Which equation could you use for the following bar model...?

Finding the whole and the parts when using a bar model

Key Stage 1

Maths

Multiplication and division: 3 and 4

Which equation below matches this bar model?

﻿Hello, everyone. I'm Mrs. Crane, and welcome to today's lesson. In today's lesson, we're going to be finding the whole and the parts when we look at a bar model, I'll explain exactly what that means as we're going through the lesson. Don't worry just yet about getting your equipment. What I would like you to do, though, for me please, is, if you can, turn off any notifications on your phone, tablet, or whatever device you're using to access today's lesson. And then, if you can, try and find somewhere nice and quiet in your home, so that you're ready for some maths learning. When you're ready, let's begin. Okay then, let's run through today's lesson agenda. So, we're going to start off by looking at the whole and the different parts that a bar model can represent. Then for let's explore today, it'll be your turn. Then we're going to learn cuisenaire rods and how we find the whole and the parts, and then at your independent task, which will be today using bar models to write equations. Then at what equipment you will need, so for today's lesson, you will need a pencil and some paper. Please pause the video now to go and get those things if you haven't gotten them already. Okay then, let's get started. So, what does this bar model tell us? Have a little think about what you notice in this bar model here. Well, I've noticed that I've got one, two, three parts. I can see here that this part is labelled with four, and I can see here at the whole bar model, the whole, is labelled with 12. So, I know from that information that the whole is 12, each part is worth four, and there are one, two, three equal parts. So I actually know quite a lot of information just from this bar model. Now, can I represent it with cuisenaire rods?. Let's have a look. One, two, three. We know that whole was worth 12. And we knew that each part was worth four. Absolutely I can. We know that this cuisenaire rod represents four, and we've got one, two, three of them. So I could represent it using my cuisenaire rods. Now I don't expect you to have anything like that at home. So don't worry too much about having those to hand, but you can see here, clearly, if I did have them, I don't have them with me either, I could show you them like that. Now, my next challenge is I'm going to look at that, but with numbers, because I want to be able to solve that equation. So, I know, if I go back a moment, that my whole was 12, and each part represented four. So, I can put into my part-part-whole grid. Before we write it as our equation, we're going to write it in here. So I can put my 12 in, and then I can put in my fours. Now I know there's three of them, because there was three parts on my bar model. And I knew each one represented four. So if we wanted to roll and count up in our fours and do some skip counting together, let's see if we get to 12. All together with me. Four, eight, 12. Absolutely. What equation could we write to represent this part-whole model there? Can you write one? Can you think of an equation? Let's see what mine is. So, I'm going to write four times by three is equal to 12. So, what we're going to do now is look at another example. If you're feeling really confident, what I'd like you to do is how I got drawing out your own version of this bar model. Then I'd like you to have a go at drawing out your part-part-whole model using this information here, and my real challenge is can you write an equation that matches the bar model? If you're not so confident, that's okay. Don't worry, because we're going to go through it together now. So, hmm. I'm thinking. What do I know about this information? What's the whole? Well, the whole is 24. I can see that the whole of my bar model is telling me is 24. I can see each part is worth six here. Now how many equal parts are there? One, two, three, four. So there's four equal parts that each worth six. So let's see how I can represent it on my cuisenaire rod. I know that my whole is 24, and I know that each part is worth six. So, one, two, three, four. So I can show it like that. I can see that each person cuisenaire rod represents six, and I'm using four of them. Now, what's the next thing I need to do? I need to show it on a part, whole model. So, let's see our whole. We know our whole. Our whole is 24. Before we can do this, and before we can write our equation to show off our whole model, let's show and fill out that whole model. Now I know I had four blocks when I use my cuisenaire rods. What was each block worth? It was worth six. So let's skip count our sixes to check that we're up to 24, so, six, 12, and 18, 24. What equation could I write then? Well, I could write four or six. So I could write six times by four, or I could write four times by six is equal to 24. Did you write an equation like that? Well done if you did, because I know that these are my parts here, I have four parts each worth six, and I know here that my whole is 24. Right then, it is now time for your talk task today. And for today's talk task, it's your turn. Ooh, it's got very bright all of a sudden. So, I'll explain your talk task before you pause it. So, listen first. So you've got a bar model here. What I want you to do today is using these speaking frames here, so the whole is, each part is, there are equal parts. I'd like you to have a go at completing that. You can jot it down if you want to. If you want to just write the numbers down, if you want to just say it, that's fine. Then what I want you to do is have a go at representing the bar model by drawing out the cuisenaire rods. They don't have to be fantastic drawings. You could literally just take a piece of paper and think, "Right, well, here's my cuisenaire rod. "I can see that each one is worth two," and you could draw them out just like that, really quickly like I've just done. I didn't throw that before hand. I do that now. And then you could mark off here if it's really helpful for you. So it doesn't have to be a long, particularly brilliant artistic drawing, just some quick jotting so that you've got some information down if you like it. Now my challenge to you today is what would the equation be? So, please pause the video now to have a go at today's talk task. Okay, welcome back. So, let's have a look then at what it would look like. So your drawing of your cuisenaire rod may have looked something like this where you can see eight to represent the whole, and you can see two to represent each part. So each cuisenaire rod represents two, so I need to use four of them. Now, my equation. What would my equation be for this bar model using cuisenaire rods? Well, it would be two times by four is equal to eight, because I have two, four times. One, two, three, four, and my whole is eight. Now, what I want you to do is have a look really carefully here. What is the same? And what is different? What do you notice is the same or what is different? Well, I notice that here I have one, two, three, four, five different cuisenaire rods, and each cuisenaire rod represents three. And here, I notice I've got one, two, three cuisenaire rods, and each cuisenaire rod represents five. Now what I notice about them size wise is they seem to represent the same amount. So I can find lots of things that are similar, but the differences, these are the grid blocks of three. Well, that