Source: Cyberchase: "Sensible Flats"
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Calculating Rectangular Area
(Video)
In this video segment from Cyberchase, the CyberSquad must compare two parcels of land during a land rush. One parcel is an irregular shape and belongs to Hacker. The other parcel is a regular rectangle and belongs to Judge Trudy. By dividing each parcel into squares and triangles, they prove that the two shapes have the same area.
Download and ShareInvestigations/Scott Foresman(2006)
In Flips, Turns and Areas Grade 3
Investigation 1: Motions and Tetrominoes
Investigation 2: Finding Area
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 a piece of paper that was made up of three rows with three squares in each row, how would you find the area of that paper? If someone took a pair of scissors and cut that paper diagonally into two pieces, would those pieces still have the same total area if they were put together again?
Focus: As you watch this segment, notice how the CyberSquad has to compare the two parcels of land in the courtroom. Jackie says that even though Hacker’s land is not a regular shape, it is made up of regular shapes like triangles and squares. How does this idea help the squad solve the problem?
Follow Up: What did the CyberSquad do with the diagram of Hacker’s land to help them make a fair comparison with Judy Trudy’s land? Did they use fractions at all? What shapes were used? When you compare two different shapes, how could using grid lines or drawing squares on the shapes help?
HACKER: Enough! You're going to make me cry! Now tell me how you're going to prove I'm innocent.
INEZ: The evidence, please. We had the same problem you did, Judge. How do you measure the area of an irregular shape? One that's not a square or a rectangle? Grids just don't fit.
JUDGE TRUDY: Got me stumped.
INEZ: Us, too. Till we realized that we could turn Hacker's shape into a regular shape. Check it out. Here's a photo of Mr. Hacker's land with a grid on it.
MATT: The outline sort of looks like a house. But it's not very regular, is it.
JACKIE: But look closely and you'll see that it's made up of regular shapes we all know. See? Squares and triangles.
JUDGE TRUDY: Mm hmm. I can see that.
MATT: But if I cut off this triangle on top of the house.
HACKER: He's destroying the evidence!
JUDGE TRUDY: Pipe down! Carry on.
MATT: And then I stick the triangle down here and finish this square. It makes a new square on the third row.
SHERIFF JUDY: Hey! Yer rearranging the shape of Hacker's land! That legal, Trudy?
INEZ: Cutting and moving a piece doesn't change the total amount of area - so long as we put it back somewhere. Right, Judge?
JUDGE TRUDY: Sounds right to me.
MATT: Okay. Next, I cut out these two triangles.
SHERIFF JUDY: If that don't beat all!
JACKIE: Wait! It gets better. Now Matt cuts off the square up here... Moves it down...and voila! A row of three squares!
DIGIT: Ooh-ooh! Lemme do the last move! We take this whole top row of three squares. Turn it right side up and move it...uh... Wu-oh! Where does it go? Oh, right. (nervous laugh) I knew that.
INEZ: And what does Mr. Hacker's land measure out to now? Three rows of five squares - or...an area of fifteen squares.
SHERIFF JUDY: Just like yer land, sis!
JUDGE TRUDY: Yep! Three times five - the same area exactly.
HACKER: (chuckle) See? I told you!!
JUDGE TRUDY: Never thought I'd say this, mister, but I'm wrong and you're right. A clear-cut case of mistaken area. Case dismissed.
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