Lesson video

Hello, welcome to today's math lesson.

My name is Miss Sew, and today we're going to be multiplying decimals by whole numbers.

I hope you're feeling really well today, and I'm excited to start.

Let's get going! Welcome to today's math lesson.

Today, we're multiplying decimals by a whole number, using 2 different methods.

The first method is using our bar model.

And our second method is using our area model.

You might be familiar with these two different strategies from earlier math lessons, but it might be the first time that you are using decimals today.

For today's lesson, you will need a pencil and some paper.

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

Now that you have everything you need, make sure you're in a calm, quiet space and make sure if you have any apps running, you turn notifications off.

So you don't get distracted during this lesson.

To start with, we're going to be looking at some decimals and fractions to a warm up, and I'm going to be explaining their relationship to you.

Then we're going to have a go at our bar model method.

After that we'll carry out our area method.

And at the end of the lesson, you'll have a chance to show what you know with an independent task and quiz.

Let's get started.

So decimals and fractions are related.

Can you think of any ways in which they are related? Hm, I'm going to show you what I know.

What whole is equal to 10/10? I can write ten tenths in words, or I can write it as a fraction as I have done here.

There are 10 parts, and the whole is worth 10.

In my bar model, I have shown the whole, and I've shared the whole into 10 equal parts.

Each part is shaded to show it has a value of 1/10.

Together, 10/10 make 1 whole.

0.

5 is equal to 5/10.

I can write this in words or as a fraction.

There are five parts, and there are ten equal parts in the whole.

One, 2, 3, four, five.

Five equal parts are shaded, and the whole is worth ten parts.

Another way of saying this is half.

0.

2 is equal to 2/10.

I have 2 parts shaded, and 10 parts in my whole.

There are still 10 parts in our whole.

Our whole is worth 1 whole, and 2 parts are shaded.

I've represented 1/10 in each equal part.

In this bar model at the top here, it is equal to 1 whole or 10/10.

And our second bar model, it is equal to 5/10 or 0.

5.

And in our last bar model, it is equal to 2/10 or 0.

2.

Fractions and decimals can represent equal amounts.

10/10, 5/10, or 2/10.

Or I can represent them here with a value of 0.

1 each.

This is equal to 1 whole.

This is equal to 0.

5, and this is equal to 0.

2.

1, 0.

5, 0.

2.

Thinking about the example I've just shown you, what does this bar model represent? What decimal, what fraction, and how would you say in words? Pause the video, and write it down.

Let me show you the answers.

I can see from this whole that there are 10 equal parts, and 7 of those parts are shaded.

If 7 parts are shaded, it is equal to 0.

7 or 7/10.

And I can write that in words or as a fraction.

This decimal is 0.

7 or 7/10.

We're going to be looking at our first strategy using bar models to multiply.

Think about what we've just learned about the relationship between decimals and fractions, and that is going to help you with this method.

Multiplication with bar models.

I've got a word problem here to help you understand the context in which we might use a bar model method.

Bar models are really helpful for representing problems and showing me what I need to find out next.

Lisa has 3 litres of water, and she drinks 2/10 of this.

How many litres of water did she drink? How else could we represent this problem? Hm, if I have 3 litres of water, and I want to find out what 2/10 of it is, I want to find out what 2/10 of 3 litres is.

Hm, another way of finding out what 2/10 of 3 litres is multiply.

If I want to know what 2/10 of 3 litres is, that's the same as doing 2/10 multiplied by 3 litres.

Or, 0.

2 multiplied by 3.

Remember what we just learned? 2/10 is equal to 0.

2.

Our decimals and fractions can represent equal amounts.

2/10 multiplied by 3 is the same, it is equal to 0.

2 multiplied by 3.

Remember what we learned earlier, 2/10 is equal to 0.

2.

Okay.

To put that in the corner there to help us remember.

Let's take a look at this bar model.

Unlike earlier, a whole represent 3.

In our earlier presentations, the whole was represented by 1 whole.

This is represented by 3 wholes.

It is 3 times larger.

My whole has still been divided into 10 equal parts, underneath it in a second bar model.

So 3, our whole, 3 holes divided or shared into 10 equal parts means that each equal part will be worth 0.

3.

If I am looking at what 2/10 of 3 is equal to, 2/10 times by 3, I want to look at the value of 2 equal parts.

If I want to look at the value of 2/10, I'm going to look at 2 bars in this bar model.

Now, if I'm looking at 2/10, I know what the value of this is going to be.

If I know that 2 multiplied by 3 is equal to 6, then I know that 0.

2 multiplied by 3 is equal to 0.

6.

I know this because 0.

2 is 10 times smaller than 2, 0.

