ALBERTO AND THE CASE OF
THE PYTHAGOREAN STEAL
By Robert Frankel
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SYNOPSIS: In Pythagorean Steal, our teenage hero Alberto is puzzling
over why his baseball coach told him that it's easier to steal second base than
third base. His brainy younger sister, Elizabeth, overhears and offers to help.
Together with Alberto’s earthy older sister, Terri, and best friend Justin, they
recreate a baseball diamond and use the Pythagorean Theorem to find the
answer. Mom and Dad get it all confused creating a humorous, memorable
ending!
The Mastering Math Series aims to inspire knowledge and mathematical
concepts through story theatre. Each ten-minute play uses theatre to actively
engage and enhance students' conceptual understanding of five different
mathematic basics: Pythagorean Theorem, Probability, Quadratic Equation,
Significant Figures, and the irrational number Pi. The Mastering Math
Series offers a non-traditional, interdisciplinary approach to effective
mathematics teaching while instilling the love of drama in students at the
same time. The plays can be fully performed or simply read aloud in the
classroom.
In this play, the Pythagorean Theorem is overviewed in the context of a
baseball game. The practical application of this theorem to the baseball
diamond and its triangles helps bring this principle to life - - both for Alberto
and his friend Justin, as well as for your audience.
CAST OF CHARACTERS
(3 MALES, 3 FEMALES)
ALBERTO (m) ...............................Athletic, bright, but constantly dealing
with unwanted-but-needed academic
help from very smart sisters whom he
loves.
ELIZABETH (f)..............................Alberto’s sister, a year younger, a math
whiz, and an occasional smart aleck.
THERESA (f)..................................Alberto’s older sister, a science whiz,
very Earthy, optimistic and a bit of a
“flower child.”
JUSTIN (m) ....................................Alberto’s best friend - - easy-going with
a crush on Theresa.
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MOM (f) .........................................Alberto’s mother, Molly, sweet and
understanding.
DAD (m) .........................................Alberto’s father, Hank, a playful nerd.
PROPERTIES
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Baseball
Two baseball mitts
Book of math puzzles
Pencil
Calculator
World globe
PRODUCTION NOTES
The set should not be elaborate. It need only suggest a house SR - - a chair
and table can be enough. And SL is a backyard which can be simply an
open stage or contain a variety of "backyard items" strewn on the ground.
This is first and foremost a comedy, so the kids should have fun with it. But
since it is introducing some math concepts, it's important that when technical
words are introduced and demonstrations are made, they not be rushed. This
play can also easily be produced as a simple in-class, stand-up-and-read play
as an introduction to the given math topic. If done this way, the
demonstration will be better understood if either, a) Kids are on their feet
doing some illustrative movement, or b) Teacher is at the whiteboard
visually illustrating some of what's said.
To Judy Replin, my once and still favorite teacher in the world.
SETTING:
ALBERTO'S family room and backyard. HIS family room is SR,
suggested by a couch, chair, TV, bookcase, and a dinner table set
with five chairs. It opens into SL, which is the large backyard that has
some baseball equipment in a pile.
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AT RISE:
Five p.m. In the darkness, we hear an umpire call, "You're out!"
followed by some moans and groans. LIGHTS UP on ALBERTO, age
13, trudging to CS, bat over HIS shoulder and mitt under HIS arm.
Reluctantly, HE stops CS and talks to audience. HE acts out what
HE describes.
ALBERTO: I blew it. Our team's down by a run, and I haven't had a
hit all day, man, the pitcher's like lights out, you know? I finally get
on in the bottom of the ninth inning - - hit by a pitch. (Rubs HIS
butt.) Ouch. So there's one out, right? And I'm fast. So I take a
lead and first pitch, voom, I take off for second, right? And the
catcher is just throwing the ball to second when I'm sliding in.
SAFE! It’s a beautiful thing, you know? So there I am on second
and my teammate Bobby Crandall strikes out. Two outs. So I'm
thinking, hey, if it's that easy to steal second, swiping third oughta
be a piece o' cake, right? So I get the same lead and next pitch,
voom, I take off for third. Never been faster, I swear. And as I
slide, I look up and the third baseman, my best friend Justin, is
smiling with the ball in his mitt, just waiting for me to slide into the
tag. I'm out, and that's the game. And the worst thing is, Coach
calls me over. He says, "Alberto, stealing second was fantastic,
man, and your slide was perfect.
