Lesson video

In progress...

Hello, how are you today? My name is Dr.

Shack, and I am really excited to be learning with you today.

We're going to have great fun as we move through the learning together.

Today's lesson is from our units calculating with decimal fractions.

This lesson is called Solve Measures Problems using Knowledge of Multiplying Decimal Fractions.

As we move through the learning, we are going to focus on exploring how we can use our known facts, so our times table facts, and our knowledge of measures to solve problems that include decimal fractions.

Sometimes new learning can be a little bit tricky, but that is great.

It means we can work really hard together and learn lots of new things.

So let's get started, shall we? How do we solve measures problems using our knowledge of multiplying decimal fractions? Our key word in the lesson today is convert.

You might have heard that before, but let's practise that anyway.

My turn, convert.

Your turn.

Brilliant.

And when we convert, we mean to change a value or an expression from one form to another.

So in the context of this lesson, convert means to change from one unit to another.

So, for example, we might convert a measure from centimetres to millimetres.

Look out for that keyword as we move through our learning today.

So we are going to start by looking at solving problems involving measures.

And in our learning today, we have Lucas and Sophia to help us.

Let's have a look at this.

In school, Sophia and Lucas decide to build a tower of blocks.

I'm sure in the past, you have built a tower of blocks at some point, have you? But I wonder if you measured yours like they did.

They measured each block to be 0.

8 centimetres tall.

How tall could the tower become? What do you think? Well, Lucas is saying that we could give the height in centimetres because we know each block is 0.

8 centimetres or we could convert, that's the key word isn't it, and we could also give the height in millimetres.

So let's investigate this with Sophia and Lucas, shall we, and present our results in a table.

A table is a really clear way of presenting any data that we might collect.

So, Lucas is saying if we use one block, the height of the tower would be just 0.

8 centimetres.

We've got one block, one lot of 0.

And if we think about what that height would be in millimetres, so if we're going to convert, we know that one centimetre is equivalent to 10 millimetres.

Well, what does that mean? How does that help us? That's right, it also means then that 0.

1, or one tenth of a centimetre is equivalent to one millimetre.

In which case, that 0.

8 centimetre block must be equivalent to eight millimetres.

So at the moment, our tower is 0.

8 centimetres tall, or we could say that it is eight millimetres tall.

What if we use two blocks? What would happen then? How tall would the tower be? That's right.

Well, we know, we're going to use our known times table fact here, we know 2 times 8 ones is 16 ones.

So, 2 times 8 tenths is 16 tenths.

And we know 10 tenths are the same as one whole.

We've got 16 tenths, so that's one whole and another 6 tenths, and we write that as 1.

So if our tower was two blocks tall, its height in centimetres would be 1.

6 centimetres and we can then use our known facts that one centimetre is 10 millimetres to convert to millimetres.

So we have 16 millimetres.

What about if we have three blocks? Well, then we would have three lots of 0.

And we can use our known times table facts to help us.

Three times eight ones is 24 ones.

So three times eight tenths is 24 tenths.

And 24 tenths is the same as 2.

So if the tower was made of three blocks, it would be 2.

4 centimetres tall.

We can then use our known facts that one centimetre is equal to 10 millimetres to convert to millimetres and we would have 24 millimetres.

Do you spot a pattern? Have you noticed anything? That's right.

The height of the tower could be any multiple of 0.

8 centimetres or any multiple of 8 millimetres, because that's each block is always 0.

8 centimetres tall or eight millimetres tall.

Let's check your understanding with this.

Could you complete the table to show the height of the tower if four blocks were used? Remember, one block has a height of 0.

8 centimetres.

But this time, I want you to complete the table for four blocks.

Pause the video while you have a go.

Maybe talk to somebody about it.

And when you are ready for the answers, press play.

How did you get on? Did you say, well, it must be four lots of 0.

8; four eights are 32, so four lots of eight-tenths must be 32 tenths, which is the same as 3.

2, and if we convert that to millimetres, well, we know one centimetre is equal to 10 millimetres, so that must be 32 millimetres.

How did you get on with that? Well done.

Let's look at this problem.

At the weekend, Lucas went to see Big Ben in London.

I wonder if you have seen Big Ben? And Lucas found out a very interesting fact.

Did you know that Big Ben is 0.

096 kilometres tall? Wow.

Sophia, she went for a walk with her parents at the weekend.

They climbed up the tallest mountain in England.

I wonder if you knew what that was called.

