Video Transcript
Adding Tens to Two-Digit
Numbers
In this video, we’re going to learn
how to add a multiple of 10 to a two-digit number, and we’re also going to learn how
to model this with place value equipment. So let’s begin with a two-digit
number. What about 29? But as we said at the start, we’re
going to take two-digit numbers like this, and we’re going to learn how to add
multiples of 10 to these. But what’s a multiple of 10? Let’s go through some examples of
multiples of 10 and see if you remember.
50 is a multiple of 10. 10, 20, 30, 40, 50. 30 is a multiple of 10. 10, 20, 30. Can you see what these multiples of
10 have in common? They all end in a zero, which means
they don’t have any ones at all. But there is a digit greater than
zero in the tens place. And we can see just by looking at
all these different ways to model multiples of 10 that a multiple of 10 is a number
of tens. It’s what we get when we count in
tens or when we multiply a number by 10. Five 10s are 50, one times 10 is
10, and so on. So these are the sort of numbers
that we’re going to be adding to some two-digit numbers. And as we come across multiples of
10 in this video, let’s keep thinking of them as a number of tens.
Now let’s pick a multiple of 10 to
add to our two-digit number. What about the number 60? To find 60 more than our number, we
need to add the two together. 29 plus 60 equals what? Now, as we said at the start, we’re
going to try to model what we do using equipment. Let’s find the answer to this
question using 10 frames. We’re going to need quite a few
counters, but we’ll have a go.
The number that we’re starting
with, 29, is made up of two 10s, which we can model using two full 10 frames, and
then nine ones, which we can model in a 10 frame containing nine counters. And as we’ve seen already, the
number that we’re adding is going to be a multiple of 10. It’s going to have a number of
tens, which is six, but no ones at all. So if we’re going to model the
number 60, we’re just going to need six full 10 frames, one for each of our six
10s. 10, 20, 30, 40, 50, 60.
Now all we need to do is to add our
two numbers together. Let’s start by adding the ones, in
other words, the 10 frames that aren’t completely full. Our first number, 29, has nine
ones. But then, if you remember, our
second number was just made out of a number of tens. There weren’t any ones. That’s why we’ve got an empty space
down here. There are no more ones to add, and
nine ones plus no more ones makes nine ones. In other words, the number of ones
that we have isn’t going to change at all.
Now let’s add the tens, in other
words, the full 10 frames. In the number 29, we have two full
10 frames because two 10s are worth 20. But then we had to add on 60, which
is worth another six 10s. So how many tens is that
altogether? Let’s count on from two. So we have two and then three,
four, five, six, seven, eight. If we put all our full 10 frames
together, we’ll have eight 10s or 80. So that’s eight 10s and nine
ones. 29 plus 60 equals 89.
Let’s try a different question. Let’s have the two-digit number
57. And what multiple of 10 should we
add to it? Let’s go with 40. We need to find the sum of 40 and
57. This time, let’s use place value
equipment. What about some base 10 blocks? First of all, we’ll think about the
tens and the ones in our two-digit number. The number 57 contains five 10s,
which we can model using five 10s blocks, and the digit seven is in the ones
place. This tells us we’re going to need
seven ones blocks.
Now, we can tell by looking at the
number that we’re adding, 40, that it’s going to be a multiple of 10. This is because there’s a zero in
the ones place. There aren’t any ones there at
all. But we do have a digit in the tens
place. 40 is the same as four 10s. 10, 20, 30, 40. Now we’ve made both of the numbers
out of base 10 blocks, we can combine them to find out what the total is. Let’s start by putting together our
ones. Our first number, 57, has seven
ones. But because our second number is a
multiple of 10, there aren’t any ones to add. Those seven ones in our first
number aren’t going to change at all. We’ve got nothing to add to
them. So our answer is going to have
seven ones, too.
