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Hi, my name is Mr. Peters.
Thanks for choosing to learn with me today.
In this lesson, we're gonna be thinking about describing and writing decimal numbers with hundredths in lots of different ways.
If you're ready, let's get started.
So by the end of this lesson today, you should be able to say that you can describe and write decimal numbers with hundredths in lots of different ways.
Throughout this lesson, we're gonna be referring to several different keywords.
I'm gonna say them first, and then you can have a go afterwards, are you ready? My turn, hundredth.
Your turn.
My turn, decimal number.
Your turn.
My turn, fraction.
Your turn.
My turn, multiple.
Your turn.
So, let's think about what these mean then.
A hundredth is the name we give to one part from a whole that has been divided into 100 equal parts.
A decimal number is a number that has a decimal point in it, and shows fractional parts after the decimal point with digits.
A fraction shows us how many equal parts there are in a whole.
And a multiple is the result of multiplying a number by an integer.
For example, two multiplied by five is equal to 10.
So 10 is a multiple of both two and five.
Okay, let's think about what's ahead in this lesson.
This lesson's gonna be split into three parts.
The first part is thinking about counting and representing hundredths up to one whole.
The second part is gonna be counting and representing multiples of hundredths.
And the final part is gonna be counting and representing hundredths above and beyond one whole.
When you're ready, let's get going.
Throughout this lesson today, we're gonna have both Sofia and Andeep helping us with their thinking as we go.
Let's start here.
At the moment, I have a square, and this square is going to represent my whole.
What do you notice? That's right, the whole has been divided into 100 equal parts, hasn't it? And each one of these parts represents one hundredth.
And we can record one hundredth as 0.
01.
Now that we know each part has a value of one hundredth, when we start combining them together, we can start counting forwards and backwards cumulatively with our hundredths.
We're gonna start counting today in hundredths, up to one whole.
And we're gonna do so looking at our hundredth square here, and we're gonna use the language of 0.
01, decimal language.
Are you ready? Let's get started.
0.
01, 0.
02, 0.
03, 0.
04, 0.
05, 0.
06, 0.
07, 0.
08, 0.
09, 0.
1, or 0.
10.
0.
11, 0.
12, 0.
13, 0.
14, 0.
15, 0.
16, 0.
17, 0.
18, 0.
19, 0.
2.
0.
21, 0.
22, 0.
23, 0.
24.
0.
25, 0.
26, 0.
27, 0.
28.
0.
29, 0.
3.
0.
31, 0.
32, 0.
33, 0.
34, 0.
35, 0.
36, 0.
37, 0.
38, 0.
39, 0.
4.
0.
41, 0.
42, 0.
43, 0.
44, 0.
45, 0.
46, 0.
47, 0.
48, 0.
49, 0.
5.
Hmm, halfway there.
0.
51.
0.
52.
0.
53, 0.
54, 0.
55, 0.
56, 0.
57, 0.
58, 0.
59, 0.
6.
0.
61, 0.
62, 0.
63, 0.
64, 0.
65, 0.
66, 0.
67, 0.
68, 0.
69, 0.
7.
0.
71, 0.
72, 0.
73, 0.
74, 0.
75, 0.
76, 0.
77, 0.
78, 0.
79, 0.
8.
0.
81, 0.
82, 0.
83, 0.
84, 0.
85, 0.
86, 0.
87, 0.
88, 0.
89, 0.
9.
0.
91, 0.
92, 0.
93, 0.
94, 0.
95, 0.
96, 0.
97, 0.
98, 0.
99, one.
Well done for keeping up with the counting there, fantastic.
We can also do that backwards.
And this time we're gonna exactly that, but we're gonna count backwards using our number line here to show the representation.
We're gonna use the same language again of 0.
01.
However, obviously, this time we're gonna start at one.
Are you ready? One, 0.
99, 0.
98, 0.
97, 0.
96, 0.
95, 0.
94, 0.
93, 0.
