Lesson video

Hello there.

My name is Miss Coe.

I'm really excited to be learning with you today.

I know we're going to have lots of fun, and I know that you are going to put loads of effort into this lesson.

If you're ready, let's get going.

So this lesson is the last lesson in thinking about three digit numbers, and by the end of the lesson, you're going to be able to solve problems by counting in multiples of 2, 20, 5, 50, and 25.

Let's get going.

Our keywords today are multiple and pattern.

I'm going to say them, I'd like you to say them back to me.

My turn, multiple.

Your turn.

My turn, pattern.

Your turn.

Well done.

Let's look at what those words mean.

A multiple is the result of multiplying a number by another whole number.

So 10, 20, 30, are all multiples of 10.

Two, four, six and eight are all multiples of two.

A pattern is when objects or numbers are arranged following a rule.

A pattern is a repeated set of numbers, shapes, or objects.

And you might be familiar with some patterns already.

Our lesson today has two cycles.

We're going to first look at number lines with missing labels, and then we're going to think about problems with bar charts.

Let's get started with the first part of our lesson.

In this lesson today, you're going to meet Sofia and Andeep.

They're going to be helping you with your learning and asking you some tricky questions to deepen your understanding.

Andeep and Sofia are counting in multiples of two and 20.

So Sofia is reminding you of something you might already know.

When you count in multiples of two, the ones digit is always two, four, six, eight, or zero.

So if we look at an example here, we have 32 and 34.

Let's carry on that count.

Are you ready? 36, 38, 40.

We've counted in multiples of two, and you can see the ones digits is two, four, six, eight, and zero.

That is always true when you count in multiples of two.

Andeep is reminding you of something else you might know, that when you count in multiples of 20, the tens digit is always two, four, six, eight or zero.

So if we think about 320, we're counting in 20 so the next number will be 340, then 360, 380, 400, and you can see that the tens digits have the same pattern as the ones digits in multiples of two.

This is gonna be really helpful for spotting some missing numbers.

These patterns repeat any time you count in multiples of two or 20.

Andeep and Sofia are also going to count in multiples of five and 50.

And again, you might be familiar with the idea that when you count in multiples of five, the ones digit is always a five or a zero.

So if we look at these numbers, counting in fives, you can see that the ones digit is a zero or a five.

"When you count in multiples of 50," says Andeep, "the tens digit is always five or zero." Let's take a look at an example.

Here, we are counting in multiples of 50, and you can see that the tens digit is a five or a zero.

This pattern, like the twos and 20s, repeats any time you count in multiples of five or 50.

Andeep and Sofia are also counting in multiples of 25.

And Sofia is reminding you of something else you might know, that when you count in multiples of 25, the ones and tens digits follow a pattern.

Let's count together.

We're going to start at 200, and count in 25s.

Are you ready? 200, 225, 250, 275, 300, 325, 350, 375.

Well done.

What do you notice about the tens and ones numbers in these numbers? That's right.

The pattern goes 25, 50, 75, 0.

And that happens anytime you count in multiples of 25.

So let's apply that understanding to missing numbers on this number line.

We have a number line here, and we can see that we have two marked intervals.

200 at one end, 300 at the other end.

"What count is the number line representing?" asks Sofia.

Andeep says we can try and solve this problem by counting in different numbers.

So let's try that together.

Andeep tries counting in multiples of five.

So where we see a mark on the number line, we're going to try and count in multiples of five.

Can we count with him? 200, 205, 210, 215, 220.

Oh dear.

Well that doesn't work, because the next number should be 225, but we've got 300 at the end of our number line.

So it's not representing counting in fives.

Hmm.

"It can't be in multiples of two, either," says Sofia, "because the last number would be even smaller." That's a great spot, Sofia.

Sometimes we don't need to check every single multiple that we can count in.

So they try counting in other multiples.

Sofia is going to count in multiples of 25.

Let's see if we can count with her.

200, 225, 250, 275, 300.

oh.

Oh, I've got two 300s now.

Oh dear, that can't be right.

300 is reached too soon.

So it can't be counting in multiples of 25 either.

Sorry, Sofia.