Now, let’s add our 10s blocks. The number 57 has five 10s, but we
need to add on 40, which is four more 10s. What’s five 10s plus four more
10s? Let’s count them: five and then
six, seven, eight, nine. Five plus four is nine, isn’t
it? And so five 10s plus four more 10s
is nine 10s. Let’s combine our tens together to
show that we have nine 10s altogether. And we know that if our answer has
nine 10s and nine in the tens place, this is worth 90. We started off with a number that
has five 10s and seven ones. Then we added four 10s to this, and
we’ve ended with an answer that has nine 10s and seven ones. Can you see once again our ones
haven’t changed? We’re just thinking about tens all
the time in this video, aren’t we? 57 plus 40 equals 97.
And, you know, if we understand
that we’re just adding tens here, we don’t even need place value blocks. We could just use a pen and
paper. Let’s see how quickly we can add
together 41 and 30. 41 is made up of four 10s and one
one. And instead of using place value
blocks or some other kind of equipment, we could just do a quick sketch to help. We could draw lines to represent
the tens and dots to represent the ones. So that’s 10, 20, 30, 40, one.
And we know that number we’re
adding, 30, is a multiple of 10. Three 10s are worth 30, so let’s
sketch our three 10s. 10, 20, 30. We don’t need to draw any dots
because there are no ones. It’s a multiple of 10, so we can
quickly find the answer because there are no ones we need to add. The number of ones that we have to
begin with doesn’t change. We’ve still got one one in our
answer. One plus zero equals one.
And now, if we add together our
tens, we’re going to see that they’re going to change. We have four 10s in the first
number, but we need to add three more. We know that four plus three is
seven. So our answer is going to have
seven 10s. 41 plus 30 equals 71. By adding 30 or three 10s, we went
from a number with four 10s to a number with seven 10s. Let’s have a go at answering some
questions now where we need to add multiples of 10 to some two-digit numbers. And each time we’re gonna have a go
at breaking apart our two-digit numbers into tens and ones and thinking about how
the number of tens are going to change.
Complete the number sentence: 88
plus 10 equals what.
In this question, we’re given a
two-digit number, 88, and we need to find 10 more than it. Now, the number 88 is made up of
some tens already, some tens and some ones. And to help us understand what
happens to 88 when we add 10 to it, let’s break it apart into its tens and ones. 88 is one of those numbers that has
the same number of tens as it does ones. It’s made up of eight 10s and eight
ones. And the number that we’re adding,
10, is just the same as one 10, isn’t it? There aren’t any ones. So if we look at our place value
blocks, we can see we already have eight 10s and we just need to add one more
10. Can you see how many tens we’re
going to get? Our number of tens has increased by
one. Instead of eight 10s, we now have
nine 10s.
But the ones in our number haven’t
changed at all. We haven’t had anything to add
there. And because we’ve added 10, our
part–whole model doesn’t quite make sense now, so let’s rub out 88 on the top. And we’ll replace it with our
answer, which has nine 10s, eight ones. 98. To help us add 10, we broke apart
88 into eight 10s and eight ones. And by adding one more 10, we ended
with a number that has nine 10s and eight ones. 88 plus 10 equals 98.
Use place value to add numbers. Pick the correct way to break apart
37 into tens and ones. Add 40 to 37 by adding four
10s.
The main calculation that we need
to do in this question comes right at the end. We need to add 40 to 37. But before we get to the answer,
there’s one or two things we need to do. Our third sentence tells us that
this question is all about using place value to add numbers. Do you remember what place value
means? It’s all about the way that the
digits in a number have different values depending on where you write them, isn’t
it? And we can see just by quickly
looking through this question, we’re thinking about two-digit numbers.
The first thing we need to do in
our question is to pick the correct way to break apart 37 into tens and ones. We know from later on that 37 is
one of the numbers that we’re going to be adding, and it seems that it’s going to be
helpful to us to split it up into its tens and its ones. We’re shown four different place
value grids, and each one shows a different number of tens and ones, but which one
is correct? Seven 10s and three ones; seven
10s, zero ones; three 10s, seven ones; or three 10s, zero ones.
