Lesson video

Hi everyone, thank you for joining me here today for your math lesson.

My name is Ms. Jeremy and today we are focusing on ordering and comparing five digit numbers.

Get yourself sorted with a nice private space, free from distractions and when you're ready, press play to begin your lesson.

Okay, let's begin by looking at our lesson agenda.

We're going to begin with a warmup where we find the greatest value using a place value charts.

We are then going to be looking at placing numbers on a number line, and then calculating missing intervals before our independent task and quiz at the end of the lesson.

For today's lesson, you will need a pencil and some paper and a nice quiet space.

So get yourself sorted with those resources, pause the video and press play when you're ready to begin.

Let's start with our warmup for today.

So we've got a question here that says, which number has the greatest value? How do you know? We're looking at two different numbers, both of them are actually quite similar, they use the same digits, but they have different values and we need to work out which one has the greatest value.

So recapping, just having a little think, how could we use a place value charts to identify which of these two numbers has the greatest value.

I'm going to give you five seconds.

Okay, so there are a couple of different ways we can do this, but the way I like to do this is to put both of those numbers into the place value chart and compare them using the place value columns to help us.

So let me get started.

I'm going to put 71,561 into our place value chart first, and just below it, I'm going to put in 71,516.

And actually see these numbers are very, very similar, it's just the last few digits that are different.

So what we're going to do to compare these numbers and work out which one is greater, is we're going to start with a ten thousands column and work our way across the screen from left to right making comparisons with those digits.

So I can see the numbers in the ten thousands columns are both seven there, the digits are both seven, that means they're both equal to 70,000.

There aren't any differences there, I can't make a comparison.

I'm going to have to move over and take a look at my thousands.

Again here, we can see the digits are exactly the same, so we're going to have to look at the hundreds.

Again, the digits in the hundreds are also exactly the same, so we'll have to look at the tens.

Looking over at the tens you can see that actually in the tens column, we do have a difference.

We can see that the first number has a six in the tens, which is equal to 60 where the second number has a one in the tens, which is equal to 10.

So therefore my first number, 71,561, must have the greater value.

It must have the greatest value.

So that shows you how we can use a place value charts to make comparisons between numbers and work out which one is greater.

Okay, let's move on to our main task.

Today we're going to be looking at placing numbers on a number line.

So I've got number line just here on our screen, and you can see I've got some blue arrows pointing to different numbers that haven't been marked on our number line.

And our challenge today is to try and work out what those arrows are pointing to.

I've got a little success criteria to help us with this.

The first thing that we're going to do is calculate the intervals.

Now an interval is a space on a number line.

On our number line here, we have two types of intervals.

We have our larger intervals, which are denoted with this longer lines here, and these are actually already been marked for us.

We've got 1,000, 2,000, 3,000, 4,000.

That means they're spaced 1,000 spaces apart because they're going up at a 1,000.

So our larger intervals are equal to 1,000.

We've also got these small intervals here and I need to calculate what those small intervals are equal to.

Well, let me explain how I do it.

If I know my large intervals are equal to 1,000 and there are 10 small intervals in each large interval, and I can count them, I can see one, two, three, four, five, six, seven, eight, nine, 10.

There are 10 in between.

Then if I do 1,000 divided by 10, that will tell me what a small interval is worth.

1,000 divided by 10 is equal to 100.

So one of those very small intervals is equal to 100.

So I've done the first step on our success criteria.

I've calculated that my large intervals are equal to 1,000 and my small intervals are equal to 100.

The next step that we need to do to work out what this first blue arrow, and I'm going to call it arrow a, is pointing to, is to look at the number that comes before it and the number that comes after it, because whatever is before and whatever is after this will help us work out what that number is in the middle.

Well I can see that the number before it is 2,000 and the number that comes after is 3,000.

And for arrow a, it is, and you might have noticed it's directly between 2,000 and 3,000, it is halfway between.

what is the number halfway between 2,000 and 3,000? Well, I know that must be 2,500 because 1,000 divided by two halfway between, it's 500.

So a must be equal to 2,500.

Great stuff.

I looked at the number before and I looked at the number after, and then I identified the value.

Let's look at arrow b, which is just this arrow here.

Let's see if we can work out what this one is equal to.

This one is a little bit more tricky.

