Transcript: Coins, Stones and Shells | Mar 26, 1999

(music plays)

The opening slate pops up with a countdown timer from 10 seconds and the title “TVO’s Virtual Classroom. Get connected.”
The “V” in “Virtual” is a tick, the “A” in “classroom” is an at sign with an extended loop that turns into a power cord with a plug at the end, and the first “O” in “classroom” is a spinning globe.

Mister C sits in the studio. He’s in his mid-forties, with a dark beard and wavy black hair. He’s wearing glasses, a black T-shirt with Einstein’s face and patterned suspenders.

Mister C says GOOD MORNING.
IT'S MISTER C. BACK IN THE
VIRTUAL CLASSROOM.
HOPE YOU'VE HAD
A GREAT MORNING.
HOPEFULLY, IT'S NOT
SO BAD AS TRYING
TO GET TO SCHOOL
LAST MONDAY.
MIND YOU, HERE IN TORONTO
IT'S STILL A MESS.
IT TAKES ME A LONG
TIME TO GET IN
EVEN IF IT'S
NOT SNOWING.
NOT AT THIS
POINT ANYWAY.
THE FIRST THING I'D
LIKE TO DO IS TAKE UP
THAT LITTLE PROBLEM
THAT I LEFT YOU WITH
RIGHT AT THE END
OF THE PROGRAM.
WE'LL TAKE A
QUICK LOOK HERE
AT WHAT THE
PROBLEM WAS.
OH, WE'RE A LITTLE
BIT CROOKED.

A blue piece of paper under the title “The Fewest Moves” appears. It reads “Horizontal, vertical or diagonal to reverse the positions of the pennies and the nickels.” The paper shows 2 horizontal rows of 3 boxes. Two boxes read “P “ and other two read “N.”

He continues I'D INVITE SOMEBODY TO
PHONE IN AT THIS POINT AND
PERHAPS GIVE ME AN IDEA OF
WHAT THE FEWEST NUMBER
OF MOVES IS AND MAYBE GIVE
ME SOME INSTRUCTIONS.

He appears in a small window on the right bottom of the screen.
He continues WE'RE READY FOR ANYBODY.
AH, I SEE WE'VE
GOT SOMEBODY.
AND WE ARE CONNECTING,
SO IT'LL TAKE US
A MOMENT OR TWO.
AND I THINK WE'RE
GOING TO ELGIN AVENUE.
WHO AM I SPEAKING TO?

He speaks with a spectator via a telephone conversation.

Sarah says SARAH.
SARAH.

He says AH, SARAH OR LINDSAY, CAN
YOU PICK UP YOUR PHONE?

Sarah says SARAH.

He says AH, THERE YA ARE.
HI, SARAH.

Sarah says HELLO.

OKAY, WHAT'S THE
He says FEWEST NUMBER OF MOVES
TO DO THIS PUZZLE?

Sarah says SIX.

He says SIX, OKAY.
ACTUALLY, I SHOULD
HAVE SOME COINS
OUT HERE TO DO THIS.
ALTHOUGH I HAVE
SOME OBJECTS HERE,
I'LL USE THEM
INSTEAD.

He places two small stones on the boxes that read “P” and two dices on the boxes that read “N.”

He continues CAN YOU SORT OF DESCRIBE
WHAT I SHOULD DO?

Sarah says MOVE THE RED DICE UP
BESIDE THE RIGHT STONE.

He says YEP.

Sarah says AND THEN MOVE THE
STONE BESIDE IT DOWN.

He says YES, THAT'S TWO.

Sarah says AND THEN MOVE
THE DICE UP.

He says THIS ONE HERE?
THERE?
[chattering on phone]

Sarah says NO, MOVE IT OVER,
THE BLUE ONE OVER.

He says OVER HERE?

Sarah says YEP.

He says OKAY, THREE.

Sarah says MOVE THE STONE DOWN.

He says FOUR.

Sarah says AND THEN MOVE
THE DICE OVER.

