Lesson video

Hello, I'm Mrs. Cayley and I'm going to work with you in today's lesson.

So today we're going to estimate the position of multiples of 10 on a zero to 100 number line.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson.

So by the end of the lesson you'll be able to do this.

I can estimate the position of multiples of 10 on a zero to 100 number line.

Here are the key words for today's lesson.

Can you repeat them after me? My turn, estimate, your turn.

My turn, number line.

Your turn.

My turn, multiple.

Your turn.

Well done.

You might have seen these words before.

Look out for them in today's lesson.

Here's today's lesson outline.

We're going to estimate the position of multiples of 10 on a zero to 100 number line.

We'll start off by looking at the position on a number line and then we'll estimate multiples of 10 on a number line.

So let's start on the learning.

Here are some children that are going to help us today.

We've got Jacob and Laura.

Here's a 100 square, multiples of 10 end in a zero.

We can show them on a hundred square.

Let's chart the multiples of 10.

So we're going to start at 10.

Can you count with me all of the multiples of 10? 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

What do you notice about the multiples of 10? They end in a zero, don't they? And they've got a different tens number.

The tens number is going up by one each time.

Jacob and Laura are using sticks of 10 cubes to measure things in the classroom.

They're measuring the height of a cardboard box.

How many sticks tall is the box? So here we've got one stick of 10, two sticks of 10 and three sticks of 10.

Let's say the stem sentence together.

There are three sticks of cubes.

How many cubes tall is the box? Remember, each stick of cubes has been made of 10 cubes.

So we've got 10, 20, 30 cubes.

Let's say the stem sentence together.

There are three groups of 10, so there are 30 cubes.

If you've got some cubes you could put them into sticks of 10 and try measuring some things around you.

They have put their sticks of cubes in a line.

Can you see the three groups of 10 have been put in a line? So we've got 30 cubes.

Let's say the stem sentence together.

There are three sticks of 10.

There are three groups of 10.

So there are 30 cubes.

What is the next multiple of 10? So if we put another stick of 10 with them, how many cubes would there be? It's 40, isn't it? Let's say the stem sentence together.

There are four sticks of 10.

There are four groups of 10.

So there are 40 cubes.

What is the previous multiple of 10? So if we took away a stick of 10, how many cubes would there be? It's 20, isn't it? Let's say the stem sentence together.

There are two sticks of 10.

There are two groups of 10.

So there are 20 cubes.

You could try this with cubes if you've got some.

These cubes are in groups of 10.

How many groups of 10 and how many cubes in total can you count them as they appear? One group of 10, two groups of 10.

Three groups of 10.

Four groups of 10.

Five groups of 10.

Six groups of 10.

Seven groups of 10.

Eight groups of 10.

Nine groups of 10 and 10 groups of 10.

Can you see how many cubes there are altogether? You can count them in tens.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

So there are 100 cubes.

I've put them on a number line here.

Can you see we're counting in tens all the way to 100.

Each group of 10 is shown as another 10 on the number line.

How many groups of 10 did we have? It's 10 isn't it? And how many cubes in total? It's 100.

Let's say the stem sentence together.

There are 100 cubes, there are 10 groups of 10.

So there are 100 cubes.

We can represent the groups of 10 and total cubes on number lines.

So here are our cubes.

Here are the groups of 10.

We've got 10 groups of 10 altogether.

So the total number of cubes is 100 and we can count them by using the multiples of 10.

What do you notice? Do you notice anything the same or different about the two number lines? So the groups of 10 are going up by one each time and the total cubes are going up by 10 each time.

They start with the same number, but the multiples of 10 have a zero on the end.

What do you notice with these number lines? Can you see the first number line is going up in ones.

Jacob said the top number line goes up in ones.

So on the middle number line, I'm going to count in tens.

We've got one 10 that is equal to 10.

Two tens is equal to 20.

Three tens is equal to 30.

Four tens is equal to 40.

Five tens is equal to 50.

60 tens is equal to 60.

Seven tens is equal to 70.

Eight tens is equal to 80.

