Lesson video

Hello there, how are you? My name is Mr. Tilston.

I'm a teacher and I really love maths.

I'm really excited to be teaching you this math lesson, which is all about dividing by 10.

And you might already have some experience and confidence in this field.

So if you are ready, I'm ready.

Let's begin the lesson.

The outcome of today's lesson is this.

I can use place value to explain removing the zero in the ones from a multiple of 10, when we divide by 10.

Let me give you an example there.

What about 80 divided by 10? That's equal to eight.

It appears that we've removed the zero, but what's actually going on there? Let's explore.

We've got two keywords today.

If I say them, will you say them back please? My turn, placeholder.

Your turn.

And my turn, magnitude.

Your turn.

Now they're not exactly what we'd call common everyday words, but you might have encountered them recently.

Do you think you could have a go at explaining what they mean, hmm? Well let's have a reminder.

A placeholder is where we use the digit zero to hold a place in a number and maintain place value.

And the magnitude of a number is its distance from zero.

So the greater the distance from zero, the bigger the magnitude.

And our lesson today is split into two parts, or two cycles as we call them.

The first will be two digit numbers and there'll be multiples of 10, such as 70.

And the second will be three digit numbers, and there'll also be multiples of 10, such as 150.

If you are ready, let's start by really focusing on those two digit multiples of 10.

And in this lesson you're going to meet Alex and Aisha.

Have you met them before? They're here today to give us a helping hand with the maths, And very good they are too.

Let's have a look at the example.

Here is a two digit multiple of 10 that's 90.

So, 90 divided by 10, do you know the answer? Say it if you do.

Alex knows the answer, so does Aisha.

She says it's nine.

But how did you know it's so quick? Did you know it quickly as well? Alex says, "Easy to divide by 10, you just take away zero." Now that might be something you've heard before.

It might be something you've thought before.

It might even be something you've said before, but what's really going on? Aisha's not sure.

She says, "Hang on, are you sure? That would look like this." If we subtract zero from 90, it would give us 90.

Hmm.

Alex says, "You are right, so what's happening? Let's explore." Here, we've got a place value grid, and we've got a counter.

It's in the ones position, so it's worth one.

Now it's in the tens position, it's worth 10.

And now it's in the hundreds position, it's worth 100.

What do you notice? Alex notices as the counter moves to the left, its value increases.

Did you notice that? So here it's worth one.

Now it moves to the left, it's worth 10.

Now it moves to the left, it's worth 100.

Its value's increasing the further it moves to the left.

Let's refer to this as movement is magnitude.

That is our keyword, or one of our keywords for today.

Aisha says," It gets 10 times the size each time it moves a place value column to the left." Let's investigate.

It's going to move one place to the left and become 10 times the size.

One becomes 10.

Now it's going to move another place to the left.

It's going to become 10 times the size.

What will it become? 100.

"What happens if we go from bigger to smaller," wonders Alex.

What do you think? Let's see.

Let's investigate.

Well, here it's worth 100.

Now it's worth 10.

It's moved one place to the right, and it's moved another one place to the right, and now it's worth one.

What do you notice? What could you say? Aisha says, "as the counter moves right, its value decreases." The opposite of increases, it decreases, it's going down.

Another example, that movement is magnitude.

The value gets one 10th times the size each time it moves along to the right on the place value chart.

Let's see.

Here it's worth 100, and now it's one 10th times the size as it moves right, and it becomes 10.

And then as it moves one more place to the right, it's gonna become one 10th times the size again.

What's one 10th times the size of 10? It's one.

Let's have a check.

Label the arrows on the place value chart below with the correct number to show the magnitude of the movement.

So, mm mm times the size.

Pause the video.

Mm is one 10th times the size and again one 10th times the size.

Well done if you've got that.

They represent the equation 90 divided by 10 is equal to nine.

And Aisha says, "Let's make 90 using base 10 blocks." Yes, good idea.

Have you got base 10 blocks with you? You can make it first before we show you.

Let's have a look there.

Here's 90 made up of 10 blocks.

Now let's divide by 10.

What's going to happen if we divide each of those blocks by 10? This is what's going to happen.

Each of those 10 blocks becomes one.

Each 10 is one 10th times the size after dividing by 10.

We had nine tens.

Now we have nine ones.

That's what happened when we divided by 10.

