Which of the following is a way to write 36?

What other way can 2 x 2 x 8 be written?

What is the 8th square number?

What is the 5th prime number?

What is the difference between the 6th square number and the 6th prime number?

Representing integers

﻿Hello and welcome to another video. In this lesson we'll be looking at exposing factors. Again, my name is Mr. Maseko. Before getting on with today's lesson, please make sure you have a pen, or a pencil and something to write on. If you don't have those things, go and get them now. Okay, now that you have those things, let's get on with today's lesson. So, try this activity: fill in the blanks. Pause the video here, and give this a go. Okay, let's see what you've come up with. So, eight is four lots of for us, four lots of two. And eight, well that is four multiplied by two. And then you have 12 is three lots of something lots of something. Well, 12 is three lots of what? Three lots of two lots of two. How do we know? Cause two lots of two, that's four. And then three lots of four, that is 12. So three multiplied by two multiplied by two. Now, 24 is four lots of what? 24 is four lots eight, and eight, well, eight is four lots of two. So it's four lots of four lots of two. Or you could have said four lots of two lots of four. And then 24, that is four multiplied by four multiplied by two. Now how many ways can we fill in the blanks for 18. Well, 18 could be two lots of, well, it's two lots of nine, so you can do two lots of three lots of three. So what we're looking at today is different ways of representing numbers that exposes their factors. Now how does this image, show that three is a factor of 30? What can you see? Well, we can see that in this image, we have three lots of something. So, because we have three lots of something, That shows that three is a factor. Can you see anymore factors? Well, we have three lots of 10, because inside each big group, there is ten. So we know that ten is a factor. What other factors can you see? Well, we have three lots of two lots of, this is three lots of two lots of five. So we know that five is also a factor. So we can see the factor three, through the three lots, we can see the factor five, because we have groups of five, we can see the factor two, because we have two lots of fives, inside the big bundles of three, and we can also see the factor ten, because those two fives make ten. Now let's look at this other image. How many dots can you see in this image? How do you know? And what factors of the represented number can you spot? Pause the video here, and give this a go. Okay, so how many dots can you see in this image? Without counting them all individually, what can we say? What can we see? Well, I can see four lots of something, because there is four big groups. So I can say I can see four lots, if this pen writes, I can see four lots of, well, four lots of what? Well, we can see four lots of, well, four lots of, what's inside there? Well, there is fives, so I see four lots of five lots four lots of five lots of, well, what's inside the smallest groups? Well, that is three. So I can see four lots of five lots of three. So that is four, multiplied by five multiplied by three. And that gives us, well, four multiplied by five is 20, times three is 60. So we know this image represents 60 dots. By grouping them, we didn't have to count them individually, and that's how we know, by looking at the groups. So what factors can you spot? Well, we can spot the factor four, we can spot the factor five, we can spot the factor three, what else? Well, four lots of five, well, that gives us the factor of 20. So we can also spot that. Well, you've got five lots of three, and five lots of three gives you the factor 15. Inside the big groups we've got five lots of three. Is there anything else you can spot? Well, right now, using this grouping, these are the only factors that we can see visibly. Now, here's an independent task for you to try. Pause the video here, and give this a go. Okay, now that you've tried this, let's see what you've come up with. So, how many dots can you see? Well, it's how you counted them, so these two questions are, would come together. So how would we count these? So what can you see in that first image? Well, I can see five lots of something, so I can see five, lots of what? Well I can see five lots of, well there's threes inside the fives, so five lots of three, that's a three, I can see five lots of three lots of four. So that's five multiplied by three, multiplied by four. Five multiplied by three, well that is 15, multiplied by four, that is another way to represent 60. Now what can you see in this big group? Well, I can see, well that is three lots of, well, what else? Three lots of, and then inside the three lots of, there is two groups, so, three lots of two lots of, and inside those two groups, you have two lots of three. So, that is three lots of