Lesson video

Hello Oak team.

I'm Miss Sew, and welcome to today's lesson all about multiplying and dividing decimals by 10, 100 and thousand.

I really liked learning about multiplying because when we multiply, we take one thing like my little plant here, and when we multiply it, we make it greater.

So that it will always be more of something.

When we divide, the opposite happens.

We take something larger, we divide it and turn it into something smaller, which is really good if it's something you don't really want lots of.

Maybe if I divided my homework, I would have less of it.

I wouldn't ever want to do that though.

Maths is great fun.

I love doing more equations.

So, today we're learning all about multiplying, where we make things greater and dividing, where we make things smaller.

These are some parts of my garden.

I've been multiplying and trying to grow more of.

I hope that you're ready for some learning today.

I'm so excited for our lesson together.

In this lesson, we're going to be multiplying and divide decimals by 10, 100 and 1000.

You will have multiplied by 10, 100 and 1000, in previous lessons and in other units of work.

But today we're applying our knowledge to decimals.

We'll start with a warm-up, multiplying and dividing integers by 10.

Next we'll apply our new learning to multiplying decimals by 10, 100 and a 1000.

We will also be dividing them.

After that, we will be comparing different numbers of different decimal values.

At the end of the lesson, you will have an independent task and quiz, which you are going to do really well at, if you focus, for the next part of our learning.

For today's lesson, you'll need something to write with and something to write on.

If you don't have those, pause the video and go and get them now.

Make sure you have everything you need, and make sure you have a calm, quiet space.

If you have any apps running, turn off notifications and make sure you're ready to do your learning.

Let's start by multiplying integers.

An integer is a whole number, that can be positive or negative.

For example, 26 is an integer.

It's a whole number.

432 is an integer.

It's also a whole number.

Minus 27 is an integer.

It's also a whole number.

Six is an integer, but 0.

6 is not.

An integer is any whole number.

Here I have one whole, which is an integer, and I also have 0.

6, which is a decimal.

Pause the video and write down three integer numbers and three decimal numbers.

What's the difference? Did you notice the difference between your whole numbers, your integers and your decimals.

First, we're going to warm up by multiplying and dividing these integers by 10.

Pause the video and have a go.

Right.

Let's look at the answers.

Here are my multiplication answers, and here are my division answers.

Mark your work, and check to see what you got correct.

How did you do this? Often in my class, I hear my students say this.

Or this.

You add a zero or you take away zero.

Is this true? Or is this false? Thumbs up.

That's all we need to do.

Thumbs down.

There's something more to it.

Thumbs up or thumbs down.

Let's go find out.

It is false.

We do not add or take away zero.

If I was just adding or taking away zero, I wouldn't be doing anything.

We aren't affecting our numbers at all.

When we multiply and divide by 10, we move our digits along the place value house.

Let's look at this example of 526 multiplied by 10.

First, let's put 526 into my place value house.

When I multiply by 10, I am increasing the value of every digit.

Five hundreds becomes five thousands.

Two tens become two hundreds and six ones become six tens.

All of my digits, move to the left.

And then I've got an empty space here in the ones.

In my blank space, I add a placeholder.

I did not add a zero, but I represented the empty place value house with a placeholder.

When we divide, the same thing happens.

When I divide 526 by 10, I move my digits to the right.

The digits are all decreasing in value.

In my place value house, I have a decimal point.

Point to my decimal point.

Six ones becomes six tenths.

Two tens becomes two ones, five hundreds becomes five tens.

My answer is now 52.

6.

Let's see what we now know.

Pause the video and explain the mistake.

What is the correct answer? Are you ready for the answer? The correct answer is 20.

4.

We did not take away the digit zero.

We had to move our digit one place value house to the right to decrease the Value.

I am going to use my beams to represent my numbers as I multiply by ten.

First, I have one one.

If I multiply it by 10, I've got 10, 10 ones.

If I multiply it by 10 again, it will be 10 times greater.

What's it going to be? A hundred.

What's it going to be if I multiply this by 10 again? It's going to be, a thousand.

I have shown, that if I multiply by 10, I can increase my value.

From one to 10, to a hundred, to a thousand.

What do we multiply by? Have I multiplied by 10, 100 or 1000? Pause the video to complete your task.

Ready for the answers.

I'm multiplying first by 10.

One times 10 is equal to 10.

10 is 10 times greater than one.

I am multiplying by a hundred.

A thousand is a hundred times greater than 10.

Now, let's see what happens when I divide.

If I have a thousand and I divide it by 10, I am left with a hundred.

If I divide a hundred by 10, it's 10 times smaller and becomes 10.