First of all, I'm calculating my intervals, I've already done this, I know my larger intervals are equal to 1,000 and my smaller intervals are equal to 100.

So I've done that.

I'm going to look at the number of before and after, I can see the number before is equal to 4,000 and the number after is 5,000.

So this just somewhere between that.

In this case, it's not exactly halfway though.

Actually in this case, I can see that there are four small intervals after 4,000 to get to this number.

So I'm going to count up in my hundreds.

I'm going to start with 4,000, 4,100, 4,200, 4,300, 4,400, b must be equal to 4,400, I'm going to write that in there.

Again, following my success criteria really simply.

last one, let's look at c, I'm going to write c up here, this is c just here.

First thing I'm going to do is calculate my intervals, I've already done that, my larger intervals are equal to 1,000, my smaller intervals are equal to 100.

So I've done that, I'm now going to look at the number before which is 8,000, and the number after which is 9,000.

And this one is extra challenging because it actually points in between two small intervals.

So let's see if I can work out what those two small intervals are.

Well, here I go with counting up in my hundreds until I get close to the arrow.

I'm starting at 8,000, 8,100, 8,200, 8,300, 8,400, 8,500, 8,600.

It's gone slightly over 8,600, but it's not quite at 8,700.

It's halfway between.

So the number halfway between 8,600 and 8,700 is 8,650, because I know the halfway between my 600 and my 700 is 650.

So here I followed my steps, look at the number before, look at the number after, let that help you identify the value that the arrow is pointing to.

So in this case, our intervals was spaced, our larger intervals were spaced 1,000 apart and a smaller intervals of space 100 apart.

Let's have a look at another example.

For this one, we've got a slightly different scale, we've got slightly different intervals.

We're starting here at zero and the next number is 10,000 for our larger interval.

Let's count upwards, 10,000, 20,000, 30,000, 40,000, and so on and so forth.

If our larger intervals are equal to 10,000, I wonder whether you can work out what our smaller intervals are equal to.

There are 10 small intervals and one large interval, and one large interval is equal to 10,000.

Let me give you five seconds to work out what those small intervals are worth.

So you might have seen that if a larger interval is equal to 10,000, well, 10,000 divided by 10, which will tell us what one small interval is equal to is equal to 1,000.

So our larger intervals, our LI, are equal to 10,000 and our small intervals, our SI, are equal to 1,000.

That is going to help us a lot, and actually we've done our first success criteria there, we've calculated the intervals.

What I'd like you to do now is pause the video and see if you can use that information, and use the success criteria to identify the values that arrow a, b and c are pointing to.

Okay, how did you get on? Let's have a look at the answers and see how they match up.

So answer a, for a we've got, it's between 30,000 and 40,000, is equal to 35,000.

For b, We've got a number between 50,000 and 60,000 and is equal to 53,000.

And for c it's a number between 70,000 and 80,000, and it's equal to 76,000.

How did you get on using our strategies and our methods? Shall we make it a little bit more challenging? Let's have a look at our next example.

So in some cases, you will have to calculate the missing intervals on a number line when we don't have many denoted, and that means kind of shown numbers on our number line.

So in this case, we can see that we've been given the starting number, 40,000 and the finishing number 90,000, but we don't know what the larger intervals are in between, and we don't know what the smaller intervals are either.

We're going to have to calculate those first.

So remembering back to our success criteria, we're going to calculate our intervals first.

I like to use a little method here called trial and error.

Trial and error is when you give something a go, test it out and see if it works.

If it doesn't work, you try something else.

Trial and error is a really good method to use if you're unsure of what the missing intervals are on a number line.

So let's have a practise at this, when I'm looking at my starting number, I can see it's 40,000 and I can see my finishing number is 90,000.

I wonder whether these larger intervals here are going up in thousands, in one thousands.

I'm going to test it out, let's see.

I going to count up in one thousands to see if it gets me to 90,000 when I count up.

Let's try it.

40,000, 41,000, 42,000, 43,000, 44,000, 45,000, it doesn't work.

That doesn't work.

So it doesn't go up in one thousands.

Let's have a think about what else it could be.

What if it's not one thousands, could it maybe be, could those large intervals be ten thousands? Let's try, let's count up in our ten thousands.

40,000, count with me, 50,000, 60,000, 70,000, 80,000, 90,000, yeah, that works.

So I know my larger intervals are spaced 10,000 spaces apart.

