# Lesson video

In progress...

Hi again, everyone, and welcome to the lesson.

Today's lesson is going to be multiplying a decimal number by a whole number.

But before we get to the lesson, let's have our joke of the day.

So, why are fish so clever? Because they live in schools.

It's a good one.

Right down with the lesson.

So, let's have a look at today's lesson agenda.

So we're going to have a look at some related multiplication facts, get our brains buzzing a little bit with multiplication.

We're then going to think about applying word problems to our knowledge of multiplication.

And we're going to do some multiplying with decimals greater than one as well.

And all the way through we think about the representations we use, and the use of manipulatives to support our knowledge of multiplication.

And you guys are going to do an independent task for me.

So, making sure as always, you've got pencil and paper that you're ready to go.

And we can make sure we have anything for jottings, or doing some work as we go.

Now a bit of a warm-up for you.

I'm going to leave this on here, what I want you to do is fill in the multiplication grid with your knowledge of multiplication.

So pause the video now, complete that on your paper.

And then when you're ready, play it and we'll look at the answers.

Okay, how did we do? Great, so let's have a look at those all-important answers.

Now, I am not going to spend ages going through every single answer for you.

So what I recommend is you pause the video now, check all your answers, make sure you're right, and then when you're ready, play the video and we'll move on.

So, those multiplication part is really important for this lesson 'cause we're going to be using and applying them as much as we can.

Now just to go back a step.

I just want us to think about related multiplication facts and get our brains worrying a bit in relation to decimals.

So first of all, nice and easy, no trick question, what multiplication and division facts could this represent? Could this represent? have a bit of a think.

Try and think more than one, more than two different ways of saying it, different ways of writing it, different ways of representing it if possibly.

Pause the video and jot same down and then we'll play and I'll show you some examples.

Okay, what did we come up with? Well, some of the things that we may have come up with, well, we could have had a look at it like this.

So this could be the first way you looked at it.

So you may have thought, Well, two multiplied by three is equal six, or three multiplied by two is equal six.

We may have written down some of these options to groups of three, two lots of three, three, multiplied by two, three times two, two equal parts each with a value of three.

There's so many different ways that we can express multiplication, we have to be familiar with all of them.

We might have thought about it in terms of division, saying our whole is six, we could split it or group it into two parts or three parts and that will leave us with six divided by two is equal to three or six divided by three is equal to two.

And some of the ways we could have said that could have been looking at sharing it too.

You may have looked at it in this way, now very, very similar in the ways that we express it.

Again, some of those values may have had or may have grouped differently.

We may have started asking questions.

well, this could be, how many twos are therein in six? For example, or this is six shared into three equal groups of two.

It's a lot of different ways that we can start representing this now.

Compare that for this.

Think about what we've just done.

And think what's the same and what's different about the representation I'm now showing you.

Okay, pause the video.

What multiplication facts did this now represent? Okay, let's have a look at them.

What we've got here is similar representation in terms of what we're looking at, but the value of each part is now 10 times smaller.

Okay, so we've gone from one to 0.

1.

When you think about multiplying and dividing by 10, so the whole is also going to be 10 times smaller.

So have if our whole was six, then our hole is now yes, 0.

6.

And we can see that in this representation here.

So we'll link to that when we express these multiplication facts, we can also do a similar thing.

We can group it like that, we can now say that two lots of 0.

3 is equal to 0.

6.

We can start expressing and writing it down in lots of different ways, we can talk about groups, and talk about lots, just in the same way with any multiplication.

And that's the sort of familiarity and confidence we need, even when we talk about decimals, just as we would with integers.

3 multiplied by two or three tenths.

So we might even start thinking about it in terms of fractions.

And this familiarity is really important in making those connections.

Also, we've got those division facts really important as well.

So we've gone from 0.

1, obviously, now we can look at it in that other way, as well.

We first looked at the rows, then we're looking at the columns.

So this time, we've got three, lots of 0.

2.

And, again, we can still express it in those different ways, and we can have all of these different possibilities of how we're talking about it.

And when we're in classrooms, when we're in schools, or when we're talking about math, we need to be familiar and understand all these different ways that people may be expressing the math.

There isn't just one way of talking about math and is having that confidence to be able to see these.

So that's why it's really important to have a look at a number of examples.

Again, linking everything back to division is really important as well.

Moving on from that, then we've now got slightly different.

So thinking about what we did before with the whole numbers when we have one, then we had 0.

1.

Look at the representation we've got now.

Thinking about our knowledge of multiplication and division particularly, a place value, can we complete this missing sentences, so the value of each part is now how many times smaller? So the whole is going to be how many times smaller? So yeah, the value of each part now is 100 times smaller therefore our whole is going to be 100 times smaller, but we can still use that same multiplication path that we used right at the start with the integer to support our understanding here.

So thinking about it first in this way, we can say that two multiplied by 0.