He says FIVE.
SIX - OKAY?
SUPER.
HAS ANYBODY GOT
ANOTHER SOLUTION?
THAT'S A GOOD ONE.
SIX MOVES IS THE BEST
WE'VE DONE SO FAR.
OKAY, THANK YOU,
SARAH.
LET'S SEE.
IS THIS SARAH
FROM TRILLIUM?

Sarah says YES.

He says OKAY, HOW MANY
MOVES DO YOU THINK?

Sarah says SEVEN.

He says SEVEN, OKAY.
DESCRIBE IT TO
ME, GO AHEAD.

Sarah says OKAY, PUT THE
STONE THE OTHER WAY.

He says THIS ONE HERE?
OKAY, ONE.

Sarah says PUT THE DICE DOWN.

He says TWO.

Sarah says PUT THE STONE
WHERE THE PENNY IS.

He says GOTCHA, THREE.

Sarah says AND THEN MOVE
THE DICE DOWN.

He says FOUR.

Sarah says AND MOVE THE STONE LEFT,
THE OTHER STONE LEFT.

He says FIVE...
ACTUALLY, YOU DID
IT IN SIX AS WELL.
THAT'S OKAY, YOU
DID IT IN SIX.
HEY, THAT'S PRETTY GOOD.
THANK YOU VERY MUCH,
SARAH, BY THE WAY.
I DID GET A FAX FROM,
I THINK, THREE PEOPLE.
I'VE GOTTA MAKE
SURE, LET'S SEE:
DAN, TRISTAN,
AND ALEX.
SO, LET'S SEE, ALEX HAS
THIS SOLUTION HERE,
WHERE HE SAYS THAT IT
CAN BE DONE IN FIVE.

He shows the paper Alex faxed. It features arrows inside the boxes in different directions.

He continues AND I'LL TRY TO FOLLOW
HIS INSTRUCTIONS.
AND I'LL PUT THE
SAME THINGS ON HERE.
HE SAYS THE FIRST MOVE
IS TO MOVE OVER HERE;
THAT'S ONE.
THEN HE SAID PULL
THE STONE DOWN HERE;
THAT'S TWO.
PUT THIS UP
HERE, IS THREE.
CRISSCROSS, BRING THAT
DOWN HERE, IS FOUR.
FIVE.
SO, IN FACT, YOU
CAN DO IT IN FIVE.
THAT'S REALLY
GOOD, ALEX.
AND I BELIEVE THAT THERE
WERE A COUPLE OTHER PEOPLE
THAT PROVIDED
SOLUTIONS AS WELL.
HERE'S ONE,
AND HERE'S ONE.
AND I BASICALLY THINK
THEY'RE EITHER
SIX OR FIVE.
THIS ONE'S FIVE AND I
BELIEVE THAT THIS
ONE DOWN HERE AT THE
BOTTOM IS SIX.
NOW, INTERESTINGLY ENOUGH,
THOUGH - NOT THAT YOU CAN
READ THIS TERRIBLY EASILY.
SOMEBODY SUGGESTED, LET'S
SEE - ALL THREE OF THEM
SUGGESTED - THAT YOU COULD
SIMPLY TAKE THE PUZZLE...
I'M GOING TO DO IT BECAUSE
I THINK IT'S REALLY,
REALLY NICE TO SEE
CREATIVE IDEAS.
SO, I'M GOING TO
PUT THEM HERE,
AND REMEMBER WHAT THE
CHALLENGE WAS: TO REVERSE
THE POSITION OF THE
STONES AND THE DICE.
THEY SIMPLY SAID,
ROTATE IT 180 DEGREES
AND WE COULD CALL
THAT A SINGLE MOVE.
AND THERE YOU ARE.
SO, I GOTTA ADMIT, IT'S
ANOTHER WAY OF DOING IT.
WELL DONE.
OKAY, I'VE GOT A NEW
PUZZLE FOR TODAY.
HERE IT IS.
I'M GOING TO
GO RIGHT TO IT.