And if I want to, I can actually fill in the numbers here, so I know that's 50,000, the next large interval is 60,000, what's the next one? 70,000, I'm running out of space here so I'll just write it here, 80,000, and we know the last one is 90,000.

Great, we've used trial and error to work out on larger intervals.

Now let's see using that information, whether we can work out what the small intervals are worth.

What if I know my larger intervals are spaced 10,000 apart, and there are 10 small intervals in one large interval, using our division, can we work out what the smaller intervals are worth? I'm going to give you five seconds.

So hopefully you've seen that they are worth 1,000 each.

So I know my larger intervals are 10,000 and my smaller intervals are 1,000.

Now I can complete the rest of my success criteria.

So I've calculated the intervals, I'm now going to look at the numbers before and after my different arrows and see if that can help me to work out what they are equal to.

So for a, I can see that the number before a is equal to 40,000 and the number after it is 50,000.

And if I count up in my thousands, I can work out what a is equal to.

So here I go, 40,000, 41,000, 42,000, 43,000, 44,000, 45,000, 46,000, a is equal to 46,000.

A nifty little method that you might like to use is to actually just work out the midway point.

I can see here, this is my midway point, that must be 45,000, one more 1,000 above that is 46,000.

That's a much quicker way than counting up all the way from 40,000, but either method works absolutely fine.

Let's look at b.

B is a nice easy one because it's halfway between two of the intervals.

It's halfway between 70,000 and 80,000.

Which number is halfway between 70,000 and 80,000? It must be 75,000, b is equal to 75,000.

And if you wanted to count upwards, you could do that as well.

And c its a slightly more challenging one because it's between two small intervals, let's have a look at it.

So I can see it as between 80,000 and 90,000, and here, this little interval here must be 81,000, so the next one must be 82,000, it's halfway between 81,000 and 82,000, c must be equal to 81,500.

And that explains to me exactly where c is located using that method looking at the number before and looking at the number after.

So you can see one of the key points I want you to pay attention to here, is how important calculating your intervals is.

If we had just gone with my initial assumption, that the larger intervals were equal 1,000 instead of 10,000, I would have actually found that I would have got completely the wrong answers here.

So you must check those intervals first because they will change according to the scale that your number line is using.

Let's have a look at another example.

So again, same method, but this time we started with 60,000 at the beginning, and the last number on my number line is 70,000.

And I can see that there are 10 spaces on my number line.

So I wonder whether I can use this to help me work out what those larger intervals are.

I'm going to use that method, that trial and error method I spoke about.

I'm going to have a guess.

I'm going to guess that b's larger intervals, these ones here that are the longer lines, are equal to 1,000.

And I'm guessing that.

It's an educated guess because I've got 60,000 here and 70,000 here.

The larger intervals equal to 10,000 this time.

It wouldn't work because if I was counting up in 10,000, that first large interval will be 70,000 and that's actually my own number.

It can't be that.

So I'm going to guess the larger intervals are equal to 1,000 but I need to test out first.

I'm going to count up in my thousands and see if it works.

Starting with 60,000, count with me.

60,000, 61,000, 62,000, 63,000, 64,000, 65,000, 66,000, 67,000, 68,000, 69,000, 70,000, brilliant.

The larger intervals are equal to 1,000.

My educated guess was correct.

So, if my larger intervals are equal to 1,000, and there are 10 small intervals in between my larger intervals, what are those smaller intervals equal to? Going to give you five seconds to work it out.

They are equal to 100.

Yeah, that's right.

So it's 100 for our smaller intervals.

So, if we know that information, let's have a look at what the arrow a is pointing to.

So first of all, I need to remember that these larger intervals, and I haven't written them in this time, I need to remember exactly what they are.

So this arrow a is between 61,000, 'cause I remember that that is going up at a thousands, and 62,000, and it is at 200 after 61,000.

So it must be equal to 61,200.

Because I can see and if I want to, I can count up in hundreds.

I can go 61,000, 61,100, 61,200, perfect.

What about b? See if you can work out what b is.

I'm going to give you five seconds.

Is pointing to one of our larger intervals, but you might need to count upwards to just remind yourself what that is.

You can either count up from 60,000 or backwards from 70,000.

It's up to you, five seconds.

Okay, did you get it? Let me count upwards and see if we get the same answer.