03 is equal to 0.

06.

I'm still using that knowledge of two multiplied by three is equal to sick to support me.

We can still discuss it and express it in the ways of talking about groups of 300, or two groups of 0.

03, or two lots of 0.

03.

And then conversely, we could talk about is 0.

03 multiplied by two as well.

And we can look at it in terms of division, okay? So lots of different ways that we're doing it but really important that we're still going back to that base fact, that base multiplication fact.

Okay, and obviously, we can group it in a different way as well with this time got the columns instead of the rows.

So, we're still getting all those different groups together and seeing that knowledge of multiplication.

So let's now take that understanding and start applying it for word problems to help us solve some problems. Here I've got a problem.

Zakia, has three litres of water, and she drinks two-tenths of this, how many litres of water did she drink? So what do we need to do in order to work this out, so maybe a few seconds, you might want to pause the video and have a go with it.

But we're going to walk through this one together and then I'm going to give you one to do yourselves.

Okay, so I'm going to model this one, then give you another example.

So essentially, what we're trying to do is we need to find two-tenths of three 'cause she drinks two-tenths of the three litres of water.

So my whole is the three litres and she's drinking two-tenths of it.

Now, in order to help me to solve this, I'm looking for two-tenths of three and I know that two-tenths is equal as a decimal to 0.

2.

So I can use that to help me.

Essentially, if I rewrite this, I'm looking for three tenths it multiplied by three.

I'm looking for three lots of 0.

2.

Okay, 'cause I know that 0.

2 is two tenths and there are three of them in the whole.

So there's three litres.

Now that's awfully confusing because I'm doing lots of talking and lots of writing and there's lots of numbers flying around everywhere.

It's better if we can represent this using some sort of model to be able to express it in a sort of a picture.

So, perhaps the bar model might help me here.

Now you can see that I've got my whole here.

So I've got my bar.

So my whole is three litres.

And we can also see that I split here into tenths because she drinks two tenths.

So I know that I'm looking for two tenths and I want three lots of that two tenths and what is two tenths? We get 0.

2.

But I know that I need three lots of that.

In this case, I can see that I've got 0.

2, 0.

2, 0.

2.

Which means in total, I've got 0.

6 litres that Zakia drinks, okay? So, there we go.

I've managed to solve it.

I want you to have a go and think about the different strategies you could use to help you to solve this problem.

So a group of friends had a pizza party, they have seven pizzas, and eight, seven-tenths of the pizzas, how much pizza did they eat? Now you might want to write things down, you may want to jot things down, you might want to use a bar model to help you to solve this.

So pause the video now have a go and then when you're ready, play the video.

Okay, let's then pick that and see how we did.

So we know, that there are seven-tenths and we're looking for seven-tenths of seven which is the whole.

And we know that seven-tenths is equal to 0.

7 as a decimal, and we can say that we're looking for seven-tenths multiplied by seven.

So let's use our bar again.

We know that the whole is seven and we're Looking for, we know there's 0.

7 in each part.

And we're going to be looking for seven of those parts so seven lots of 0.

7.

So in this case, I can add them all up, or I can do 0.

7 multiplied by seven to show, and this is a really good example of where we can show something very clearly, that is going to be how much pizza they eat with the 4.

9 pizzas.

Okay, let's move on then.

Now we're going to have a look at multiplying with decimals greater than one.

Now, in order to do this, we're going to use the distributive property of multiplication.

It sounds complicated, but you probably already used it previously.

Essentially, we're going to be looking at numbers, and rather than if I wanted to do, for example, 23 multiplied by three, rather than trying to do it all at once.

I might distribute my number, I might partition you may have before, my number.

So I'm going to do 20 multiplied by three, or I'm going to do three, multiplied by three, and then I can put them together to get my answer, okay? Now in order to support this, it's quite important to think about the ways that we can represent it.

In this case, we're looking at place value counters.

And this is a nice way to be able to represent the different problem we've got 23 in the top row, and then we've got three lots of that.

So that's a nice way that you can do it.

But that takes quite a lot of time to be able to draw represent it, particularly if you don't have place value counters at home.

So another great way that we can do it is use of an area model.

The area model is essentially drawing a rectangle and then partitioning the rectangle as I've done here, into the number.

So we've got 23, but I distributed it to 20 and three, and I'm multiplying it all by three here.

Now I simply need to multiply the parts, the 20 multiplied by three, and three multiplied by three.

So I've got 20 multiplied by three is equal 60.

And I've got three multiplied by three is equal to nine, so I add them up, and my answer is 69.

Now, you'll notice that what we haven't done here is anything to do with decimals.

But that's fine because it's coming now.

So this time, we can use our knowledge our existing knowledge, but supporting everything during multiplication into decimals.

So this time, instead of 23, we've now got 2.

3 multiplied by three.

Again, I can distribute my number.

So this time, I've got two multiplied by three, plus 0.

