Think More Deeply- does the Representation Match the Expression?

Key Stage 1

Maths

Multiplication: equal and unequal groups

﻿Hello everybody. My name is Ms. Omanivich and I will be teaching you today. So we're going to continue learning all about equal groups and how to represent equal groups using a repeated addition expression. So I've brought a little friend along with me today. His name is Little Ducky. Can you give them a wave? Excellent. Thank you. Now Little Ducky is a little bit shy. He loves Maths, but he sometimes he makes mistakes. So your job today is to help him out when this happens. Do you think you can do that? Great. Thank you everybody. So we'll see more of Little Ducky later on in the lesson. Now let's review the practise activity from the previous lesson taught by Mrs. Perry. So she asked you to represent four groups of six with a drawing, a bar model, and a repeated addition expression. She then asked you to do the same to represent six groups of four. Now I hope that you've got your drawings, and pictures in front of you. I want you to have a look at what you've done and have a look at what I decided to do to show this. And I want you to have a think about whether it's similar or different to your example that you've done. Have you noticed that with my example, in the top picture we've got four equal groups and in the bottom picture we've got four dots in each group? And have you also noticed that in the top picture, there are six dots within each group, but in the bottom picture, there are six equal groups? So for that bottom example, we've just swapped, the number representing the number of groups with the number representing the group size. And do you remember that Mrs. Evans Puppet Number Bear found this a little bit tricky in her lesson? Let's have a look at these three pictures. We can see a picture of some coins. Now we've been learning a lot about money recently. Haven't we? Do you remember what the value of a two pence coin is? That's right. One two-pence coin has a value of 2p. So we don't need those pre-money tokens anymore now that we've gone over that. So we can also see a picture of some children in some bumper cars with a repeated addition expression underneath. And we can see a picture of some blue counters with a number underneath. So first of all, I want you to have a look at all three of those pictures, and I want you to think about what's the same and what's different about them. And then I'd like you to pause the video and explain this. Okay. Now let's have a look at the picture of coins first. How many 2p coins can you see? That's right. There are two 2p coins. Do we remember our sentence stems from lesson six? Let's see if we can use them to help us to describe this picture. Now, I want you to say the sentence stems with me, okay? So remember to speak loudly and clearly, otherwise I won't be able to hear you. Let's have a go. There are two groups of two. There are two and two. We can write this as two plus two. Excellent. Now let's have a look at the picture of the bumper cars. How many bumper cars can you see? There are two bumper cars. And how many children are in each bumper car? There are two children in each bumper car. So let's see now, if we can use the same sentence stems to describe this picture. Off we go. There are two groups of two. There are two and two. We can write this as two plus two. Now, have you noticed what's the same, about this picture of coins and this picture of bumper cars? So there are two 2p coins and there are two bumper cars. Each two pence coin has a value of 2p and there are two children in each of the bumper cars. So we can use the same sentences, can't we, to describe both of these pictures, even though both of these pictures show different objects. Now let's have a closer look at these blue counters. How many blue counters can you see? That's right. I'm sure most of you got the answer straight away. There are four blue counters and we can see that really clearly, can't we? And I don't know about you, but they remind me of a pattern on a dice. So Little Ducky has noticed something about these blue counters that he wants to tell me about. Little Ducky says that he can see two groups of two. And I wonder if some of you have seen these counters as two groups of two. Now Little Ducky is going to show you what he means by this. So he's going to draw one group of two by circling two counters, and then he's going to draw another group of two. And by doing this, he can say that he can see two groups of two. Now there's another way that we can show those groups of two, and I wonder, if you've thought of it already. I'm going to show you now. So we can show all groups of two in a different way by drawing all groups like this. And we've still got two groups of two, haven't we? Some of you might have seen it differently, and you might have even seen four groups of one because there are four blue counters. Let's think carefully about that number four. What do you think the four represents in this picture? The four represents how many counters there are in each group. So what does that tell you about the number of groups? There are four counters in each group. So that must mean that there are four counters in one group, and I'm going to show you how that can be represented. So I'm going to draw my one circle, making one group around my four blue counters. So let's use that sentence stem again, to describe this picture now. I want you to say it with me. There is one group of four. The one represents the number of groups and the four represents the number of counters in the group. Now, if there's any one group of four, do you think that we can use the repeated addition expression to represent this? We can't, can we? Because we are not adding the same equal group again, there's only one equal group here. So this is why the picture of the counters is a little bit different to the picture of the coins and the picture of the bumper cars. With the counters, there is one group of four, and with the coins and with the bumper cars, there are two groups of two. Now I want you to have a look at this picture. What have you noticed? There are lots of pineapples in some boxes, aren't there? Do you like pineapples? I do, they're one of my favourite fruits. Okay. So we've got a true and a false question for you now. I want you to have a look at that statement. Shall we read it together? This picture shows five plus five plus five plus five. Now do you think that's true or do you think that's false? In a moment I want you to explain your answer, pause this video and then we'll come back, after you're done. Shall we see if you got it right? Okay. Well done if you said that this statement was true, but how do we know it's true? Shall we use those sentence stems again to describe the picture? They've been really handy, haven't they, and helped us with our reasoning. Okay. Let's have a go together. There are four groups of five. There are five and five and five and five. So have a look at the number of fives we've got. We can also say that there are four fives. Now, I bet you can think, of the repeated addition expression now. Let's say it together. We can write this as five plus five plus five plus five. So I want to know what does