It's Scarfell Pike.

I wonder if you might have climbed it.

And Sophia found out an interesting fact about Scarfell Pike.

Scarfell Pike is about 10 times the height of Big Ben.

So using this information, we can determine the height of Scarfell Pike.

We can form an equation to help us.

We know the height of Big Ben is 0.

096 kilometres.

And we know Scarfell Pike is 10 times that height.

So we're going to multiply by 10.

And remember, when we multiply by 10, the digits move one place to the left.

So 0.

096 kilometres multiplied by 10 is equal to 0.

96 kilometres.

So the height of Scarfell Pike, that tallest mountain in England, is about 0.

96 kilometres.

So, what do we notice about 0.

96? That's right, it's just smaller than one, isn't it? Four hundredths smaller than one.

So not quite one whole kilometre tall.

We could also calculate the height in metres, Lucas reminds us, when we convert, couldn't we? We know there are 1,000 metres in one kilometre.

So we can convert from kilometres to metres by multiplying by 1,000.

We can take that distance in kilometres and multiply it by 1,000 to give us the distance in metres.

We know the height of Big Ben is 0.

096 kilometres.

If we multiply that by 1000, well, we know when we multiply by 1000, the digits move three places to the left.

So, that would be 96 metres.

So, Big Ben is 96 metres tall, and that's equivalent in height to 0.

096 kilometres.

We can then form an equation to calculate the height of Scarfell Pike in metres.

We know Big Ben is 96 metres and we know Scarfell Pike is about 10 times that height.

96 multiplied by 10.

When we multiply by 10, the digits move one place value place to the left, which would be 960 metres.

So the height of Scarfell Pike is about 960 metres and that's equivalent in height to 0.

96 kilometres.

Let's check your understanding with this.

Could you convert the given height in kilometres to metres and using the given equation, write an equation to calculate the height in metres.

So, you've got 7 multiplied by 0.

04 kilometres is equal to 0.

28 kilometres but I'd like to find out what that is in metres.

So pause the video while you have a go, and when you're ready to go to the answers, press play.

How did you get on? Did you realise that we can use our knowledge that one kilometre is 1000 metres, so 0.

04 kilometres must be equal to 40 metres? We can then multiply 7 by 40 metres to get 280 metres.

So, 0.

28 kilometres is equivalent to 280 metres.

Your turn to practise now for question one.

Could you solve this problem? Sophia fills a jug using 0.

3 litre cups.

How much water could be in the jug? Use the tail to record your thoughts, and explain what you notice about the possible volumes.

For question two, could you solve these problems? For part A, Sophia runs 0.

4 kilometres.

Izzy runs five times as far.

How far has Izzy run? Could you give your answers in kilometres and in metres? For part B, Lucas has a jug filled to its capacity of 0.

2 litres.

Sophia's jug has a capacity that is six times the capacity of Lucas's jug.

What is the capacity of Sophia's jug? Give your answer in litres and in millilitres.

And for part C, Lucas's cat has a mass of 0.

09 kilogrammes.

His dog has a mass that is 50 times the mass of his cat.

What is the mass of his dog? Give your answer in kilogrammes and in grammes.

And if I may make a suggestion, it might be useful to represent some of these in a bar model to help you.

Pause the video while you have a go at both questions.

When you are ready for the answers, press play.

How did you get on? Let's take a look.

For our first question, it was about Sophia filling a jug using 0.

3 litre cups.

And we had to work out how much water could be in the jug.

So I said, well, she could have used one cup, so that would be 0.

3 litres or 300 millilitres.

She might have used two cups, so that would be 0.

6 litres or 600 millilitres.

She may have used three cups, which would be 0.

9 litres, or 900 millilitres, or she might have used four cups, which would be 1.

2 litres or 1,200 millilitres.

I wonder if you thought it could be a different volume.

You might have said that you noticed the volume in litres was always a multiple of 0.

3, 0.

6, 0.

9, 1.

They are all multiples of 0.

And that, given in millilitres was always a multiple of 300.

300, 600, 900, 1,200, and that's because there are 1,000 millilitres in one litre.

For question two, you had some problems to solve.

For part a Sophia ran 0.

4 kilometres, Izzy ran five times as far.

So you can see I have represented that in my bar model, which would help me form an equation.

4 kilometres multiplied by five is equal to two kilometres.

I can use my timetable known facts to help me there, couldn't I? Four fives are 20.

So four tenths times five is 20 tenths, which is equal to 2.