3 multiplied by three.

So I have now partitioned 2.

3 or distributed it into two and 0.

3.

Again, I could use my place value counters to support me here.

So again, we can see that we've got 2.

3 multiplied by three, all linked to that connect quite nicely.

I can use my area model which you're drawing things using a piece of paper is probably slightly more efficient.

So I've got two multiplied by three is equal to, yeah, and 0.

3 multiplied by three.

Okay, so we should end up with six plus 0.

9 is equal to 6.

9.

Okay, now, we've had a good go at that, now is over to you.

So I'd like you think about the representations you're going to use.

You can use place value counters, or you can use that area model that I was using, can you solve 4.

2 multiplied by three? Okay, pause the video now, and then when you're ready, play again.

Okay, so let's have a look at how we did.

You may first have distributed it, and said well actually I want to do four multiplied by three and I want to do 0.

2 multiplied by three.

You may have done place value counters, which looked a little Like that, so I've got 4.

2 three times, or you may have done using area models to help you.

So you've got four and 0.

2, and I've got three, then I can multiply out to try and find the answer.

So in this case, four multiplied by three is equal to 12.

And 0.

2 multiplied by three is equal to 0.

6.

6.

Well done if we did that, okay.

Just as a bit of an alternative, there is another strategy that you may have used previously.

So I did want to mention it as well.

Now you can see here I've got a number fact 32 multiplied by four is equal to 128.

Now, this isn't a decimal yet.

So if I had the decimal 3.

2 multiplied by four, but I didn't want to use decimals, I can use my knowledge of 32 multiplied by four is equal to 128 to help me with this, because I know that 32 is 10 times greater than 3.

2.

So because I know this fact, I can then use that to help me.

So if I solve this part of the problem, then I know that my answer just needs to be because 32 is 10 times greater than 3.

2, then my answer, my product is going to be 10 times greater as well.

So if I get my answer and divide it by 10, then I'm going to find the answer to 3.

2 multiplied by four.

So I know 128 divided by 10 is 12.

8.

Therefore I know that 3.

2 multiplied by four is equal to 12.

8.

Okay, guys, we've had a bit of a practise, I've shown you lots of different faculties that we could use.

I want you now to go to your worksheets, and there's some problems for you to solve.

As you're solving these, do think about the representations and the strategies that you're using.

If you're really happy with using a bar model, sorry, a bar model, or an area model, then use those to help you to solve it.

If you'd rather use that place value counters then use those.

So just thinking really carefully about the strategy that you're using.

And if you do want to check it, maybe use that alternative model that we looked at to support that.

Okay, pause the video now, and then when you finish, we'll come back and have a look at the answers together.

Okay, let's have a look at some of those answers then.

So 10.

8 multiplied by seven.

First thing we may have done is maybe use that distributive law and may have partitioned it 10 multiplied by seven plus 0.

8 multiplied by seven.

Wow, yeah, we could have used place value counters if you do have place value counts, and you probably don't have this many, right? If you did spend time drawing that, brilliant, but probably not the most efficient way of doing it, right? Yeah, so what is then, I think the area model is possibly the most efficient way here.

So we know that we've got 10 multiplied by seven is equal to 70.

And we've got 0.

8 And I know that eight multiplied by seven is 56.

So I know that 0.

8 multiplied by seven is equal to 5.

6.

6.

Now those of you who were using that alternative strategy may have said actually, I'd rather do 108 multiplied by seven, and then divide my answer at the end by 10.

You did that, it may have looked something like that same answer.

Okay, next one 24.

3 multiplied by six.

The first thing we should have done is think about our partitioning, distributing it, then once we've done that, we may have gone straight into that area model 'cause it probably don't have a place to go to those place value counters just yet.

So thinking about it now, we may have partitioned into 24 and 0.

3 and then gone from there.

So 24 multiplied by six equal to 144.

And 0.

3 multiplied by six equal to 1.

8.

So we could then have had, if you've chosen that alternative method, 243 multiplied by six divided by 10.

But both should have got the answer of 145.

8.

6.

5 multiplied by three.

Hopefully, we first thought about our partitioning, distributing, then perhaps we went for our area model to support us.

So three multiplied by six is equal to 18 and then 0.

5 multiplied by three is 1.

5.

We may have used in this case partition.

So to use our place value counters possibly may be useful.

We should have found that our answer is equal to 19.

5.

So well done if you did that.

3.

9 multiplied by four.

Now three multiplied by four and 0.

9 multiplied by four.

So, three multiplied by four is equal to 12.

And 0.

9 multiplied by four is equal to 3.

6.

Or you might use alternative strategy.

So 39 multiplied by four, and then divided by 10.

Hopefully, we found that our answer was 15.

6.

Well done if you did that.

Okay, lots to get through today.

Hopefully, we've been able to get through it all, and we're feeling a lot more confident with multiplying by decimals.