Copyright © MMVIII by Robert Frankel. All rights reserved. Caution:
Professionals and amateurs are hereby warned that ALBERTO AND THE
CASE OF THE PYTHAGOREAN STEAL is subject to a royalty. ALL
INQUIRIES CONCERNING PERFORMANCE RIGHTS, INCLUDING
AMATEUR RIGHTS, SHOULD BE DIRECTED TO HEUER
PUBLISHING LLC, PO BOX 248, CEDAR RAPIDS IA, 52406.
www.heuerpub.com
But stealing third, you don’t do it in a close game." So I say,
“Why?” And he says, "Because it's a lot harder to steal third than
it is to steal second." And before I can ask him why again, he pats
me on the back and starts talking to the parents.
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As HE talks, HIS older sister THERESA, ENTERS SR into house and
moves outdoors US of ALBERTO. She is in hippie-like garb and
carries a world globe.
ALBERTO: So I've been going over it the whole way home and it
doesn't make any sense. Why would it be easier to steal second
than third?
TERRI: WOO-hoo, little bro! You better not let Dad hear you were
stealing. You'll have bathroom chores for the next year.
ALBERTO: Oh, ha, ha, you’re SO funny. And I'm not little.
TERRI: (Moving to HIM - - concerned.) Hey, what’s the problem?
Ya know, if you need any help, I could. . . .
ALBERTO: Naw, It's all right. I'll figure it out.
TERRI: Okey-dokey, but you’re missing out on a BEA-U-tiful day,
little bro.
HE glares at HER. SHE EXITS with globe SL as JUSTIN ENTERS
SL and passes HER.
TERRI: Hiya, Justin.
JUSTIN: (Waving to HER OFFSTAGE.) Hey, yo, hi, Terri. Bye! (HE
drops the baseball HE's holding and scrambles for it. To
ALBERTO.) Must be nice having a sister like Terri, huh?
ALBERTO: Oh yeah, slice o' heaven. You come to gloat?
JUSTIN: Naw, I wouldn't do that, man. Close game, close game.
Coulda gone either way. And you're just too slow, bro!
HE laughs and ducks as ALBERTO tries to grab HIM. THEY wrestle
a bit, laughing.
ALBERTO: Hey, you ever hear that it's harder to steal third than
second?
JUSTIN: It is for YOU!
ALBERTO: No, seriously man. It's the same ninety feet, right?
ELIZABETH, bespectacled, ENTERS through house to edge of family
room with a book of Math Puzzles and a pencil. SHE wears a
calculator on HER belt. SHE overhears this discussion and becomes
curious.
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JUSTIN: Well, yeah. Ninety feet from home to first, first to second,
second to third, third to home.
ALBERTO: Yeah, right, so Coach is wrong, right? I mean it should
be just as easy stealing third as it is second.
JUSTIN: Yeah, I guess. But ya don't see it happen as much, for
some reason.
ELIZABETH can't stand it any more and strolls in US of JUSTIN.
ELIZABETH: (Mock coughing into HER hand as SHE says.)
Pythagoras.
ALBERTO: Huh?
JUSTIN: Oh hey, Lizzie.
ALBERTO: Hey, we're in DEEP CONVERSATION, trying to figure
something out here. Has nothing to do with math. Its sports.
Baseball. (Turning back to Justin.) So if its ninety feet all the way
around, I don't see why - ELIZABETH: (Mock coughing again.) Pythagoras!
ALBERTO: What was that? The Aflac duck?
JUSTIN: (To LIZZIE.) Hey, did you say Pythagoras?
SHE jumps on this chance and joins THEM DS.
ELIZABETH: Uh, no. But, uh, now that you mention it, Pythagoras is
this ancient Greek mathematician, and he’s got a theorem named
after him that just may help you with your DEEP
CONVERSATION.
ALBERTO: Yeah? What's his name again?
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ELIZABETH: Pythagoras. Born around 570 B.C. And the theorem’s
called the Pythagorean Theorem. Duh.
ALBERTO: Well, baseball wasn't invented until the 1700's . . . in
England. I don't see how a Greek mathematician born that long
ago could ever help us.
JUSTIN: Hey, no, wait, Alberto, that's the next section in Keller's
math class.
