Video: Factor pairs

﻿Hello everybody. Good to see you again. My name is Mr. Ward, and we're going to continue our unit on multiplication and divisions today with a creative lesson when we look at factor bugs, which is a great strategy that you can use to allow you to identify factor pairs for any given number. Now, if you're free distraction, in the quiet place, and ready to begin your lesson, I'm excited about teaching this lesson. So I think we're about ready to go on. Let's make a start. Okay, before we make a start on our main lesson, there is of course always time for a mathematical joke of the day. I hope you enjoy this one, but I have a little confession. It's not my joke, so if you don't like it, please don't blame me. However, it has been making me chuckle and tickled me pink ever since I heard it a few weeks ago. Why do so many pupils wear glasses during maths lessons? It improves their di-vision. Very appropriate for our unit of work. Now if you think you can do better than me, and let's be honest, you probably could due to the material that I've been sharing recently on Oak National Academy, you can share your work and mathematical jokes with us here at Oak National Academy. Details of course, I will be sharing at the end of the lesson, so please keep watching the video until the last few slides. Just a quick overview of the lesson today. We'll start by introducing the new learning. Then you're going to have a go at the Talk Task in which we discuss that new learning in the context of a challenge or a task or an activity. Then we're going to take our learning a bit further by introducing a new concept to our learning today. And then I'm going to hand it over to you. You'll going to have a go independent task before having a go at the end of the lesson quiz. And hopefully you're going to leave today's lesson more confident and familiar with the concept of factor bugs and how to use them to identify factor pairs. It is important that you are equipped for the lesson. And you've got everything you need. So you're going to need something to write on, pencil, ruler, and some paper or a notebook that your school may have provided. As always, it's great to use squared paper in math, but if you haven't got that, you've only got plain paper or lined paper, absolutely fine. And if all you've got is the back of your cereal box or something to write on, anything will do. Make sure you've got something that you can write down ideas. Should you not have any of the equipment that you actually need today, please pause the video go and get exactly what you need and then resume the video when you are ready to begin. Let's get ourselves warmed up. And to remind ourselves of multiples, I've got an activity for you on your page. Please pause the video after I finish the instructions and spend a few moments or as long as you need to complete this task. You're going to use a Venn diagram. You may recognise these from previous years. I want to know how many numbers can you place within the Venn diagram? Look carefully at it where you might place those numbers. How many numbers can you place within the Venn diagram? See you in a few minutes. All right, let's just share a few ideas that you may have come up with. We could have listed endless amounts, and as you can see, I went up into the hundreds. Could have gone to thousands. And just to remind yourself that a Venn diagram all numbers within the grey circle will be multiples of four. All the numbers of within the red circle will be multiples of three. And any number in between the two circles are both multiples of four and three, and should we have put the numbers on the outside, that would indicate that they're neither multiples of four or three, but we haven't done that though. Just everything inside the Venn diagram. So examples are multiple of four, 76, 56. Multiples of three are 90 and 39. And multiples that include three and four, so they're both factors of these numbers are 36 and 240. You could have come up with anything. It would be great to see how many you came up with A good way of using the terms multiples and factors as a reminder of what they are. I've got a challenge for you, a question for you. Okay, there's a group of 20 children. I want to know how many ways are there of grouping them into equal sized groups, so I'm going to split them up into groups that have to be equal size groups. How many different ways are there of doing that? Pause the video now. Spend a few minutes discussing this and having a go, maybe writing down, jotting down some ideas, and then let's feedback and see how many you came up with. See you in a few minutes. I came up with six ways of grouping them. I wonder if you came up with all six. You shouldn't find any more than six, so if you've got a greater number than six, you probably made a mistake or repeated one of your groupings. Now, you can see that I've got whole groups. I can have one group of 20. I could then have in this context 20 groups at one. Now, in maths, when we calculate inference, we might say one times 20 is the same as 20 times one. That is correct to the calculation, but conceptually, that's not always the case. And in this case, it's not the same thing. One group of 20 is not the same as 20 groups of one because this is one group of 20 here, but if they were all standing individually on their own social distancing, then they would be 20 separate groups of one, so that's two. Then you can split them into pairs. Ten groups of two because a pair means two. Then you might have had groups of four, so you could have five groups of four. Or you could switch that around and have five, four groups of five. And finally, going back to that 10 groups of two, if I split, if I turn that around, I could have two individual groups of 10. So there's six possible ways of splitting a group of 20 into equal sized groups. And I can demonstrate that because they're all factors. And I can demonstrate that using something called a factor bug. Now, you will notice why we call them factor bugs because lo and behold, they look like bugs, don't they? They've got antennas at the front. And then, they've got legs. And as we know, within insects and bugs, they have multiple legs. So actually, the number of factors will indicate how many legs our factor bug will have. So I've fitted all of those factors in there. from the six groups. We know that one is a factor of 20. And of course, a factor means that you could take a number, and you can multiply it