A new blue sheet of paper under the title “Equal shares” appears. reads “A farmer and a friend bought an 8 litre container of apple cider. They wanted to share the cider equally but only had a 3-litre and 5-litre container. How did they do it? More mathematical activities, Brian Bolt.”

He continues HOW DID THEY WORK IT OUT
SO THAT THEY GOT EXACTLY
FOUR LITRES EACH?
THAT'S RIGHT, THAT'S
WHAT THEY WANT.
THE WAY WE'RE GOING TO
SIMULATE THIS IS WITH THIS.
SO, YOU'VE GOT
EIGHT LITRES.
AND WHAT I'VE DONE HERE IS
EACH ONE OF THESE LITTLE
SQUARES THAT I'M PUTTING
ON - OR RECTANGLES,
I SHOULD SAY - REPRESENTS
A SINGLE LITRE.

He grabs a piece of paper that shows three vertical containers. The first one reads “8 litre,” the second one reads “5 litre” and the last one reads “3 litre.”

He continues AND WHAT WE CAN DO IS POUR
BACK AND FORTH BETWEEN THE
EIGHT, THE FIVE, AND THE
THREE TO EVENTUALLY END UP
WITH EXACTLY
WITH TWO FOURS.
THERE WE ARE; WE HAVE
A FULL EIGHT-LITRE CONTAINER.
THANKFULLY, I CUT
ENOUGH OF THOSE.
AND IF YOU THINK
YOU SEE A SOLUTION,
LET'S GO AHEAD AND START.
WHAT MIGHT YOU DO FIRST?
IT'S KIND OF A TRICKY
LITTLE SITUATION.
WE SEE WE HAVE A
CALL FROM USBORNE.
AND AS SOON AS WE CONNECT
HERE, IT WILL BE,
I THINK, EITHER
GREG OR SARAH.
SARAH IS A VERY POPULAR
NAME THIS MORNING.
GOOD MORNING,
GREG OR SARAH.

Sarah says SARAH.

He says HI, SARAH.
OKAY, WHAT WOULD YOU
LIKE ME TO DO FIRST?

Sarah says YOU PUT ONE OF THE EIGHT
LITRES IN THE FIVE.

He says OKAY, SO...
ALL FIVE OF THEM HERE?
REMEMBER THAT
WHEN I SOLVE THIS,
ALTHOUGH I'VE GOT THEM
DIVIDED INTO INDIVIDUAL
LITRES FOR DEMONSTRATION
PURPOSES, IT'S LIKE WATER.
YOU DON'T KNOW EXACTLY
WHAT ONE LITRE IS.
SO, YOU'VE GOT TO POUR
EITHER COMPLETELY INTO
THIS, OR COMPLETELY INTO
THIS KIND OF THING.
YOU FOLLOW ME?

Sarah says YEP.

He says LET'S START WITH POURING
FIVE INTO THE FIVE-LITRE.
OKAY, THERE WE ARE.
SO, WHAT WE HAVE
NOW IS FIVE IN HERE.
WHAT MIGHT YOU DO NEXT?

Sarah says THEN YOU PUT THE THREE
IN THE THREE-LITRE.

He says IS THAT GOING
TO HELP ME OUT?
OKAY, WHAT THE HECK, I'LL
PUT THREE IN THE THREE.
NOW, WHAT DO I DO?

Sarah says OH, NO, YOU PUT
THE THREE BACK,
AND THEN YOU TAKE THREE
OF THE FIVE-LITRE.

He says AH, OKAY, THAT'S
A BETTER MOVE.
YOU'RE DOING
REALLY WELL, SARAH.
SO WHAT WE HAVE
NOW IS THIS SITUATION.

Sarah says THEN YOU PUT TWO LITRES
IN THE FIVE-LITRE ONE?

He says THAT'S...
HOW DO I DO THAT?

Sarah says LIKE, PUT THE...
TWO IN THE EIGHT-LITRE.
YOU TAKE TWO OF
THOSE PIECES...