ALBERTO: (To JUSTIN.) It can't have anything to do with baseball,
man. C'mon.
ELIZABETH: But it DOES have to do with baseball, because it
DOES have to do with triangles.
ALBERTO: So okay, Miss Know-it-all, but the baseball diamond is a
SQUARE, not a TRIANGLE.
ELIZABETH: (Slyly.) Hmmm, I wonder what you get when you cut a
square in half at its corners.
JUSTIN: Hey, I know! Two triangles! Right?
ELIZABETH: Absolutely right. RIGHT TRIANGLES, in fact. You
know, triangles with a right angle in them.
JUSTIN: Oh, I remember now - - and a right angle is one that has
ninety degrees.
HE holds up HIS fingers in an “L” shape. ALBERTO is confused.
ELIZABETH: You got it.
THERESA reenters SL without the globe.
ELIZABETH: Here, lemme show you. Hey Terri, need your help a
sec.
TERRI: (Comes DS with enthusiasm.) Sure. But you're not going to
make me do math problems are ya? You know how queasy I get
with quadratic equations.
ELIZABETH: No, no, it's nothing like that.
TERRI: All right, then.
JUSTIN: Uh . . . hi, Terri.
TERRI: Hiya. Again!
ELIZABETH: All right, so each one of us is going to be a base. Let's
see, I'll be first base.
SHE positions HERSELF DSL and aligns the OTHERS as
appropriate on the stage given sightlines.
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ELIZABETH: Okay, Alberto, you're second.
ALBERTO: (With impatient sarcasm.) Great.
ELIZABETH: Terri, you're third.
TERRI: YES! (THEY give HER a look.) Well, all good things in
science come in threes.. Sun, moon, Earth. Solid, liquid, gas.
Crust, mantle, core. Inertia, momentum and reciprocal actions.
ELIZABETH: Yeah. In math, too! Hour, minute, second. Scalene,
isosceles, equilateral.
Mean, median, mode.
Hyperbolic,
Euclidean, elliptic.
ALBERTO: Whoa, you two. We’re talking baseball.
ELIZABETH: Right. And so Justin, you're home base.
ALBERTO: Plate. It's called "home plate," duh. And besides, a
whole baseball field can't fit in this backyard.
JUSTIN: Well, that's okay. As long as we're in a square - - the same
distance from each other - - the idea still works, right?
ELIZABETH: Exactly. Okay, so. The distance from home-Justin to
me-first is supposed to be ninety feet.
JUSTIN: Right.
ELIZABETH: And me to Alberto, and Alberto to Terri, and Terri to
Justin, all ninety feet. Or in this case, all maybe twenty feet. But
that doesn't matter, just that they're the same length. That means
we've got a square, and we've got right angles at every corner.
ALBERTO: But that just proves my point. When I ran from first to
second, it was ninety feet, and second to third - - Terri - - it's still
ninety feet.
ELIZABETH: Yeah, but what about the catcher?
ALBERTO: So what about the catcher? He just throws it to either
base. Same difference.
TERRI: I like the name “catcher.” Very grounded.
Eyes roll.
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JUSTIN: So if I'm the catcher, I throw to second, buh-BING . . . (HE
mimes the throw.) . . . when you try to steal second. And if you try
to swipe third, buh-BING . . . (Mimes the throw again.) . . . I throw
to third.
ELIZABETH: That's it! That's it!
ALBERTO: That's what?
ELIZABETH: Well, how far is it when Justin, the catcher, throws from
home to Terri at third?
ALL: Ninety feet.
ELIZABETH: Right, 'cause he's throwing right along the baseline,
which we know is ninety feet. BUT how far is the catcher throwing
when he throws to second?
JUSTIN mimes a throw to ALBERTO. THEY consider this in silence.
JUSTIN: Um, well, just a guess here, but wouldn't it be, like, ninety
feet?
ALBERTO: Yeah. Same-o, same-o.
ELIZABETH: But it isn't.
TERRI: This is that Pythagorean thingy, isn't it? Never got that.
ELIZABETH: Yeah. The Pythagorean Theorem states that, for any
right triangle, the square of the HYPOTENUSE is equal to the sum
of the squares of the adjacent legs.
Pause.
JUSTIN: Uh, could you go back to the part about the pot and the
goose?
