In this video segment from Cyberchase, The CyberSquad is trying to figure out the patterns followed by each of four musicians who play a song together. They start by charting the pattern of each instrument, and in doing so they use their knowledge of factors. After testing a few possibilities, they are able to successfully find the pattern that represents the song. Watch "Performance by Music of the Spheres" to hear the whole song performed by the musicians.
Investigations/Scott Foresman (2006)
Investigation 1, Session 3: pp. 9-10
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: Sometimes when we hear music we clap our hands or tap our feet. When we do this, what are we keeping track of? If one person hits the drum every two seconds, while another person blows into a trumpet every three seconds, and another person strums a guitar every six seconds, at what point will all the musicians being playing a note at the same time? How do bands manage to play together so that all the different instruments are coordinated?
Focus: As you watch this video segment, notice how the CyberSquad keeps track of the beats in the different musicians' playing patterns. What does the CyberSquad discover to be the key to getting everyone to play the song correctly?
Follow Up: What was the beat pattern that the drummer needed to follow? Did all the other band members have to follow the drummer’s exact same pattern? Why or why not? How do you think musicians and songwriters develop the beats and patterns in music they produce?
JACKIE: Guys, I've got the horn part. After the Beast starts, Himeropa counts and toots her horn on the fourth count. One-two-three-four. One-two-three-four. And they all play together on one beat just before the song repeats.
MATT: Alright! We've got a sound pattern for each musician!
INEZ: But our chart doesn't show us any time when they all play together!
JACKIE: Maybe they have to play longer before it all repeats. Try repeating Apollo and Calliope's parts a few more times and see what happens. It's going to work. Add one more of Himeropa's part.
MATT: We did it. Look, we found a place where they all play together. Cool! All three patterns match up on the 12th note!
JACKIE: And if they keep playing the same patterns, the music will repeat over and over again.
INEZ: Yeah...but that still doesn't tell us when the Beast plays.
JACKIE: You've got a point there... Let's get the band to rehearse - maybe then we can tell what's missing and figure out the Beast's pattern!
MATT: Come on! Oh man, it sounds worse than before!
JACKIE: They're playing their parts the way they told us they do...
INEZ: But something's definitely missing!
PIN: Oh, no! The sun is setting!
PAN: We're running out of time!!!
MATT: Come on, guys - think! What do we know?
INEZ: We know that each musician plays their own sound pattern - over and over.
JACKIE: And without the Beast, their parts don't seem to fit together. His drum part must be the pattern they all depend on - or they wouldn't sound so bad without him!
INEZ: But how do we figure out what that pattern is?
MATT: Back to the chart! I'll mark each beat in the pattern with a number. So now what do we know?
INEZ: We know the Beast starts playing on the first beat.
JACKIE: And we also know he plays on the 12th beat with the others. Himeropa told me.
INEZ: Look! Look! No one plays on the fifth, seventh or eleventh beats - maybe the Beast plays there, too.
JACKIE: I think we're getting somewhere. Let's hear what it sounds like with the real instruments!
MATT: Inez, you play the drums for the Beast.
INEZ: Me? Oh, why me?
JACKIE: Desperate times call for desperate measures.
INEZ: Who said that?
JACKIE: You did!
INEZ: Ah? No good? Well, I guess that wasn't the right pattern.
JACKIE: No wonder it didn't work! Look, the drum doesn't have a regular pattern like the others! Don't you see?
INEZ: I'm not sure.
MATT: Jackie's right! We need to find a pattern for the Beast that repeats.
JACKIE: Something simple - something that helps the others play. Remember when we saw the video of the band? How I was tapping my foot?
MATT: Yeah, and I was snapping my fingers.
INEZ: And I was trying to clap. What's your point, Jax?
JACKIE: What was the pattern when I tapped my foot?
MATT: Beats me.
JACKIE: Exactly! A simple, steady beat! Watch. The same beat, over and over. One...one ...one...one.
INEZ: So are you saying the Beast plays on every beat?
JACKIE: I think so. They all started off together!
INEZ: But that pattern sounds so simple.
MATT: Let's chart it! Touchdown! All the patterns fit together.
JACKIE: And look...you can repeat the song after 12 beats.
INEZ: That's got to be it! The beat of the Beast's simple pattern keeps the other three together.
MATT: Let's play it on the big board and see what we've got.
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