We could also have done that in metres.

We know 0.

4 kilometres is equal to 400 metres.

400 metres times 5, well again, I can say 4 fives are 20, so 400 fives must be 20 hundreds or 2,000.

So Izzy runs 2 kilometres, which is equivalent to 2,000 metres.

For part B, Lucas has a jug filled to its capacity of 0.

2 litres.

Sophia's jug had a capacity of 6 times that.

So you can see, I have represented that on my bar model.

And I can use that to form an equation.

2 litres multiplied by 6.

Well, I can use my known facts, 2 sixes, to help.

2 sixes are 12.

So 2 tenths times 6 must be 12 tenths, or 1.

2 litres.

We could also look at this in millilitres.

2 litres is equal to 200 millilitres multiply that by 6.

We get 1,200 millilitres.

So, we can say Sophia's jug has a capacity of 1.

2 litres and that is equivalent to 1,200 millilitres For part C, Lucas's cat had a mass of 0.

09 kilogrammes, and his dog had a mass that is 50 times that mass.

So we can use that information to form an equation.

09 multiplied by 50.

Well, we know 9 multiplied by 5 ones would be 45 ones.

We've got 9 hundredths multiplied by 50.

Well, 9 hundredths multiplied by 5 would be 45 hundredths.

But then we need to make that 10 times bigger because we're multiplying by 50.

So that's 4.

5 kilogrammes.

We could also have converted the amount in kilogrammes to grammes.

09 kilogrammes is equal to 90 grammes.

90 multiplied by 50 is equal to 4,500 grammes.

So his dog, Lucas's dog, has a mass of 4.

5 kilogrammes, which is equivalent to 4,500 grammes.

How did you get on with all those questions? Fantastic.

Brilliant learning so far.

I am really impressed with how hard you are trying.

We are going to move on now and look at some problems involving money.

So, let's have a look at this one.

Sophia saves 60 pence from her pocket money each week.

Can you visualise that? What does 60 pence look like? That's right, I've got three 20s here.

You might have visualised a 50p and a 10p or six 10ps, , or maybe some other amounts.

So what might the question be here, do you think? At the moment, there is no question, is there? How much money could be in her money box? So let's investigate this, and like we did before, let's present our results in a table.

We can give the amount in pence, but we could convert.

Remember, that's our key word remembering to change from one form to another.

So we could convert from the pence and give the amount in pounds.

So after one week, we know Sophia will have saved 60p.

One lot of 60 is 60 pence.

We know that one pound is equivalent to 100 pence.

So 10 pence, or 0.

1, one-tenth of a pound is equivalent to 10p.

And 60p then must be equivalent to 0.

60.

Well, what about after five weeks? Well, she would have five 60s, and we can use our known facts to help.

We know five times six ones is 30 ones.

So five times six tens is 30 tens, or 300.

So after 5 weeks, Sophia would have saved 300 pence.

And then we can use our known facts to help us convert that into pounds.

We still know that 5 sixes are 30, so 5 times 6 tenths would be 30 tenths, which is equal to 3.

You might notice something here.

That's right, I've got some zeros, some placeholders in my tenths and hundredths place, haven't I? And that's because we are discussing money.

And when we write amounts of money, we can put the zeros to show that there are no pence.

It's 3 whole pounds, 3.

00.

3 whole pounds and no pence.

But what about after seven weeks? Well, we can say seven sixes are 42, so seven lots of six tens would be 42 tens or 420, and we can do the same for pounds.

We know 7 sixes 42, so 7 lots of 6 tenths would be 42 tenths, which is the equivalent to 4.

2, or because it's money, we would write 4.

20 to show we have 4 whole pounds and 20 pence.

Let's check your understanding with this.

Could you complete the table to show how much money would be saved after six weeks? Pause the video while you have a think about that.

And when you are ready to go through the answers, press play.

How did you get on? Did you say, well, after six weeks, you must have six 60s, which is 360 because six sixes are 36, and we could convert that into pounds, which would be six six tenths, so 36 tenths, which is three pounds, 60, 3.

60.

How did you get on with those? Well done.

It's your turn to practise now.

For question one, could you fill in the blanks in these equations? For question two, could you solve this problem? Lucas saves his pocket money.

He saves 90p each day.

How much money might he have saved? Could you record your thoughts in the table? Explain what you notice about the possible amounts.

For question three, could you solve these problems? For part A, Lucas saves 30 pence a week.