92, 0.
91, 0.
9.
0.
89, 0.
88, 0.
87, 0.
86, 0.
85, 0.
84, 0.
83, 0.
82, 0.
81, 0.
8.
Can we do it really quietly now? 0.
79, 0.
78, 0.
77, 0.
76.
0.
75, 0.
74, 0.
73.
0.
72, 0.
71, 0.
7.
0.
69, 0.
68, 0.
67, 0.
66, 0.
65, 0.
64.
0.
63, 0.
62, 0.
61.
0.
6, 0.
59, 0.
58, 0.
57, 0.
56, 0.
55.
0.
54, 0.
53, 0.
52, 0.
51, 0.
5.
0.
49, 0.
48, 0.
47, 0.
46, 0.
45, 0.
44, 0.
43, 0.
42, 0.
41.
0.
4, 0.
39, 0.
38, 0.
37, 0.
36, 0.
35, 0.
34, 0.
33, 0.
32, 0.
31, 0.
3.
0.
29, 0.
28, 0.
27, 0.
26, 0.
25, 0.
24, 0.
23, 0.
22, 0.
21.
0.
2, 0.
19.
0.
18, 0.
17, 0.
16, 0.
15, 0.
14, 0.
13, 0.
12, 0.
11, 0.
1.
0.
09, 0.
08, 0.
07, 0.
06, 0.
05, 0.
04.
0.
03, 0.
02, 0.
01 and zero.
Well done for keeping up.
Fantastic counting.
So far, we've been counting using decimal number language.
Now we can start thinking about counting using fractional language.
Have a look at the number line this time.
We're not gonna count all the way up.
We're gonna count the short portion of this, but focus on how we're representing each number each time as a fraction as well.
Are you ready? Zero hundredths, one hundreth, two hundreths, three hundredths, four hundredths, five hundredths, six hundredths, seven hundredths, eight hundredths, nine hundredths.
10 hundredths, 11 hundredths, 12 hundredths, 13 hundredths, 14 hundredths, 15 hundredths, 16 hundredths, 17 hundredths.
18 hundredths, 19 hundredths, 20 hundredths.
Can you see how the fractions are progressing as it moves along the number line? Let's count back from 20 hundredths as well.
20 hundredths, 19 hundredths, 18 hundredths, 17 hundredths, 16 hundredths, 15 hundredths, 14 hundredths, 13 hundredths, 12 hundredths, 11 hundredths, 10 hundredths, nine hundredths, eight hundredths, seven hundredths, six hundredths, five hundredths, four hundredths, three hundredths, two hundredths, one hundredth and zero hundredths.
Well done.
Fantastic counting again.
So, so far we've counted using decimal numbers, and now we've just started counting using fractions.
Being able to move between both of these types of counting is known as dual counting.
We can also use what's called a gattegno chart to do some of our dual counting.
This is a really special chart, and it allows us to really highlight the parts that make up the decimal numbers that we're counting.
So let's start counting using our decimal number language to start off with.
Okay, if you've got a gattegno chart in front of you, you can tap each number as we go along.
If you don't, you could point at the numbers on the screen, but be careful not to touch the screen.
Are you ready? 0.
01.
0.
02, 0.
03, 0.
04, 0.
05.
0.
06, 0.
07, 0.
08.
0.
09, 0.
1, 0.
11.
Ah, at this point, when we've got both a 10th and a hundredth, you'll need to tap it twice or use two fingers to tap both of them at the same time.
0.
12, 0.
13, 0.
14.
0.
15, 0.
16, 0.
17.
0.
18, 0.
19, 0.
2.
0.
21, 0.
22, 0.
23, 0.
24, 0.
25, 0.
26.
0.
27, 0.
28, 0.
29, 0.
3.
Can you see what's happening each time there? Each time we're having to tap the tenths and the hundredths and combining them together as we say it as a decimal number, aren't we? Let's change over now to start counting up in the fractional language of hundredths.