If I divide 10 by 10, it becomes 10 times smaller and becomes one.

Now, we're going to imagine we're going to zoom into this one block.

Look at it really closely, We're zooming in.

Get your telescopes out, zoom in.

We have zoomed into our one block.

And we're going to repurpose the value of our other beams. Have a look at our one.

we're going to explore the place value numbers that are less than one whole.

Goodbye for our one block.

Now, let's imagine that this thousand cube, the orange cube has a value of one.

I've written the fraction one whole and also shown there is one whole in the place value chart.

If the value of the orange cube is one whole then the blue square now has a value of one 10th.

10 tenths are equal to one whole.

If I divide one whole by 10, I would have one 10th or 0.

1.

Our greenstick now has a value of one hundredth.

100 hundredths are in one whole.

How many hundredths are in one 10th? There would still be 10 green sticks in one blue square.

From this, I know that there are 10 hundredths in one 10th.

I say this decimal number 0.

01.

One block is now worth one thousandths.

I would take 1000 of these to fit inside our orange cube, which represents one whole.

I want you to say the number with me.

Let's read it digit by digit.

0.

001.

Take two minutes to check you understand what we've done so far.

Pause the video to read these questions and have a go.

If you need help, I will share a clue in the next five seconds.

Pause it now and try it yourself first.

This is our representation of one hundredth, which is the same as 0.

01.

What do I multiply this by to equal one whole, our orange cube? Are you ready for the answers? 0.

01 multiplied by 100 is equal to one.

100 hundredths is equal to one whole.

Let's move on to our let's explore part of the lesson.

Why is 0.

132, 10 times smaller than 1.

32? Let's look at this example with beams. First, let's look at how I've represented 1.

32.

I have one whole, my orange cube, three tenths, my three blue squares and two hundredths, my two green sticks.

Now let's make it 10 times smaller.

First I will look at my hundredths.

I have two hundredths represented with these beams. I will make these 10 times smaller, replace them for two thousandths.

Let's move across on the place value chart.

My two hundredths are now worth two thousandths.

I have got three tenths.

I will replace three tenths, to three hundredths.

I will move my three in the place value house, along to the hundredths.

I have got one whole, which I will replace with one 10th.

I will move my one in to the 10th place value house.

I now have a blank space in my ones.

I will put a placeholder zero to represent that there is nothing in the ones column.

0.

132 is 10 times more than 1.

32.

How can I explain the relationship between 1.

32 and 0.

132? Pause the video to complete.

At the operation, multiply it by 10 and divide by 10 into each one of the boxes.

Which way do the arrows go? Are you ready for the answers? I multiply 0.

132 by 10 to make 1.

32.

I divide 1.

32 by 10 to make 0.

132.

Now we are ready for your independent task.

I have got different numbers here.

I have a range of integers and decimals, and I want you to write, whether I have multiplied or I have divided by 10.

Take a look at my arrows and check which way they are travelling.

1,320 divided by 100 is 13.

2 and 13.

2 times by 100 is 1,320.

I need to look really carefully at my place value and check to see how many decimal places the numbers have moved.

If I look at 13.

2, I can see that my digits have moved to the left one way.

So if they've moved to the left, they've increased in value.

I have multiplied to get 132.

If they've increased by one decimal place, I have multiplied by 10.

And to move the other way, I've divided by 10.

Let's look at the next example, 132 and 0.

32.

I have had to move one, two, three decimal places to the right.

If I've moved three decimal places to the right, I have divided my number by three decimal places.

I have divided it by 1000.

Which means I have times by 1000, the other way.

Let's look at the last two numbers I'm comparing.

I have 0.

132, and 1.

32.

I have moved by one decimal place.

1.

32 is greater than 0.

132.

So I've increased, which means I have multiplied.

I have multiplied by 10 and I have divided by 10.

Go to your worksheet now and have a go at your independent task.

You are doing the same thing as me, but you are showing the relationship between a whole range of numbers in a circle.

Now it's time to check what you've learned in this lesson.

Pause the video to complete your task.

If you're not feeling confident, rewind and try watching my examples again.

Are you ready for the answers? Let's take a look.

Pause the video and check your work.

Here are the answers for the second question.

Pause the video and check your work.

That brings us to the end of today's lesson.

A really big, well done, in all the fantastic learning you've achieved today.

First, look back in your notes and think about the most important thing you've learned today.

It's up to you what that is.

This will help you get ready for the quiz.

Second, if you're able to, please take a picture of your work and ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Now it's time for you to go and join in with your quiz.

Thank you for learning with Oaks today and have fun on your next lesson.

Bye.