How much does he save in six weeks? Give your answer in pence and in pounds.

For part B, Lucas has 90 pence.

Sophia has four times as much.

How much more money does Sophia have? Give your answer in pounds.

And for part C, Sophia saves 540 pence.

Lucas has won six times this amount.

How much less money does Lucas have? Give your answer in pounds.

Have a go at all three questions.

Pause the video while you do that.

And when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

For question one, you were asked to fill in the blanks in these equations.

We could have used our known facts for these ones, that three nines are 27.

So three tenths times nine must be 27 tenths, or 2.

But because it's money, we would say £2.

70.

And then we could look at that amount in pence.

We know 0.

30 pounds is equal to 30 pence.

Multiplying that by 9 we get 270 pence.

For the second set of questions we could have used our known fact that 8 sevens are 56.

So 8 tenths multiplied by 7 is 56 tenths, or 5.

6, and in this case because it's money £5.

60.

We could have looked at converting that into pence.

80 pounds is equal to 80 pence.

Multiplying that by 7, we get 560 pence.

And for the last set of equations, we could have used the known fact 9 sixes are 54, so 9 tenths multiplied by 6 is 54 tenths, or five pounds 40.

We can then look at the amount in pence.

90 pounds is equal to 90 pence.

Multiply that by six.

We get 540.

For question two, you were asked to solve this problem about Lucas's pocket money.

And he saved 90 pence each day.

We had to record our results in a table to see how much money he might have saved.

I chose three days, five days, and eight days.

You may have chosen something different.

After three days, he would have saved 3.

90, which is 270, or 3.

9, which is 27 tenths, or £2.

70.

After five days, he would have saved 5.

90, which is 450 pence, which is equal to £4.

50.

After eight, he would have saved 5.

90, which is 450 pence, which is equal to £4.

50.

After eight days, he would have saved 8.

90, which is 720 pence, or 8.

9, 10, 7th, which is equal to £7.

20.

You might have said that you noticed that the amount in pence was always a multiple of 90, and the amount in pounds was always a multiple of 0.

90.

And this is because there are 100 pennies in one pound.

For question three, you had some problems to solve.

The first one was about Lucas saving 30 pence a week.

So how much does he save in six weeks? And I can represent this in a bar model, and that will help me to form an equation.

30 pence times 6, well, I know 3 6s are 18.

So, three tens times six would be 18, or 180.

We could also have looked at that in pounds and converted the amount in pence, so 30 into pounds 0.

30.

We can still use that same times table, 3 6s are 18, so 3 10s times six would be 18 tenths, which is the same as 1.

8, or in this case, £1.

80.

So we could say in six weeks, Lucas saves £1.

80, which is equivalent to 180 pence.

For part B, Lucas has 90p and Sophia has four times as much.

Again, I can represent this in a bar model to help me form an equation.

9 times 4 is 36, so 9 10 times 4 must be 36 10s or 360 pence.

We could look at that amount in pounds.

90 pence is the same as 0.

90 pounds, and we can multiply that by 4.

We can still use 9 4s are 36, but 9 tenths times 4 would be 36 tenths, or £3.

60.

So Sophia has £3.

60, but we were asked to find out how much more money Sophia has.

So Sophia has £3.

60, and we're going to subtract the 90 pence that Lucas has, which is £2.

70.

Sophia has £2.

70 more than Lucas.

For part C, Lucas saves 540 pence.

Lucas has 1 sixth times the amount.

So we can use this information to draw a bar model and then form an equation.

This time he has 1 sixth times the amount, so we have to divide by 6.

We can use our known facts to help us.

54 divided by 6 is 9, so 540 divided by 6 must be 90 pence.

We could also have looked at this in pounds.

540 pence is equal to £5.

40.

Divide that by 6, and we get 0.

90.

So Lucas has £0.

90.

And this is £5.

40 subtract that 0.

90, which is equal to £4.

50.

So Lucas has £4.

50 less than Sophia.

How did you get on with all those questions? Well done.

Fantastic learning today, everybody.

You have really deepened your understanding of how we can solve measures problems. We know that we can use knowledge of multiplying by decimal numbers with whole numbers, and that can help us solve these measure problems. We can use that stem sentence, m times m ones is equal to m ones, so m times m tenths or hundredths is equal to m tenths or hundredths.

You should be really proud of how hard you have tried today.

I have had great fun learning with you, and I look forward to learning with you again soon.

I've finished the video