He says YOU PUT THOSE BACK THERE.

Sarah says YEAH, AND THEN YOU PUT
THE THREE IN THE FIVE.

He says OKAY, GOTCHA.
SO FAR, SO GOOD.

Sarah says AND THEN YOU ADD AS MUCH
AS YOU CAN IN THE FIVE
OUT
OF THE EIGHT.

He says OKAY, SO I GO BACK
TO HERE, RIGHT?

Sarah says YEP.

He says OKAY.
KIND OF TRICKY, EH?

Sarah says THEN YOU PUT...
I CAN'T FIGURE IT OUT.
[chuckling]

He says THIS IS PRETTY TRICKY,
I'LL TELL YOU THAT RIGHT NOW.
I'LL SHOW YOU WHAT
THE NEXT MOVE IS.
YOU WERE SITTING IN
THIS POSITION BEFORE,
WHICH IS A GOOD MOVE.
BUT WHAT YOU DID NEXT
WAS NOT THE RIGHT MOVE.
WHAT YOU DID IS PUT
THE TWO BACK HERE.
WHAT'S THE ONLY THING I
CAN POSSIBLY DO NOW THAT'S
DIFFERENT FROM PUTTING
THE TWO BACK HERE?
OR NOT PUTTING
THE THREE HERE?
SEE THIS ONE?

Sarah says MM-HMM.

He says ONE THING YOU HAVEN'T
TRIED YET IS TO TAKE THOSE
THREE AND PUT
THEM BACK HERE.
SO, WHAT YOU HAVE NOW IS A
SIX AND TWO SPLIT, OKAY?

Sarah says MM-HMM.

He says NOW, WHAT MIGHT
YOU DO NEXT?

Sarah says PUT...
THE THREE IN THE FIVE?

He says THAT PUTS US RIGHT
BACK WHERE WE STARTED.
WHAT ABOUT THESE TWO?
WHAT'S THE ONLY THING YOU
CAN DO WITH THEM THAT'S A
LITTLE BIT DIFFERENT?

Sarah says I DON'T KNOW.

He says YOU COULD ACTUALLY JUST
DUMP THEM INTO HERE, RIGHT?

He puts them in the 3 litre container and continues
IS THAT GOING
TO HELP AT ALL?
IT ACTUALLY DOES,
BELIEVE IT OR NOT.
BECAUSE WHAT
YOU HAVE HERE,
WHAT YOU CREATED IS
ONE LITRE LEFT OVER.
REMEMBER, WE
WANT FOUR LITRES.
CAN YOU SEE A WAY OF
MAKING FOUR LITRES NOW?
NOW, WHAT I'M GOING TO ASK
FOR IS I KNOW THERE ARE
OTHER HANDS UP,
AND I THINK, SARAH,
YOU'VE DONE A GREAT JOB.
I'M GOING TO LEAVE
AT THIS POINT
AND ASK SOMEBODY
ELSE TO CALL IN.
AND ACTUALLY,
THEY'RE CALLING IN.
NOT A PROBLEM THERE.
TO CONNECT TO SOMEBODY
ELSE AND SEE IF WE CAN
JUST FINISH THE PROBLEM.
HELLO.
WHO AM I SPEAKING
TO, TRISTAN?
WHO IS IT?

Tristan says THIS IS TRISTAN.

He says OKAY, GOOD.
YOU SEE WHAT THE
SITUATION IS HERE?
WHAT MIGHT YOU SUGGEST?

Tristan says PUT FOUR IN FIVE, IN
THE FIVE-LITRE BUCKET.
AND LEAVE FOUR IN
THE EIGHT-LITRE.

