In this video segment from Cyberchase, Matt and Digit need to set up tables so that 20 workers will each have a spot at a table in order to assemble their circuit boards. Matt and Digit want to know the number of tables they need so that they can transport them all at once. Matt decides to use small shingles to represent the tables and washers to represent workers. He tests his ideas by positioning the washers around the shingles. Check out "Arrangement 2" and "Arrangement 3" to view Matt's other attempts to solve the problem.
Investigations/Scott Foresman (2006)
Patterns of Change: Tables and Graphs, Investigation 1, Sessions #1-4: pp. 18-39
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 were planning a big dinner party for 100 guests, you would need to figure out how many tables and chairs are needed to seat all the guests. How would you go about doing this? What do you have to know about the tables?
Focus: As you watch this video segment, you’ll see that Matt and Digit have to figure out how many tables they need to seat all of the workers. How do they figure this out without actually bringing in the actual tables and workers?
Follow Up: How many tables do Matt and Digit decide they need? Once they figured out how many workers fit at one table, did they need to keep modeling the rest of the problem with the shingles? How could they have done it with numbers?
DIGIT: Hey! Are you guys lifting your end or what? This is heavy!
EUKIE: Really heavy!
MATT: Of course we're lifting! Are you?
REEKA: Can we just move t-the table?
MATT: OK, you four - to work!
AQUA WORKER: Need a Torx Driver!
PINK WORKER: Seen my soldering iron?
GREEN WORKER: Where's my wire wrapper?
MATT: Guys, guys...find your own tools! I can't do everything! Get to work!
OTHER WORKERS: What about us?/Where do I sit?/What about me?/And me?
MATT: Didge...we need more tables!
DIGIT: What happened to please?
MATT: Didge, "please" isn't gonna get these circuit boards done on time! We need more tables!
DIGIT: Fine, but why not figure out how many we need, so we can bring 'em all down at once - instead of one at a time!
EUKIE: Good idea!
REEKA: Why didn't you think of that?
MATT: I don't even know how many workers are here.
MATT: Okay. That's a start.
PINK WORKER: Screw twister!
GREEN WORKER: Glue! Glue! Glue!
MATT: Get it yourself... please! Man, there's gotta be some simple way to figure out how many tables we need. Wait a second! I just might have an idea! Let's make believe this shingle is a table...and these washers are the workers.
EUKIE: Don't forget, we need twenty places!
REEKA: Yeah, twenty!
MATT: I know. We'll get to them. Right now, I need to keep the problem simple. Now, if we put one worker on each side of the table...one table will give us room for four workers.
DIGIT: Um… we already know that Matty. We need more tables!
EUKIE: But how many?
MATT: Well… Let's add more shingles and count up places. The first table gives us four places... the second one gives us eight...then twelve...and one more gives us sixteen total.
EUKIE: Not enough Places!
REEKA: What do we do?!
DIGIT: Uh… How 'bout we add one more table?
MATT: Touchdown, Didge! And another four makes twenty. We need 5 tables for 20 workers.
REEKA: A place for every worker.
EUKIE: And a worker for every place.
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