Are you ready? We started on 30 hundredths.
30 hundredths, 31 hundredths, 32 hundredths, 33 hundredths, 34 hundredths, 35 hundredths, 36 hundredths, 37 hundredths, 38 hundredths, 39 hundredths, 40 hundredths, 41 hundredths, 42 hundredths, 43 hundredths, 44 hundredths, 45 hundredths, 46 hundredths, 47 hundredths, 48 hundredths, 49 hundredths, and 50 hundredths.
We're going to stop counting there, but it's really good practise to continue practising counting forwards and backwards using a range of representations here.
Okay, time for you to check your understanding now.
Which of these are ways that you can say this number here? Is it A, B, C, or D? Take a moment to have a think.
That's right.
Both A and D.
This number could be read as 0.
34, or it can be read as 34 hundredths.
Just a reminder about C in particular, how we don't pronounce it as zero point 34.
We say the digits separately.
Here's another true or false.
Look at this sequence of hundredths.
Is this how we count up correctly? That's right.
It's false.
It's not how we count up correctly is it? Let's look at our justifications for A and B.
Which one of these help us answer why it is not the right way to count up correctly? That's right.
It's B, isn't it? The justification of B helps us because when you reach 10 hundredths, it should be regrouped for one 10th.
So it would be 0.
1 or 0.
10.
We can see the mistake here we've made, can't we? That when we've got to nine hundredths, we've not regrouped the 10 hundredths to make it into one 10th.
Well done if you managed to spot that.
Okay, so your first task today is to use each one of these representations to practise all three of these.
So what I'd like you to do is count from 100 to 34 hundredths, to count from 0.
08 to 0.
31, and also to count from seven tenths and four hundredths to nine tenths and nine hundredths.
I would do that across each representation if you can.
Good luck and I'll see you again shortly.
Okay, welcome back.
So you can see here on the left hand side on the hundredth square, we've counted from one hundredth to 34 hundredths.
And I've highlighted that in the yellow to show you where those numbers that we counted would be positioned within our hundredth square.
In the second part, we can see that it starts at 0.
08.
And we could use our decimal number language here or our fractional language here.
If it starts on 0.
08, then maybe we could have used our decimal number language.
But if we wanted to use our fractional language, and we could have said that that is eight hundredths and continued counting, for example, nine hundredths, 10 hundredths, 11 hundredths, 12 hundredths.
And finally, we could have also used gattegno chart here.
Now we can see how 99 hundredths would be represented as nine tenths and nine hundredths on the right hand side.
And as I said earlier, using a gattegno chart to count forwards and backwards is really helpful to help identify the number of tenths and hundredths each number has when you are counting.
Okay, let's move on to phase two of our lesson now, counting in multiples of hundredths.
So as Andeep's pointed out so far, we've been counting in multiples of 100, haven't we so far? We could also use our times tables to count up in multiples of hundredths.
Let's use Sofia's idea as an example to get us going.
Why don't we start counting using our 10 times table knowledge to help us? That means we're going to need to count up in lots of 10 hundredths.
Are you ready? Zero hundredths, 10 hundredths, 20 hundredths, 30 hundredths, 40 hundredths, 50 hundredths, 60 hundredths, 70 hundredths, 80 hundredths, 90 hundredths, and a hundred hundredths.
And let's count backwards.
100 hundredths, 90 hundredths, 80 hundredths, 70 hundredths, 60 hundredths, 50 hundredths, 40 hundredths, 30 hundredths, 20 hundredths, 10 hundredths and zero hundredths.
Sofia's pointed out that it's actually the same as counting up in tenths isn't it? 'Cause we know that one tenth is equal to 10 hundredths.
So let's do that as well.
Are you ready? Zero tenths, one tenth, two tenths, three tenths, four tenths, five tenths, six tenths, seven tenths, eight tenths, nine tenths, and 10 tenths.
And we could do the same counting backwards, couldn't we? So we've now counted up in multiples of 10 hundredths or one tenth.