2 is 10 times smaller than 2.

If I am using a number that is 10 times smaller, then my answer is also going to be 10 times smaller.

Thinking back to our original question, Lisa drinks 0.

6 litres of water.

I've just shown you an example of how a bar model can be used to help us multiply decimals.

Now, I want you to have a go, finding 3/10 of 2.

3/10 is equal to 0.

3, our decimal number.

And if I want to find 3/10 of 2, that's the same as 3/10 multiplied by 2, or 0.

3 multiplied by 2.

In this problem, our whole is worth 2, and I still have a bar model made up of 10 equal parts.

I want you to have a go finding out what 3/10 of 2 is and telling me your if-I-know-then-I-know sentence.

If you'd like a clue, I'm going to share one in the next five seconds.

Otherwise, pause the video and have it go on your own now.

If you'd like a clue, I'm going to show you what the value of each part in this bar model is.

I know if the whole is 2, and I divide 2 by 10, and I have 10 equal parts, each equal part will be worth 0.

2.

Now, if I want to know what 3/10 of 2 is, I have to look at 3 equal parts.

I've highlighted it in the bar model here.

Have a go at your if-I-know-then-I-know sentence.

Okay, it's time for the answers now.

If I know that 3 multiplied by 2 is equal to 6, then I know 0.

3 multiply by 2 is equal to 0.

6.

This is because 0.

3 is 10 times more than 3.

I've used my bar model to help me.

We're now going to look at our second way of multiplying decimals using our area method.

Have a look at my place-value counters over here.

My place-value counters can be used to represent numbers of different value.

For this equation, I am doing 23 times 3.

I've got 10, 20 in my 10s, and 1, 2, 3 in my 1s.

My 10s are worth 20, my 1s are worth 3.

I have got 3 groups of 23.

When I am multiplying 23 by 3, I need 3 groups of 23, or 3 lots of 23.

I have 1 group of 23, 2 groups of 23 and 3 groups of 23.

I can represent this using my area method rather than my place-value counters.

Here, I've drawn my area method.

I've separated my area into two sections.

The first section here, the largest section is my 20, my 10s, and my section to the right is my 3s, my 1s.

20 multiplied by 3 is equal to 60, and 3 multiply by 3 is equal to 9.

I've partitioned and multiplied each area separately.

The answer is equal to 69.

I've just shown you an example of how we can use the area method to solve multiplication equations.

Now, I want you to have a go applying what I showed you to decimals.

If I know that 23 most played by 3 is equal to 69, then I know 2.

3 multiplied by 3 is equal to, and think about the relation between 23 and 2.

3, 2.

3 is 10 times smaller.

I'm going to show you a clue in the next five seconds.

Otherwise, if you want to have a go on your own, pause the video to complete your task.

Draw your own area model.

Off you go.

If you'd like to clue, I'm going to have a look at the value of the place-value counters.

I've got 2, and I have got 0.

3.

I have got 3 groups of 2.

3.

I need to multiply 2 by 3, and 0.

3 by 3.

The two equations I need to solve this are 3 multiply by 2 and 0.

3 multiplied by 3.

Let's have a look at the answer.

First, let's look at value of place-value counters.

I have 3 groups with a value of 2.

3.

Then I have to do 2 multiply by 3 in the larger part of my area, and then 0.

3 multiply by 3 in the small part of my area.

Then I have to add both these numbers up, and the answer is 6.

9.

If I know 23 multiplied by 3 is 69, then I know 2.

3 multiplied by 3 is 6.

9.

Because 2.

3 is 10 times smaller than 23.

Thank you so much for listening and joining with my explanations earlier.

It's now time for you to have a go at your independent task.

For the first part of your independent task, I want you to solve these multiplication problems with our bar model method.

If you need some help, there's a support sheet later on.

For the second part of our independent task, I want you to solve these equations using our area method or arrays.

You can always track your answer using if-I-know-then-I-know or another method that you are aware of.

Here's the support sheet to help you with our bar models.

I've told you the value of each of the parts, and I've highlighted how many parts we need to look at.

Here's the support sheet with some of the area models drawn for you.

You need to work out which numbers you have to multiply and add them together.

Pause the video to complete your task.

Okay, it's time to you the answers.

Take a look and mark your work.

Here are the answers to the area multiplication problems. Here are the answers for the bar model multiplication problems. Thank you so much for joining in with your math lesson today.

If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnwithOak.

You have worked fantastically hard to make it to the end of this lesson.

And we've learned not just one, but two strategies to help your multiplications today.

Now it's time to show what you know by going to complete the quiz.

Good luck, and thank you so much for joining you today.

Have a great day learning for the rest of your lessons.

Bye!.