Source: Cyberchase: "A Perfect Fit"
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In this video segment from Cyberchase, the CyberSquad must build a path to cross a stream of hot lava. They find a pile of triangle shaped tiles which float in the lava and don’t melt. Unfortunately, they run out of triangle tiles when they are only half way across the stream of lava and must figure out what other tiles they can use to complete the path.
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: Fitting together the same size shapes with no gaps or overlaps is called tessellating. Do you think you could create a tessellation using rectangles? Why or why not? Do you think it is possible to create a tessellation using different shapes together, such as triangles and rectangles?
Focus: In this video segment, you will see the CyberSquad attempt to finish the tile path across the lava, even though they have run out of triangles. Notice what shapes they try instead. Which ones work and which ones don’t? Why?
Follow Up: How was it possible for the CyberSquad to create a tessellating path out of triangles and hexagons? Do you think a tessellating path could have been made out of ovals or circles? Why or why not? How about a path made out of triangles and circles?
MATT: Way to go, guys - we're half-way across!
JACKIE: Only one thing...we don't have enough triangles to finish the path!
DIGIT: Just when things where goin’ good!
INEZ: Wait! What about those other tiles?
MATT: These tiles don't work! Game over!!
INEZ: You sure? That's what we said about the triangles.
MATT: Okay, what do we have here? A pentagon: five sides all the same length - equal angles, just like the squares and triangles. But here's the difference. Five pentagons together leave a big gap...And there's no way to add one to fill that gap, without an overlap!
JACKIE: And the lava could ooze through the overlap!
MATT: What we have here is a failure to tessellate!
DIGIT: All right! Pentagons are out! Next! Ow ow eww!
INEZ: How about these hexagons? Six straight sides, equal length, equal angles. All the same size. Two together leave a big gap but a third one fills it exactly...A perfect fit! JACKIE: And look! Every time we add a hexagon, we have more gaps that other hexagons can fill! So we can make this tessellation as big as we want it!
MATT: Game on, guys! Let's finish this bridge over troubled lava!
DIGIT: And make it snappy, okay? In exactly nine, make that eight minutes, the sun will reach high noon...AND GIGABYTE WILL LIVE AGAIN!!!...Just slide these hexagons into those empty spaces like so...and the Big T is done! Yes! No gaps - no overlaps! Tessellation complete!
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