To help us, we could think about
what might happen if we put the digits in 37 into a place value table. If we were doing this, we’d write
the three in the tens column and the seven in the ones column. In other words, we could model 37
out of base 10 blocks by using three 10s blocks and seven ones blocks. And this will help us identify the
correct answer. Can you see it? It’s this place value table, isn’t
it? It contains three 10s and seven
ones.
In the final part of the question,
we’re told then to add 40 to 37 by adding four 10s. The numbers that we need to add
together, which are 37 and 40, have been written in a place value table. Now the calculation could have been
written like this, but by writing the digits in a place value table, we’re really
doing what we’ve done in the first part of the question. We’re splitting them up into their
tens and their ones.
Can you see that both the tens
digits are above each other and both the ones digits are above each other, too? Now, we’re told we need to add 40
to 37 by adding four 10s. This is because 40 is worth four
10s. If we look at it in our place value
table, can you see that there’s a four in the tens place and there aren’t any ones
to add at all? 40 is just worth four 10s. 10, 20, 30, 40.
So our starting number has three
10s and seven ones, and we need to add to it four 10s. If we start by thinking about the
ones, we know that we’re not adding any ones. 40 is just four 10s. So we started off with seven ones,
and we’re going to end with seven ones. Seven plus zero equals seven, but
our tens digit is going to change. 37 has three 10s, and we need to
add four more 10s. And three plus four more equals
seven. If we combine our 10s blocks,
you’ll see how our number changes.
Our answer still has seven ones,
but our tens digit has changed from three to seven. We’ve used our knowledge of place
value to add together a two-digit number and a number of tens. The correct way to break apart 37
into tens and ones is three 10s, seven ones. And to add 40 to this number, we
just needed to add four more 10s. 37 plus 40 equals 77.
All the robots have been working
hard to make new numbers. Which multiple of 10 have they
added?
In the picture, we can see three
robots, and they seem to have been programmed to do a job involving numbers. We’re told that they’ve been
working hard to make new numbers. Can you see what’s happening in the
picture? Each robot is taking in a
number. It’s then doing something to that
number. But then finally, a new number
comes out of the robot. Now, in the next sentence, we’re
given a clue as to what’s happening here. We’re asked, which multiple of 10
have they added? We can tell a few things from this
sentence. Firstly, we can tell that all the
robots are doing the same thing. The question doesn’t ask us which
multiples of 10. It’s just one multiple. They’re all doing the same
thing.
The next thing we can tell is that
they’re adding a number to the number that goes into them, and also we know what
sort of number they’re adding. Each robot is adding the same
multiple of 10. Now we know that a multiple of 10
is a number in the 10 times table. It’s what we get when we multiply
another number by 10. So the robots could be adding 10,
20, 30, 40, and so on. But which multiple of 10 have they
added? To find out the answer, we need to
look at how the numbers change from the numbers that go in to the numbers that come
out. And we could do this using place
value grids.
With the first robot, the number
that goes in is 22. So that’s two 10s, two ones. And the number that comes out is
62. So that’s six 10s, two ones. This is interesting, isn’t it? We started off with two ones, and
we’ve ended with two ones. No ones have been added at all, but
the number of tens that we have has gone from two to six. Can you see how many tens have been
added by this robot? Two plus four more 10s makes six
10s, don’t they? And as we say, the robot hasn’t
added any ones at all. And if we’ve got the right answer
here, we’d hope that the other two robots have done exactly the same thing.
Our second robot has taken the
number 14, which is one 10, four ones. And we can see that the new number
it’s made is 54, five 10s, four ones. Once again, the number of ones
hasn’t changed, but we’ve got four more 10s. The multiple of 10 that these
robots are adding is 40, isn’t it? And if we just check the last
robot, if we have six 10s or 60 and we add four 10s or 40, we’re going to end up
with 10 10s, which is the same as 100. By adding a multiple of 10 each
time, we notice that the number of ones doesn’t change. The number of tens, however,
does. And these robots have increased the
number of tens by four. And that’s how we know the multiple
of 10 that each robot has added is 40.
What have we learned in this
video? We’ve learned how to add a multiple
of 10 to a two-digit number. We’ve also learned how to model the
answer using place value equipment.
