Embedding the language of factor & product, making connections between different representations

Key Stage 1

Maths

The two times table

﻿Welcome back. My name is Mrs. Harris, and I'd like to revisit the practise activity from the last lesson that you had with Mrs. Akers. I even had a go myself. So Mrs. Akers asked you to make your own bar models, and that you had to write the equation to go with your bar models, and then explain them to someone as well. She even asked you to use the language of product and factors. I'm going to show you mine and go through them. Using the Anchorage product and factors. I did get a bit of a bluey mess though. Did you? Okay, I did four examples. We've got four different bar models to show my different equations. In this one, my product is eight, and I have four equal groups of two. Two is a factor. Four is a factor, 'cause I have four groups of two, and eight is the product. I remembered to write my equations as well. I remembered my equations here. Six is the product of three times two. Three times two equals six. I did get in a bit of a muddle here. I had to cross something out, but that just shows that I'm learning and that I knew what I'd done wrong, so I can correct it just there. Here, my product is 10. One of my factors is two. See, all my groups are equal groups of two, and I've got five groups. And this is my last one down the bottom. Oh, I forgot to write in what the product was. Let's count in twos to find out what the product is. Two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24. Just write that in. I find knowing the product helps me write my equations. There's my 24. Thanks for your help. How many twos did I have? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. 12 is a factor. And I've got 12 lots of two, 12 lots of two equals... There's a clue on my bar model. Yeah, 24. And we know, don't we, I could write it with the product first as well. 24 is the product for 12 times two. Brilliant. Okay, so now we're going to practise even more writing equations and really, really thinking about what numbers we're using and whether they are factors or products. Now, these children, they agreed to help me. And I know that they're going to do this lesson at home just like you are now. We're going to get all the information we need to write our equation from these pictures. The first thing I want to look at is one of the factors. And the factor I want to look at is the one I'm going to write first. And that is going to represent the number of groups. So, really, I want to know how many bicycles we have here. What's that? We've got five. Ah, yes. One, two, three, four, five bicycles. Fantastic. That's going to be one of my factors. Next, I've got my other factor, and that's going to be the number of wheels on each bike, the number of wheels in each group. Yeah, so I've just looked at all my bicycles. They've all got two wheels. So I've got my factors of five telling me the number of bicycles and two telling me how many wheels on each bicycle. Hey, I've got two bits of my equation, but I still need to know the product, and to know the product we could count in twos, but maybe you already know it. But I'm going to count in twos just to check. Maybe you can join them with me. Two, four, six, eight, 10. We've got all the information we need now to write our equations. I'd like you in a second to pause the video and write me the equation with factor, factor, product, and then write me the equation with the product first and then the factors. Okay, pause it now and give it a go. Okay, I hope you remembered all the information that we'd found out together. We'd remembered. We found out, sorry, not remembered. We found out that we had five groups. We had five bicycles. We found out that in each group, we had two wheels. They're our factors. I'm going to write them up on my board. We have five lots of two. I've got factor and factor. And then together, we worked out the product. Do you remember, we counted in twos, and what was our product? Come on, you can say it louder than that. That's right, our product was 10, but that was just one of the equations I wanted you to write. Do you remember, I asked you to write it like this with my factor, factor, product? And I asked you to write it with the product first. Our product was 10. That represents the total number of wheels. And 10 is the product of five lots of two. Remember, our five bicycles each with two wheels. Well done if you got that right, but if you didn't, don't worry, 'cause we're going to practise some more, because these weren't the only children who wanted to be in this lesson. She did too. Now, I think these equations, they no longer match my pictures. I'm wondering what's changed. Has my product changed? Have I still got 10 wheels all together? Have my factors changed? Oh, you think one of my factors has changed? Well, each bike still has two wheels. doesn't it? So I'm going to keep my factor of two the same, but you're quite right. The number of groups has changed. The number of bicycles has changed. This time, I've got six bikes. Remember, we had five and now we have one more. Five and one more, six. One, two, three, four, five, six. So my factor of five, well that can't stay, can it? So I'm going to rub that out, but maybe on your piece of paper, you'd like to write a new equation underneath. I'm going to have six groups of two. I've got six bicycles all with two wheels on each of them. Is this right now? What you mean it's not? Yes. My product has changed as well. I no longer have 10 wheels altogether. How many wheels do I have altogether? What is the product of this equation? Pause the video and have a go yourself at just finishing my equation here and my equation here. No peeking at mine though. We do want you to have a go first. Welcome back. Thank you for having a go. Now, I set you the challenge of finding me the product of six lots of two. Maybe some of you were very resourceful and just knew that two more than 10 is 12. Maybe some of you counted in twos. And if you counted in twos, you would have got to 12 as well to find our product. Let's just find it together to check. Two, four, six, eight, 10. I remember that 10. And two more, 12. Our product here is 12. You're getting really good at this. Point to the product on your equation. Did you point to 12? Point to the factor that shows how many in each group. Yeah, that was the two, wasn't it? And that actually hasn't changed from our last equations. That leaves me one factor left. Just tell me, what does the factor six represent? It does. It represents the number of groups here. It represents how many bicycles. One more challenge for you. There was another child that wanted to be in our lesson today. This one's a bit bigger though. It doesn't make a difference. 