Here's nine place value counters, each of them with a value of 10.

Have you got place value counters with you in your classroom? Again, you could recreate this with us as we go along.

So here is 90 using place value counters.

Altogether that's equal to 90, so let's divide them by 10.

What's going to happen? Could you recreate that before we show you? This is going to happen.

Each 10 becomes one.

There are still nine counters here.

The number of counters hasn't changed.

That's what happens when we divide 10 by 10.

We had nine tens, now we have nine ones.

Use place value counters to represent the division below.

40 divided by 10 is equal to four.

Could you represent that? If you don't have place value counters with you, you can draw them.

Pause the video.

How did you get on? Well, here's 40, what's going to happen to that 40? Those four tens, they're going to become four ones or four.

Alex says," Let's use counters in a place value chart." We've got 90 divided by 10 is equal to nine.

Here are nine tens.

Each 10 is divided by 10 to become a one in the next column.

Now we've got nine ones.

They've all moved and changed place value from 10 to one.

There are still nine counters, but now they are ones.

We had nine tens, we now have nine ones.

That's what happens when we divide by 10.

Aisha says, "How about we change the counters for digits, starting with the tens?" Okay, so how many tens have we got there? We've got nine, so let's use a digit nine.

Let's swap the nine tens for the digit nine.

Here we go.

We need to use a zero as a placeholder here.

That's our other key word for today.

A zero placeholder, why? Hmm, could you explain that? What's the purpose of that zero? What do you think? Well, Aisha says, "If we didn't have the place value chart, how would we know it was nine tens?" Let's see.

That's the place value chart gone.

What does it look like now? It doesn't look like nine tens does it? It just looks like nine.

Alex says, "I see, the placeholder shows us there are nine tens, not nine ones." So, there we go.

Now it looks like 90, now it is 90.

That's nine tens.

That is a placeholder zero in action.

That 90 has become nine, when we divide it by 10.

The zero is no longer needed as a placeholder to show the value of the nine.

Have a look at these representations, what do you notice? What have we got? What's the same? What's different? Now, what have we got? Again, what's the same and what's different? What did you notice? Well, Alex says, "I noticed that they all show nine tens becoming nine ones after being divided by 10.

This shows us that all the digits have moved one place to the right." And that's really what's happening.

It's not that we're removing a zero, it's that the digits are moving one place to the right, and are one 10th times the value that they were before.

A digit changes magnitude when it moves its place value either left or right, and in this case it's moving right.

It's moving closer to zero.

To divide a multiple of 10 by 10, remove the zero from the ones place.

"That's what I meant by take away zero.

But I see now it's not the same," says Alex.

Now he understands, hopefully you do too.

Well, let's find out true or false.

To divide by 10, you just subtract zero.

Is that true or false, and can you explain why? Have a think and pause the video.

True or false? True or false? It's false.

But why? Although you are removing a zero, that is what's happening.

It's a placeholder to show that the digits had a greater magnitude.

By removing it, the digits become one 10th times their size.

That's really what's happening.

Let's do some practise.

Number one, for each of the following equations, use a place value chart to represent them, drawing counters in for before and after the division.

Then complete the stem sentence below.

We had mm, mm, now we have mm, mm.

We're going to start with 40 divided by 10 is equal to four.

And for B, 50 divided by 10 is equal to five.

Can you draw that with counters before and after? Can you fill in the stem sentences? Number two, write down the equation being represented below, and then complete the sentence describing it.

Again, we had, mm, mm now we have mm, mm.

And number three, which opinions do you agree with and why? Alex says, "When you divide by 10, you remove the zero from the ones place, because there are no ones." And Aisha says, "The placeholder is removed from the ones column when dividing to allow all the digits to become one 10th times their size.

This means the tens digit moves to the ones digit so the zero is no longer needed." Who's right? Is it Alex? Is it Aisha? Is it neither, is it both? You decide and see if you can explain as clearly as you can, but using mathematical language.

Wonder if you could use the words placeholder and magnitude, our keywords today.

Okay, pause the video.

Good luck with that and I'll see you soon for some feedback.

Welcome back, let's see how you got on.

Let's give you some answers.

Number one, first of all, we're doing 40 divided by 10 is equal to four.

This is how we could represent that 40.

That's the before, four tens is the same as 40.

We had four tens, and now we can draw four counters in the ones.