with another number to get to a total number. So the 20 has a factor of one and 20, because I can multiply one by 20. So that becomes a pair. 20 also has two factor two is a factor of 20 because I can multiply two with ten, and that gives me 20. That becomes a pair. Two and ten is another pair. Four is a factor of 20 because I can multiply four by five to give 20. So there are three pairs of factors in the number 20. And I can represent that with a factor bug. So let's try that again with a different number this time. This time you're going to have a group of 24 children. So same question, but now it's with 24 children. How many ways can we divide or split 24 children into equal sized groups? Again, pause the video, spend a few moments jotting down some ideas or talking about it if you're in a group or in a pair, and let's see how many ideas you came up with. Okay, I'm going to reveal the answers. And I'm sure you've come up with, hopefully, a number of pairs by creating a factor bug to demonstrate it. So the first thing you can see, as with every number, is that itself and one. Okay, so we got one and 24. That's the first pair of factors because one multiplied by 24, or 24 multiplied by one will give us a total of 24. So that's our first factor pair. And then no, because it's an even number, I can divide it by two. So 24 divided by two gives me 12. So 12 times two or two times 12 gives me 24. So that's my second factor pair. Because I know my multiplication tables, my times tables, I know that three is a factor 24. I know that three goes into 24. Because I know three lots of eight makes 24. So that's my third factor pair. And also, I recognise 24 has been in the four times table as well and the six times table, so I knew that four times six, or six times four would give me 24 as well. So that is my fourth factor pair. So there's eight factors in 24. Have I exhausted all possibilities? Let's think. I've got one, two, three, four. Does five go into 24? No, five doesn't go into 24, does it? Five, ten, 15, 20 because five is five is a factor in multiples of five or 10, so five goes into 15, for instance, or 25, or 35. It also goes into 30, 40, and 50, but five does not go into 24. So therefore, if I've got one, two, three, four, five is not factor pair, then I've got six, and I got eight, 12, 24. I've got all of my factors right there. So there are eight total factors in 24, four pairs of factors. So we're going to move on to the Talk Task part of the lesson, and just a reminder that a Talk Task generally take part three to one. So we're going to move on now to Talk Task part of our lesson. And reminding that Talk Tasks generally take place in schools, in groups, pairs, or whole class scenarios where we can talk and discuss the math using the vocabulary. Now, if you happen to be sitting at home, or working on your own at the moment, that's perfectly fine. You can still get involved. You can still pause the video, have a go at the task, articulate some of your ideas by writing them down or verbalising them to yourself, and then be ready to share when we discuss our answers. Of course, if you've got somebody close to you, an adult, parent, care, a sibling, a pet, or somebody nearby that you grab, bring them over, and show them what you're learning and try and get engaged in a conversation, that would be really useful as well. So we're going to take our learning further in terms of factor bugs. So let's explore by creating our own factor bugs. On the screen, you will read a statement. Factors come in pairs, and therefore all numbers must have an even number of factors. I want you to think about what's been said. Factors come in pairs, and therefore all numbers must have an even number of factors. Now, is that statement true? Is it sometimes true? Or is it false? I would like to explore this by creating factor bugs for the following numbers. So you pause the video. Spend as long as you need on this task. You can get to draw as many factors bugs as you can. Play around. Your knowledge of timetables will help as well. But draw your factor bugs, and seeing if you can prove with the evidence you create, whether that statement is true, sometimes true, or never true. Like I say, pause the video, spend as long as you like, resume the video when you're ready to share some of your findings. Good luck. See you in a few minutes. Bye for now. Welcome back, everybody. I'm hoping you've got lots of jottings and drawings of factor bugs on your page. And if you have done factor bugs for the six numbers below, you should have enough evidence there to come to the same conclusion that I did. And that is that the statement of factors come in pairs and therefore all numbers must have an even number of factors is only sometimes true. That is not true all the time because there are occasions where there are an odd number of factors. And the two examples we had that prove that was 16 where there's five factors, and 25, where there's only three factors. This was proof that we needed to support our hypotheses or our conclusion that the statement was not always true, only sometimes true. We take that newfound learning then, a newfound understanding that sometimes there are an odd number of factors, and we're going to put it into our new task now as we take our understanding a little bit deeper. So there are an odd number of factors for some numbers. And that begs the question, why? Two questions for you to consider and discuss if you're with somebody right now or to think about on your own. What is special about these numbers? And do these special numbers have a name? Now if you're familiar with it, fantastic. You can move on. If you aren't, have a think when you may have heard those numbers before. 16 and 25. They're special numbers because they have an odd number of factors. Why? Special numbers because they are called square numbers. And a square number is the product of a number multiplied by itself. So in this case, 16 is the product of four multiplied by four, multiplied by itself to make 16. 