Nine tens is equal to 90 and 10 tens is equal to 100.

What are we counting up in and what do you notice about the bottom number line? Laura said then we are counting in tens.

Jacob said the numbers are the same distance apart on each line.

So they're equally spaced, aren't they? Laura said that's because one unit of 10 is the same as 10.

Jacob said so four tens and 40 have the same position.

So you can look at the number four and four tens and 40 and they are all in the same position, aren't they? On the number lines? Knowledge of counting to 10 can help you counting tens to 100.

So if you are good at counting in ones, like the top number line, you can use that to help you count in tens on the bottom number line.

What do you notice here? Can you see we are counting in ones and then counting in tens and the numbers can have the same position on the number line.

Jacob said we can count in tens or ones.

Laura said one 10 is the same as 10, two tens is the same as 20.

Counting in tens is like counting in ones.

The tens numbers look like the ones numbers but end in zero.

Here we've got the two number lines.

The top number line is counting in ones and the bottom number line is going up in tens.

What multiples of 10 are missing and how do you know? Look at the bottom number line.

There are two numbers missing.

What do you think they are? Jacob said 30 is missing, which is three tens.

Do you know where it's going to go? Laura said, I agree.

It is between two tens and four tens.

So there it is on the number line.

What other number is missing on the number line? Jacob said eight tens is also missing.

We write this as 80.

Laura said, agreed it is one 10 less than 90, which is nine tens.

So there's 80 on the number line.

Let's check your understanding.

Can you spot the mistakes here? We've got a number line going up in ones and a number line going up in tens.

Can you spot any mistakes? Pause the video while you think about this one.

Did you spot any mistakes here? Jacob has found the number 15 is wrong.

This should be 50, not 15.

Did you spot that one? 15 sounds a bit like 50 doesn't it? But it's not the same number.

Did you spot any other mistakes here? Laura has spotted one near the end here.

She said this should be 90, not zero nine.

She's got the two digits the wrong way round, hasn't she? So it should be 50 and 90.

Is that what you thought? Here's task for you to have a go at.

Can you use the zero to 10 number line to help complete the missing multiples of 10 on the zero to 100 number line? So the top number line is complete.

It's going up in ones, but there are some numbers missing on the bottom number line that's going up in tens.

See if you can work out what the missing multiples of 10 are.

Here's the second part of your task.

Can you use the zero to 10 number line to put the multiples of 10 on the zero to 100 number line? So at the bottom here we've got the multiples of 10, 30, 60, and 90.

Can use the top number line to help you put them in the right place on the bottom number line? So pause the video while you have a go at your tasks.

How did you get on with your tasks? Did you complete the number lines? So here we had the top number line going up in ones from zero to 10 and the bottom line going up in multiples of 10 from zero to 100.

The missing numbers are 10, 20, 40, 50, 70 and 80.

I can see we can use the top number line to help us work out the multiples of 10 on the bottom number line.

They look the same but they've got a zero on the end.

How to get on on the second part of your task.

Did you use the zero to 10 number line to put the tens numbers on the zero to 100 number line? So the multiples of 10, 30, 60 and 90 go here on the number line.

I can see that 30 is in the same position as three.

60 is in the same position as six and 90 is in the same position as nine because we know that 30 is the same as three tens.

60 is the same as six tens and 90 is the same as nine tens.

Is that where you put them? Let's move on to the second part of the lesson.

We're going to estimate multiples of 10 on a number line.

Multiples of 10 can be put on a zero to 100 number line.

So here we've got a number line from zero to 100 with some marks on it.

What number is the arrow pointing to? The arrow is halfway along the number line.

So what number is halfway between zero and 100? It's the number 50.

50 is halfway along the number line.

It is the midpoint.

The midpoint can be used to estimate where other numbers go.

So the midpoint can be really useful to mark on a number line to help you find other numbers.

We can show the midpoint even when the number line doesn't have marks.

Jacob said 50 is the midpoint.

It is halfway between zero and 100.

So Jacob has put 50 in the middle of the number line.