Now we have four ones.

And what about this one? 50 divided by 10 is equal to five.

How do we represent that? Five counts of five circles in the tens.

We had five tens and then five counters of five circles in the ones.

Now we have five ones.

Number two, A, let's look at the equation first.

What's going on here? That 70 divided by 10 is equal to seven, and our stem sentence completed is this.

We had seven tens, now we have seven ones.

And for B, the equation is this.

That's 40 divided by 10 is equal to four.

We had four tens, now we have four ones.

And then who did you agree with? Well, Aisha was correct in this case.

All whole numbers are made up of ones, but they are arranged into different place value columns.

The zero in the ones column is removed to show that the other digits are now one 10th times the size.

Well done if you use one 10th times the size in your explanation.

Okay, well let's look at three digit multiples of 10 now.

For example, 120.

Alex wants to explore further.

So far we've only used two digit multiples of 10 for division, let's try three digit.

I like your spirit.

Alex is ready for the next stage.

Let's look at this example.

140, it's a multiple of 10, it's three digits.

140 divided by 10, do you know the answer? "To divide a multiple of 10 by 10 remove the zero from the ones place" says Aisha.

The answer should be 14, but let's make sure we know why.

Did you get 14 by the way? Did you get that really quickly? Well done if you did.

They represent the equation.

Aisha said, "Let's make 140 using base 10 blocks, then let's divide." Okay, again, if you've got base 10 blocks in front of you, go for it.

How could you make that? Just like this, that's 140.

Now we're going to divide.

What's going to happen to each of those blocks? This is what's going to happen.

That 100 when divided by 10 became 10, and each 10 when divided by 10 became one.

This shows one 10 and four ones which is equal to 14.

140 divided by a 10 is equal to 14.

Now Aisha says, "Let's represent 140 using place value counters instead." Okay, let's do that.

If you've got place value counters in front of you, you could recreate this yourself.

We're looking for 140, so that's 104 10, that's what 140 looks like with place value counters and we're going to divide them by 10.

We're going to divide each one by 10.

What's going to happen? What's going to happen to that 100? What's going to happen to each of those tens? Now we can divide each by 10, removing the zero from the ones column of each, so that 100 becomes 10 and the tens each become one.

Each counter is one 10th times the size.

Now we have one 10 and four ones.

That's equivalent to 14.

Let's have a little check.

Use place value counters, or if you don't have them, draw them to represent the division below.

150 divide by 10 is equal to 15.

Pause the video.

If you drew those, you might have drawn those as a before and after.

This is what the before looks like, that's 150.

Now we're going to divide it by 10.

We're going to divide each of those counters by 10, and this is what we get.

So that 100 has become 10, and each of those tens has become one when divided by 10.

Aisha says, "Here's a place value chart.

We have 104 tens." This represents 140, but now let's divide it by 10.

What's going to happen, can you picture it? Can you visualise it before it happens? Each counter becomes one 10th times the size.

So moves down a place, or as it will appear on here one place to the right.

Now we have one 10 and four ones.

How about we change the counters for digits, starting with the tens? Okay, let's do that, sounds good.

Let's swap the hundreds and tens for their digits.

Here look, we've got 100 and we've got four tens.

Let's use those digits one and a four.

Now we're going to need to use a placeholder zero, aren't we? "We do need a placeholder here as well." You're right Aisha, make sure we put it.

Alex says, "Again, why?" What do you think? Can you explain why we need it? Think about what we looked at before.

"If we didn't have the place value chart, how would we know it was 104 tens?" It just looks like 14 there, doesn't it? "I see, the placeholder shows us that there is 104 tens, not one 10 and four ones." That zero is really important there.

Now to divide by 10, by turning 104 tens into one 10 and four ones.

Let's have a look at that.

Each one's going to move one place to the right, and now that's what we've got.

The zero is no longer needed as a placeholder, because the digit four replaces it.

That's what's happening to the zero really.

"Let's try some other numbers.

How about if we have more hundreds to start?" Oh, okay, that's ambitious, so 430 divided by 10.

Do you think you know it? Do you think you could do that quickly? We have four hundreds and three tens here that's equivalent to 430 with a zero placeholder.

"Let's make each digit one 10th times the size by moving them right a place value position." What's going to happen to each of those digits? What's going to happen to those four one hundreds? What's going to happen to those three tens? What's going to happen to that zero one? Let's move a place to the right.