So I'm here at 62,000, 63,000, 64,000, 65,000, 66,000, 67,000, b is equal to 67,000.

And that's a simple one because it's right on one of our larger intervals.

And this one should say c here, I'm just going to change that for you, we've got c, let's have a look what c is equal to on our number line.

So I can see that c is past my next 1,000, so this is 68,000 here, and this one be 69,000.

So it's between 68,000 and 69,000, and it is, if I have a look, it's past 68,200, but it's not quite 68,300.

What is halfway between 68,200 and 68,300? So it must be 68,250.

I know that 50 is halfway between my hundreds, so, 68,250 is the value for c.

How did you get on with those ones? Ready for a bit of a challenge? Let's try this one.

I'd like you to have a go at this on your own and use the same method that we've been using.

It's going to be very important that you calculate those intervals first, because here, your larger intervals are not necessarily what we've been working with so far.

Have a look at this question, pause the video when you're ready, calculate your larger intervals, your smaller intervals, and then those values in between.

okay, how could you get on? So you might have noticed, that in this case, our larger interval are a lot smaller, if that makes sense, than we've previously been working with, because actually my first number here is 65,000 and my last number 66,000.

They can't be going up in ten thousands, they can't be going up in thousands, those larger intervals are going up in one hundreds.

So each larger interval hear, is equal to 100.

That means that my smaller intervals were equal to 10.

Did you get that correct? If so, you might have managed to get the answers that we've got on screen here.

A is equal to 65,120, b is equal to 65,700, and c is equal to 65,825.

That was really tricky because it was in between 65,820 and 65,830.

We had to look at the halfway point.

So this one was a little bit more challenging because the intervals were actually a lot smaller than we've previously been working with.

And it shows you larger intervals could be equal to 10,000, they could be equal to 1,000, they could be equal to 100, they might even be equal to 10.

You can be dealing with intervals that are equal to any different number, they might even be equal to a number that isn't a multiple of 10, so they might be equal to seven or 29.

The thing about intervals to always remember is that they're always equal to each other.

So if one larger interval is worth 100, the next one that must be too, if your scales are accurate.

So this is our independent task for today's lesson.

What I'd like you to do, I'll just rub this out so you can see it nice and clearly, is to look at these three number lines.

I want you to use the success criteria that we've been working with to calculate the larger and smaller intervals first, and then identify the numbers that are located at the different arrows.

We've got arrow a, b and c for the first number line, d, e and f for the second, g, h and i for the third.

But each of those number lines, there will be a different scale, there will be different larger intervals and different smaller intervals.

So you are going to have to calculate each one individually before you work out what those arrows are pointing to.

Pause the video when you're ready and come back to complete your activity and come back once you've completed your activity to have a look at the answers.

Okay, you ready to go through the answers together? Let's have a look.

So, I've got you the answers for a, all the way through to f and you can see them now on the screen, we had different larger intervals and smaller intervals to calculate.

But I wanted to have a look at g, h and i together.

'cause I think this one was probably the most challenging.

So let's have a little peak at g, h and i together and use our success criteria to work out what these arrows are pointing to.

Okay, so you might have seen that in terms of this number line here, our larger intervals are equal to 10 and our smaller intervals equal to one.

So we're going up in tens to help us first of all.

This first one here is 51,210, and that is going to help us work out what g is, because g is between 51,210 and 51,220.

And I can count up in my ones, those are the smaller intervals to work out what g might be.

So I'm going to start with 51,210, go up in ones, 51,211, 51,212, 51,213.

I should see that g is equal to 51,213.

Again, using that same method, I'm going to work out h.

So this one would be 51,220, 51,230, 51,240, 51,250, and that's two above, so it's 51,252.

And the last one, I'm again counting up in my tens first of all, I knew this one was 51,210 51,220, 230, 51,240, 51,250, 51,260, 51,270, 51,280, and this one is three above 51,283.

So in this case, our larger intervals were a little bit smaller than what we'd worked with previously, hopefully you managed to use that to help you work out what those arrows were pointing to.

So we've come to the end of our lesson.

If you would like to, please ask your parent or carer to share your work, the work you've done today on Twitter, tagging @OakNational and #LearnwithOak.

Now it's time to complete your quiz.

Thank you for joining me today, it's been great to have you.

Join me again for some more math soon.

Bye.