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# Triangles

Media Type:
Video

Running Time: 2m 01s
Size: 5.5 MB

or

Source: Cyberchase:"A Perfect Fit"

### Collection Developed by:

Collection Credits

### Collection Funded by:

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 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. They work together to try to figure out how to create a path made of the triangle tiles that has no gaps and no overlaps. Check out the video segment "Hexagons" to see if the CyberSquad makes it across the stream of lava.

Connections

Everyday Math (2004)
Teacher Lesson Guide, pp. 105, 462, 920
Teacher Reference Manual, pp. 145-148
Student Reference Book, pp. 69

Teaching Tips

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: Fitting together the same size shapes with no gaps or overlaps is called tessellating. Do all shapes tessellate? Why or why not? What kinds of shapes do you think will tessellate?

Focus: In this video segment, you will see the CyberSquad attempt to build a path made of triangle tiles with no gaps or overlaps. You’ll notice their first attempt leaves many gaps. What does Matt do with some of the triangles to remove the gaps?

Follow Up: Does it look like the CyberSquad will be able to build a path of triangles that has no gaps or overlaps? What do you think the shape of the path will be? When you are tessellating with shapes, do all the shapes have to face in the same direction?

Transcript

DIGIT: But the floor's red hot! We'll never get across! Hacker's gonna win!

MATT: No way. That is not gonna happen.

INEZ: Hey! What's this? Tile?

JACKIE: Let me see. Whoa! W-whoops! Sorry!

INEZ: Look! It floats and it shields the heat!

JACKIE: Maybe we can make a path across the lava with tiles - just like we made a raft to get across the river!

MATT: But these tiles are so small! We’ll need lots and lots to make a path wide enough to walk on!

DIGIT: And they have to fit tight - no gaps. Or our toes will be toast!

JACKIE: No problem! Let's tessellate ‘em!

DIGIT: Problem! None of these are squares! Only squares give us no gaps or overlaps right?

JACKIE: We don't know that for sure, Didge. Maybe we can do it with triangles!

DIGIT: How? These have three sides, not four.

MATT: Wait! At least the sides are all the same length, like the squares.

INEZ: And every triangle is the same size, too!

JACKIE: That helped with the squares. Let’s try 'em! Nope. Oh not working. Gaps everywhere.

MATT: What if we slide this top row over a bit, so the corners meet, like the squares did?

JACKIE: Hey! The gaps look just like our triangles - only upside down!

MATT: So flip the triangles!

DIGIT: The triangles fit together exactly - no gaps, no overlaps! It worked!

INEZ: Let's see what happens if we add more triangles here...A tessellation! As long as we use the same pattern of triangles we can make the pattern as big as we want! Start tessellating!

Standards

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