He says YOU CAN'T QUITE
DO IT THAT SIMPLY,
ALTHOUGH YOU'RE GOING
IN THE RIGHT DIRECTION.
REMEMBER, I'VE GOT TO
COMPLETELY FILL THIS
IF I'M GOING TO
MOVE THERE.
I DON'T KNOW WHAT
A LITRE IS, REALLY.
IF I TAKE FIVE HERE
YOU SEE THAT?
He puts 5 litres in the 5 litre container and continues
WHAT MIGHT I BE ABLE
TO DO TO CREATE FOUR?
REMEMBER WHAT'S
LEFT OVER HERE.
HOW MUCH IS
LEFT OVER HERE?
WHAT AM I MISSING HERE?

Tristan says BRING ONE OVER.

He says BRING ONE OVER, EXACTLY.
IF I FILL THIS UP, I NOW
HAVE ONE LITRE HERE.
HOW MUCH DO I FINALLY
END UP WITH HERE?
HOW MANY LITRES HAVE
I ENDED UP WITH HERE?

Tristan says THREE.

He says NO, FOUR: ONE, TWO,
THREE, FOUR, RIGHT?

Tristan says MM-HMM.

He says IN THE MIDDLE
ONE I'VE GOT FOUR,
SO I BASICALLY
SOLVED THE PROBLEM.
ALL I HAVE TO
DO NOW IS...

Tristan says TAKE THE THREE AND
PUT IT IN THE EIGHT.

He says YOU GOT IT.
IT'S A PRETTY TRICKY
LITTLE PROBLEM,
BUT THEY'RE KIND OF
NEAT TO PLAY WITH.
I THINK MY ONLY SUGGESTION
THERE IS THAT WHEN YOU
HAVE A PROBLEM LIKE THAT -
AND I KNOW YOU DIDN'T HAVE
IT IN FRONT OF YOU - IS
TO ACTUALLY PLAY WITH IT.
YOU GOT TO LOOK FOR
SITUATIONS THAT ARE
SLIGHTLY DIFFERENT FROM
ONES THAT YOU'VE TRIED
BEFORE THAT MAY
NOT HAVE WORKED.
YOU KNOW, IT'S BEEN A
WHILE SINCE WE TALKED TOO
MUCH ABOUT THE MYSTERY.
AND I JUST THOUGHT I'D TRY
TO BRING US BACK UP TO DATE,
OR AT LEAST GET US
BACK INTO THE GROOVE,
SO TO SPEAK.
SO, I'VE CONNECTED
TO DANIEL,
ONE OF THE TWO
NATIVE CHILDREN.
HE'S ON THE
LINE RIGHT NOW.
SO, HI, DANIEL,
ARE YOU THERE?

Daniel says HELLO, MISTER C.

He continues JUST BEFORE THE BREAK,
I HAD A CHANCE
TO TALK TO SOLANGE
AND I UNDERSTAND
THAT YOU AND
YOUR SISTER AND
THE TWO OF THEM ARE
ACTUALLY INVOLVED IN SOME
KIND OF MYSTERY.

Daniel says WHICH MYSTERY IS THAT?

He asks THERE'S MORE THAN ONE?

Daniel replies THERE'S THE MYSTERY
OF OUR NATIVE LEGEND.
AND IF WE CAN SOLVE IT,
WE'LL BECOME FULL MEMBERS
OF OUR TRIBE.
BUT WE'RE ALSO TRYING
TO FIGURE OUT WHICH
OF THE ELDERS IS PUTTING
US THROUGH THIS TORTURE.

He says TORTURE?!
WHAT KIND OF TORTURE?

Daniel says EVERY WEEK, WE HAVE TO DO
ALL THESE MATH EXERCISES,
AND WE STILL
DON'T KNOW WHY.

He says I SUGGEST THAT THERE
MIGHT BE TWO REASONS.
ONE REASON IS THAT THE
SOLUTION TO THE MYSTERY
MIGHT BE BURIED IN
THE MATHEMATICS.
BUT THERE'S PROBABLY
A SECOND REASON.
I JUST HAVE A FEELING THAT
THE ELDERS OF THE TRIBE
KNOW THAT THE MORE
MATHEMATICS THAT YOU LEARN,
THE MORE YOU
CAN CONTRIBUTE
TO THE COMMUNITY
LATER ON.