ELIZABETH: (Little chuckle.) That's close Justin. It's actually hyPO-te-NUSE. And . . .
ALBERTO: (Interrupting.) I still don't see a triangle here. Just a
square.
ELIZABETH: But look! (SHE walks away from HER position at first
base.) See? The three of you form a triangle, a right triangle.
ALBERTO: Oh, I get it now. So from Justin to Terri is one side of the
right angle and from Terri to me is the other side.
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ELIZABETH: Correctumundo, big bro. And those two sides in a right
triangle are sometimes called “legs.”
JUSTIN: Okay, so what's this line, the one that goes from me, home
plate, to Alberto? 'Cause that's the line the catcher is throwing on,
right? What's that?
ELIZABETH: THAT is your “pot” and “goose,” otherwise known as
the hypotenuse!
(SHE giggles, then continues, pointing
appropriately.) So those are the two legs, and this is the
hypotenuse. We know the length of each of the legs. It's . . . ?
ALBERTO: Ninety feet?
ELIZABETH: Right. What we WANT to know is the length of the
hypotenuse here. The Pythagorean Theorem is made exactly for
figuring that out. It says . . .
ALBERTO: English this time, okay?
ELIZABETH: Promise. So it says that . . . (Points to line between
JUSTIN and TERRI.) . . . if you square the length of that leg . . .
TERRI: Oh right, I remember. So that's ninety squared - - ninety
times ninety.
JUSTIN: (Quickly.) Which is exactly eight thousand one hundred.
All look at HIM astonished.
JUSTIN: Well, it is.
ELIZABETH: Correct. And the square of the length of THAT leg
is . . .
Points to line between TERRI and ALBERTO.
ALBERTO: Same thing. Ninety squared or eight thousand one
hundred.
ELIZABETH: Yep. And now just two last steps. The theorem says
the "sum of the squares of the legs" so . . .
ALBERTO: So that's just, what, adding the two squares we just
calculated. So, eight thousand one hundred plus eight thousand
one hundred is . . . sixteen thousand two hundred.
JUSTIN: Feet? Naw. That can't possibly be the distance between
me and Alberto!
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ELIZABETH: (Smiling.) It's not. The last step of the theorem says
that the sum is equal to the SQUARE of the hypotenuse. So if the
hypotenuse SQUARED equals sixteen thousand two hundred, to
get the actual hypotenuse you have to just . . .
JUSTIN: . . . take the square root of sixteen thousand two hundred?
ALBERTO: Naw, that can't be - ELIZABETH: Yes, exactly right!
ALBERTO: Uh, good one there, Justin.
ELIZABETH takes out HER calculator and pushes some buttons.
ELIZABETH: And the square root of sixteen thousand two hundred
is . . . one hundred and twenty-seven. (Pause.) Point three!
ALBERTO: (Getting excited as HE "gets it".) Wait, wait, I get it! So
whether I steal second or third, the distance I run is the same.
BUT. When I steal second, the CATCHER has to throw the
distance of the hypotenuse, which is one hundred and twentyseven feet. When I steal THIRD, he only has to throw NINETY
feet. And THAT'S why it's easier to steal second - - the catcher
has a longer throw!
JUSTIN: Cool.
TERRI: But I always thought it was just A-squared plus B-squared
equals C-squared.
ELIZABETH: Well, yeah, it’s that too. (SHE walks to the lines and
points appropriately.) A-squared is the hypotenuse here, and it
equals the sum of the two legs B-squared, here, and C-squared.
Just another way of saying it.
TERRI: Hmmm. Well, TTFN! Got a science project to do!
ELIZABETH: WAIT! I wanna show you the coolest thing about the
Pythagorean Theorem - - the PROOF!
THEY ALL hold THEIR breaths, looking at EACH OTHER unhappily.
DAD suddenly ENTERS into house and yells out to THEM.
DAD: Dinner, everyone! Alberto, Terri, Lizzie, dinnertime!
JUSTIN: Well, too bad there, Lizzie, really looking forward to that
proof. But gotta go. See ya, Alberto!
ALBERTO: Yeah, bye.
JUSTIN has almost EXITED SL when HE stops and turns.
JUSTIN: Like, see ya 'round, Terri.
TERRI: (Teasing him a bit.) Like, yeah!