Here we go.

The placeholder was removed and now we have four tens and three ones, and that's 43.

430 divided by 10 is equal to 43.

Aisha says, "What if we have a multiple of 100? That's a multiple of 10, but with two placeholders." Can you think of a multiple of 100 we could use here? How about this one, 700 divided by 10, what's that equal to? Hmm, did you know that quickly? We have seven hundreds, that's equivalent to 700 with two zero placeholders this time.

Alex says," Let's make each digit one 10th times the size by moving them right at place value position." What's going to happen this time? What's going to happen to that seven in the hundreds column? What's going to happen to that zero in the tens column? What's going to happen to the zero in the ones? They're going to move one place to the right.

That seven hundreds has become seven tens and the zero tens has become zero ones.

Now we've got 70.

700 divided by 10 is equal to 70.

The same thinking and the same processes apply even when it's a multiple of 100.

Let's do some practise.

Number one, use the place value chart to represent the following equations by drawing counters in for before and after the division.

Then complete the stem sentence below.

A is, 130 divided by 10 is equal to 13.

Can you draw that with counters? What does that look like before, what's it look like after? And can you complete the stem we had? Mm and mm, now we have mm mm and mm mm.

And B, you're going to do that for 250 divided by 10 is equal to 25.

And C, you're going to do that with this multiple of 100.

500 divided by 10 is equal to 50, is still a multiple of 10.

And number two, complete the ratio chart below by filling in the missing numbers.

Number three, tick the statements true or false.

And you might like to have a go at explaining why as well.

If a multiple of 10 is divided by 10, the ones digit can't be zero.

True or false? Only two digit multiples of 10 can be divided by 10.

True or false? To find one 10th times the size, divide by 10, true or false? To divide a multiple of 10 by 10, remove the zero from the ones place.

True or false? And digits that move to the right by one place value position become one 10th times the size.

True or false? Okay, good luck with that.

Pause the video, and I'll see you soon for some feedback.

Welcome back, how did you get on? Are you feeling confident? Well, let's give you some answers you can check.

Number 1, A, 130 divided by 10 is equal to 13.

That is the case, but can you represent that? What does it allow before and afterwards? Well, it looks like this before.

One circle of one counter in the one hundreds, and three circles or three counters in the tens that's before.

We had 103 tens, and then this is what it looks like after.

Now we have one 10 and three ones.

And for B, 250 divided by 10 is equal to 25.

What does that look like? It looks like this.

We had two hundreds and five tens.

Then after it looks like this, now we have two tens and five ones.

And then 500 divided by 10 is equal to 50.

This time a multiple, not just a 10, but of 100.

This is what it looks like before, we had five hundreds.

And this is what it looks like after, now we have five tens.

And complete this ratio chart below by filling in the missing numbers.

We're dividing each of these numbers by 10.

20 divided by 10 is equal to two.

30 divided by 10 is equal to three.

150 divided by 10 is equal to 15.

200 divided by 10 is equal to 20.

370 divided by 10 is equal to 37, and 990 divided by 10 is equal to 99.

And true or false, the first one, if a multiple of 10 is divided by 10, then one's digit can't be zero.

That's false.

Multiples of 100 divided by 10 have a zero in the ones column, and only two digit multiples of 10 can be divided by 10.

That's also false.

Multiples of 10 with any number of digits can be divided by 10.

To find one 10th times the size divided by 10, that's true.

To divide a multiple of 10 by 10, remove the zero from the ones column.

That is true.

And digits that move to the right by one place value position become one 10th times the size.

That is true.

We've come to the end of the lesson.

You've been amazing today.

I hope you are proud of your accomplishments and your achievements, and I'm sure your teacher is too.

We've been using place value to explain removing the zero in the ones from a multiple of 10 when we divide by 10.

In our place value system movement is magnitude.

Moving left, each column is one 10th times the size.

To divide a multiple of 10 by 10, remove the zero from the 10th place.

This makes a number one 10th times the size.

The zero is a placeholder, it works for any multiples of 10.

This is not the same as saying take away zero.

Well, I've had great fun today, and I'd love to spend another maths lesson with you in the near future.

But until then, have a fantastic day and whatever you do, be the best and most successful version of you that you could possibly be.

Take care and goodbye.