're now going to need those strips of paper that I asked you to prepare, okay. And in this lesson, rather than cutting out the parts to check whether they're equal, we're actually going to be folding these strips of paper to look at the parts. So here are two strips of paper. The first one has been folded and opened out again, and this is what it looks like. What do you notice? How many parts has the whole length of paper been folded into, and are they equal or unequal? What do you think? Yes, there are four equal parts. So can we use this sentence to describe the whole length of paper? I have folded my whole length of paper into four equal parts. Well done. Now the second one has also been folded. What do you notice this time? What's the same about this second strip of paper and what's different? Did you notice there are still four parts but now that unequal. So let's use this sentence again. I have folded my whole length of paper into four unequal parts. So we're now going to need those strips of paper. I've got mine ready. And what I'd like you to do, is I'd like you to take one of the strips of paper and see if you can fold it into equal parts. So I'm going to make it easy for myself. I'm just going to fold it down the middle like that and there we go, I put two equal parts there. I then like you to take a second strip of paper and you're going to fold it into equal parts again, but can you see whether or not you can fold it into a different number of equal parts? So I'll I do that first whole but then I'm going to fold it again down the middle, and now I've got four equal parts. So that's different. Now to the tricky bit, we're going to take the final strip of paper, and this one, I'd like you to have a go and see if you can fold it into unequal parts. This can be quite difficult. So I'm going to fold it sets not quite to the end there, and then if I just do that tiny bit there, and you can see that those are definitely not equal they're unequal parts. So you might want to pause the video at this point to go away and have a go at doing those folds, but once you've got those three strips two with equal parts, one with unequal parts. Would you like to just take one of them and see whether you can use the sentence on the slide to describe what you've done with your strip? So for this one, I would say I have folded my whole length of paper into three unequal parts. That's what I need to say. So again, maybe pause the video, go find someone that you can describe your strip to, might be your Teddy that you need to do it too. Would you like to do that now and then come back to the video? So here are some more examples of strips of paper that have been folded into different numbers and parts, some are equal, some are unequal. Have a closer look and see if you can spot which of the strips have been folded into an unequal parts. I'm going to give you a little bit of time to have a look and see if you can work out, which ones are unequal parts. Are you ready for me to show you? There we go. Did you get that right? Now have a close look and see if you can find the strip that's been folded into eight equal parts. So you're going to need to count now as well. So I'll give you a little bit of time to do that. Are you ready? That's the one, did you spot that one as well? Well done. Are you ready for a challenge now? These three children have each folded their strips of paper in different ways, but can you spot which one is the odd one out? Now, here's the challenge. Can you actually find a reason each of these strips could be the odd one out? This sentence might help you come up with your reasoning. So use this, and I'm going to suggest that you pause the video to give yourself time to think about each of your reasons, and you might want to practise them with someone else in your house or your Teddy, and when you've done that, would you like to start the video again? So have you come up with reasons why each one of these strips could be the odd one out? Okay, let's see what these children have got to say. So Jimmy says, I think my strip is the odd one out because it has unequal parts and both Holly's and Ravi's have equal parts. Did you spot that as well? Now let's have a look at seeing whether we can use this same sentence to describe Jimmy's folding. He has folded the whole length of paper into three unequal parts. Well done. And now let's see what Holly's got to say. So she says, I think my strip is the odd one out because it has five parts, and both Ravi's and Jimmy's only have three parts. Did you come up with that one too? So again, let's see if we can use this same sentence and let's all say it together to describe Holly's folding. She has folded the whole length of paper into five equal parts. Great. And finally, let's hear what Ravi's reason is. So he says, I think my strip is the odd one out because it's shorter than both Holly's and Jimmy's strip. Did you spot that one, that was quite straightforward, or wasn't it? So again, let's see if we can use this sentence one more time. And would you like to say it? I won't feel the bits, then you do it on your own. He has folded the whole length of paper into parts, great. So let's move on. I've now drawn a line and I divided it into three parts. But look closely, and can you tell me, are these parts equal or unequal? Have a think, I wonder, would this help you if I were to give you the size of the parts? You have to change your mind there. So what we will now agreed. The parts are unequal, that's right. Now, what I'd like you to do now, and you might have to pause the video to do this in a minute, I'd like you to use your ruler, and a pencil, or a pen, and would you have a go at drawing your own line and dividing your line into three unequal parts as well? Now you need to think about how you can prove that those parts are unequal. And would you also show it or tell someone in your