Adding Tens to Three-Digit
In this video, we’re going to learn
how to model adding a multiple of 10 to a three-digit number. And as we do this, we’re going to
investigate which digit in the number change.
Now, let’s begin with a three-digit
number, 231. And let’s imagine we want to find
out what 40 more than this number is. We’re going to need to find the
answer to an addition, aren’t we? 231 plus 40. Let’s think about this number that
we’re adding for a moment. What can we say about it? Well, we know that if we are
modeling it out of base 10 equipment, we just need some tens blocks. We’d only need tens counters if we
wanted to model it out of place value counters. And if we wanted to record it in a
place value grid, the only digit we’d need that wasn’t a zero would be a four in the
tens place. Obviously, we’d still need a zero
in the ones to show that the four is in the tens place.
So, all of these facts show us that
40 is what we call a multiple of 10. It’s a number we get by multiplying
10 or counting in tens. 10, 20, 30, 40. These numbers all end in zero. They’re all multiples of 10. And these are the sorts of numbers
that we’re going to be adding in this particular video. So, with this particular question,
the multiple of 10 that we’re thinking of is 40.
Now, one way we can find the answer
quickly to a calculation like this is by using place value blocks to help. So, let’s start by modeling our
three-digit number using place value blocks. 231 is made up of two hundreds,
three tens, which are worth 30, and one one. Now, as we’ve said already, we’re
going to be adding a multiple of 10 to this number. And we model 40 using four 10s. Can you see where we need to add
this to our place value blocks?
We can add the four 10s to the
three 10s blocks that we already have, and three plus another four equals seven. Our number now has seven 10s in
it. We still have two 100s; that hasn’t
changed. And we still have one one; that
hasn’t changed. But our three-digit number has gone
from having three 10s to seven 10s. That’s because by adding 40, we’ve
added four 10s. 231 plus 40 equals 271.
Now, we don’t have to use place
value blocks to find the answer to a question like this. Because we’re adding a number of
tens, we could count on in tens to find the answer. And we could use a number line to
help us do this. Let’s start with the number
147. And let’s imagine we want to find
the sum of this number and 50. And we know that finding the sum
means adding. So, we need to find the answer to
147 plus 50.
The first thing we can do is look
at the number that we’re adding and see that it’s a two-digit number that ends in a
zero. It must be a multiple of 10. And when we think about our times
tables facts, we know that five 10s make 50. So, we need to add five 10s to
147. And because we know how to count in
tens, we could skip count in tens five times from 147 to find the answer. So, we could sketch a number
We could mark 147 on the left
because we’re going to be counting onwards. We’re going to need the rest of the
number line to show what we’re doing. And we could put an arrow on both
ends of the number line to show that it continues in both directions. And now, we simply need to practice
counting in tens five times. So, we can say 147 and then 157,
167, 177, 187, 197. Did you notice which digit changes
as we counted on in tens? The number 147 is made up of one
100, four 10s, and seven ones. And because we were skip counting
by ten, it was the tens digit that began to change. Four 10s became five 10s, then six
10s, seven 10s, eight 10s. And we ended up with an answer that
had nine 10s.
We started off with a number that
had four 10s. We added five more 10s. And because we know four plus five
is nine, we’ve ended with a number with nine 10s. And you know you can hear the tens
digit change as we read the numbers. 147, 157, 167, 177, 187, 197. You actually hear it changing,
can’t you? So, this is another way we could
add a multiple of 10 to a three-digit number by counting on in tens. 147 plus 50 equals 197.
Now, let’s try one more
example. And this time, it’s going to
involve separating out the tens so that we can look at them on their own. Let’s imagine that we want to find
the answer to 844 plus 30. Once again, we’re starting with a
three-digit number, and we’re adding a two-digit number that ends in a zero. It’s a multiple of 10. And we know that 30 is the same as
three 10s. And we know if we’re adding a
number of tens to a three-digit number, it’s going to affect the number of tens in
that number. So, the first thing we could do is
to separate out the tens to look at them.
And what we’re about to do, you
could do in your head. But we’re going to use a part–whole
model just to show exactly what we’re doing. So, we’re going to take our number
844. And because we know we’re adding a
number of tens, we could separate out the tens part of 844 because we know there is
a four digit in the tens place; we know that’s worth 40. And the other part is the rest of
the number. So, we’ve still got our eight 100s
and our four ones, 804.
Can you see why we split the number
up like this? We know that we want to add 30 to
our number, which is worth three 10s. So, we’ve taken our four 10s out of
the three-digit number so we can think about them separately. Now, we know that four plus three
equals seven. And so, four 10s plus three 10s
must equal seven 10s, or 40 plus 30 equals 70. The four 10s that we started off
with are now seven 10s. And we just need to combine our two
parts back together to find the answer. It still has eight 100s, and it
still has four ones. Those digits haven’t changed, but
our tens digit has changed. And by separating out the tens like
this, we could find the answer quickly. 844 plus 30 equals 874.
Let’s have a go to answering some
questions now, where we have to add tens to some three-digit numbers, and we’ll try
putting into practice some of the different strategies we’ve talked about.
Add the two numbers 328 and 20.
In this question, we’re given two
numbers to add together. We’ve got the three-digit number
328 and the two-digit number 20. Now, the number that we’re adding,
20 here, is a multiple of 10. We know this because it ends in a
zero, and a multiple of 10 is a number that we can get by multiplying 10 several
times. We know that two 10s are 20. Now, we know the number 328
contains three 100s, two 10s, and eight ones.