represent three, sorry. And these are blocks that represent five. So, what multiplication equations do you think you could say about these bar models? You think of any? Let's have a look then. well, I could say three times by five, one, two, three, four, five is equal to 15, or I could say that five times by one, two, three is equal to 15 as well. So they show different ways of the same equation, and we can call that commutative. So with multiplication, we have something that's called commutativity. Whoa, sounds like a long word, and it is quite a long word, but what it means is that I can do three times by five, or five times by three, and it gives me the same answer. So sometimes if I look at an equation, I think, "Three times by five, it's a bit tricky. "I'm not sure how I do that," but I think, "I know my fives. "I'm just going to roll my fives three times." That's a much quicker way of doing it. So you can switch them around in your head if you want to to be able to answer an equation, multiplication equation, sorry, much more efficiently, or more quickly. So these two bar models here are just showing that, so showing us visually exactly the same as this here. So, if we can say that about multiplication questions, what can we say about the division equations? Now I know that in both of these two bar models, my whole is 15, so I need to use my whole as the first number in my equation. I cannot use either of my parts, because I will not get the correct answer. So I could say 15 divided, so share deeply, into groups of three, and there's five of them. Can you think of the other equation that I could write for this bar model here using the same numbers as here? Well, I have to start with my 15. This time I've split 15 into groups of five, and there are one, two, three of them. So 15 divided by five is equal to three. Okay, if you're feeling really confident, I want you to have a look at these two cuisenaire rod bar models, and have a look and think about what's the same and what is different. If you're feeling super confident, you could even have a go at writing the different multiplication and division equations that these two bar models could represent. If you're not feeling super confident, that's fine, because we're going to go through it together now. So, the first one, I noticed is the same. I can see here they're about the same length. So I know there's some similarities between what the whole represents. Now I know here that each part represents six. I know that there's one, two, three parts. And I know here, there's one, two, three, four, five, six parts that each part represents three. So I can see that relationship between the three and the six. So, what I'm going to do is think about the equation, the multiplication equations, that I could say about these bar models. So, I'm going to start off by saying six times by three is 18. Now I know that, because I know my six times tables. I can say six, 12, 18. You might not feel as confident on your six times tables. That's okay, because we could also use the commutative equation, which is three times by six. We can see here here's our three. We can see at one, two, three, four, five, six times. So let's roll our threes until we get to 18. It should take us six times. So, again, three, six, nine, 12, 15, 18. Absolutely. So, if we find it easier, we can switch those two numbers around and use the rule of commutativity to help us solve our equation and write our equation down. Now, again, I'm thinking, "If I've done a multiplication equation, "what division equations could I also use? Now, I know I have to start with my whole, and my whole in this example is 18. So here, I've split 18 into three, and each one represents six. So I'm going to write 18 divided by three is equal to six. Can you think of what my other division equation will be? Have a think. Well, I'm still going to have 18 as my whole. This time I've split it into six groups. One, two, three, four, five, six, and each of those is worth three. So my second division equation is 18 divided by six is equal to three. Okay then, it's now time to look at your independent task today, which is using bar models to write equations. So, you are going to have a few different questions, and I'll run through them now with you, so you know what to do. What I'd like you to do is write one multiplication, so you can see here, the boxes are blank for you, and one division for each bar model like we've just been doing. Can you write it using the part-whole model? That is your challenge today for me. So here's question one, and here's question two. Here's question three, and here is question four. Please pause the video now to complete your task. Don't forget to resume it when you're finished, and we can go through the answers together. Okay, welcome back. I'm going to put so that you can see me as we go through the answers together, 'cause it's always nice to see what's going on when we're answering them. So here is our first question. You can see our whole is worth nine. Each part is worth three. So I'm going to say three times by one, two, three is equal to nine, and I can put that in here. Now, I have to use my whole here in my division. So I'm going to say nine divided by three is equal to three, because if I split nine into three groups, there's three in each of them. Next one, question two then. Which is my whole? Well, my whole is 12. My parts are four, and there are one, two, three of them. So I'm going to say four times by three is equal to 12. Now I know my whole is 12, so my 12 has to go here in this box, and then I'm going to split it into fours, and there are three of them. One, two, three. So my whole has been split into three. You may have got it so that it says 12 divided by three is equal to four. That is correct too. And you may have got it so it says three times by four is equal to 12 just like over here. Although over here actually, you won't have got that, because three times by three, you won't have that, because the digit is the same. The parts are the same. So, let's have a look at questions three and four. Now I can see here, oh, which is my whole? Well, I know my whole is 12. I know I have one, two, three, four parts, and that each part is worth three. So I'm going to say three times by four is 12, or I could say four times by three is 12. Then I'm going to take that whole, I'm going to say 12 divided into groups of three. There is one, two, three, four of them. Next one then, question four, our last question. Which is our whole? Fantastic. It is 16. And which are our parts? Well, we have parts that are worth four, and we have one, two, three, four of them. So let's put in here four times by four is equal to 16. Now to do our division, I need to take my whole, so my 16, I'm going to put 16 here, and I'm going to divide it into groups of four, one, two, three, four, and there are four in each group. Okay then, if you'd like to, please ask a parent or carer to share your work from today on Twitter by tagging @OakNational and using the hashtag #LearnwithOak. Fantastic work today. I've been really, really impressed. It's been super. Don't forget to show off all your fantastic bar model learning in today's quiz by completing it. Hopefully I'll see you again soon for some more maths. Thank you and goodbye.

Finding the whole and the parts when using a bar model

Finding the whole and the parts when using a bar model

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UnitMaths / Multiplication and division: 3 and 4

Maths