We can now extend this to think about a different times table.
Why don't we think about this time, the two times table, and how we can relate that to counting up in multiples of two hundredths.
Are you ready? Two hundredths, four hundredths, six hundredths, eight hundredths, 10 hundredths, 12 hundredths, 14 hundredths, 16 hundredths, 18 hundredths, 20 hundredths, 22 hundredths, 24 hundredths.
We don't have to stop here.
We could carry on, couldn't we? 26 hundredths, 28 hundredths, 30 hundredths.
Can you see that we're moving up in multiples of two hundredths each time, aren't we? Finally, we can also use our gattegno chart again, couldn't we? And this time we're gonna change from thinking about the two times table to maybe the five times table and how we can apply that to counting up in multiples of five hundredths.
Are you ready? Andeep's given us the first few examples here.
Five hundredths, 10 hundredths, 15 hundredths.
Are you ready? Five hundredths, 10 hundredths, 15 hundredths, 20 hundredths, 25 hundredths, 30 hundredths, 35 hundredths, 40 hundredths, 45 hundredths, 50 hundredths.
Well, let me change this now to start counting up using our decimal number language as well.
So 0.
5, 0.
55, 0.
6, 0.
65, 0.
7, 0.
75, 0.
8, 0.
85, 0.
9, 0.
95, one, one whole.
Well done for keeping up with that.
So, so far we've been counting up in different multiples of hundreths, haven't we? We can also record this as an addition or subtraction equation as we move forward.
Let's have a look here, for example.
At the moment I've got 24 hundredths.
If I was to add on two more hundredths, I could record this as an addition equation.
0.
24 plus 0.
02 is equal to 0.
26.
We could also do the inverse of this and record it as a subtraction equation.
Now I've got 0.
26 or 26 hundredths, and I can subtract two hundredths from that, which would mean our subtraction equation would look like this.
0.
26 minus 0.
02 is equal to 0.
24.
Not only have we just recorded those addition subtraction equations using decimal numbers, we could also do it using fractions.
Have a look here.
At the moment, I'm starting with 24 hundredths, and then I'm adding on two more hundredths, so I could record this as 24 hundredths plus two hundredths is equal to 26 hundredths.
And for the inverse of that, we could say 26 hundredths minus two hundredths is equal to 24 hundredths.
Okay, time for check our standing again.
What's the missing number in this sequence? That's right, it's B.
The missing number is 0.
1.
How did we figure that out though? Well, I noticed that each of the numbers in the sequence were going up in a multiple of two hundredths.
So if I get to 0.
08 and I'm adding on two hundredths to 0.
08, that would make me up to 10 hundredths or 0.
1, one tenth.
Here's another question.
Which equations match this representation? That's right, it's both A and C.
Let's have a look in a little bit more detail.
Well, our number line is there, and you can see it's going up in hundredths.
The arrow on our number line starts at 0.
40 or 40 hundredths.
So that would be represented by the first addend in both A and C.
We then add on 10 hundredths or 0.
10 or 0.
1.
So that's again represented in the second addend in both A and C.
And finally, it ends at 50 hundredths or 0.
50, again, which is demonstrated in the sum of both A and C.
Okay, onto our second task now.
What I'd like you to do this time is think about using these representations again, but counting up in different multiples of hundredths.
Maybe you could choose some of your own times tables that you'd like to count forwards and backwards in.
Once you've done that, I'd like to have a go at question two here.
I'd like to fill in the missing numbers for each of these equations, thinking about what we've just said about representing it as an addition or subtraction equation when counting forwards or backwards from a multiple.
Good luck.
I'll see you again shortly.
Okay, welcome back.
Andeep has finished the first task and decided to count up using the understanding of the four times table to help.
Great thinking, Andeep.
Well done you! Okay, and here are the answers to the second part of our task.
You might like to tick them off as you go.