Daniel says HOW SO?

He says MATHEMATICS ALLOWS YOU TO
DO EVERYTHING FROM HELPING
OR PREPARING TO CONSTRUCT
BUILDINGS FOR YOUR
COMMUNITY; TO PERHAPS
LOOK AT YOUR FINANCES
AND UNDERSTAND THEM
BETTER; TO UNDERSTAND,
WHEN YOU READ
THE NEWSPAPER,
STATISTICS AND PROBABILITY
AND UNDERSTAND
THE ISSUES OF POLITICS.
I THINK THERE'S ALL KINDS
OF THINGS THAT MORE
MATHEMATICS WILL
HELP YOU DO.
AND WE'LL HELP YOU
ANY WAY WE CAN.

Daniel says SARAH AND I APPRECIATE
YOUR HELP, MISTER C.
AND I GUESS I'M JUST GOING
TO CONTINUE TO WORK HARD
AT MY MATH CLASSES.
SO LONG FOR NOW.

He says BYE-BYE, DANIEL.
TALK TO YOU LATER.
ANYWAY, THAT BRINGS US
BACK SLIGHTLY UP TO DATE.
WHAT I WILL TELL YOU IS
THAT SOMETIME WITHIN
THE NEXT TWO WEEKS OR SO,
YOU WILL RECEIVE ONE MORE
SHEET THAT WILL ACTUALLY
HELP YOU BEGIN
TO UNDERSTAND THAT ALL THESE
MATH EXERCISES ACTUALLY
CONNECT TO THE MYSTERY
BECAUSE YOU HAVE TO FILL OUT
SINGLE ANSWERS FROM YOUR
PREVIOUS MATH EXERCISES.
AND AT THE END OF IT,
YOU'LL HAVE A VERY
INTERESTING TASK TO DO
WHEN WE GET CLOSE
TO THE END OF OUR SERIES,
WHICH IS SOMETIME
IN THE MIDDLE OF
FEBRUARY.
NOW, RIGHT NOW, I'D LIKE
TO TAKE UP THE HOMEWORK
FROM THE LAST TIME.
SO, I'M GOING TO GET
RID OF THE PUZZLE HERE.
AND IF YOU RECALL
CORRECTLY,
WHAT WE HAD WAS,
LET'S SEE.
I DON'T KNOW THAT I
HAVE A PICTURE OF IT.
YES, I DO, ACTUALLY.
THERE IT IS.
IT'S IN WHITE,
BUT THAT'S...
OKAY, REMEMBER THAT WHAT
WE WERE DOING WAS WE WERE
TAKING ALL THESE
DIFFERENT PARTS.
AND THEN WE ADD A SERIES
OF INSTRUCTIONS WHERE
WE HAD TO TAKE THESE PARTS
AND PUT THEM THERE
IN THEIR
APPROPRIATE PLACES.

He shows a piece of paper with a grid and different black lines, semi arches and arrows.

He continues SO, WHAT I'M GOING TO DO
FOR TAKING THIS ONE UP
IS I'LL GO THROUGH
THE INSTRUCTIONS.
AND WE'LL SIMPLY JUST
TAKE A LOOK AT THIS ONE
AND DECIDE WHAT YOU
SHOULD HAVE DONE.
LET'S GO THROUGH
THE INSTRUCTIONS.
THERE'S INSTRUCTION NUMBER 1.

A blue sheet of paper reads “Object number 1. Translate 9 squares to the right and 14 squares down. Object number 2. Translate 10 squares to the left and 15 squares down.”

He continues WHAT I'LL ASK YOU TO
DO IS TO PHONE IN
AND SORT OF COACH ME.
AND I'LL BASICALLY SET
UP ON HERE EXACTLY
WHERE THESE THINGS GO.
He grabs again the paper with the grid and continues
SO, WE'LL START
WITH - LET'S SEE,
WE'LL MAKE A
CONNECTION THERE.
WE'RE LOOKING TO A
STUDENT FROM ELGIN,
LINDSAY OR SARAH.
GOOD MORNING.