Andeep is gonna try and count in multiples of 20.

Let's count with Andeep.

200, 220, 240, 260.

280, 300.

Hurrah! Brilliant.

Well done, Andeep.

The count is in multiples of 20.

So we had to try a few different times, but we got there in the end.

Well done, Andeep and Sofia.

They're going to look at another number line now.

So this time our count starts at 320, ends at 360, and we have some missing intervals there.

So Andeep is saying to help us out a bit, he knows that 320 is not a multiple of 25 or 50.

So we're ruling out the count being in 25s or 50s.

So it's not one of those.

That's a good start, I think.

Sofia says, "Well, it can't be in 20s either because we're only going from 320 to 360.

If we were counting in 20s, we'd go 320, 340, 360.

We'd meet 360 very quickly, so it can't be that either." So they think the count is in multiples of two or five.

Let's have a look.

Sofia is going to check by counting in multiples of two.

Let's count together.

320, 322, 324, 326.

328, 330, 332, 334.

Oh.

My next number isn't 360.

Sorry, Sofia.

It can't be that, because the next number in my count would be 336, not 360.

So I think Andeep might be right, but let's count together to check.

We're going to count in multiples of five.

Are you ready? 320, 325, 330, 335, 340, 345, 350, 355, 360.

Great job, Andeep.

The count is in multiples of five.

Sofia and Andeep label another number line.

So this time the count starts at 400, ends at 500, and we have a few missing intervals.

Andeep has spotted something.

He says "There is a difference of 100 between 400 and 500." So whatever this label is, to get from 400 to 500, we're going to count 100 in some sort of step.

So Sofia says, "Well because of that, the count can't be in multiples of two or five because there aren't enough intervals, there aren't enough gaps between 400 and 500.

If you imagine how many numbers you have to say to get from 400 to 500.

If you're counting in twos, that's a lot more than those intervals.

It's a really good spot, Sofia.

Well done.

So they think it must be in multiples of 20 or 25.

Sofia counts in multiples of 20.

Let's have a look.

400, 420, 440, 460.

Oh, that's really close, isn't it? But not quite because the next one would be 480, not 500.

So Andeep's going to count in multiples of 25.

Let's count together.

400, 425, 450, 475, 500.

The count is in multiples of 25.

Well done both of you for working that out.

Time to check your understanding.

I'd like to find the missing labels.

So we have a number line here with 200 at one end, 210 at the other end.

Think about is the count in 2s, 20, 5s, 50s, or 25s? Pause the video here, have a go.

Welcome back.

How did you get on? Sofia is reminding us that we need to look really carefully at the difference between the start and end numbers.

So 200 and 210 are really close.

I don't think it's counting in 50s because my next number would be 250, which is far too big.

Well done if you identified that the number line was counting in twos, and realised that the missing numbers were those shown on the screen now.

And so this time they have 400 and 800 at one end.

Andeep is reminding us that there is a difference of 400 between 400 and 800.

So Sofia says, "Well actually, that must mean the count must be quite a big number." Again, if we tried to count in twos from 400 to 800, we'd be there for quite a long time.

So is the count in multiples of 25 or multiples of 50? Andeep is going to count in multiples of 25.

So let's see, 400, 425, 450, 475, 500, 525, 550, 575.

Oh dear.

We're still quite a way from 800.

The next number should be 600 and not 800.

So it's not that.

Sofia is going to count in multiples of 50.

So we've got 400, 450, 500, 550, 600, 650, 700, 750, 800.

Excellent work, Sofia, the count is in multiples of 50.

So Sofia and Andeep are labelling yet another number line and this time they're going from 250 to 270.

Andeep has identified that the count cannot be in 20s because 250 is not a multiple of 20.

So we can't be going up in 20s.

And 270 isn't a multiple of 25 or 50.

So we're discounting some of the different counts there.

So Sofia says the count could be in multiples of two or five.

Have a little look at that number line.

What's your prediction? What do you think the count's going to be? Let's have a look.

So who is right? Sofia thinks that the count is in multiples of two.

Andeep thinks it's multiples of five.

Who's correct? Work it out for yourself.