Did you find any of those trickier than any of the other questions? The key here was to find out the difference between the numbers that you had, so you could identify what multiple it was being counted up or backwards in, in order to identify how much you needed to add or subtract or what the final total would be for the equation you're working with.
Well done if you managed to get all of those right.
Okay, moving into the last part of our lesson now, we're gonna start thinking about counting and representing hundredths beyond one.
You can see here we've got a number line again, and I'd like us to use our decimal language to count up and above one whole.
Are you ready? 0.
9, 0.
91, 0.
92, 0.
93, 0.
94, 0.
95, 0.
96, 0.
97, 0.
98, 0.
99.
Hmm.
What happens here then? That's right.
We need to regroup the nine hundredths to make one extra tenth which would then be placed into the tenths column.
Then we'd have 10 tenths.
So we'd need to regroup those 10 tenths to make one whole, which is why we are now at one.
1.
01, 1.
02, 1.
03, 1.
04, 1.
05, 1.
06, 1.
07, 1.
08, 1.
09, 1.
10, or 1.
1.
Be careful not to say one point 10! 1.
11, 1.
12, 1.
13, 1.
14, 1.
15.
Why don't we count backwards from here now as well? Are you ready? 1.
15, 1.
14, 1.
13, 1.
12.
1.
11, 1.
1 or 1.
10.
1.
09, 1.
08, 1.
07, 1.
06, 1.
05, 1.
04.
1.
03, 1.
02, 1.
01, 1.
Or here, 1.
00.
0.
99, 0.
98, 0.
97.
0.
96, 0.
95, 0.
94, 0.
93, 0.
92, 0.
91, 0.
9.
Well done.
Hopefully you feel a bit more confident counting over the one's boundary as we count up in hundredths.
Now that we've done that on a number line, we can also start thinking about doing it with our hundredth squares.
So here you can see I've got one whole completely shaded in, and I've also got an additional one hundredth in the second hundredth square.
So this represents one whole and one hundredth altogether.
I wonder if you could carry on counting with me using this language.
Are you ready? One whole and one hundredth, one whole and two hundredths, one whole and three hundredths, one whole and four hundredths, one whole and five hundredths, one whole and six hundredths, one whole and seven hundredths, one whole and eight hundredths, one whole and nine hundredths, one whole and 10 hundredths.
Have you noticed what's happening each time? That's right.
The numerator on our fraction is increasing by one each time, isn't it? And that increase represents one hundredth.
One and 11 hundredths, one and 12 hundredths, one and 13 hundredths, one and 14 hundredths, one and 15 hundredths, one and 16 hundredths, one and 17 hundredths, one and 18 hundredths, one and 19 hundredths, one and 20 hundredths.
Well done for keeping up with that.
We've got one more way to investigate with our counting and how we can represent that as well.
At the moment, I've got one whole and it's all shaded in, and that would make 100 hundredths 'cause the whole has been divided into a hundred equal parts.
If I was to add one more hundredth, I would then have 101 hundredths.
Notice how it's changed on my fraction as well now.
The fraction is turned into an improper fraction where the numerator has a greater number than the denominator.
Let's continue counting using this language as well, and keep an eye on the fraction as it increases each time.
101 hundredths, 102 hundredths, 103 hundredths, 104 hundredths, 105 hundredths, 106 hundredths, 107 hundredths, 108 hundredths, 109 hundredths, 110 hundredths.
111 hundredths, 112 hundredths, 113 hundredths, 114 hundredths.
115 hundredths.
Well done.
Can you see how the number changed each time? All of these are representing exactly the same thing, but we can just represent it in different ways.
So let's have a look at this in a little bit more detail and why these are the same.
Well, if we think about the fraction we just finished on, One whole and 15 hundredths, when we say this is a decimal number, I say 1.
15, but I think one whole and 15 hundredths.
And we can see how these can be used interchangeably and represented in equations or written down as numbers exactly like this, and they would represent the same thing.
On the left, we have the decimal number, and on the right, we have the mixed number.
