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Hello, how are you today? My name is Dr.
Shorak and I am really happy that you have chosen to do your maths learning with me today.
We are gonna have a lot of fun as we move through the learning together.
Today's lesson is from our unit calculating with decimal fractions.
The lesson is called use known multiplication facts and unitizing to multiply hundredths with whole numbers.
As we move through the learning today, we're going to deepen our understanding of hundredths, what they are, what they are composed of, and then we're going to use this to help us multiply.
Sometimes new learning can be a little bit tricky, but it is okay.
I'm here to guide you and I know if we work really hard together, then we can be successful.
Shall we get started then? Shall we look at how we use our known multiplication facts to multiply with hundredths? Our keyword for the learning today is hundredth.
Now, I know you've probably heard this word before, but it's always good to practise.
Let's have a go.
My turn, hundredth, your turn.
Nice.
And a hundredth is just one part in 100 equal parts.
We are going to start today's learning by thinking about hundredths.
We have Lucas and Sofia to help us.
Lucas has one pound.
Sofia has one penny.
Lucas is saying that he has 100 times as much money as Sofia has.
Why is he saying that? What do we know? That's right, there are 100 pennies in one pound.
So Lucas has 100 times the amount that Sofia has.
Sofia is saying that her one pence is 1/100 of one pound.
Remember hundredth? That's one of our keywords.
It means one part in 100 equal parts.
She has one penny, which is one part in the 100 equal parts that a pound has.
There are 100 hundredths in one whole.
Let's practise counting in hundredths using our number line and as Sofia says, we can count up in different ways.
We're going to start by counting up in fraction vocabulary of hundredths.
We start with zero, one hundredth, two hundredths.
Can you continue? Let's count together, shall we? Three hundredths, four hundredths, five hundredths, six hundredths, seven hundredths, eight hundredths, nine hundredths.
What would come next after nine hundredths? That's right, it would be 10 hundredths and 10 hundredths are equivalent to 1/10.
What would come next then after 10 hundredths? That's right, 11 hundredths, 12 hundredths.
Can you keep going? 18 hundredths.
19 hundredths.
What would come next then? That's right, it would be 20 hundredths and 20 hundredths is the same as 0.
2.
What would come next after 20 hundredths? That's right, 21 hundredths.
Should we also have a go at counting backwards? So 21 hundredths, 20 hundredths, 19 hundredths.
Can you keep going? 15 hundredths and then forward again.
16 hundredths, 17 hundredths, 18 hundredths, 19 hundredths, 20 hundredths.
What would come next? That's right, 21 hundredths.
Can you keep going? 25 hundredths, 26 hundredths.
29 hundredths.
What would be next? That's right, 30 hundredths.
30 hundredths is the same as 3/10 or 0.
3.
Well done, but we can also count up using decimal fraction vocabulary.
So zero, 0.
01, 0.
02.
Can you continue? Let's count together.
0.
03.
0.
04.
You keep going.
0.
08, 0.
09.
Ooh, what would come next? That's right, 0.
1.
We don't say 0.
10 'cause it's 0.
1.
It's 1/10, so 0.
1.
What would come next then? That's right.
0.
11, 0.
12, 0.
13.
Can you see how I'm saying the digits rather than the number? I'm not saying 0.
13, I'm saying 0.
13 and that's really important when we learn about decimals.
0.
14, 0.
15.
Can you keep going? 0.
19.
What would be next? That's right, 0.
2, which is equivalent to 2/10.
0.
21, 0.
22, 0.
23.
Can you continue? 0.
26.
0.
27.
Let's just have a go at counting backwards.
0.
27, 0.
26, 0.
25, 0.
24.
You keep going.
And before 0.
21? 0.
2, 0.
19, 0.
18.
Let's count up again.
0.
18, 0.
19.
0.
2.
0.
21.
0.
22.
0.
23.
Can you keep going? 0.
28, 0.
9 and then 0.
3.
30 hundredths is the same as 3/10 and we say 0.
3.
We can also practise counting up in hundredths using a Gattegno chart.
Again, we could count up in decimal fraction language or in hundredths fraction language.
Let's count up in the fraction language of hundredths.
Are you ready to count with me? Let's start.
One hundredths, two hundredths, three hundredths, four hundredths.
Can you keep going? Nine hundredths.
What would come next? That's right, 10 hundredths and 10 hundredths is the same as 1/10, and we can keep counting.