And so, one way to find the answer
might be to count on from this number in tens twice. Let’s count aloud and see where we
end up. So, we start with 328 and then 338,
348. Look out, the tens digit in our
number has gone from two 10s to four 10s. This is because our number had two
10s to begin with, and we needed to add 20 which is the same as two more 10s, which
makes four 10s altogether. We counted on to find the
answer. If we add together 328 and 20, we
get the total 348.
Count in tens to find the sum. 643 plus 40 equals what.
Our question begins with a
three-digit number, 643. Can you see it labeled on this
number line? And we need to add to it a multiple
of 10. We know that a multiple of 10 is a
number that we get by multiplying another number by 10. In other words, it is a number in
the 10 times table. It’s a number of tens. And we can recognize the number 40
as being a multiple of 10 because it ends in a zero. And also, we know a times tables
fact to help us, don’t we? Four 10s are 40. And that’s why we’re told in the
question to count in tens to find the sum or we could even say count on four
Now, if we look at our starting
number, we can see that it contains four 10s already. So, we’ve got four 10s and we need
to count on four 10s. How many tens do you think our
number is going to have by the time we finished? Let’s count on to find out, and
we’ll use the number line to help us. So, we have 643 and then 653, 663,
673, 683. The number 40 is the same as four
10s. So, we counted on in tens four
times to find the sum. Our starting number had four
10s. We added on four 10s, and our
answer has got eight 10s. And we can see why this is, can’t
we? Because four plus four more equals
eight. 643 plus 40 equals 683.
Find the sum by adding the tens
first. 321 plus 40 equals what.
In this question, we need to find
the sum of two numbers. And we know that finding the sum
means finding the total, adding together. And the two numbers that we need to
add together are a three-digit number, 321, and a two-digit number, 40. And we’re told to find the sum by
adding the tens first. Can you see why we might want to do
that? It’s because the number that we’re
adding, 40, is a multiple of 10. It’s a number of tens. We know that four 10s are worth
40. And so, we can take out the tens of
our number, 321, and just add our four 10s onto this, as long as we put the whole
thing back together again at the end. And that’s what the part–whole
model underneath the number 321 shows us.
Let’s show what we mean using arrow
cards too. So, here’s our number 321. And because we want to add on four
10s to it, we’re going to take out the tens from this number. There we go. So, we’ve split the number 321 into
two parts. We’ve got our tens that we’re going
to be working with. That’s two 10s, which are the same
as 20. And we’ve got the other part, which
is the number we’ve left behind. We’ll come back to that at the end,
and that’s 301. So now that we’ve separated out the
tens, we can add them.
What is 20 plus 40 or what are two
10s plus another four 10s? Well, we know that two plus four
equals six. So, the answer is going to be six
10s or 60. Let’s record our answer using
another part–whole model. So, two 10s plus four 10s equals
six 10s. And in the other part, we’ve still
got that 301 that we left behind. So, to find the overall answer, we
just need to quickly put back together our two parts, 301 and 60. Can you see what the numbers are
going to be? Well, we know those six 10s are
just going to slot neatly into the tens place of our answer, aren’t they?
321 plus 40 equals 361. We found the sum of 321 and 40 by
adding the tens first. 321 has two 10s, and we added on
four more 10s. And so, our answer has six 10s. The sum of 321 and 40 is 361.
If I add together 436 and 60, what
will the tens digit of the sum be?
This is an interesting question
because it starts off by looking like we need to add together 436 and 60. But as we read the rest of the
question, we can see that we’re not being asked for the sum of these two
numbers. We’re being asked what the tens
digit in the sum is going to be. And you might think to yourself,
“Well, I’m gonna have to work out the answer and then just look at what the tens
digit is.” But there’s a quicker way to solve
the problem, and it involves us understanding what it means to add a multiple of 10
to a three-digit number. So, let’s have a go at solving this
problem the quick way.
And it’s not that difficult; it
just involves us understanding the place value of the numbers that we’re adding. So, if we think about the number
we’re starting with, 436 contains four 100s, three 10s, and six ones. And the number that we’re adding to
this contains six 10s and zero ones and, of course, zero 100s as well. Now, the really important bit about
what we’ve just said is this digit here. The number that we’re adding on to
436 contains six 10s. It doesn’t contain any hundreds,
doesn’t contain ones, just six 10s because six tens equals 60.
Now, as we’ve said already, our
starting number 436 has got three 10s. So if we already have three 10s and
we’re adding on six 10s, what will the tens digit of the sum be? Well, we know that three plus six
equals nine. So, three 10s plus six 10s is going
to make nine 10s. Our answer is going to have the
digit nine in the tens place. So, although we don’t have to,
let’s just write down what the sum would be. It’s still going to have four 100s,
and it’s still going to have six ones. Those digits aren’t going to
change. But the three tens that we started
with are now going to become nine 10s. 436 plus 60 equals 496.
We’ve used our knowledge of place
value here to work out what the tens digit is going to be. If we add 60 to a number that has
three 10s — in this question, it was the number 436, but, you know, it could have
been any number at all — we found that the answer will contain nine 10s. So, the tens digit of the sum of
these two numbers is nine.
So, what have we learned in this
video? We’ve learned how to model adding a
multiple of 10 to a three-digit number. We’ve also investigated which
digits change when we do this.