The use of a repeated addition expression to represent equal groups

Key Stage 1

Maths

Multiplication: equal and unequal groups

﻿Hello everybody. My name is Mrs. Evans, and I'm going to be with you in the next two lessons. My friend number bear is also going to be with you. He's going to need a bit of help because he's finding the work that we're doing at the moment a little bit tricky. In the last two lessons with Mrs. Martin, I know that you've been thinking about the language to describe equal groups of things. And today we're going to practise using that language, saying things like, I have three groups of five. And we're also going to begin to represent using numbers and symbols those equal groups that we've been thinking about and describing. Now, I know that Mrs. Martin gave you some tasks to do, so we'll start by having a look at those. So in this task, you are asked to use our sentences to describe what's in the picture of the eggs in the nests. So the first sentence says, there are how many equal groups of eggs? Now, we're really good at counting groups, you know to do it like this; one group, two groups, three groups. You could probably see that. There are three equal groups of eggs. So how about the next sentence, there are how many eggs in each group? Now, I can see that they're equal groups, so I only need to look at one nest and see how many eggs are in it to answer that question. So here I can count one egg, two eggs, three eggs, four eggs, five eggs. There are five eggs in each group. So can you put those numbers into the last sentence? There are how many groups of how many? There are three groups of five. That last sentence is going to be really important in this lesson. We're going to be using it a lot saying there are so many groups of so many. So we'll have a bit of a practise and make sure that you're really confident with that. So Mrs. Martin gave you a picture, didn't she? And she asked you to complete it. She said, I have four groups of three. Now, in Mrs. Martin's picture to start with, I can see some groups of three, but only two groups. So I needed to draw some more groups, didn't I? So I've got two groups and another picture of the ice cream cone is three groups. Still not enough is it for four groups of three, so I needed to draw another one. Did you draw your picture like that with four groups of three? Four groups of ice cream cone, there were three scoops of ice cream. Mrs. Martin gave you another challenge, didn't she? With ice cream cones. She asked you to draw three groups of four. Now, I had a go at this. I had to think really quite hard about it. To help me, I wrote down three groups of four so I could check back. I drew my first ice cream cone and that's when I had to think really hard how many ice cream scoops should I put in it? And I looked at the sentence again, it said three groups of four, and I realised that the of four bit was my clue. So here's my first group, my first ice cream cone with four scoops in. Did you draw that to start with? After that, it got a bit easier. Once I'd got one group, I knew the other groups had to look the same and I knew that there are three groups. So this is the rest of my picture. One group, two groups, three groups, each with four scoops of ice cream in. Did yours look like that? Well done if you got that right because I think that was quite a challenge. So I've got some true or false questions here and they're for number bear to check that he's getting this right. And you can do it too. So this says, there are four groups of three. All right, number bear, what do you think? Number bear says there's definitely four groups, but he think it's really good to underline them to make sure that he's right, so we can do that together, can't we? one group, two groups, three groups, four groups. There are four groups, aren't there? Now, are they groups of three? Number bear is having a think. He said yes, he thinks that's right because in each boat, there are three children. They are groups of three, aren't they? So number bear says yes, that's true there are four groups of three. Do you agree with him? I think he's right, that's true. Here's another true or false question for number bear and you to have a go at. So this one is a pineapple question. It says, there are five groups of two. That was quick number bear. Number bear says that one is true as well. He thinks there are five groups of two. Do you agree with him? We could check by counting the groups, couldn't we? Shall we do that to start with? It says there were five groups, one group, two groups. There aren't five groups, are there? Are they groups of two? Is that part of the statement correct? Well, no, because look, one, two, three, four, five, there are five in each group, aren't there? So there are not five groups of two. That's false. So why do you think that number bear might have thought that there are five groups of two? Could you pause the video and see if you can think of a way of explaining to number bear why he was wrong that time? Did you notice something? I noticed that if you swap round the numbers in that statement like this, then it is true. If write there are two groups of five, that's true. We counted the two groups, didn't we? And we saw that there were five in each group. So they were groups of five. So I think that's why number bear might've got it wrong. But if we do swap the numbers around, then it will be true, won't it? So number bear is going to have to think really carefully on the next questions that he gets those numbers the right way round. I've got some representations here that I'd like you to think about. The first one is of some buckets, and I'd like you to imagine that those buckets are full of water. I've got a picture of some bears. The third representation is a bar model with the number five written in it. And the last one is some pieces of numicon. I'd like you to look really hard at the picture. Could you explain to somebody or explain to yourself what's the same about those representations and what's different? Pause the video and have a really good think. Let's start by thinking about what's different about the representations. I think that's quite easy. The picture of the buckets is quite different to the picture of the bears. On the bar model, I can't see any objects of anything at all. And the new numicon pieces are different to the bar model as well and the other pictures. So four really different representations. So did you find anything that you could say is the same about the representations? Did you spot that we can still talk about equal groups here? Let's start by thinking about those buckets. I asked you to imagine them full of water, didn't I? I can see on the bucket it says five litres. It says five litres on each of those buckets, doesn't it? To help you imagine that, perhaps you could think about a bottle of squash, I've got one here nearly empty. If it was full, it would have one litre. And I know it would have one litre because it says here one litre. So I'd like you to imagine I empty out my squash and then I fill my squash bottle with water and I pour it into a bucket. If I did that five times one, two, three, four, five, that would be one of those buckets filled. So if I did that with three buckets, that would be the same as what's in the picture. And then I think I could say I've got three groups of five, three buckets each with five one litres in, three groups of five. Let's look at the teddies now. That's a bit easier I think. I can see there's five teddies on each plate and there are three