11 hundredths, 12 hundredths, 13 hundredths, 14 hundredths.
Can you keep going? 19 hundredths.
Then we would have 20 hundredths, which is equivalent to 2/10 or 0.
2.
We could then switch to counting up in decimal fraction vocabulary.
0.
21, 0.
22, 0.
23, 0.
24.
Can you continue? 0.
29.
What would come next? That's right, 0.
3.
Well done on that counting.
Let's check your understanding.
Could you use the number line to complete the sequences? Pause the video while you have a look and when you are ready to go through the answers, press play.
How did you get on? Did you see that the first sequence was increasing in hundredths? We had 17 hundredths, 18 hundredths, 19 hundredths, then 20 hundredths.
20 hundredths can be written 0.
20 or you may have just written 0.
2.
And for sequence B, it was counting down in hundredths.
12 hundredths, 11 hundredths.
It would be 10 hundredths, then nine hundredths.
Well done.
But what do we know about the composition of hundredths? What are they made from? Let's look at 0.
03 or three hundredths.
I can represent what three hundredths is composed of on a bar model.
You can see that three hundredths is composed of three one hundredths, three equal parts of 0.
01.
We could add the three parts together to give us 0.
03.
We could say that three times 0.
01, three lots of one hundredth are equal to three hundredths or 0.
03.
What about 0.
43? What's that composed of? "0.
43," Sofia is telling us, "is composed of three one hundredths." What do you think? Do you agree with Sofia? Ah, Lucas doesn't.
Lucas is respectfully challenging Sofia.
I wonder why.
That's because there is a three in the hundredth column.
We can see that, but actually, 0.
43 is composed of 43 hundredths, not just three hundredths.
Sofia gets it now.
1/10 is composed of 10 hundredths and we have 4/10 and this is 40 hundredths and three more.
So we can represent 0.
43 as 4/10 or 40 hundredths and three more hundredths.
Let's check your understanding on that.
0.
38 is composed of eight hundredths.
Is that true or false? Pause the video while you have a think.
Maybe talk to somebody about this.
When you're ready to see the answer, press play.
How did you get on? Did you say that has to be false? But why? Is it because the three represents 3/10, which are not hundredths or is it because 1/10 is composed of 10 hundredths? So 3/10 will be composed of 30 hundredths and we have eight more hundredths.
This is 38 hundredths.
Pause the video while you think about which option it is and when you are ready to hear the answer, press play.
How did you get on? Did you say it must be B? 1/10 is composed of 10 hundredths and we have 3/10, so that must be 30 hundredths and then eight more.
38 hundredths.
Your turn to practise now.
For question one, could you complete the equations? For question two, Sofia says that 0.
48 is composed of eight hundredths.
Do you agree or disagree? And could you convince me that you are correct? Pause the video while you have a go at both questions.
When you are ready to go through the answers, press play.
How did you get on? Let's have a look.
Did you notice that for a lot of these, you could use your known number facts? If we know four ones and six ones are 10 ones, we know four hundredths and six hundredths are 10 hundredths, which is equivalent to 1/10 or 0.
1 and the same here.
If we know three ones and seven ones are 10 ones, then three hundredths and seven hundredths are 10 hundredths, which is equivalent to 1/10 or 0.
1.
Four hundredths and six hundredths are equal to 10 hundredths, which is equal to 0.
1 or 1/10.
And the same, five hundredths and five hundredths will be equal to 10 hundredths, which is equal to 1/10 or 0.
1.
And then 0.
1, well, that must be made of nine hundredths and one hundredth or two hundredths and eight hundredths and we have 1/10 subtract three hundredths is equal to seven hundredths, and 1/10 subtract six hundredths is equal to four hundredths.
1/10 subtract five hundredths is equal to five hundredths and 1/10 subtract eight hundredths would be equal to two hundredths.
1/10 subtract one hundredth would be equal to nine hundredths.
1/10 subtract three hundredths would be equal to seven hundredths.
And eight hundredths would be equal to 1/10, subtract two hundredths and five hundredths would be equal to 1/10 subtract five hundredths.
For question two, you are asked to say if you agree with Sofia that 0.
48 is composed of eight hundredths.
You might have said you disagree with Sofia and given a reason like there are 10 hundredths in 1/10, we have 4/10, which is equivalent to 40 hundredths and we have eight more hundredths.