two lots of two lots of, that's a two, lots of three. So, altogether this is three times two, which is six times two, which is 12, times three, which is 36. Now what factors can you see that are visible? Well, the ones that are written here, so, five, three, and four for 60, three and two for 36, what else can you see? Well, here we've got two lots three, and two lots of three, that gives you a factor of six, so I can see six. Well, you've got three lots of 12, so you know that 12 is a factor, because inside those you've got four threes, so that gives you 12, and you know you've got four threes, so you know that four is also a factor, because you can see that. What else can you see? well 36 would be another one, and also one because you can see groups of one. Those are the visible factors we can see. But we know that there are other factors, we know that, what other factors...do you know? Well, nine would other be a factor of 36, but in this representation, we can't really see the factor of nine clearly. What about from this image? Well, you can see five, three, and four. Well, you can see three lots of four, so you know that 12 is a factor. What else can you see? Well you can see five lots of three, five lots of three, that gives you 15 as a factor. Well, five lots of four also you can see in there, and so that gives you twenty as a factor, we've got five lots three lots of four. And with this representation, these are the factors that are visible to you. Other representations will show you different factors. In this explore task, a student is asked to draw a diagram showing three lots of two lots of five, which is wrote, written as, three multiplied by two multiplied by five. I'll draw a diagram for these statements and find an expression also. Pause the video here, and give this a go. Okay, let's see what you should have come up with. Well, our diagram for two lots of three lots of two, well, you see what we have? We've got two lots, I should have said, two lots of and then inside we have three lots of two. Can you see that? So how can we write this? This is two lots of three lots of two. And what does that give us? Well, three lots of two, that is six, multiplied by two, that is 12. This diagram, you can see that we have three lots, and then inside that, we've got two lots of two. Can you see that? Good. So that is three, this one would be three multiplied by two multiplied by two, which gives us, another way of writing 12. And then here, you've got two lots of two lots of three. Well, if you look at this, you've got two lots of what? Two lots of three. That should have been, around the three. Can you see that? So that is, two lots of and again, that gives us 12. This should be brackets, but my pen today doesn't seem to want to work. Well, if you look at these, these are all different representations of 12. Each representation helps us expose different factors. What factors can you see from the first diagram? Well, you can see the factors of three, and the factors of two, and also, three lots of two, well that gives you the factor of six. What about the second diagram? Well, you can see the factor of two, which you've already seen, you can see the factor of four, what else can you see? Well, three lots of four, that gives you 12, well, two lots of six gives you 12, so we know that 12 will be a factor of 12, and also you've got 12 ones. And then in this diagram, you can see the factors of three, and six. So, if you can see, these three representations of 12 helps, help us to expose all of the factors of 12. So, all of the factors of 12 have been exposed in these three different representations of 12. So, I hope that you enjoyed today's lesson. If you want to share your work, ask your parents to to share your work on twitter, tagging @OakNational #LearnwithOak. I will see you again next time. Bye for now.

Which of these is not a factor of 36?

What do we call numbers that have exactly two factors?

What type of number has an odd number of factors?

Which of these numbers in a common factor of 12 and 18.

Which of these numbers is not a common factor of 20 and 24

Exposing factors

In this lesson, we will be looking at how different representations of numbers can help us expose factors of numbers.

Maths

Y7 Maths

Key Stage 3

Year 7

Factors and multiples

Number

THEME

UNIT

Factors and primes

Prime factors

Square numbers

Factor polygons

Common multiples

Number grids

Which of these is not a factor of 24?

What is the lowest common multiple of 2, 3, and 5?

Which algebraic expression represents multiples of 8?

Which expression can be used to represent all the following set of numbers?   3, 5, 7, 9, 11...

What is the first prime number?

What are the prime factors of 18?

Which of the following is not a prime factor of 42?

Write 144 as a product of 2 square numbers both bigger than 1.

Lesson overview:Exposing factors

Core Content

Factors and multiples: