Lesson video

Hello there.

My name is Mr. Tilstone, how are you? I hope you're having a great day today.

Let's see if we can make that day even better by having a successful maths lesson.

Today's lesson is all about multiplying by 10, and that's an area that you might already have some confidence with and have found some success with.

Well, let's see if we can take you even further along that journey.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is this, I can use place value to explain placing a zero after the final digit when we multiply whole numbers by 10.

Have you ever noticed that that's what we do? Well, let's find out why.

Our keywords today are my turn placeholder, your turn, my turn magnitude.

Your turn.

Hmm.

I bet there's one word at least outta those two that you are not familiar with.

So let's have a look.

A placeholder is where we use the digit zero to hold a place in a number and maintain place value and we'll explore that today.

And the magnitude of a number is it's distance from zero.

And again, we're going to practise lots of examples of that today, so you'll be very familiar with that word by the end.

Our lesson today is split into two parts or two cycles.

The first is movement is magnitude and the second two digit numbers.

Let's start by focusing on the concept that movement is magnitude.

And in this lesson you will meet Sofia and Jun, have you met them before? They're here today to give us a helping hand with the maths.

Okay, so we've got six multiplied by 10.

Do you know the answer to that? Hmm.

Well, Jun does.

He says, "I know the answer." And Sofia does.

She says, "So do I.

It's 60." Did you know that? But how did you know it so quick? And were you quick too? And Jun says, "Easy to multiply by 10, you just add zero." Hmm.

Sofia says, "Hang on, are you sure? That would look like this?" Six add zero and that would equal six.

Hmm.

"You are right.

So what's happening? Let's explore." So we've got a place value chart here and we've got some counters.

So we've got one counter in the ones, and if we've got the same counter in the tens, it's now not worth one.

It's worth 10.

And if we've got a counter in the hundreds, it's not worth one or 10.

It's worth 100.

What do you notice? Jun says, "As the counter move to the left, its value increases." Did you notice that? So it's one, now it's 10, now it's 100.

It's increasing the further we move it to the left and Sofia says, "It gets 10 times the size each time it moves one column to the left." So it's one when it's in this column and then it gets 10 times the size and it becomes 10 and that becomes 10 times the size and becomes 100.

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 hmm, times the size.

Pause the video.

Did you get it? It is 10 times the size.

So when we move one place to the left, our number becomes 10 times the size.

They represent the equation six multiplied by 10 is equal to 60.

And you can do that in lots of ways and they're starting off with base 10 blocks.

So Sofia says, "Let's make six ones using base 10 blocks and then let's multiply." You could do this if you've got base 10 blocks with you.

So we've got six ones and each of them is going to be multiplied by 10, and this shows six groups of 10, which is equal to 60.

Here are six place value counters.

Let's multiply each by 10.

So the same kind of thing this time with counters.

So we've got now instead of one of those 10 of those, what could we do instead of having 10 ones? We could exchange 10 ones for one 10 and it's still worth this same.

We could do that with all of them.

So instead of counting 10 times each, we can exchange a one for a 10 to make it 10 times the size.

There are still six counters here, just like they were before.

Yes, but each counter now has a value of 10, not one.

So its value has changed.

Let's do a check.

Use place value counters to represent the multiplication below.

If you don't have place value counters, you can draw them.

Pause the video.

Let's see.

So here are five place value counters, each worth one, and we're going to multiply them by 10.

And we could do this, make 10 of that one, or we could exchange it for one 10 and do the same for the others.

So each of those one counters has been exchanged for a 10 counter.

"Let's use counters in a place value chart," says Jun.

So, we've got six multiplied by 10 is equal to 60.

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

So this one becomes one 10, this one becomes a 10, this becomes a 10, this one becomes a 10, this one becomes a 10 and this one becomes a 10.

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

There are still six counters, but now they are tens.

How about we change the counters for a digit starting with ones? So instead of having six ones, what could be right? What digit could be right? "Good idea," says Jun, "Six counts means a digit of six." Yes.

"Let's multiply it by moving it in the same way," so it's going to become 10 times the size.

It won't be six ones anymore, it will be six tens.

"Now," says Jun, "We have six tens shown by the six in the tens position." What about the zero then, where does that come from? Let's take away the place value chart and that's what we would be left with.

Without place value this still reads as six or six ones.

Let's bring the place value chart back.

We need a zero to show it's six tens.

There are zero ones and six tens in 60, and this is called a placeholder.

So that zero is a placeholder.

We had six ones and now there are six tens, and that zero is helping us to show that.

Let's have a look at some different representations together.

What do you notice, what can you see? What could you say? I notice that six is shown in all of them, but it's six tens, not six ones.

A digit changes value when it changes its place value.

To multiply a whole number by 10, place a zero after the final digit of that number.

And that's why that rule works.

That's what I meant by add a zero.

But I see now that it's not the same.

True or false, to multiply by 10, you just add zero.

Is that true or is that false and why? Pause the video.

True or false? Hmm, it's false.

But why? Although you are writing a zero on the page, it's a placeholder to show that the digit now has a greater value because it's in the tens column and not the ones column.

So that's what we mean by placeholder.

That's zero.

Let's see if you pick that up.

Let's do some practise.

Number one for each of the following equations, use a place value chart to represent them.

Drawing counters in four before and after the multiplication.

Then complete the stem sentence below.

So we've got A, four multiply by 10 is equal to 40.

So what does that look like before and what does that look like after? And then can you fill in that stem sentence.

We had mm mm, now we have mm, and the same for B.

This time we've got five multiplied 10 is equal to 50.

Again, can you represent that with the charts? Can you fill in that stem sentence.

Number two write down the equation being represented below and then complete the sentence describing it.

So we had mm mm, now we have mm mm, so do that for A and for B.

We've got some different representations there.

Number three, which opinions do you agree with and why? Jun says, "The placeholder is used in the ones column for any multiple of 10 to show that there are no extra ones." And Sofia says, "The placeholder is put in to show that there are no ones whatsoever, only tens." Who do you agree with Jun, Sofia? Both or neither.

See if you can explain that right here, pause the video and away you go.

Welcome back.

How did you get on? Are you feeling confident? Let's give you some answers.

So number one, we've got four multiplied by 10 is equal to 40.

So here are our four ones.

We had four ones and here are our four tens.

Now we have four tens, and this is five multiplied by 10 is equal to 50.

So we had five ones, now we have five tens.

2A let's begin with our equation.

Seven multiplied by 10 is equal to 70.

So we had seven ones.

Now we have seven tens.

And for B, different representation, place value counts this time starting with our equation, we've got four multiplied by 10 is equal to 40.

So we had four ones, now we have four tens.

And which opinions do you agree with and why? Well, in this case, Jun is correct.

The placeholder is used in the ones column for any multiple of 10 to show that there are no extra ones.

That's what zero does.

That's what that placeholder zero does.

There are ones in every whole number, but they can be arranged into the tens column and columns greater so that there are none leftover.

This is when zero is used as a placeholder to show this.

Okay, you're doing really, really well.

Let's see if you are ready for the next cycle, which is two digit numbers.

So let's look at this equation 12 multiply by 10 is equal to 120.

What do you notice? Sofia says, "Let's use the representations again to explore what happens." Jun says, "So far we've looked at single digit numbers multiplied by 10." Let's look at two digit numbers multiplied by 10.

So they represent the equation.

Let's make 12 using base 10.

Lots of choices here.

Sofia's gone for base 10.

Then let's multiply.

In 12 there are two ones and one 10.

So it looks like that.

That's 12.

Now to multiply that by 10, here we go.

So we're multiplying the one 10 by 10 and we're multiplying the two ones by 10.

Now we are showing 10 groups of 12.

It is equal to 102 tens or 120, that's 100, that's two tens or 20.

Let's have a check.

Use base 10 to represent the multiplication below, 11 multiply by 10 is equal to 110.

If you don't have base 10 equipment, perhaps you could draw some sticks and dots to represent that.

Okay, pause the video.

How did you do? Well, here's 11.

So that's one 10 and one one.

And we can multiply that by 10.

And that gives us 100 and one 10 or 110.

So 12 multiplied by 10 is equal to 120.

We've established that.

Let's look using a different representation this time, let's use place value counters.

So we've got 12.

As one 10 and two ones.

Let's multiply by 10.

Let's do that indeed.

10 lots of each of those counters.

Now what could we do instead of having 10 tens, we could exchange for 100.

What's about those 10 ones, one 10 and those 10 ones a different one 10.

Each counter's value has become 10 times the size.

The 10 became a 100, the one became a 10.

Now we've got 12 multiplied by 10 is equal to 120.