Lindsay says IT'S LINDSAY.

He continues HI, LINDSAY.
SO, WE'RE LOOKING
AT OBJECT NUMBER 1.
WHERE DID THIS END UP
GOING TO WHEN YOU DO
THE TWO TRANSLATIONS?

Lindsay says ONE, TWO, THREE...
AT THE FOURTH SQUARE FROM
THE BOTTOM ON THE RIGHT.

He continues OKAY, THE FOURTH SQUARE
FROM THE BOTTOM ON THE RIGHT.
IT'S OVER IN HERE
SOMEWHERE, RIGHT?

Lindsay says NO, IT'S FROM
THE MIDDLE LINE.
IT'S FROM THE MIDDLE.

He says YEAH.

Lindsay says AND IT GOES...
ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN...
SEVEN OF THE
LITTLE LINES OVER.

He says OKAY, I'M GOING TO
ACTUALLY JUST...
ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN,
EIGHT, NINE.
SO, THAT END COMES
DOWN THERE, AND 14.
AND HOW CLOSE TO THE
BOTTOM DO I END UP?

Lindsay says THREE SQUARES
FROM THE BOTTOM.

He says OKAY, I'M GOING TO...
IT'S ABOUT IN
THERE, ISN'T IT?
THIS MAY NOT BE EXACT
BUT IT'S PRETTY CLOSE,
ISN'T IT?
He draws a red line and continues
OKAY, THANK YOU
VERY MUCH.
NEXT INSTRUCTION.
THAT WAS LINDSAY.
SO, WE'RE LOOKING AT
THIS ONE RIGHT HERE.
SEE IF YOU CAN HELP
ME OUT WITH THIS ONE.
HELLO, IS IT
CHRIS OR TYLER?
USBORNE, YES, OKAY,
CHRIS OR TYLER?

Tyler says TYLER.

He says OKAY, TYLER, WE'RE
DOING OBJECT NUMBER 2.
AND I THINK, LET'S SEE,
TRANSLATE 10 TO THE LEFT
AND 15 DOWN.
WHERE DID THIS
ONE END UP?

Tyler says I DON'T KNOW.

He says IF I'M TAKING THIS AND
TRANSLATING 10 TO THE LEFT,
WHAT DO I DO -
THIS OBJECT UP HERE?
OKAY, I THINK, TYLER,
I'LL GIVE YOU ANOTHER
CHANCE LATER ON.
BUT I'M GOING TO CONNECT
TO SOMEBODY ELSE, OKAY?
LET'S SEE,
WHO'VE WE GOT?
I THINK WE'RE GOING
TO ELGIN AVENUE.
JESSIE OR SAVANNA.
HELLO?
AH, THERE, YOU'VE
GOT YOUR PHONE.

Savanna says HELLO?

He says HELLO, JESSIE OR
SAVANNA?

Savanna says SAVANNA.

Savanna says OKAY, WHERE
DOES NUMBER 2 END UP?

Savanna says IT ENDS UP, OKAY...

He says IT'S DOWN IN HERE
SOMEWHERE, ISN'T IT?

Savanna says YEAH, IT'S THE FOURTH
SQUARE UP FROM THE BOTTOM.
AND TWO SQUARES
FROM THE MIDDLE.

He says AND THREE FROM
THE MIDDLE.
SO, ABOUT IN
HERE SOMEWHERE?

Savanna says TWO, TWO FROM
THE MIDDLE.

He says OKAY, TWO FROM THE
MIDDLE, GOOD ENOUGH.
SO, ABOUT IN
HERE SOMEWHERE.
NOW, I'M NOT GOING TO
BE PERFECTLY EXACT.
I'M JUST TRYING TO GET
SORT OF IN GENERAL
WHERE IT GOES.
SO, WE'VE DONE THAT
ONE AND THAT ONE.
WOULD YOU LIKE
TO DO ONE MORE?

