Freddie has 3 sweets. Connell has 5 times as many sweets.  How many sweets does Connell have?

Can the same calculation be used to solve different number stories?

Does the product change when the order of the factors change?

Looking at multiplication strategies and the effect on the product

Key Stage 2

Maths

Deriving multiplication and division facts

﻿Hi, and welcome to our first lesson together. My name is Mrs Behan. I'd love to get to know you. What's your name? It's a little bit dark and gloomy today in my recording studio. But I'm sure after spending some time with you, my day is going to get brightened right up. So go and find a quiet place in the house where you're not going to get disturbed for our first lesson. And when you ready, let's make a start. Let's take a look at our lesson agenda. Firstly, we're going to have a look at some multiplication number stories. Then I have a talk task for you. Following that. We're going to develop our learning some more, and then we're going to have a practise activity. And lastly, there is an independent task for you to have a go at. And I'm sure you're going to want to know how you got on. So I'm going to share the answers with you. There are a few things you're going to need to take part in this lesson. Make sure you have something to write with. So either a pen or a pencil. Make sure you have some paper to write on, and it might be helpful to have some small objects nearby, that you could use as counters. Lego blocks or pastel would do the job perfectly. If you haven't got those things to hand, make sure you pause the video now and go and grab them. You'll see that I've put my avatar intimate little teddy suit. I'm sure, you're wondering why. Well, in my spare time, I like to sew and I can make teddies. Here is a picture. I'm sure you have a favourite teddy. I'd love for you to tell me what it looks like. Now, I'm not sure what you think, but I think this teddy would look better with a jacket or a coat on. The jacket I want to give it will have two buttons. So I need to buy two buttons. My pink circles represent the buttons, but I have more teddies, and here they are. Blue one, a green one and a pink one. I'm going to need two buttons for every teddy. Can you tell me how many buttons I need for three teddies? That's right. We will need six buttons. You can see three equal groups of two. So we've got two, three times. You can see here that I've represented the buttons with the written number two, and I've pushed our equal groups together to create a bar model. So you can see that we have three equal groups of two. The product is six. And you can see the word product on your screen. The product is the result of multiplying one number by another number. This is a really key word. So we're going to have a go at my turn, your turn. I'm going to say the word, then you say it. Product. Product. Can you do it in a whispering voice, product. And allowed voice product. Fantastic. Okay. So we can see here that we've got our buttons represented as the pink circles. We squished them all together. So we've got our bar model. We can see our three equal groups of two here. And our product or the total is six. We can also write this as a repeated addition. So say it with me. We can say two plus two, plus two is equal to six. We also know that two multiplied by three can be used in this calculation. Because we have two buttons three times. So two multiplied by three is equal to six. We can also use this calculation because we have got three groups of two. So three groups of two is equal to six. Can you tell me what you notice about the product in all of these representations? That's fine. The product is the same. So all of these different ways, these pictures, the bar model, the written calculations, they can all help us with my question, of how many buttons do I need to put buttons on three teddy bears, if each teddy has got two buttons. Okay. So here is a quick activity. Which of these representations does not help me. You have no products here, just so you know, coming up. Okay. I need two buttons for five teddies. Option one is an incomplete bar model. Option two, I've got two times five. Option three, you can see there is a repeated addition. And option four, there is another multiplication. So like I said earlier, you have no products here. And if you were to work them out, it might give you a clue. I need two buttons for five teddies. Pause the video. wish to have a think. And when you're figuring it out, also have a think why the odd out does not help. Welcome back. Did you find out which representation was not helpful? I hope you picked option three. Yes, that one doesn't help us at all. We can see number five, five times. So that tells us we've got five groups of five here. One group of five, two groups of five, three groups of five, four groups of five, five groups of five. And in my little number story over here, I said, I need two buttons for five teddies. So at no point can we see the number two here in the groups, or with the amount represented in option three. All of the other representations do help us, because if we change this here, if we found a total of two plus two plus two plus two plus two, it would be, can you tell me yes, it's 10. We already know that two multiplied by five is 10. And we know that five times two is 10. Can you tell me what five groups of five would be? I'm sure you're all calling out 25 right now. Well done. So we've just had a look at different ways of representing one number story. But I would like to know can calculations be the same for different number stories. So in our previous example, with our teddy bears and our jackets, we had just the one number story. I need two buttons for five teddy bears, and we had lots of different ways of representing it. But I wonder if the same calculation could be used if the story that we used was different. And if we do use the same calculation, would the product be different? Just pause the video and have a quick think about it. And if you've done that, could you try to prove your thinking. Okay. So I'm sure you've got some thoughts and ideas on that. Let us explore this and see if you thought I have helped. So in this story, Zara has three teddies that have five buttons on the jackets. Michael has one teddy bear. His is much larger. His teddy wears three times as many buttons as Zara's teddies do. So how many buttons does Michael's teddy have. It's very important to remember that we are looking at the number of buttons that are on the jacket. Not necessarily how many teddies there are. Let's look at the number of buttons Zara's teddy has. We can see written three times five or five times three. Because there are three teddies, each wearing five buttons. This is the same calculation as thinking we have five buttons on three teddies. So you can see our bar model here shows three teddies. These bars represent the teddies. And each of them would have five buttons. We've been told that Michael's teddy has more. So compared to Zara's three times as many. So we can take what Zara has her five and put it down here. What Michael has and multiply it by three. So now here is Zara's but this is Michael's. He's got the same, but three times. I'm sure you were telling me from home that there are 15 buttons on Michael's teddy. And if you are, well done. You can see that the bar model shows us how to scale up. When we are told something times bigger or something times as many or something times greater. This we will call a times greater problem. But Zara's because she had three equal parts. She had three teddies, all had five buttons on them, we'll call hers an equal parts problem. So Zara has an equal parts problem. Michael has a times greater problem. Just to check how many buttons are there on all of Zara's teddies? You should be saying 15 as well. The calculation is the same for both stories. And the product is the same. There are 15 buttons on Zara's teddies. And on one of Michael's teddies, it also has 15 buttons, because his teddy has three times as many as Zara's. The school presentation day, the children received some awards. Have you ever worked so hard that you've given a certificate at school? Michael has four awards. He was given two stickers for each award he won. Zara received one award, but it was larger. She received four times as many stickers as Michael. So my question is how many stickers did Zara receive? So Michael gets the same number of stickers for each award he receives. He gets four awards. So there are four equal parts. He gets two stickers for each certificate. So each part has a value of two. Four multiplied by two or two multiplied by four. For Zara She received four times the number of stickers that Michael received. So in the bar, we can see here that the first bar has a value of two. And the second bar is four times greater. So it has the same value as four equal parts of two. What do you notice about the calculations? That's right. Even though the stories are different, the same calculation can be used to find the answer to both. Does it matter which order you multiply? No. When you understand what the story is telling you, you can change the order of the factors to make it easier to multiply. So we now know that Zara gets eight stickers. Let's do a thumbs up, thumbs down checks. So the question that I gave to barely and the talk task was can calculations be the same for different number stories? Thumbs up or thumbs down. What do you think? Thumbs up. Well done. Calculations can be the same for different number stories. Zara and Michael stories have proven that. one of them had an equal parts story, one of them had a times greater, but the same calculations were the same for both of them. Okay. Thumbs up, thumbs down. If we do use the same calculation, would the product be different. Thumbs down? Yes, of course. We've seen it that Michael and Zara both had 15 buttons. They would just spread out a different amount of parts. And we saw that they had the same number of stickers as well is just that Zara had a larger award, rather than the more awards that Michael had. Well done everyone. Let's go a bit further now. On this screen are two word problems. and we're going to have a think about the calculations we need to solve both. You might want to pause whilst you have a little think. I'm going to read the first purple box to you. Each day Milo eats two sandwiches for his lunch. After three days, how many sandwiches has he eaten? So I have a let's think about a calculation you might need to use to solve that problem. In the green box it says, Stu spent two pounds on a present for his sister. He spent three times as much on a present for his mom. How much did his mom's present cost? I wonder what Milo had to miss sandwiches. Tell me what your favourite is. Hmm. It's making me hungry. Milo eats the same number of sandwiches each day for three days. So there are three equal parts. He eats two sandwiches each day. So each of the parts has a value of two. Three multiplied by two, simple. So let's