So this is equivalent to 48 hundredths, not just eight hundredths.
How did you get on with both of those questions? Well done.
Fantastic learning so far, everybody.
I can see how hard you are trying.
We're going to move on now and have a look at how we can use that information that we've learned to multipling with hundredths.
Let's have a look at this.
Sofia is saving her pocket money.
She is given four pounds each week.
Can you visualise that? Can you imagine being given four pounds every week? What might the question be, do you think? That's right.
How much money could she save? Not how much money did she save.
We don't know how many weeks she saved over, so how much could she save? And let's start by representing this on a number line and writing the related equations.
We can see that before the first week, she had no money, so she had zero pounds.
After the first week, she was given four pounds.
After the second week, she had another four pounds, so she had two lots of four pounds, she had eight pounds.
After the third week, we added another four pound.
Three multiplied by four is equal to 12.
So she would have 12 pound and she would continue to get another four pounds every week.
We can represent that in a table.
What do you notice? That's right, Sofia could save any amount that is a multiple of four because each week she got another four pounds.
And we know multiplication is commutative, so we could represent the equations the other way round.
Let's have a look at Lucas though.
Lucas is also saving some money.
He is saving 0.
04 pounds each week.
How much money could he save? Can you visualise that? What does that look like? That's right, 0.
04 is the same as four pennies.
We can start by representing this on the number line and writing the equations.
So at the beginning, he has nothing.
After the first week, he has 0.
04 pounds or four pence and then he gets given another four pence, which would be eight pence or 0.
08 pounds.
He then gets given another four pence, so he's got three lots of 0.
04 pounds, which is equal to 0.
12 pounds.
And he continues, doesn't he? Getting 0.
04 pounds every week.
So let's have a look at this table showing our results.
What do we notice? That's right, Lucas could save any amount.
That is a multiple of four hundredths.
And we know multiplication is commutative.
So we could also write the equations like this.
Let's now compare multiples of four and 0.
4.
The multiples of four is how much Sofia could be saving and the multiples of 0.
04 is how much Lucas could be saving.
What do you notice about them? That's right, we've got three fours are equal to 12, but what does that mean? So it means three four hundredths are equal to 12 hundredths and 12 hundredths is written 0.
12.
Lucas and Sofia look at this equation.
Seven multiplied by 0.
05 or five hundredths and we can use a stem sentence to help us.
Seven times five ones is equal to 35 ones.
So seven times five hundredths is equal to 35 hundredths and we can represent that as an equation.
Seven fives are 35.
So seven times five hundredths is equal to 35 hundredths.
35 hundredths is equivalent to three tenths and five more hundredths.
So we can write seven multiplied by five hundredths is equal to 35 hundredths or 0.
35.
Let's check your understanding now.
Could you complete the equations? And use the stem sentence to help you.
Pause the video while you do that.
When you're ready to go through the answers, press play.
How did you get on? Did you work out that eight multiplied by four is equal to 32? Eight multiplied by four ones is equal to 32 ones.
So eight times four hundredths must be equal to 32 hundredths.
Eight multiplied by four hundredths or 0.
04 is equal to 0.
32.
And we could have used our stem sentence to help us.
Eight times four ones is equal to 32 ones.
So eight times four hundredths is equal to 32 hundredths.
Well done.
Let's look at this using arrays.
You can see here I have got three groups of four ones.
Three times four is equal to 12.
Three times four ones is equal to 12 ones.
We can use that to help us when the value of each of our counters is 0.
01.
So now you can see I've got three groups of 0.
04 or four hundredths, and that equals 12 hundredths or 0.
12.
We could say three times four hundredths is equal to 12 hundredths.
And we can use the stem sentence to help us.
Three times four ones is equal to 12 ones.
So three times four hundredths is equal to 12 hundredths.
Let's have a look at these different arrays.
We've got the arrays where the place value counters have a value of one, a value of 0.
1 or 1/10 or a value of 0.
01, one hundredth.
What do you notice? That's right, to support us when we multiply with hundredths, which is what we're learning about in this lesson, we could think about multiplying with tenths first.
So we know three multiplied by four ones is 12 ones.
So three multiplied by 4/10 is equal to 12 tenths and 12 tenths is equal to 1.
2.
So three multiplied by four hundredths is 12 hundredths, which is 0.
12.