We know we can also take this a step further and write it as an improper fraction.
And as we can see, we can write that as 115 hundredths, where the numerator is 115, and the denominator is a hundred.
Have a look at this example here.
What'd you notice this time? That's right.
Well spotted.
This time, we've got two wholes, haven't we? And we've got an additional eight hundredths.
So to write this as a decimal, I would need to write it as 2.
08.
I say 2.
08, but I think two wholes and eight hundredths.
We also know we can represent this as an improper fraction.
Altogether, there are 100, 200, and eight hundredths, aren't there? 208 hundredths.
And we can record that like this as an improper fraction.
Okay, our last checks for understanding today then, are you ready? I say one point one eight but I think A, B or C.
Have a little think for yourself.
That's right.
It's C.
I say one point one eight, but I think one whole and 18 hundredths.
Okay, and the next one, true or false, 1.
07 can be written as 107 hundredths.
Do you agree or do you disagree? That's right.
It's true, isn't it? Which justification can be used to help us reason it? Yep.
B, can't we? 1.
07 represents 100 hundredths and seven hundredths, and altogether, 100 hundredths and seven hundredths makes 107.
So that would be 107 hundredths, which can be recorded as the improper fraction that we can see.
Well done if you managed to get that as well.
Okay, onto our last task for today.
What I'd like to do, first of all, is use the base 10 blocks to either draw or create each of these numbers here that we have got.
Once you've done that, I've got a table here for you.
And what I'd like you to do here is either convert from a decimal number to a mixed number or fraction, or from a mixed number or fraction to a decimal number.
Good luck, and I'll see you again shortly.
Okay.
Welcome back.
Have a look at this here.
Hopefully you can see how we've represented using the base 10 blocks each of these numbers.
The first one, 0.
35, is represented with three tenths and five hundredths.
The second one, 3.
00 is actually just three wholes or three ones.
So we've represented that with three one blocks.
Underneath that we've got 3.
86.
I'm gonna need three ones.
I'm gonna need eight tenths and additional six hundredths.
Then I've got 4.
50.
Well, that would be represented with four ones and five tenths because the five represents five tenths and it changes slightly for the bottom one.
Now we've got 4.
05.
That can be represented as four ones, zero tenths and five hundredths.
Well done if you managed to do that.
And finally, this task here, I can use my stem sentence to help me on some of these.
I say 0.
05, but I think zero wholes and five hundredths.
So I'd record that as five hundredths.
Hmm.
Well, if I think zero wholes and eight hundredths, I can record that as 0.
08.
This time I've got 86 hundredths.
Well, I know that I've got zero wholes this time, so I'm gonna need a zero point.
And then the 86 hundredths can be represented by eight tenths and six hundredths.
So we can record that as 0.
86.
Now I've got 1.
00 or one whole, and we know, how many hundredths are in one whole? That's right.
A hundred hundredths.
Then I've got two wholes and 24 hundredths.
Hmm.
So this time I'm going to need to record a two before the decimal point to represent the two wholes.
And then I'm gonna record a two and a four after the decimal point to represent the 24 hundredths.
So we've got 2.
24.
And then finally the last one.
What did you notice this time? I've given you three digits for the whole number, haven't I? The number is 108.
74, and we can record that as a mixed number by writing it as 108 and 74 hundredths.
Well done if you managed to get that.
Okay, that's the end of our lesson today.
Hopefully you feel a lot more confident about the different ways that we can count up in hundredths.
So, we can count up in hundredths using the language of tenths and hundredths.
For example, there are two tenths and five hundredths.
We could also use our language of hundredths counting up just simply by counting up the number of hundredths that we've got.
For example, there are 34 hundredths, and finally, we could say and write hundredths as a decimal number, for example, 0.
06, as you can see.
Thank you for joining me for our learning today.
I've really enjoyed teaching you that, and hopefully you feel a lot more confident.
Take care, and I'll see you again soon.
