Video Transcript
Part–Whole Bar Models: Numbers up
to 100
In this video, we’re going to learn
how to solve one-step addition and subtraction problems with numbers up to 100 by
drawing a part–whole bar model to help.
This is a type of part–whole
model. You’ve probably seen one
before. Let’s complete it with some numbers
to help us understand it. There we are. In models like this, we know the
two circles that feed up into the top circle are the parts. Eight is a part. Three is a part. 11 is the whole amount. We know this because if we add the
two parts together, we get the whole amount. Eight plus three equals 11.
But you know there’s another sort
of part–whole model that we can use to represent calculations, and that’s a
part–whole bar model. Let’s use this bar here to
represent the number eight. We could draw another part next to
it to represent the number three. These are the two parts that make
up the whole. And where is the whole amount on
our diagram? The whole amount is the whole
distance when we put both bars together. Why don’t we draw one large bar to
represent the whole amount? And because we know that eight and
three go together to make 11, we know that this bar represents the number 11.
This is what we mean by a
part–whole bar model. It’s not always labeled to show us
the parts and the whole. It’s not always colorful. And sometimes the numbers are
labeled differently, but it’s still a way of showing different parts that make up a
whole.
We can use bar models to help
represent additions and subtractions. For example, what if we know the
two parts in the bar model, but we don’t know what the whole amount is. This could even represent a word
problem. There were 13 children in the
school hall eating dinners, and then 42 more children joined them. How many children were then in the
hall altogether?
By looking at our bar model, we can
see that the numbers that we know are the two parts and the number that we want to
find is the whole. And what do we know about parts and
wholes? A part plus a part is a whole. We’re not going to work out the
answer now. But we know that to find this
missing number, we’re going to have to add together 13 and 42.
But what if we have a problem where
we know the whole amount and we also know one of the parts, but we don’t know the
other part? Again, this bar model could
represent a word problem. There are 86 children going on a
school trip. 24 of them are boys. How many are girls?
By looking at our bar model, we can
see that to find the answer, we need to find the number that goes with 24 to make
86. This is going to be a subtraction
problem, isn’t it? Because we know the whole amount
take away one of the parts will leave us with the other part. And again, we won’t work out the
answer now, but we know to find the missing part, we need to find 86 take away
24.
Let’s try putting into practice
what we’ve learned now. We’re going to use bar models to
solve some word problems.
Liam has 62 blocks to build
with. He used 29 blocks to build one
house. He wants to build a second house
with the leftover blocks. Is the number of leftover blocks
bigger or smaller than 62? Do you need to add or subtract to
find how many blocks he has left to build the second house? How many blocks are left to build
the second house?
There are a lot of words in this
problem, and there are three parts to it. To help us understand the problem,
we could sketch a bar model. This isn’t going to tell us what
the answer is, but it is going to help us to picture the problem and to work out how
to solve it. Firstly, we’re told that Liam has
62 blocks to build with. Now this is the total amount of
blocks that he has to begin with. Our bar model is going to be made
up of a whole amount and some parts. And because we know Liam starts off
with 62 blocks, we know this is the whole amount. We could draw a bar to represent
this.
Next, we’re told that he used 29 of
those blocks to build a house. 29 is part of the whole amount, so
we can draw another bar that’s not as long as 62 and it shows part of 62, and we’ll
label it with the number 29. We’re then told that Liam wants to
build a second house with the leftover blocks. Now, we don’t know how many blocks
he has left over. But what we do know is that this is
another part that goes together with 29 to make 62.
This is a part–whole bar model. 62 is the whole amount. 29 is a part, and we don’t know the
other part. Now, we can use this to help us
answer the question. Is the number of leftover blocks
bigger or smaller than 62? Well, we can look at our bar model
and see that 62 is the whole amount. Liam had 62 blocks to start
with. The leftover blocks are what’s left
over after he’s used 29 of them. So, we know that the number of
leftover blocks is smaller than 62.
Do you need to add or subtract to
find how many blocks he has left to build a second house? By looking at our bar model, we can
see that the missing number is one of the two parts that go together to make 62. So, to find our missing number, we
need to start with the whole amount, which is 62, and then take away one of the
parts, the part we know which is 29. Our bar model hasn’t given us the
answer, but it certainly showed us how to find it. We need to subtract to find how
many blocks Liam has left.
And now, we need to work out the
answer. How many blocks are left to build
the second house? We need to subtract 29 from 62. The number 62 is made up of six 10s
and two ones, and the number 29 is made up of two 10s and nine ones. Let’s take away the two 10s first:
one, two. Six 10s take away two 10s leaves us
with four 10s.
Now, all we have to do is to take
away the ones: 42 take away nine. Here’s where we could work out the
answer in our heads. We know that 42 take away 10 would
give us the answer 32. But we don’t want to go as far as
taking away 10. We only want to take away nine. 42 take away nine is going to give
us an answer one more than 32. The answer is 33.
We used our part–whole bar model to
help us every step of the way. We knew that the number of leftover
blocks was going to be smaller than 62 as though we knew that we needed to subtract
to find out the number of blocks that Liam had left. And in the final part of the
question, we actually did the subtraction. 62 take away 29 leaves Liam with 33
blocks.
A farmer has 43 ducks and 24
hens. Find the total number of birds that
he has.
Sometimes when we’re answering
problems like this, we can need a little help in imagining the problem and working
out what we need to do to find the answer. And so, we can use bar models to
help. Let’s use a bar model to work out
what we need to do to solve this problem.
First of all, we’re told that a
farmer has 43 ducks. Let’s draw a bar to represent those
ducks. And we’ll label it with the value,
which is 43. We’re also told that the farmer has
24 hens. Now, this isn’t part of the group
of ducks; this is a separate group. In fact, these two groups, the
ducks and the hens, are two parts that make up a whole amount, because in the final
part of the question, we’re told to find the total number of birds that he has, in
other words, the total of the ducks and the hens put together.
We can draw one long bar to
represent this whole amount. This is a part–whole bar model. 43 is a part, 24 is a part, and —
well, we don’t know what the whole is, do we? That’s the bit we need to find
out. So, how are we going to find the
total number of birds? We need to add together the two
parts. In other words, we need to add
together 43 ducks and 24 hens.
Now that we know what we need to do
to find the answer, let’s work it out. We know that the number 43 is made
up of four 10s and three ones. And the number 24 is made up of two
10s and four ones. Let’s start by adding the ones. We’ll add four ones to three ones,
so we’ll count on from the number three: three, four, five, six, seven. Three ones plus four ones equals
seven ones. Now, let’s add our two 10s to four
10s, so we’ll start counting on from four 10s: four, five, six. Four 10s plus two 10s equals six
10s. And so, we’re left with an answer
that has six 10s and seven ones; it’s 67.
We used a part–whole bar model to
work out what to do, and then we actually did it to find the answer. The total number of birds that the
farmer has is 67.
So, what have we learned in this
video? We’ve learned how to solve one-step
addition and subtraction problems with numbers up to 100 by drawing part–whole bar
models.