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Welcome to Algebra I: Modeling Real-World Situations

9 minutes

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.

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In this program, students will learn to model real-world situations with algebraic expressions in a variety of representations. Part of the "Welcome to Algebra I" series.

Media Details

Runtime: 9 minutes

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