house or maybe your Teddy once you've done it. So just pause the video now to go and do that, and then start again once you've completed it. We've looked at how online can be divided into three unequal parts, but I'm now wondering, how could we divide a line into three equal parts? That's a bit more tricky. Have a think about what you might need in order to make sure those parts were equal. What do you think? I think we're going to need to use that ruler that I talked about. And what you can see is I've used a ruler not only to make sure that my 9 is straight, but also to measure a line that's exactly six centimetres long. So I've started at the zero, not at the end of the ruler and I've drawn a nine that is six centimetres long. And then I'm going to need to think about how I would divide that six centimetres into three equals. Ooh, what's that? Mr. Ted thinks he knows a times table fact that might help you divide that six centimetres into three equal parts. He says that he knows that three dots of two is equal to six. So what we're going to need to do is to use our ruler to measure from zero to two centimetres, and then another two centimetres, and that way we can make sure that you've definitely divided the line into three equal parts. Now I'd like you to think about whether or not you can do that as well. So your challenge is to this time, draw a line, not at six centimetres, but could you draw a line using your ruler that measures nine centimetres. So that's from the zero to the nine, and once you've done that, you're going to need to think about a timetable fact that's going to help you divide that nine into three equal parts and have a go at doing that yourself. So you're going to need to pause the video again, and when you finish that and drawn your line, come back and start it again. How did you get on? While you've been doing that, I've been thinking of another way that you might have been able to draw your nine centimetre line and divide it into three equal parts. I realised that if I measured three centimetres, and then I measured another three centimetres from the end, and then I measured another three centimetres from the end again, that way I've drawn a line that has got three equal parts, each part measures three centimetres. So that might be an easier way. If we know the size of one part, what we can do is we can keep repeating that part to make the total line. So in this instance, my nine has three equal parts and I can measure one part and then another part, and then another part to draw my whole line. What do you think, would that'd be an easier way to do it? I think you need to practise both methods to decide which one you think is the easiest. So have a go yourself, and I'd like you to look at trying to lines of 12 centimetres, 15 centimetres and 18 centimetres. And in each case, dividing those lines into three equal parts, and try both methods and decide which one you like best. So you're going to need to pause the video again while you go away and practise yourself. Let's end this lesson with a challenge, shall we? Okay, so we've got two children, and Liz has folded her paper strip into three equal parts but Lara has folded her paper strip into four equal parts. Now, as you can see, part of their strips are hidden, but using that information I've just given you, can you work out whose strip is longer? Is it Lizzie's strip that has been divided into three equal parts, or Lara's strip that has been divided into four equal parts? What do you think? Now before I reveal the answer, do you want to go and share your ideas with someone in your family or with your Teddy? Okay, you ready for the reveal? Here we go then. Where you write it's Lara strip that's longer, but why, why is it that you were able to work that out when you couldn't see the full length of her strip? Can you explain how it is you knew that Lara's was going to be the longer strip? Again explain it to someone in your family or explain it to your Teddy. Did you tell them that the reason you knew that Lara's would be longer was because although her equal parts are the same size as Liz's, she has four equal parts in her strip and Liz only has three, well done. So, we've come to the end of this lesson. Well done once again for all your hard work. Before you have your next lesson, I'd like you to see if you can create a similar problem to the one that we've just done with Liz and Lara. But I'm thinking you could use some items that you can find in your house. For example, you might want to use an item of cutlery, or some toy cars, or rolling sticks, or maybe even some sticks that you collect while you're out on your daily walk. What you need to make sure is that each of the parts is the same length, and then you're going to create two lines, one has to have more parts than the other, of course. And if you then cover up some of those parts and then see whether or not you can test someone in your house to work out who has got the longest line. Of course, if they can't work out the answer, you're going to need to explain to them afterwards how you can use the information about how many parts there are in each line, to be able to work out which is the longest. So good luck with that, bye.

Lesson summary: Embed the concept of equal parts and unequal parts

In this lesson we will explore the concept of 'equal' and 'unequal' parts demonstrated through three strips of paper. We will be looking at shapes and deciding if they have been cut up into equal or unequal parts.

Maths

Y3 Maths

Key Stage 2

Year 3

Embed the concept of equal parts 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

Explore the Concept of 'Equal' 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

Embed the concept of equal parts and unequal parts

Video

Lesson summary: Embed the concept of equal parts and unequal parts

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