Lesson video

Hello, and welcome to another lesson.

In this lesson, we'll be looking at Representing Integers.

I am Mr. Maseko.

Before going on with today's lesson, make sure you have a pen or pencil and something to write on.

If you don't have those things, please go and get them now.

Okay, now that you have those things, let's get on with today's lesson.

First try this activity.

Pause the video here and give this a go.

Okay, now that you've given this a go, let's see what you've come up with.

So filling in the gaps, six would be equal to two multiply by, well three.

Correct.

12 as two multiplied by three, and then multiply by two.

Plus two times three gives you six, times two it gives you 12.

18 could be three times two times three.

36 could be six times two times three.

36 another way to write 36 you could write, two times two times nine times one.

Is there another way we could've written, any of these numbers? Well, 12 you could've written this as, two times six times one.

What about 18? Is there another way we could've written that? Well, you could've written, three times six times one.

36, is there another way you could've written 36.

Well let's do that on filling in the blanks, or you could've written, three times three, times okay that's nine times four.

Another way, nine times two, times two.

Okay, are there any other ways that you came up with? Good, as long as your multiplications, multiply to give you 36, that is an equally valid way to do it.

Now let's look at this picture.

Now in this picture, we have the integers one to 12, and there represented using different diagrams. What do you notice about the multiples of three? What do you notice about the multiples of four? And is there another way we could've drawn, any of those diagrams? Pause the video here and give this a go.

Okay, let's see what you've come up with.

Well, if we look at all the multiples of three.

This is three, and all the multiples of three, the next one is six have that triangle structure in them.

So three, six, and nine, they all have that triangle structure in them.

Look at the multiples of four, the multiples of four all have this square structure in them.

If you look at the number 12.

12 is both a multiple of three and a multiple of four.

But the way it's been drawn, it's been drawn with a base of four in mind.

How could we show that 12 is also a multiple of three, using the base structure for three? Instead of drawing, three lots of four, we could have drawn four lots of three.

Now pay attention to the language am using.

So instead of drawing three lots of that square structure, that show that 12 is a multiple four, we could have done four lots, of the triangle structure, that shows, that three is a multiple of 12.

So that triangle structure remember contains, three dots in it.

Now let's see if we can explore this idea of representing numbers in this way any further.

Well we have two students, that discussed a strategy for counting dots in this diagram.

Who do you agree with and why? Pause the video here and give this a go.

Okay, let's see.

Well student one says I can see three lots of 12.

Well is still the one correct firstly? Can you see three lots with 12? Well yes, there three lots of 12 here.

We've already seen the picture for 12 in our previous slide.

So we can see three lots for 12.

The next student says, I can see three lots of three lots of four.

Well, this student is also correct because yes you can see, three lots of three lots, of four.

So we've got, three lots, think the big circle, there's three big circles and inside them, there's three lots of four.

So we've got three lots of three lots of four.

Both students are correct.

Is there a different way you could've counted these dots? You could have grouped these in many different ways.

Think back to the pictures that we saw at the start of this, that represented the integers from one to 12.

Well you could've said, you've seen nine lots of four.

Where do you see nine lots of four? Once you count them individually, all of these, are all fours and there is nine of them.

So you can see nine lots of four.

Or if you count the dots individually you can say, you can see 36 lots of one.

If you count them, as twos you can see 36.

Not 36, 18 lots of twos.

And if you count them, as three lots of six lots of twos.

Well, if you look at them as, this three big bundles last we had three lots, and then inside that you have six lots of two.

So you've got three lots of six lots of two.

Now another student drew two pictures, to visualise four multiplied by six.

This is a representation of four.

This is a representation for six.

Can you see how she created the diagrams? And can you draw a similar diagram to represent five multiply by three? Pause was the video here and give that a go.

Okay let's see what you've come up with.

Well if you look at that first diagram, how does she create it? Well, she has four lots of six.

That's a bad circle, she has four lots of six.

For the second diagram, what the second diagram, instead of four lots of six, she has six lots of four.

Can you see that? Good.

So what picture could you have drawn to represent five lots of three? Well, if we take this to represent five and this to represent three, you could've done.

Three lots of five, or you could've done, five lots of three.

Now here's an independent task for you to try.

Pause the video here and give this a go.

Okay, let's see what you've come up with.

So fill in the gaps.

Some of the missing words slash numbers, can used more than once.

Representing a number of using diagrams can reveal some of its properties.

One of the ways of representing, what numbers add to that is 10.

One of the way the representing 10 could be this.

This representation shows what? what can you see? Well, we can see that 10 has five lots of two in it.

So it shows that five and two are both factors of 10.

This is one way of representing seven.

This representation helps to show that, seven only has two factors, because all you can see is seven lots of one, or one lots of seven, and is therefore a prime number.

Really well done, if you got this in this.

In this explore task.

Can you figure out what sequence of numbers this group of dots is representing? What could the next pattern look like? And what can you tell, about the numbers from the representations? Pause the video here and give this a go.

Okay, now that you're trying this, let's see.

Well, what can you see? These numbers are one, four, nine, 16.

This pen is refusing to write.

This is 16 and 25.

Let's change that nine, there we go.

So what are those numbers? Well, these numbers are all the square numbers, good.

So what could the next pattern look like? Well, what's the next square number after 25? It is 36, and this is what 36 could look like.

So what can you tell about the numbers from the representations? Well, if you look at 36, you can tell that 36 well that is, six lots of six.

Within a six, what can you see? Well, within a six you can see that there are, three lots of two.

So you could tell that two is a factor of 36, and you could also tell that three is factor 36.

Did you come up with similar things for the other numbers? Well, if you look at 16, that is four lots of four.

And within each cluster of four, what can you see? We can see two lots of two.

So the same way you can tell that two, is a factor of 16.

The same way that four is a factor of 16.

If you come up with other things that, you could tell.

Ask your parent or carer to share your work on Twitter, tagging @Oaknational and # learnwithOak.

Thank you for participating in today's lesson.

Bye for now.