12 groups there. Okay, I'm actually going to rub mine off. I would like you to write me an equation to match these groups now. Remember to find both factors. I think one stayed the same from last time. And find me the product. Pause the video now and have a go. Well done. I'm wondering, did you start with the factors or start with a product? I'm going to start with the factors and the first factor I'm going to find is the number of groups. One, two, three, four, five, six, seven. There are seven groups. Seven is a factor. Next, I'm going to find how many in a group. Yeah, that hasn't changed, has it? Our bikes all still have two wheels on each of them. So we have seven lots of two. Let's just check that together. One lot of two, two lots of two, three lots of two, four lots of two, five lots of two, six lots of two, seven lots of two. We got it, didn't we? So I've got my two factors. What am I missing? Ah, I'm missing the product. But what is that product? Oh, I could count in twos to find it. Yeah, I could remember my product from last time, and I had two more to it. Maybe I even just know it, but I'm going to count in twos to check. Two, four, six, eight, 10, 12, 14. My product is 14. Okay, let's write that the other way. 14 is a product of seven times two. I'd like you to pause the video and tell somebody in your house what are the products, what are the factors, and show them the photographs and explain to them where the pictures have come from. Great job, everybody. Ah, I told you, you'd see these generalisations again. And, look, here they are. Let's say them together, so we can keep them in our minds as we go through this picture. So, let's have a look at factor times factor is equal to the product. Did you say it with me or did you forget? Let's do it again. Factor times factor is equal to the product. The product is equal to factor times factor. I didn't hear you. Again. The product is equal to factor times factor. Okay, we've got them, haven't we? We're going to keep them right in here. Let's look at the picture together, because then we might be able to use these generalisations to help us make our equations. So, how many groups of children are there? I hope you said four, because there are. There are four groups of children. One, two, three, four. How many children are in each group? One, two, one, two, one, two, one, two. Yep, there's two children in each group. How many children are there altogether? I hope you're being really efficient in counting in twos. Two, four, six, eight. What I'd like you to do is just pause the video in a second and write the multiplication equations to go with this picture. And I would like two. I'd like one with the factors first and the other with the product first, Think carefully about what your factors are as well and where you got them. I'll do it as well. No peeking. Okay, are you ready? Let's have a look at the answers together. So, first of all, I asked you to write it with the factors first, and I had factor times factor is equals to the product. I had four. Where did I get that four from? The groups of children. I then had my nice multiplication symbol. Then I had my other factor. What was that? It was two, because that represents the number of children in each group. And four times two is equal to the product, which was? Eight. Fantastic. And then I asked you to write it with a product first. So what's the product? Eight. And eight is the product of? Four times two. Well done. You're really getting the hang of this now. Have a little look at this picture. What are my factors? The bumper cars are the groups. The children in each car are the number in the group. So what are my factors? Oh, you know what? This picture, it's just so busy. I can see that there's two children in each bumper car, but there's so much for me to look at. I'm going to try replacing each bumper car with a counter. I'm going to ride two on each counter. Maybe you can count in twos as I do it. Two, four, six, eight, 10, 12. Oh, 12 is the product. That's the total number of children altogether, but it's still really busy. I do prefer things when they're lined up. I think I'll line all my counters up. Oh, that's better. These counters look so neat all in a line, much easier as a counter, and much easier to work with to write our equations. I still put my bumper cars down here, though, just in case you need convincing that that's where our counters came from. Now we know that there was two children in each group, two children in each bumper car. So I'm thinking, two is a factor, because they're in groups of two. How many groups was there though? How many bumper cars was there? We're going to need to count our counters and see how many counters we've got to find out our factor. One group of two, two groups of two, three groups of two, four groups of two, five groups of two, six groups of two. So we've got six and two as factors, but we still need to do the product. We're going to need to count in twos again, aren't we? Two, four, six, eight, 10, 12. We've got all the information we need here to write our multiplication equations. You know what I'm going to ask you to do? I'm going to ask you to pause the video and write the equations for me. Did you give it a go? Well done if you did. So, let's write it with our factors first. And I haven't got our generalisations up, have I? But I think we can remember them now. Factor times factor equals the product. Let's write that. Not the generalisation, the actual numbers that are the products and the