Hey, guys.
Welcome to Algebra I.
Today we'll be working on
modeling real-world situations.
If you've had practice
translating expressions,
you've already got
a bit of a handle on this.
Let's take a look
and get started.

(Describer) She touches a screen and a phrase appears.

Okay. So, "a number
increased by 5."
You've dealt with situations
like that
when you were
translating expressions, right?
How would you translate that
to something numeric? Remember?
I see "increased by," so that
gave you a hint you were adding.

(Describer) She underlines it.

You're increasing
some number by five.

(Describer) She writes.

So, you had some practice
translating x plus 5.
Let's keep jogging your memory.
"The product of 7
and a number."
You remember "product" let you
know you were multiplying.
So, product 7 and a number.

(Describer) 7x.

Okay. All right.
"Seventeen more dollars
than Kenny."
All right,
that's a real-world situation,
but how you translate
something like that
is not much unlike
how you would translate
every good old
algebraic expression.
Let's keep going.
You'll see how you handle that.

(Describer) She changes the screen.

Step 1:
Decide what you want
your variable to represent.
You've got
a real-world situation.
You've got to figure out
what's your unknown.
Step 2: Identify the keyword,
'cause that'll tell you
what operation you've got to do:
add, subtract, multiple, divide,
if you've got an exponent.
The keyword gives you
a hint on that.
The final step
is writing that expression.
Remember those three steps.
You can even write
a note to yourself.
That's gonna help us
work through these problems.
Let's keep going.
"Example 1: Three more points
than the other team scored."
Now, what I don't know
in this case
is how many points
the other team scored.
That's what I'm gonna let
my variable represent,
and you can pick any letter
you want for your variable.
Many times you'll notice
that they'll choose a variable
that reminds them
of the situation.
For example, the "points
the other team scored."
Let me catch that.
It's the points
the other team scored.
I'm gonna let p
represent those points.

(Describer) She writes "P: points".

So, p is the points
that the other team scored.
And there were 3 more points
than that team scored.
So, you remember that "more,"
that told you you were adding.
So, I have 3 more points
than the other team.
You translated that
real-world situation: 3 plus p.
Or you could've said,
"p plus 3."
Either one's fine.
Okay? Let's try the next one.
"Four years younger
than Kendall." Okay.
What I don't know here
is how old Kendall is.
So, that is what my variable
is gonna represent.

(Describer) Kendall.

I'm gonna let k
represent Kendall's age.

(Describer) She writes, "K: Kendall's age."

That's my unknown. I have
no clue how old Kendall is.
What I do know is
I need to represent a situation
of 4 years younger than Kendall.
Think about younger
in the real world.
If you're younger than someone,
then your age
is less than theirs.
So, remember "less than"?
That told us
we were subtracting.

(Describer) She connects the word "younger" to "less than".

So, 4 years less than Kendall.
I've got Kendall's age,
and I need 4 less than that.
So, I could represent that:
k minus 4. Okay?
Are you seeing
how it's not much different
than translating expressions?
You have that extra step
of interpreting the situation
and deciding what your variable
needs to represent, okay?
"Example 3:
The bill at the restaurant
was split evenly 4 ways."
I like to eat,
so this happens sometimes to me.
What you don't know here
is what the bill is.
So, I'll pick b.
I'll let b represent the bill.
We're gonna split the bill
evenly 4 ways.
So, that split?
We're dividing.
We're dividing that bill up
4 equal ways.
So, I have b divided by 4.
That is how I just modeled
that real-world situation.
All right, example 4.
I know you saw
all those words.
And in math,
you see the word problem,
and it's like, "I don't
want to bother with it."
Take a deep breath,
take it in chunks,
and they're easier that way.
Take your time and it
won't be too bad at the end.

[inhales]
Got our deep breath.

"In a football game,
"a team earns seven points
for a touchdown
"and one point
for a field goal.
"Write an expression
to represent the total number
of points a team earns."
So, I read my way through it.
Let's break it down
and get this expression going.
You have two unknowns
in this situation.
That's how this one's different.
The team earns seven points
for a touchdown,
but I don't know how many
touchdowns they've made.
And they earned one point
for a field goal,
but I don't know how many
field goals they've made.
Those are my unknowns.
I'm gonna let t represent
the number of touchdowns.

(Describer) She writes.

And I'm gonna let f represent
the number of field goals.
These are my variables because
I don't know what they are.
But I do know
that the team earned
seven points for each touchdown.
So, seven for each.
You're multiplying there.

(Describer) She writes 7t.

And then I've got
one point for a field goal.
So, I get one point
for each field goal.

(Describer) Plus 1f.

And you've translated
that expression.
You wrote one,
and it modeled that situation.
It wasn't too bad, was it?
Just break it down.
All right. Now you've got
four examples to try.
Hit pause, take your time
and work through these.
Then we'll get back together
and compare our answers.

(Describer) Number One: Six years older than Ray.
Number Two: One-half the amount of Jacob's car.
Number Three: Four dollars less than Samantha spent.
Number Four: In a baseball league, teams are ranked using points. A team earns five points for each win and two points for each tie. Write an expression to represent the total number of points a team earns.

(female describer)
Number one:
Six years older than Ray.
Number two: One-half
the amount of Jacob's car.
Number three: Four dollars
less than Samantha spent.
Number four:
In a baseball league,
teams are ranked using points.
A team earns five points
for each win
and two points for each tie.
Write an expression
to represent the total number
of points a team earns.
Let's see how we match up.
"Six years older than Ray."
Let me switch to my arrow tool
so I can move
these answer boxes.
There you go: r plus 6.
Maybe you picked
a different variable.
You're not wrong if you did.
You may have picked Q to
represent Ray if you wanted to.
Or maybe you wrote, "6 plus r."
You're still right.
Either one's right.
Okay, "one half the amount
of Jacob's car."
So, I have 1/2 times j.
I let j represent Jacob's car,
or the cost of his car.
"Four dollars
less than Samantha spent."
I've got s minus 4,
'cause I let s represent
what Samantha spent.
"In a baseball league,
teams are ranked using points.
"A team earns five points
for each win
"and two points for each tie.
"Write an expression
to represent
the total number of points
a team earns."
I let w represent
the number of wins
and t represent
the number of ties.
So, 5w plus 2t.
All right.
Okay, guys, you just modeled
real-world situations.
I hope you saw the connection
to translating expressions.
If you can handle one,
I bet you can handle the other.
See you soon.
See you next time.
Accessibility provided by the
U.S. Department of Education.

(Describer) Accessibility provided by the U.S. Department of Education.