have a look at the second problem. Stu spent two pounds on his sister and three times as much on his mum. So this first bar here, shows us the value that he spent on his sister. And the second bar shows us that it was three times as much that he spent on his mum. It has the same value as three equal parts of two. So what calculation did you write down? This is what I came up with. Two multiplied by three equals six, because in each of these examples, there are three parts and each has a value of two. So there are two, three times. A little challenge for you now. So here is a word problem. And I'm going to show you two more word problems, that come up on the page in just a moment. And I want to see if you can find the problems that use the same calculation. So the stories that use the same calculation. So this is our first one, One Sunday Aaron found five conkers in his grandma's garden. The week after he found five times as many. How many conkers did he find the second time? Okay, so this isn't equal parts question. This is a times greater problem. So our first option is that, Sam bought two packs of erasers with four erases in each pack. How many reasons did Sam buy? If you're not sure what an eraser is? It's a rubber that you use to get rid of your pencil marks. Ella bought five packs of Christmas cards. If each pack contained five cards, how many cards did she buy altogether? Can you tell me the calculation that we need? Yes. We have five multiplied by five. Aaron found five conkers in his grandma's garden. And then the week after he found five times as many. So five multiplied by five. Well done. But now I need to decide which of these is the other store that uses five multiplied by five. Can we use five multiplied by five in this equation? No, we can't. We need to use two because we have two packs of erasers each with four in each pack. So multiplication here would be two multiplied by four. Over here though, with Ella's question, she had five packs of Christmas cards. Each pack contained five cards. So the calculation she needs is five multiplied by five. Here if you wanted to extend your learning further, you could try and draw the bar models to represent the problem. I think you ready now for your independent task. Using this calculation, can you rate two number stories? One should be an equal parts problem. And one should be a times greater problem. The calculation I'm giving to you is four multiplied by five or four times five. It would be superb, if you could draw a bar model to go with it. When you've done that, I'd like you to much the calculation to the two word problems where it can be used. So in the centre here, we've got two times six and two times 10. And then I'm going to show you different word problems. Lola packed six pairs of shoes for her holiday. How many single shoes did she have all together? Marcus has 10 pence in his pocket. Joseph has twice as much money as Marcus. How much does Joseph have? Louie gave two sweets to 10 friends. How many sweets did he give out all together? Poppy and Ava had a snail race. Ava's snail moved two centimetres, Poppy's snail moved to six times as far. How far did Poppy snail move? So see if you can much the calculations. And if you can see if you can identify, which is the equal parts word problem, and which is a times greater problem. Pause the video once to complete your task. Once you finished, come back to me. Welcome back. I'm going to show the hundreds of different number stories out there now for the calculation, four multiplied by five. I'd love to hear what you all came up with. Here is my equal parts example. Kaylum drew four pictures every day. After five days, how many pictures had he drawn? And here's my times greater question. Bethany had four lollipops. Ava had five times as many lollipops as Bethany. How many lollipops did Bethany have? Oh, I've hidden there. Let's move me out of the way. So the calculation we have for Kaylum in these pictures is four supplied by five would give a product are 20. Sure you all work that out. And also for Bethany and Ava's problem, we can use four multiplied by five, because Bethany had four lollipops and then Ava also had four but five times greater. So actually either had 20 lollipops. Okay. I'm just going to hide my camera for now. So, match the calculations to the two word problems where it can be used. So how did we match Lola? Did we go for two times six or two times 10? I'm sure you all went for two times six. And the other two times six question, was Poppy and Ava's snail race. 'Cause they ever snail had moved two centimetres and Poppy's nail moved six times as far. So it was bit two multiplied by six. So that leaves us with Louie and his friends. We would use the calculation two times 10 to find out how many sweets he gave out all together. And also Marcus has 10 pence coins in his pockets, but Joseph has twice as much money as Marcus does have. So Joseph must have 20 pence. And we're going to use the calculation, two times 10 to work that out. Now I would love to see your work. And if you would like to, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. So I've started out a little quiz for you. Make sure you go and complete it to see what you have learned this lesson. See you again soon and thank you.

Looking at multiplication strategies and the effect on the product

Looking at multiplication strategies and the effect on the product

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UnitMaths / Deriving multiplication and division facts

Maths