In this video segment from Cyberchase, Matt and Digit need to set up tables so that 20 workers will each have their own spot at a table as they assemble circuit boards. They only have five tables, and they found out that when the tables were put together in video segment "Arrangement 1" there were not enough seats for all the workers. Since he cannot add any more tables, Matt realizes that perhaps changing the positioning of the tables will provide the extra seats they need. Check out "Arrangement 2" to watch one of Matt's other attempts to accommodate the 20 workers.
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: Let’s say you had a deck of 10 cards and some pennies and you were laying them out on a table. If you were allowed to put one penny on each side of a card, what would be the best way to arrange the cards to get the maximum number of pennies on the table? What if you had the same task, but this time there was a rule that said every card must be placed right next to another card (so that the sides touch)? How many pennies could you place down? How many pennies could you place down if there were twenty cards? How did you figure it out?
Focus: In this video segment, Matt makes a discovery about why his first arrangement did not seat enough workers. What did he realize? Using the new arrangement, how many workers can sit at a table?
Follow Up: How did Matt finally decide to arrange the tables? Why did changing the table arrangement make a difference? If the tables were spread out, with none of them touching, how many workers could be seated?
MATT: Okay, we don't have nine tables - we just have five...so I need to find a way that uses the five tables we have. Time out! Do you see what I see?
MATT: The tables aren't square! They're rectangles...like these shingles!
DIGIT: So...how does that help?
MATT: Look...these two sides are longer than the other two.
EUKIE: More room for more workers?!
MATT: Exactly! One table is the simpler case. See! One-two...three-four!
REEKA: But we still only have five tables... remember?
EUKIE: Yeah, five...only five!
DIGIT: Not to worry, the kid's a professional.
MATT: Here are the five tables we have to work with. Four workers, eight workers, twelve, sixteen, twenty. Lined up this way, five tables gives us...
DIGIT: Twenty places for twenty workers! Matty, you're a genius!
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