Pause the video here, have a go.

Welcome back.

Now it's absolutely fine if you needed to count both times to see.

That's perfectly fine.

But if we count in twos, we can see here that we've got enough intervals to get from 250 to 270 counting in twos, which means that Sofia is correct.

Well done if you said that.

Let's think about a slightly trickier task.

Let's look at the number line.

The number line counts in multiples of two or five or 20 or 25 or 50.

We know the last number is 300 and there are one two three four five empty boxes.

What could the first number be? Hmm, that's tricky.

Andeep says he's going to count backwards in multiples of 25.

Let's count backwards with Andeep.

300, 275, 250, 225, 200, 175.

If the number line is in multiples of 25, then the first number is 175.

What if it was in one of the other multiples? I'd like you to find a different answer.

You might have a different answer to your partner, so if you happen to have a partner with you, compare answers.

Pause the video here and have a go.

Welcome back.

How did you get on? There are different solutions depending on what multiples you counted in.

But if we can counted in multiples of five and we counted backwards, our first number would be 275.

Now it would depend on what multiples you counted in, so don't worry if you didn't get 275.

Time for your first practise task.

I would like you to label the missing numbers on each of these number lines.

So be really careful.

Think about what we're counting in.

The first one starts at 200, ends at 300.

There are four missing numbers.

What intervals, what steps are we counting in? For question two, I'd like you to do the same thing.

So we've got different number lines here.

We've got 450 at one end of the first one, 460 at the end of the second one.

And for question three, the number line counts in multiples of 2, 5, 20, 25 or 50.

How could you label the numbers? So we have three identical number lines.

How could you label the numbers? Pause the video here, have a go at those three tasks, and then come back when you're ready for some feedback.

Welcome back.

How did you get on? Let's look through the answers.

Here are the completed number lines for question one.

So if you think about the first number line, we can see that we counted in steps of 20.

So we have multiples of 20.

Pause the video here if you need to, to mark your work.

For question two, you also had to label the missing numbers.

So again, we had to think carefully about what steps, what multiples we were counting in.

Well done if you recognised the different multiples that we were counting in.

Three, there were different answers depending on what you were counting in.

Let's look at the first one that I've written.

900, 850, 800, 750, 700, 650.

What multiple was I counting back in? That's right, I counted back in multiples of 50 for that one.

You might have chosen multiples of two or five.

That's absolutely fine.

So have a think, make sure that you've got the right multiples.

Let's move on to the second part of our lesson, where we're looking at bar charts.

The graph that we are going to look at shows the number of children who have packed lunch each day.

So here we have the graph, and we can see that on this side we have the number of children, and then we have the days of the week.

So the bars represent Monday, Tuesday, Wednesday, Thursday, and Friday.

Now, we don't know what the count is.

So there are no numbers on my x axis, my vertical axis.

We don't know what the count is.

"It could be in multiples of 2, 5, 20, 50, or 25," says Sofia.

Let's have a look.

We can use the graph to work out the answers to the questions though.

So even though we don't know what the multiples are, we can work it out.

If five children had a packed lunch on Wednesday, how many children had packed lunch on Tuesday? Let's look at the bar for Wednesday.

The count must be in multiples of five because there is only one block for Wednesday.

So that block represents five.

So that means the count must be in multiples of five.

So we can count in multiples of five to find out the lunch on Tuesday.

So the bar before Wednesday.

Let's count up in multiples of five.

5, 10, 15.

The bar for Tuesday is the same height as 15.

So in this example we were counting multiples of five, 15 children had packed lunch on Tuesday.

If five children had packed lunch on Wednesday, so the same count, how many children had packed lunch on Thursday? So find the bar for Thursday and let's count in fives.

5, 10, 15, 20, 25, 30.

The bar for Thursday is as tall as 30.

So therefore, 30 children had packed lunch on Thursday.

So let's change the count.

This time, if 20 children had packed lunch on Wednesday, how many children had packed lunch on Friday? So this time the count must be in multiples of 20 because the Wednesday bar is the same as 20.

So we can count up in multiples of 20 to find the answer.