Laura said this can help us estimate the position of other numbers.

Estimate means we're going to have a really good guess at where it's going to be and try to be as close as possible.

A zero to 10 number line can be used to help estimate where the multiples of 10 go on a zero to 100 number line.

Estimate which multiple of 10 the arrows are pointing to.

So look closely at the top number line and then see if you can work out the multiples of 10 that would go where the arrows are on the bottom number line.

So I can see we've got the number two on the top number line.

That's going to be in the same position as 20 on the bottom number line because 20 is made of two tens.

Then we've got the number five, that's the midpoint of the top number line and that's going to go in the same position as 50.

That's the midpoint of a zero to 100 number line.

Then we've got the number six on the zero to 10 number line.

That's going to be in the same position as 60 on the zero to 100 number line because 60 is the same as six tens.

How do you know where they go? Jacob said we know two groups of 10 is the same as 20, 50 is the same as five tens and is the midpoint 60 is the next multiple of 10 from 50? We can estimate where multiples of 10 go on the unmarked number line.

We can see if they come before or after the midpoint.

Remember the midpoint on a zero to 100 number line is 50.

Can you estimate the number that the arrow is pointing to? Is it before or after the midpoint? Jacob said this number is before the midpoint.

It could be 40.

It is near where four would be on a zero to 10 number line.

What about this arrow? Can you estimate what number this arrow is pointing to? Is it before or after the midpoint? Laura said this number is after the midpoint.

It could be 60, it is near where six would be on a zero to 10 number line.

Is that what you thought? Estimate what number is being shown by the arrow here.

How do you know? Is it before or after the midpoint? Can you see the midpoint? And can you estimate what multiple of 10 the arrow might be pointing to? Jacob thinks it is more than 50 but less than 100.

Laura thinks it's a bit nearer to 50 than 100.

Jacob said 60 is 10 more than 50 but it's further away.

So he thinks the arrow is further away than 60.

Laura said I estimate the number is 70.

It is 70.

Is that what you thought? Where is 90 on the number line and how do you know? Is it before or after the midpoint? Can you see the midpoint there? Remember the midpoint is 50.

Where do you think 90 will go? Jacob said 90 is between zero and 100.

Laura said 90 is nearer to 100 than zero.

Jacob said 90 is nearer to 100 than 50.

Laura said 90 is 10 less than 100, will it go here? So this is Jacob's estimate.

Do you think that's in the right position? Laura said that is too far from 100.

Laura said will it go here? Can you see where Laura has estimated 90 will go? Jacob said that is too near.

Will it go here? Can you see where Jacob has put his estimate? Laura said yes.

That looks like the same position as nine on a zero to 10 number line.

Yes, that was 90.

Well done.

Let's check your understanding.

Estimate what multiple of 10 the arrow is pointing to on the number line and how do you know? Is it before or after the midpoint? Remember the midpoint is 50 on a zero to 100 number line.

So pause the video and see if you can estimate which multiple of 10 the arrow is pointing to.

What multiple of 10 do you think the arrow is pointing to? Jacob said it is between zero and 100.

Laura said it is nearer to 100 and zero.

Jacob said it is between 50 and a hundred.

So it's after the midpoint.

Laura said it is nearer to 100 than 50.

So what do you think the number is? 80 is a good estimate.

Is that what you thought? Jacob draws a number line showing multiples of 10.

He's going to draw his own number line from zero to 100 and mark the multiples of 10 on it.

So he's put zero at one end and 100 at the other and he's going to put the multiples of 10 on 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

What do you think of his number line? Look closely at it.

Do you think it's accurate? Jacob said I started off trying to make sure the multiples of 10 were equally spaced.

I know they are the same distance apart but I ran out of room.

Can you see near the end they're all a bit squashed.

I had to squash 70 to 90 up together.

I don't think this shows the multiples of 10 properly.

Can you think of a good way that he could have made sure they were equally spaced and in the right position? How could Jacob be more accurate? Laura has a go at drawing a number line.

You can see she's drawn a number line and she's marked zero on 100.

