Source: Cyberchase: “And They Counted Happily Ever After”
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, Bianca has volunteered to help count the number of runners participating in the New York City Marathon. She must keep track of the runners as they pass a certain checkpoint on the course. There are at least 30,000 runners, so she has to develop a good strategy for counting such a large number of people. She tests out a few options, but finds that an abacus may be her best tool.
Download and ShareInvestigations/Scott Foresman (2006)
Investigation 2, Sessions 1-5, pp. 18-35
Investigation 3, Sessions 1-5, pp. 36-51
Investigation 4, Sessions 1-3, pp. 52-58
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 your friend owns a very busy store. She wants to keep track of how many customers come into the store between 9:00 a.m. and noon. How would you keep track of something like that? Is there more than one way that you could do it?
Focus: As you watch this video segment, you’ll see how Bianca tries to figure out the best way to keep track of all the runners. She considers a few methods, but rejects them for various reasons. What method does she finally decide to use?
Follow Up: How many runners passed Bianca’s checkpoint? How was she able to use an abacus to keep track of her count? would an abacus be easier than recording tally marks?
BIANCA: When I was a kid, I was the best runner: at tag; red light; green light, at ringolevio, “olly, olly oxen free! We had so much fun, but…now that I’m older, I don’t run so well.
BIANCA: My friend Dorothy says I run like a rabbit. At first I thought she meant that I was fast, but then she said I have this hop skip and jump to my run, so then I decided to volunteer to work the New York City Marathon, maybe I could get some pointers.
BIANCA: Here’s my post. Young girl: whatcha doing?
BIANCA: There’ll be over thirty thousand runners coming through here soon, I have to count and see how many actually passes this point Young girl: how are you gonnna do that?
BIANCA; Well, it took a lot of thinking, thirty thousand is a big number and i didn’t want to loose track, at first I was gonna use a chart with tally marks.
BIANCA: I would put a tally in this column. And when I made ten marks I would put a tally in the tens column when I had ten tallies in the tens column, I would put a mark in the hundreds column, I could count that way into the millions Young girl: but wouldn’t you have over thirty thousand tallies in the ones column?
BIANCA: Oh, you figured that out? Well then I bought one of these counters, every time you press the button the number changes, but it only has four places so the .largest number it can count…
YOUNG GIRL: Is nine thousand, nine hundred and ninety nine, how are you gonna count them?
BIANCA: Well, with this… it’s got ten beads in each row: 1,2,3,4,5,6,7,8,9,10. As each runner comes across, I’ll move a bead to the right ,when I’ve moved all ten beads across, I’ll slide them back and move one bead on the next row down to the right, that’s the tens row. Then, I’ll start counting using the beads in the ones place again. When I’ve move them all over to the right again, I’ll slide then back and move another bead in the tens place.
BIANCA: Ones, tens, one hundreds, thousands, ten thousands, hundred thousands.
BIANCA: Ii’ve invented it, isn’t it cool?
YOUNG GIRL: It’s an abacus right?
BIANCA: Well, yeah…but mine has colors, it can go into the millions Look here they come!
BIANCA: That’s dangerous…
RUNNER: Hey watch out!
RUNNER: Get away
BIANCA: Aah! Keep the count
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