If we think about multiplying with tens first, we know when we multiply by hundredths, our answer must be 10 times smaller.
So we can use it to check our answers.
Let's check your understanding with this.
Could you use the arrays to complete the equations? Pause the video while you do that.
When you are ready to go through the answers, press play.
How did you get on? Did you say three times five is equal to 15? Three times five ones is equal to 15 ones and we can use that to help us.
Three times five hundredths is equal to 15 hundredths and three times 0.
05 must then be equal to 0.
15, 15 hundredths.
We can check our answer by thinking about multiplying with tenths.
Three multiplied by 5/10 would be 1.
5.
So our answer of 0.
15 must be correct because this is 10 times smaller.
How did you get on with those? Well done.
It's your turn to practise now.
For question one, part A, could you fill in the missing numbers? For part B, could you fill in the missing symbols? Less than, greater than or equals too.
For question two, could you solve these problems? Part A, it takes 0.
01 or 1/100 of a kilogramme of baking powder to make one cake.
How much baking powder is needed to make seven cakes? For part B, a blue kite is flying 0.
04 kilometres, 1/400 of a kilometre, above the ground.
A hot air balloon is flying at nine times this height.
How far above the ground is the hot air balloon? Pause the video while you have a go at both questions.
When you're ready to go through the answers, press play.
How did you get on? Let's have a look.
For the first question, you were asked to fill in the missing numbers.
So we know four eights are 32, so four eight hundredths must be 32 hundredths, 0.
32.
Five times seven ones is 35 ones, So five times 700 hundredths is 35 hundredths.
Three times six ones is 18 ones.
So three times six hundredths is 18 hundredths or 0.
18.
Five multiplied by seven is equal to 35.
Five hundredths multiplied by seven would be 35 hundredths or 0.
35.
12 multiplied by four hundredths is 48 hundredths, 0.
48.
Five hundredths multiplied by seven is 35 hundredths, 0.
35.
Zero multiplied by seven hundredths, well that has to be zero 'cause anytime we multiply by zero, the product is always zero.
Six hundredths multiplied by 10 must be 60 hundredths, which is 0.
6.
For part B, you were asked to fill in the missing symbols.
Nine multiplied by 400 hundredths is greater than six multiplied by four hundredths.
Eight multiplied by nine hundredths, well, that's greater than seven multiplied by nine hundredths.
Nine multiplied by two hundredths is greater than seven multiplied by two hundredths.
And five multiplied by eight hundredths, well, that is the same as eight hundredths multiplied by five because multiplication is commutative.
What about this one? If we've got two lots of seven hundredths and one lot of seven hundredths, we've got three lots of seven hundredths and that is equal to if we have five lots of seven hundredths and we take away two lots of seven hundredths, that would also be three seven hundredths.
So they are equal.
Did you notice that you did not actually need to calculate any of these? You could have filled in the missing symbols using your number sense and your reasoning skills.
If the multipliers are the same, we can just compare the multiplicand.
An understanding of the commutative property of multiplication and the distributive law also helps.
For question two, solving these problems. The first problem was about some baking powder and we needed one hundredth of a kilogramme to make one cake.
And I can represent this in a bar model 'cause I need to find out how much I need to make seven cakes.
So I have seven equal parts of one hundredth or 0.
01.
From this, I can form an equation.
I know seven ones are seven, so seven one hundredths must be seven hundredths.
To make seven cakes, we need seven hundredths or 0.
07 of a kilogramme of baking powder.
For part B, our blue kite is flying 0.
04 or four hundredths of a kilometre above the ground and the hot air balloon is flying at nine times this high.
So I can represent this in a bar model with nine equal parts of four hundredths.
From this, we can form an equation.
We know nine times four ones is equal to 36 ones, so nine multiplied by 400 hundredths is equal to 36 hundredths or 0.
36.
The hot air balloon is 0.
36 of a kilometre above the ground.
How did you get on with both of those questions? Well done.
Really impressed with your learning today and how hard you have tried.
You have made such good progress at multiplying hundredths with whole numbers.
We know there are 100 hundredths in one whole, and we know there are 10 hundredths in 1/10, and we know we can use the stem sentence mm times mm once is equal to mm once.
So mm times mm hundredths is equal to mm hundredths and that supports us to multiply hundredths.
I have had great fun learning with you today and I look forward to learning with you again soon.
