Source: Cyberchase: “Find Those Gleamers”
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In this video segment from Cyberchase, Harry has $100 to buy new clothes. At a bargain store, he finds a jacket that costs $20 and a pair of pants for $10. Harry has to evaluate a few algebraic expressions to figure out what combination of pants and jacket he should purchase for his new wardrobe.
Download and ShareHere are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: Sometimes in math we use symbols or letters to stand for concepts or quantities. Let’s say we are painting a room, and a can of yellow paint costs $2. If we wanted to write an equation to help us figure out how much our paint will cost, we could say that the letter "Y" stands for one $2 can of yellow paint. That is an easy way to write it. If we need 4 cans of paint for the job, we could express the cost as 4Y = $8, because each can of yellow paint costs $2, so 4 x $2 = $8. When we do this we are using Y as a variable.
Focus: In this video segment, as Harry figures out how to put his wardrobe together, what is the first step he takes? As he begins to write about the jackets and the pants, what letters does he use? Why do you think he uses these letters? Notice how Harry creates a few different equations. Why doesn’t he stop after the first one?
Follow Up: In this video segment, how did Harry approach the problem of getting jackets and pants for his new wardrobe without spending more than $100? How did he use variables? What do you think the advantages are of writing equations like this with variables? Could you give an example of how you might use variables in equations for some shopping that you have done?
HARRY: (Sigh) I need some new duds. I mean, I need a new look. I am getting nowhere with my two-toned shoes and Hawaiian shirts. Excuse me. Excuse me, that is a beautiful suit. You must be a lawyer or a banker.
MAN-ON-THE-STREET: Thank you. I'm a librarian. I just like to dress up.
HARRY: That might be my problem. I dress down. I have this 100 dollars that I've been saving from my various jobs. And I am going to create a new me, a better me. A me that people stop on the street and ask "Are you a movie star?" "You must be a millionaire."
Right idea, wrong store.
Not here. Not here either.
There's got to be someplace that has bargain clothes!
The new me is right around the corner.
I can buy a whole new me here. But what should I get? And how much can i get?
Let's see. I have 100 dollars. And I'll write down j for jackets, which are 20 dollars each. And p for pants, which are 10 dollars each.
5j, or 5 times 20, is 100. So I could buy five jackets. 10p or ten times ten is also 100 so I could buy 10 pairs of pants.
But I want a whole new look. I need to buy more than just one kind of thing.
Wow, I found some really cool stuff. Let's see if I have enough money. 4j plus 4p... 4j is 80 dollars. And 4p is 40 dollars. So 80 plus 40 is 120 dollars? Oops. I don't have enough money.
Okay, now that I've lightened my load. 3j plus 4p is 60 plus 40. That's $100 dollars! Perfect.
STORE CLERK: That's 3 jackets and 4 pairs of pants. That's 100 dollars exactly. And today when you spend $100 you get a free pair of shoes.
HARRY: No way! There is nothing like new clothes, to make you feel like a new person.
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