So this time we're looking at the bar for Friday.

Let's find the bar for Friday and count in 20s.

20, 40, 60, 80.

The Friday bar is as tall as 80, which means that 80 children had packed lunch on Friday.

Time to check your understanding.

If 50 children had packed lunch on Wednesday, how many children had packed lunch on Thursday? Think about what you're going to count in.

Pause the video here and have a go.

Welcome back.

How did you get on? So 50 children had packed lunch on Wednesday.

That means we need to count up in multiples of 50.

Hopefully you found the bar for Thursday, and you counted all the way up to 300.

So 300 children had packed lunch on Thursday, very big school.

Now we're going to start with a different bar.

If six children had packed lunch on Tuesday, how many children had a packed lunch on Monday? So this time we're starting with the Tuesday bar.

The count must be in multiples of two, because if we count 2, 4, 6, that is the same height as Tuesday.

So now we need to carry on counting in multiples of two to find out the value of the bar for Monday.

So we've got two, four, six, eight, 10.

We've reached the height of Monday's bar.

So therefore 10 children had packed lunch on Monday.

This time we're sticking with Tuesday, but Tuesday now represents 75 children.

How many children had a packed lunch on Monday? So we can count in multiples of 25.

So we can get 25, 50, 75.

That's the same height as Tuesday.

So Tuesday represents 75.

And then we can keep counting to find the value of Monday's bar.

100, 125.

That's the same height as Monday's bar.

So that means 125 children had a packed lunch on Monday.

Time to check your understanding.

This time, 60 children had packed lunch on Tuesday.

How many children had packed lunch on Monday? Sofia's reminding you to think about what you're going to count in.

Pause the video here and have a go.

Welcome back.

How did you get on? Well, if Tuesday is worth 60, then I can count in multiples of 20.

20, 40, 60 gives me Tuesday's bar and I can keep going to get to Monday.

60, 80, 100.

That's the height of Monday's bar.

So that means 100 children had packed lunch on Monday.

Well done if you said that.

For your final practise task of this lesson, you're going to use this chart here.

So we've got number of people, days of the week again, but this time we have got the number of people visiting the cinema.

So we can see Wednesday, Thursday, Friday, Saturday and Sunday, and the number of people who go to the cinema.

So this chart is the one you're going to be using for all of the questions.

We need to think about the answers to these questions.

So let's look at number one, if 10 people went to the cinema on Wednesday, how many people went on Thursday, Friday, Saturday? So to remind you, if the Wednesday bar is now worth 10, what do we need to count in to find out how many people went to the cinema on Thursday, Friday, Saturday? So use that graph to help you answer those three questions.

You've also then got D, E, and F to have a go at using the same graph.

Pause the video here, have a go at those questions and come back when you're ready for some feedback.

Welcome back.

How did you get on? I know you'll have had to do, have done a lot of counting there and a lot of concentrating, thinking about which bars you were looking at.

So if 10 people went to the cinema on Wednesday, that would mean that 40 went on Thursday, 55 on Friday, 75 on Saturday.

If 40 people went on Wednesday, that would change the numbers, remember? So that would mean that 220 people went on Friday, 300 went on Saturday.

And then if 50 people went on Wednesday, that would change the numbers again.

So you would have 200 on Thursday and 300 on Sunday.

Well done if you got those correct.

For D, if 400 people went on Thursday, so hopefully you're looking at the right bar, that meant 100 people went on Wednesday, 550 people went on Friday, 750 people went on Saturday.

160 people went on Thursday, that would mean 240 people went on Sunday.

And then finally, tricky one, if 275 people went on Friday, 375 people went on Saturday.

Well done if you've got all of those correct.

That was a lot of counting and some tricky problems. We've come to the end of the lesson and I know how much effort you have put in to answer those questions and to do all of that counting.

Let's summarise our learning.

We can use patterns to help us work out whether a number is a multiple of another one or not.

So remember, multiples of 50 always have five or zero as the 10s digit.

So that helps us find if there are multiple.

To find missing numbers, we can count in different multiples to see whether the count works.

Thank you so much for learning with me today and I look forward to seeing you again soon.