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MOM joins DAD at the door to the backyard.
MOM: Hey, you hear your Dad? Dinnertime! Make sure you wash
your hands.
TERRI: (Shaking HER head as SHE heads SR to the house.) Dirt is
VERY organic, Mother.
MOM: (Calling after HER.) It’s also very dirty.
DAD: What were you doing out here, anyway?
ELIZABETH: Nothing.
ALBERTO: Just learning about the Pythagorean Theorem, that's all.
MOM: The Pythagorean . . . what?
DAD: (To MOM.) Theorem. The Pythagorean Theorem. That’s that
Aesop fable with the tortoise and the hare, I think. They race and
the tortoise wins and . . .
THEY talk as THEY EXIT SR.
MOM: I don't think that's the same thing, Hank.
DAD: No? Well, "Pythagorean," I mean, sound it out, Molly. If it's
not that fable, then it must be some disease.
MOM: Oh my. Should I call the doctor?
DAD: Maybe?
ALBERTO begrudgingly turns to ELIZABETH.
ALBERTO: Hey, uh, you know.
ELIZABETH: Thanks?
ALBERTO: (Deadpans.) No need to thank ME.
SHE starts to protest and HE grins and hits HER lightly on the arm.
ELIZABETH: Yeah, no problem.
SHE skips off through the house and EXITS SR. ALBERTO turns
back to the audience.
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ALBERTO: So, turns out Coach was right. I wanna steal third, I'm
gonna need a bigger lead off second, because the catcher's throw
is shorter. Cool. (Considers it for a second.) I just can't believe
that Coach knows the Pythagorean Theorem!
HE races OFF SR. BLACKOUT.
THE END
MINI-LESSON: PYTHAGOREAN THEOREM
Okay, time to review!
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In brief:
The Pythagorean Theorem states that for any right triangle, the square of the
hypotenuse is equal to the sum of the squares of the adjacent legs. Another
way to state this is that, for a right triangle with legs a and b and hypotenuse
c:
a2 + b2 = c2
Definitions:
▪ A right angle is one that is ninety degrees.
▪ A right triangle is a triangle that has one right angle in it.
▪ Legs are the two sides of the right triangle which form the right
angle.
▪ The hypotenuse is the side of the right triangle that is opposite the
two legs.
When is it used?
The Pythagorean Theorem is useful whenever you know the length of two
sides of a right triangle and need to determine the length of the third side.
Example:
The length of the two legs of a right triangle are known to be 3 inches and 4
inches respectively. What is the length of the hypotenuse?
Answer: Substituting into the Pythagorean Theorem, we get . . .
32 + 42 = c2
Or . . .
9 + 16 = c2
Or . . .
25 = c2
Therefore:
c = 5, and the length of the hypotenuse is 5 inches.
MINI-TEST
A. Two legs of a right triangle are 7 feet and 9 feet, respectively. What
is the length of the hypotenuse?
B. One leg of a right triangle is 6 meters and the hypotenuse is 10
meters. What is the length of the other leg?
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C. An isosceles right triangle is a right triangle whose two legs are the
same length. If the hypotenuse of an isosceles right triangle is 12
units long, how long are each of the legs?
D. Jan is practicing her archery. For fun, she climbs to the top an
eight-foot tree and places an apple there. Then she stands six feet
away from the tree and shoots her arrow at the apple. If she hits the
apple, how far will her arrow travel?
Answers:
A. 72 + 92 = c2. Therefore, c =
130 .
B. 62 + b2 = 102. Therefore, b = 8.
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C. Since we have an isosceles right triangle, we know that the legs are
the same length, or a = b. So the Pythagorean Theorem becomes: a2
+ a2 = 122 or 2a2 = 144 or a2 = 144/2. Therefore, the length of each
leg is
72 or 6 2 .
D. Since the tree and the ground form a right angle, the straight line
formed between Jan and the apple is the hypotenuse of a right
triangle. Therefore, we can use the Pythagorean Theorem to find
the distance: 82 + 62 = c2. Since c = 10, her arrow will travel ten
feet!
Activities:
For more fun with the Pythagorean Theorem, see Coral Gables High School
in Coral Gables, Florida’s website entitled, “Measuring the Height of a
Tree:”
http://cghs.dadeschools.net/shs/EcoSearch/tree.html
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