factors. We know that six was a factor that represents our number of groups. We had six groups of two. Two is our other factor. And if we know that factor times factor equals a product, and we know the product is 12, I'm going to write my 12 here. The other generalisation was where we had the product first. Product or the product is equal to factor times factor. Well, all I need to do is move my product to the beginning, pop in my equal symbol, my factor of six representing the number of groups, my multiplication symbol, my other factor of two representing the number of children in each group. You're getting really good at working these through with me. Thank you. Oh, money. I remember working on money a few weeks ago. Take a close look at these coins. Can you remember their value? That's right. It is a two pence coin. That's its name, and it is worth two one pennies. It's the same as having two one pennies, isn't it? So I've popped them into a bar model, a bit like what we were doing at the beginning of this lesson and that you did last lesson with Mrs. Akers. So, I've got my two pence coin in each group. That must be a factor. Two is a factor, because each one of these is worth two. I've got five groups of two. So five must be a factor. So what is my product? Go on counting twos. Well done. It's 10, isn't it? We had two, four, six, eight, 10. So what's the product? That's right, it's 10. Can you write me the multiplication equations to go with these with this bar model? I hope you did give it a go. I'm going to write my products first. I know that there are five groups of two and that the product of that is 10. Now I'm going to write it with my product first. Product is equal to factor times factor. I really like how all the information we needed was in this bar model. Handy. Oh no, these counters are blank. What am I going to do? Oh, don't worry. Do you know what? They could represent anything we like. And as we have been working in twos today, let's give each a value of two. You're a two. You're a two. You're a two. You're a two. You're a two. You're a two. Well, really you're all twos, 'cause you're all exactly the same. Each of you represent two. Now, I'd like to write some multiplication equations to match this image. I know how many counters I've got. I've got one counter, two counters. Sorry, one counter, two counter, three counters, four counters, five counters, six counters. Let me just check I've got six equal size groups on my bar model. One, two, three, four, five, six. Yep. Hmm. What did I say each counter had a value of? I did, didn't I? We said each counter represents two, even though it doesn't say it on it. So what number am I going to write in each of these boxes, each of these groups on my bar model? I'm going to write a two. Two is a factor, because each of our counters represents a group of two. How many twos have I got? Yeah, I got six twos. So, I know my factors, but I don't know my product. Do you know what? I'm going to leave that out for now. I'd like you to work it out. So, can you write for me... Don't worry, it's for the last time today. Write for me, the multiplication expressions that go with this bar model, and don't forget the product. We know the factors. You know what to do by now. Pause the video and have a go yourself. Well done for giving it a try. What I did first is I found out what the product was. And to do that, I did that good old counting in twos, because we're so good at it. Two, four, six, eight, 10, 12. And then, so I didn't forget that, I popped it in the whole bar of my bar model. So now I know my product, my factors, two and six, I could quite easily write my multiplication equations. I wrote factor times factor is equal to the product. And then I wrote product is equal to factor times factor. I could say the numbers, couldn't I? Six times two is 12 Six times two is equal to 12. 12 is the product of six times two. Well done if you had a go at that challenge, I didn't give you all the information you needed, did I? But you worked out the whole, and then you had all your factors, both of your factors and the product, so you could write your equations. Great job. So now I've got your practise activity, the thing I'd like you to have a go at for next time. This is my example. And my example says the product of four and two is eight. So what I did then was I thought about all the different ways I could show that I understood it, that I understood the product of four and two is eight. I did my counters. Four counters to represent one of the factors. My counters had the number two on the other factor, and, altogether, they made the product of eight. I did a bar model just like we have done. I even did it with the blank counters and gave them a value in my mind of two. Oh, I drew some children at desks. I could have drawn the bumper cars or the bikes, maybe even some shoes. I drew some Numicon. I like working with Numicon. With my four pieces down here are the products. One, two, three, four. Each of them have a value of two. There's a two, There's a two. There's two. There's a two. And then had my product. Hey, that looks like a bar model, ooh. And then I did it with some money. The product of four and two is eight. And then just because we're so good at it, and it's what we really need to do, don't forget, is I wrote the equations. Now, you may think, "That's easy, Mrs. Harris. "You've done it for us," but, no, I know you can do it yourselves. And here it is. So your practise activity is to represent this sentence with pictures, a bar model, and equations. I'll just read it to you, but you might like to leave it up on the screen to look at when you're doing the practise activity. Remember to draw many pictures, draw many equations, maybe even a bar model, to show that the product of seven and two is 14. I'll have a go too, and I'll show you my ideas next time. Bye.

Embedding the language of factor & product, making connections between different representations

Embedding the language of factor & product, making connections between different representations

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UnitMaths / The two times table

Maths