plates. So, again, I can say there's three groups of five. On the bar model, it's got three parts and in each part is written the number five. So, again, we can say this represents three groups of five. You can't see the five in each group, but the number five in each part could represent a group of five. And in the numicon pieces, you can see that each piece has got five holes in it. It's a five piece, isn't it? And how many pieces have we got worth five? That's three pieces. So, again, we could say this represents three groups of five. Did you spot what was the same about the representations? Well done if you did, that's really good. So using these representations, I'd like us to start thinking about how we can represent using numbers and symbols this time what we can see in our equal groups. We know that both representations show three groups of five. You could imagine that the bar model represents the plates of bears. So this part of the bar with five represents these five bears, this part represents these five bears, and this part represents the last five bears. And you could describe this as five and five and five. And when we write it, we can write five plus five plus five. Can you remember how to write the plus symbol? Can you write it in the air for me? Did you go down, straight down, take your finger off, and straight across to draw a cross? Well done if you did. So I'm going to write that expression five plus five plus five. Here's my first five down and around, then I'm going to use that plus symbol, plus, then I'll write another five because I said five plus five plus five. Five plus five plus five. Why did I write five? The fives represent the plates of five bears or the part of the bar model with five on it. So why did I write three fives? That's because it's three groups of five, isn't it? There's a special name for these expressions. They can be called repeated addition. Repeat means you do something again and again. And repeated addition means you're adding something again and again, but only when it's the same number being added again and again, like here, it's always the number five. We call that repeated addition. Now it's your turn to write a repeated addition expression to match this picture of the children at their desks. Let's agree first what the groups are. I can see groups of two, there's two children at each desk. How many groups are there? How many desks? I can see four. So we could describe that as four groups of two. And I can say there's two and two and two and two. So how would we write that? We'd write, join in with me, two plus two plus two plus two. Can you pause the video now, write that expression down, read it back, and make sure that it matches the picture. So I think you should have written this. Let's read it together. Two plus two plus two plus two. I'm sure that you wrote two. Just check that you wrote it four times. Did you? You needed to write it four times, didn't you? Because there are four groups of two. Did you remember to put the plus symbol between each of those twos? Well done if you got that right, you've written a really good repeated addition expression. Here's another one for you to have a go at. I've got my pictures of buckets again, and we described this as three groups of five, didn't we? Your first task is to have a go at drawing a bar model. How many parts do you think you're going to need? There's three buckets. That's going to be three parts. What number are you going to write in each part do you think? Well, it says five litres, so I think you need to write five in each of your three parts. So your first job, pause the video and draw me a bar model. So did your bar model look like this? Did you have three parts to it with five in each part? I hope that you tried to make sure that each part of your bar model was the same size. That's important because we're trying to represent equal groups, so we need equal sized parts. And we can say this is five and five and five. And you can also write now the repeated addition expressions to go with it. So pause the video again, write the expression, and check it back with your bar model in the picture. Is what you've written the same as what I've got here, five plus five plus five? Well done if you've got that right. Now, I've noticed that we've used this expression before. Do you remember we wrote this to match the picture of the bears, five plus five plus five? So the same expression can represent lots of different pictures or groups of objects as long as they have the same number of groups and the same number in each group. In previous lessons, we've been practising using tokens, different numbers of dots on, haven't we? And also some coins to practise our counting. Now you can use these things again to work on your repeated addition expressions. So I'm going to show you how we could do it. I've chosen my two counters, two dots on each of my counters, and I've put three counters down. So to write an expression to match this, I'm going to have to write the number two. Two plus two plus two. So you could practise getting your tokens and writing some expressions, or you could swap your tokens for coins of course. I could swap my two tokens for two pence coins. Here we go. Two plus two plus two. Can you see that my expression here represents both the pictures of the tokens and also my two P coins? This time I've just put some coins on my board. I could have used my tokens. This is which coin? Can you see it's a silver coin, it's a 10 P coin, so I could have used my 10 token, but I think I'll just use coins this time. So I want to write an expression to match my three 10 P coins. Which number would I have to write? Can you tell me? I need to write 10. 10 plus 10 plus 10. Is that what you thought I should do? It's 10 because? Each coin is worth 10 P, that's right. And there are three tens because there's three coins. Now, what if I put another 10 P coin down? Still tens. Is my expression right still? No, it's not, is it? Do you think I need to start all over again, or could I just change this expression perhaps? I think actually I can just change this. So I can see that I've got this 10 P this 10 and this 10 P, and now I need to write another 10 P. But before I write 10, I need another plus sign, don't I? Plus 10. Can you read it with me now? It's getting quite long, isn't it? 10 plus 10 plus 10 plus 10. If I had more coins, I could keep going. It could get really long, couldn't it? Number bear and I have really enjoyed being with you in this lesson. And we'd like you to do some practise before next time, so this is what we'd like you to do. I'd like you to get all your tokens that you've made for the previous lessons, and also collect some coins. You're going to need to sort them out. You'll have piles of tokens which have got two on, which have got five on, which have got 10 on, sort those out. Also sort your coins into two Ps, five Ps, and 10 Ps. It doesn't matter how many you've got. And then you can practise choosing some of your coins or some of your tokens and writing repeated addition expressions. Just make sure that if you're using two Ps, it's only two Ps in your expression. Otherwise, it's not a repeated addition expression, is it? So thank you for joining us. I really hope to see you next time, so bye for now and well done everybody.

The use of a repeated addition expression to represent equal groups

The use of a repeated addition expression to represent equal groups

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UnitMaths / Multiplication: equal and unequal groups

Maths