Video Transcript
Bar Models: Numbers up to
10,000.
In this video, we’re going to learn
how to solve one-step addition and subtraction problems by modeling them with either
part–whole or bar models and writing equations. In this problem, we have to find
the total number of fans at a baseball game. There are 3,570 home team fans and
the away team has 1,050 fans. We can use bar models or part–whole
models to help us solve the problem. These models help us to see how the
quantities in our problem are related. We know there are 3,570 home team
fans and 1,050 fans from the away team.
So to find the total number of
fans, we need to add these two numbers together. We can add these two numbers using
column addition. Zero plus zero is zero. Seven plus five or seven 10s plus
five 10s gives us 12 10s. Five 100s add no hundreds plus the
one we exchanged gives us a total of six 100s. And three 1,000s plus one 1,000
gives us a total of four 1,000s. 3,570 plus 1,050 gives us a total
of 4,620 fans. Let’s try answering some addition
and subtraction word problems using bar models or part–whole models to help.
Olivia and Jennifer want to
represent 6,755 plus 2,648 on a bar model. Olivia used this bar model. Jennifer used this one. Who used the correct bar
model? What is the result of 6,755 and
2,648?
Olivia and Jennifer are trying
to represent 6,755 plus 2,648. We don’t know what the whole
amount or the total is, but we do know both of the parts. One of the parts is 6,755, and
the other is 2,648. So the correct bar model needs
to show our two parts, 6,755 and 2,648. This is Olivia’s bar model. The first part is 6,755 which
is one of our parts, and the second part is 2,648 which is our second part. And Olivia’s drawn a question
mark because we don’t know the total. This looks like the correct bar
model.
This is Jennifer’s bar
model. Her bar model shows one of our
parts, 2,648, but the other part is missing. This part should say 6,755. It looks like Jennifer’s
written this as the whole amount. She’s written this number in
the wrong place. So the person who used the
correct bar model is Olivia. Now, we need to find the result
of 6,755 plus 2,648. And we can use the standard
written method or column addition to help find the result. Let’s start by adding the
ones. Five ones and eight ones gives
us a total of 13 ones, so we need to exchange. Now we can add the tens. Five 10s plus four 10s is nine
10s and one more makes 10 10s. Again, we need to exchange.
Now we can add the
hundreds. Seven 100s and six 100s gives
us 13 100s plus the one we exchanged gives us a total of 14 100s. And we need to exchange
again. Finally, we can add the
thousands. Six plus two is eight plus the
one we exchanged gives us a total of nine 1,000s. 6,755 plus 2,648 equals
9,403. Olivia and Jennifer wanted to
represent 6,755 plus 2,648 using a bar model. Olivia drew the correct bar
model, and the result of 6,755 and 2,648 is 9,403.
There are 5,267 students in a
school. 2,247 are boys. How many girls are in the
school?
This is a word problem. We know the total number of
students is 5,267. So this is the whole amount. We also know there are 2,247 boys
in the school. This is one of the parts. We have to calculate how many girls
there are in school. This is the missing part. We can also represent these
quantities using a bar model. We know the total number of
students is 5,267 and the number of boys is 2,247. So to find the number of girls, we
need to find the difference between 5,267 and 2,247. In other words, we need to subtract
2,247 from 5,267. Let’s calculate the answer using
the standard written method.
We need to start by subtracting in
the ones place. Seven take away seven leaves us
with zero ones. Six 10s take away four 10s leaves
us with two 10s. Two 100s take away two 100s leaves
us with zero. And five 1,000s subtract two 1,000s
leaves us with three 1,000s. 5,267 subtract 2,247 is 3,020. If there are 5,267 students in a
school and 2,247 are boys, then 3,020 pupils must be girls. We represented the quantities in
the word problem using a part–whole model and a bar model. This helped us to see that we
needed to find the difference to calculate the number of girls in the school. The number of girls is 3,020.
Noah and Anthony are playing a
game. Noah scores 2,568 points, and
Anthony scores 1,287 points more than Noah. How many points does Anthony score
in total?
In this word problem, we’re being
asked to calculate the total number of points that Anthony scored in the game. We know that Noah scored 2,568
points and Anthony scores 1,287 points more than Noah. We can represent the quantities in
this problem using a bar model. We know that Noah scored 2,568
points and Anthony scored 1,287 points more than Noah. So to find Anthony’s total score,
we’re going to need to add together the two parts in our bar model, 2,568 plus
1,287. And we can use the standard written
method to calculate the answer.
We know that eight ones and seven
ones gives us 15 and we need to exchange. Six 10s plus eight 10s gives us a
total of 14 10s plus the one we exchanged is 15. Five 100s plus two 100s is seven
100s plus the one we exchanged gives us a total of eight 100s. And two 1,000s plus one 1,000 gives
us a total of three 1,000s. 2,568 plus 1,287 equals 3,855. If Noah scores 2,568 points and
Anthony scores 1,287 more points, then Anthony’s total score is 3,855 points. We used a bar model to represent
the quantities in our word problem. We realized we needed to add, so
this helped us to write our equation. Then we calculated our answer. The total number of points Anthony
scored is 3,855.
What have we learned in this
video? We have learned how to solve
addition and subtraction word problems using part–whole models and bar models.
