Source: Cyberchase: "Zeus on the Loose"
Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.
In this video segment from Cyberchase, the CyberSquad must help Pin and Pan divide fifteen gold bars equally between them. Many of the bars are different sizes, however, and the CyberSquad must add up fractional parts of the gold bars in order to give both Pin and Pan their fair share of gold.
Download and ShareInvestigations/Scott Foresman (2006)
Different Shapes, Equal Pieces,
Investigation 1, Session 5: pp. 19-21.
Investigation 2, Sessions 3 and 4, pp. 29-37
Investigation 3, Sessions 1 and 2, pp. 41-45
Here are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: If you had four candy bars of equal size, it would be easy to share between two people. How would you do that? But, what if you had seven candy bars and they were different sizes? How would you go about doing that? Are there any strategies you could use to help you make fair shares out of items that are not all the same size?
Focus: As you watch, think about the strategy the CyberSquad uses to solve the problem. How does knowing about the relationship between different fractions help them? What fractions do they encounter here? How are these different fractions related?
Follow Up: What did the CyberSquad know about these fractions that helped them share the gold equally between Pin and Pan? How did they decide which gold bars represented which fractions? For example, how did they know the bar they called one-fourth, was really one-fourth? Draw a diagram showing the equivalencies between eighths, fourths, halves, and a whole.
PIN: Pan, you are a goat-headed fool.
PAN: Pin, you are a fool-headed goat!
PIN: I want my fair share of the gold - or my share of the boat!
MATT: Sorry to butt in like this, but we need a ride across the river.
PAN: Sorry, we’re out of business!
JACKIE What is the problem here?
PIN: The problem? You want to know what the problem is? Heh! (to Pan) You tell her.
PAN: You see all this gold? Half is mine - and half is his.
PIN: And when we try to split it up one piece for you, one piece for me - there’s always one piece left over. Give it to me!
DIGIT: Hold onto your horns! I count fifteen here - I don’t know how to share fifteen either.
INEZ: Hmmm... Maybe we can! PIN: But tha-that thing with the big beak just said we can’t!
INEZ: Here’s an idea. Will you take us across to the cave if we help you divide the gold equally?
PAN: Oh and here’s an idea for you! If you can’t...(growl)
INEZ: OHHAHHHH!
MATT: That was awesome!
DIGIT: Listen, goatman. Do you realize my friends here have the power to give you both an equal share of gold? Huh?
PIN: Okay, you have a deal.
PAN: Heh, start the sharing!
INEZ: Okay. This one looks like a whole bar of gold. Maybe all these smaller ones are parts of a whole bar. You follow me?
PIN:/PAN: Uh, right!/Yeah, we knew that!
MATT: So let’s start by separating the different size pieces.
JACKIE: Try putting the bars in rows - largest to smallest.
PIN: Hey, look at that?! Two of these bars are the same as the one big bar.
INEZ: Which means each smaller bar is one-half of the whole bar.
MATT: And four of these bars also equal one big bar.
PIN: Yeah!
JACKIE So each of these is one-fourth of the whole bar.
PIN: And it looks like it takes, uh, eight of this size bar to equal the whole bar.
PAN: Which means, uh, each one of these bars must be one-eighth of the whole bar.
PIN: So how do we share them?
JACKIE Simple! You get the whole bar...
PAN: Hey! What about me?
INEZ: And you get the two half bars - the same as one whole bar.
PAN: Aha, uh, that’s better.
MATT: Now you get the four quarter bars - because four quarters is also the same as a whole.
DIGIT: And you get all eight of the one-eighth bars because, um, because...
DIGIT: Because eight-eighths is the same as a whole!
PIN:/PAN: (in unison) Hooray - equal shares of gold! Hooray!
INEZ: But your shares...you just...
PIN: It doesn’t matter! We’re friends again.
PAN: And we can divide our gold up anytime we want - now that we know how to do it.
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