25 will be the product of five multiplied by five, by itself. So they are called square numbers. Can you think why we call them square numbers? Hmm. It is a little clue. Why do we call them square numbers? Well, I can show you that with this visual representation. As you can see your page, if we were to use counters to create arrays, you would see that square numbers have an even number of rows and columns. So two lots of two, it's a square. Three lots of three, it's a square. Four lots of four, it is a square. You'll also see a small two next to the two and a small two nest to the three. Now that is, this is a symbol for squared. So if you ever see a two, a small two next number, so for the next one in the sequence, it would be five squared, five and a small square. That would mean five lots of five. As you can see, they're going squared. So literally, you can see it's a square shape in an array. So the next one will be five squared which is five lots of five which is 25 Six lots of six which is 36, and so on, and so forth. So, whenever you see, or you find a number that has an odd number of factors, the chances are that you've identified a square number. So we've breezed through a lot this learning, but that's fine, because actually, a lot of it's from our prior understanding and knowledge. We're now going to try and put it into an independent task and which is down to you. It's a fun activity today. I want you to create factor bugs. I want you to explore with the numbers. But I've given you a few guiding questions to hopefully guide your investigation. So in the process of creating new factor bugs, can you look for how many bugs you find with more than four legs? So therefore, you're going to have to have to find factor bugs that have either an odd number of factors greater than three, or have factor pairs greater than two factor pairs, so six or eight, so on so forth. How many bugs can you find with a stinger? So how many bugs can you find that are, that would have a product of a square number? How many bugs would you find with an odd number of factors? And how many bugs can you find with exactly four legs? So, I'm going to let you pause the video and spend as long as you need for this task. Jot down, draw them, you know, use your times tables if you need to, go back and refer to them, explore if you're with somebody, share your ideas, talk about it, come up with many factor bugs as you can. Try and find as many as you can with a stinger, with an odd number of factors. And then come back to the video, resume when you're ready to share some of your ideas. See you very soon. Bye for now. Okay, I'm sure you've got some fantastic examples in front of you. Obviously, we cannot spend too long, sharing all their ideas. There's so many there and I'm so I'm not with you, so I cannot physically see what you've created. Although, if you'd like to share some your factor bugs, I'd love to see them here at Oak National Academy, but I've just come up with a couple of examples. So make sure you're on the right lines. Hopefully your factor bugs look like this. It can be as plain as this. It could be a little bit more colourful. If you want to add some colour and you've got time to do so. I've come up with one which is 28. 28 had more than four factors, and it had more than two pairs of factors. It had three pairs of factors or six factors in total in 28. One, two, four, seven, 14, and 28. Now I need to work systematically through that, so I think about any times table. So I know one and two, four going to 28, but then does five go into there? No because 28 is not a multiple of five or 10. Does six go in there? No, because six times four is 24. Then six times five is 30, so I know that doesn't work, but then it comes to seven and I go, and so forth until I find those factors. So I work systematically through the options. And if the 36, you can see that there is a stinger. So it had an odd number of factors, which means it was a square number. There were seven, sorry, there was nine factors in total. There were four pairs and an odd factor. So there's one and 36, because one multiplied by 36 is 36. Two times 18, that's a second pair. Three and 12, a third pair. Four and nine was a fourth pair, and six, because six multiplied by itself, or six squared would be 36. So that has nine factors, a rather large number of factors. If we compare that to some of the other numbers we've looked at earlier today, 25, for instance, which only had three factors, you can see that actually there is a big difference from number to number. If that's all of our learning today, you still have not had enough and you want to continue creating factor bugs and exploring numbers that are greater than 100, please feel free to have a go the extension challenge slide. Pause the video, read the instructions on the screen, and take as long as you like. There's no time limit for the challenge. I just hope you enjoy this task. This almost brings us to the end of today's lesson. What a great creative lesson that was. It's now time for you to have a go at the quiz to see how much of that learning is embedded. And if there's anything you need to go and repeat, or go back over, in case you're not too familiar, but I think you're going to be absolutely fine as long as you remember the key vocabulary because you have been super during today's lesson. I've got the quiz now, and I'll see you in a few moments. I want to know how you did. I imagine you did very, very well because you have worked really, really well, every single one of you today. Now just a chance to remind you as I always do at the end of the lesson that we'd love to see the work you've created, and I bet today you created some absolutely amazing factor bugs. And some you may have some colours and you made it really attractive, drawing with the mass. I'd love to see your work, so please share your work with us here at National along with your improved mathematical jokes to improve my comic material. Ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak I'm looking forward to seeing what you have created today and across the unit as a whole. Unfortunately, that brings us to the end of today's lesson despite all the fun that we've been having with our factor bugs. I hope you found the strategies useful and they will allow you to work with more confidence when identifying factor pairs in the future. Have a great rest of the day. I look forward to seeing some of you again in the near future here on Oak National Academy. So for me, Mr. Ward, bye for now.

Worksheet: Factor pairs

Exit Quiz: Factor pairs

Completed: Factor pairs

Today we will be learning how to work systematically to identify the correct number of factors and factor pairs for given numbers, using the notion of factor bugs to help us.  We will then develop our learning further by proving that square numbers have an odd number of factors.

Maths

Factor pairs

Video

Worksheet

Final Quiz

Lesson Complete