each five in the repeated addition expression represent? Each five represents the number of pineapples in each box or each group. There are five pineapples in each box. So why are there four fives? There are four fives because there are four groups of five. There are four boxes of five pineapples. Now I'm going to write the number five next to each box of pineapples. So I've got my second five here. I'm going to write my third five and my fourth five. So four groups of five. Now here's another question, we've got another true or false question. But I bet you'll be really good at this one. So have a look, we've got a different picture this time. What can you see? There are lots of trees with apples in them. I wonder if any of you have any apple trees in your garden. So let's have a look at that first statement. Shall we read it together? There are six groups of two. So I want you to have a think, is this true or is this false? Does that statement match the picture? And you might pause the video here to explain your answer. Shall we see if you're right? Are you ready? Okay. Well done if you realised that it was true. Shall we use our sentence stems again? Let's have a go. There are six groups of two. So we know that it's true, don't we? But to explain it further, what does the six represent? The six represents the number of trees, doesn't it? Shall we count how many trees there are together? One tree, two trees, three trees, four trees, five trees and six trees. So what does the two represent? The two represents the number of apples in each tree. Okay. Can you help me with this sentence? There are two and two and two and two and two and two. Wow. That's a lot of twos. That's a really long sentence, Isn't it? I wonder how many twos there are in that sentence. Can you count them and check? That's right, we can say that there are six twos. So now I want you to have a look at that second statement underneath the first one. It says we can write this as six plus six. Now Little Ducky thinks that we can write this as six plus six. He thinks that the statement is true and he's very sure about that. Now I want you to have a think. Is Little Ducky right or has he made a little mistake? Is there a different repeated addition expression that we can write to match this picture? Have a think, pause the video and have a go at explaining. Okay. Shall we see if you're right? Little Ducky are you ready? You're sure you're not going to get sad if you've got it wrong? Okay. Excellent, let's see. It's false. Little Ducky is looking a bit confused about this so shall we help him to understand? Okay, let's have a go. So now we've got these sentences underneath the picture. It might be quite easy to know what that repeated expression should be. Shall we have a go at saying it together? We can write this as two plus two plus two plus two plus two plus two. So six twos. Now, if I was going to write six plus six, to match a picture of trees and apples, what might that picture look like? Now I've got a challenge for you. I want you to think about that expression six plus six, and I want you to get some paper and a pen or a pencil, and I want you to draw a picture of trees and apples to match this expression six plus six. And when you're finished, come back and we'll see if your picture looks like mine. So here's my picture to represent the expression six plus six. Does it look like the picture that you've drawn? I hope so. So have you noticed that I've got two trees and I've got six apples on each of my trees? Have you also noticed that the apples on my trees are of different sizes? Some of them are bigger than others, but remember it doesn't matter about the size of the apples, as long as you've got six apples on each of your two trees. Now let's say a sentence or two to go with this picture. Let's say it together. There are two groups of six. There are six and six. We can write this as six plus six. So that helps us to understand why the picture would look a little bit different to the first one. And now let's have a look at both of the pictures together, with their repeated addition expressions. So here we can see that bottom picture, the six plus six is very different to that top picture, isn't it? And we need to be really clear on what the numbers within the repeated addition expressions represent to get it right. What can you see in this next picture? We can see some coins in a purse, can't we? Now let's have a read of the question together. Sam has drawn a bar model and written an expression to match the picture below. Is he right? I'm not sure if he is right. Now can you be a detective and can you take a closer look and see what mistakes Sam has made with his bar model and with his repeated addition expression? If you're not sure, I'll give you a clue. Look closely at the type of coin Sam has in his purse. Are they 1p coins? No, they're not, are they? Are they 2p coins? No, they're not 2p coins either. Are they 10p coins? Yes, that's right. They are 10p coins. And we know this because we can see 10 pence written at the top of each coin, can't we? Okay. Now it's time to pause the video here and talk about the mistakes that Sam has made. Okay. Shall we go through this together now? Right. So we can see some 10p coins, can't we? Do you remember what the value of a 10 pence coin is? That's right. Each 10 pence coin has a value of 10p. So how many 10p coins can you see in Sam's purse? Yes, that's right. There are three 10p coins or three groups of 10. So let's say a sentence to describe this, are you ready? There are three groups of 10. We can also say this sentence. There are 10 and 10 and 10 and each 10 represents each 10p coin in the purse. Now I bet you can say the repeated addition expression to match these sentences now, can't you? Shall we say it together? Are you ready? Okay. 10 plus 10 plus 10. So we can see now that Sam was a little bit right, wasn't he? Because he knew that he had to split that bar model into three equal parts. And he knew that for his repeated addition expression, he needed to have three numbers. But the mistake that he made was that he wrote the number one instead of the number 10. So this is what it should have looked like, but he was almost there, wasn't he? Okay. And now it's over to you and it's time for your practise activity. So what I'd like you to do is to make your own true or false questions. I wonder if the grownups in your house are as good as you are at explaining your answers. Here's an example of what I've done so I want you to have a good look at it. Can you see that I kept the number of groups and the group size quite small? Can you see that I have drawn the same objects in each of my groups? So I want you to make sure that you do the same thing. Okay? And I'd also like you to bring your examples to the next lesson with you. Okay. I'm looking forward to seeing what you come up with. That brings us to the end of our lesson. So thank you very much everybody, and it's goodbye from me and goodbye from Little Ducky. Goodbye.

Think More Deeply- does the Representation Match the Expression?

Think More Deeply- does the Representation Match the Expression?

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UnitMaths / Multiplication: equal and unequal groups

Maths