She said 50 is the midpoint so I'm going to put it in the middle of the line.

That's a good idea, isn't it? Then she said the multiples of 10 need to be the same distance apart.

So they need to be equally spaced, don't they? I wonder how she can make sure they're equally spaced.

Can you think of anything she could do to help space them out equally? She said I could use a cube or my finger to try to be as equal as possible.

So she's going to mark the multiples of 10 and try to equally space them 10, 20, 30, 40, 50.

That's looking really good, isn't it? What's going to be next? 60, 70, 80, 90, 100.

I think she's spaced them out really well, hasn't she? Let's check your understanding.

Can you spot the mistakes here? We've got a zero to 10 number line and a zero to 100 number line with some of the multiples of 10 marked.

Can you spot any mistakes? Pause the video while you think about this one.

So Jacob has noticed that the midpoint should be 50, not 60.

And I can see it's the same position as five on the zero to 10 number line.

So that should be 50.

Laura has noticed that 80 and 90 are the wrong way round.

So 80 will be in the same position as eight and 90 will be in the same position as nine.

Jacob has noticed that 10 and 20 are too close to zero and they're too squashed, aren't they? So they need to go there on the number line.

10 will be in the same position as one and 20 would be in the same position as two because 10 is one 10 and 20 is two tens.

Laura has noticed one more mistake.

40 should be before 50, not after it.

So 40 should be in the same position as four because 40 is four tens and 40 comes before 50 not after it.

Did you spot all of those mistakes? Well done.

Here's a task for you to have a go at.

Can you estimate where these numbers go on the number line? Are the multiples of 10 before or after the midpoint? So we want you to mark these multiples of 10 on the number line, 10, 90, 40 and 60.

Think about what the midpoint is and decide where they're going to go.

Think about how you could get them in the right position.

When you've had a go, compare with a friend, tell a friend why you placed the numbers where you did.

Here's the second part of your task.

Can you estimate the multiples of 10 marked on the number line? So look at what the arrows are pointing to and see if you can estimate what multiple of 10 they are pointing to.

Here's a third part of your task.

Can you draw your own number line from zero to 100, mark the midpoint and all the multiples of 10.

See if you can think of a good way to equally space the multiples of 10.

Think about how Laura did it earlier.

So pause the video and have a go at your tasks.

How did you get on with the first task? Did you estimate where the numbers go on the number line and how did you know? Can you see I've marked the midpoint on the number line, that's 50 and I've used that to help me mark the multiples of 10.

Do you think I've got them in the right place? Jacob said 10 is near zero and I left a little gap between them.

Laura said I knew that 60 was 10 more than 50, so they went next to each other.

Jacob said, I knew that 40 was 10 less than 50, so they went next to each other.

Laura said, I knew that 90 was 10 less than 100 so it went before it.

And if you've got a zero to 10 number line, you can use that to help you as well, can't you? How did you get on with the second part of your task? Did you estimate the numbers on the number line? So 50 is the midpoint, so that will go halfway along the number line.

30 is going to go before 50 and 80 will go after 50.

This is where I think they go on the number line.

Do you agree? You could check by looking at a zero to 10 number line.

How did you get on with the third part of your task? Did you draw your own number line from zero to 100 and mark the midpoint and multiples of 10? So it's a good idea to start off by marking zero and 100 and then find the midpoint 50 which is halfway along the number line, and then you can equally space the other multiples of 10.

Jacob said, I knew the midpoint was 50.

Laura said I used the midpoint to help me mark the multiples of 10.

So starting at zero you should have 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100.

And all of them equally spaced.

How does your one look? We've come to the end of our lesson.

Well done everyone.

Today we were estimating the position of multiples of 10 on a zero to 100 number line and this is what we've learned.

A number line can be used to show the multiples of 10.

There are 10 jumps of 10 on a number line from zero to 100.

The multiples of 10 are equally spaced.

Knowledge of counting to 10 can help you count in tens to 100.

A zero to 10 number line can help to estimate where multiples of 10 go on a zero to 100 number line.

Well done everyone.

See you soon.