Here's 12 on a place value chart.

Let's put 120 the product underneath.

So 12 multiplied by 10 is equal to 120 again, and this is what it looks like.

So we've got 12 in the first one and 120 in the second one, what do you notice? Movement is magnitude.

Each of these counters moves when multiplying by 10, they're moving further away from zero when multiplied by 10.

Each counter's value is now 10 times the size that one 10 has become 100.

Those two ones have become two tens.

We had one 10 and two ones.

Now we have 100 and two tens.

Let's replace accounts with digits and remove the place value chart.

So what digits could we use instead? Well, that's two ones so that's two, and that's one 10.

So that's one.

And those two tens could become the digit two and those two hundreds of digit one, but we need to do one more thing.

Can you see what it is? Now what do you notice, has anything changed? Both of these look like 12 because there aren't any placeholders.

That's why the placeholders are so important.

So let's add that placeholder in.

Here's a zero in the ones column to show that the digits one and two are 10 times the size.

There is the placeholder.

So to multiply a two digit hole number by 10 place a zero after the final digit of that number.

Let's see if you are ready for some final practise.

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

Then complete the stem sentence below.

So we've got 14 multiplied by 10 is equal to 140.

What does that look like before? What does that look like afterwards? And then can you fill in that stem sentence.

And the same for B.

This time we've got 17 multiplied by 10 is equal to 170 and C, 16 multiplied by 10 is equal to 160.

Represent that with a place value charts and fit in the stem sentences.

Number two, complete the ratio chart by filling in the missing numbers.

So you're multiplying each of those numbers by 10.

Number three, tick the statements.

Are they true or false? You might like to write Y as well for each one.

When a whole number is multiplied by 10, the product is a multiple of 10.

Is that true, is that false? Only single digit numbers can be multiplied by 10.

True or false? To find 10 times the size multiplied by 10, true or false? To find 10 times the size just as zero, true or false? Digits have moved to the left by one place value position in a place value chart become 10 times the size.

Is that true or is that false? And you might like to prove it or disprove it using examples.

Okay, good luck with that.

Pause the video and I'll see you soon.

Welcome back.

How did you get on? Number one so here's 14.

So we had one 10 and four ones.

Now we have 104 tens.

Here's 17 multiplied by 10 is equal to 170.

What does that look like? Well, there's your 17.

So we had one 10 and seven ones.

And now we have, this is your 170, one hundred and seven tens.

This is 16 multiplied by 10 is equal to 160.

What does that look like? Like this this is your 16, that's one 10 and six ones, and this is your 160.

That's 100 six tens.

And complete the ratio chart, five multiplied by 10 is equal to 50, 12 multiplied by 10 is equal to 120.

42 multiplied by 10 is equal to 420.

57 multiplied by a 10 is equal to 570.

81 multiplied by a 10 is equal to 810 and 99 multiplied by 10 is equal to 990.

Under these statements, true or false, when a whole number is multiplied by 10, the product is a multiple of 10.

True or false? That's true.

Only single digit numbers can be multiplied by 10 is false.

Any number can be multiplied by 10.

And you've investigated some two digit numbers too, but three digit, four digit, basically any numbers can be multiplied by 10.

To find 10 times the size multiplied by 10.

True or false? Yes, that is true.

To find 10 times the size, just add zero.

No, that's not true.

To multiply whole numbers by 10, place a zero after the final digit, that's more accurate.

And then digits that move to the left by one place value position in a place value chart become 10 times the size is true.

So well, and if you got those.

We've come to the end of the lesson, well done you.

Today we've been using place value to explain placing a zero after the final digit.

When we multiply a whole numbers by 10, it's a useful rule, but today you've been coming to understand why that rule is true.

In our place value system movement is magnitude.

Going up each column is 10 times the size.

To multiply a whole number by 10 place a zero after the final digit of that number.

This makes a number 10 times the size.

The zero is a placeholder.

So that's our key word.

It works for single digit whole numbers or whole numbers with more than one digit.

This is not the same as saying add zero.

Well done on your accomplishments and your achievements today, I hope you've deepened your understanding.

I'm sure you have.

Give yourself a little pat on the back.

You've been incredible.

I hope you have a great day whatever you've got in store and that you are the most successful and best version of you that you could possibly be.

I hope to spend another math lesson with you again in the near future.

But until then, take care and goodbye.