Savanna says OKAY.

He says OKAY, LET'S
SEE; NUMBER 3 SAYS...

A blue piece of paper reads “Object number 3: Reflect vertically about line segment A and reflect horizontally about line segment B. Object number 4: Reflect horizontally about line segment C. Object number 5: Rotate 90 degrees counter clockwise.”

He continues SO, THIS ONE UP HERE.
WHAT DO I DO
WITH THIS ONE?

Savanna says OKAY, YOU FLIP IT,
LIKE, ON THE SPOT.

He says SO, IN OTHER WORDS, THIS
LITTLE PIECE ENDS UP
GOING DOWN LIKE THAT.

Savanna says YES, AND YOU FLIP IT...

He says THERE'S THE LINE THERE.
SO, THIS IS GOING TO
BE KIND OF LIKE THIS?

Savanna says YEAH.

He says WELL DONE.
VERY GOOD, THANK
YOU VERY MUCH.
OKAY, LET'S GO TO
ANOTHER CALLER FOR NUMBER 4.
Pointing to the paper with the grid he continues THAT'S OBJECT NUMBER 4, AND
THERE'S THE LINE SEGMENT C.
AND WE'RE REFLECTING THAT.
USBORNE, IS IT JENNIFER?

Jennifer says YEAH.

He says OKAY, WHAT DOES THIS
ONE LOOK LIKE
IF IT'S A REFLECTION
ABOUT THIS LINE HERE?

Jennifer says UM...

He says WHEN I MOVE
THIS LINE HERE,
DOES IT GO FROM THE BOTTOM
LEFT TO THE UPPER RIGHT,
OR THE OTHER WAY AROUND?
FROM THE BOTTOM RIGHT
TO THE UPPER LEFT?

Jennifer says IT GOES TO THE BOTTOM
RIGHT, I THINK.

He says SO, IS IT PARALLEL
TO THIS, THEN?
WHEN I REFLECT IT?

Jennifer says NO.

He says OKAY, SO WHAT HAPPENS IS
THIS POINT HERE GOES
FROM THE BOTTOM LEFT
TO THE UPPER RIGHT,
IS THAT CORRECT?

Jennifer says MM-HMM.

He says OKAY, THAT POINT RIGHT
THERE - YOU SEE WHERE
I'M POINTING RIGHT NOW?

Jennifer says YES.

He says WHERE'S THE REFLECTION
OF THAT POINT?
WHERE DO I ACTUALLY
GO WITH MY PEN?

Jennifer says YOU GO DOWN TO
THE LEFT CORNER.

He says WHEN YOU DO A
REFLECTION, REMEMBER
THAT YOU ALWAYS DO THIS.
THAT'S THE LINE OF
REFLECTION, ISN'T IT,
RIGHT THERE?
SO, IT'S ONE SPACE
ON THIS SIDE,
SO HOW MANY SPACES WILL
IT BE ON THE OTHER SIDE?

Jennifer says ONE.

He says RIGHT ON, OKAY.
NOW, THIS SPOT UP HERE IS
ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN
SPACES TO THAT SIDE.
SO, HOW MANY SPACES
TO THE OTHER SIDE?

Jennifer says SEVEN?

He says RIGHT.
SO, WHAT YOU DO IS
YOU DO THE ENDPOINTS,
ESPECIALLY WITH
A STRAIGHT LINE.
ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN.
AND YOU CONNECT THEM.
I THINK I'VE PRETTY
MUCH DONE THAT.
SO, THAT'S HOW YOU DO THAT
KIND OF A REFLECTION.
DOES THAT HELP YOU?

Jennifer says YEP.

He says SUPER.
LET'S GO TO THE NEXT
CALL AND DO OBJECT NUMBER 5.
I THINK WE'RE DOING
PRETTY WELL HERE,
BY THE LOOKS OF IT.
ELGIN, AND IS IT
JILLIAN OR BRITTANY?

Jillian says NO, IT'S JILLIAN.

He says HI, JILLIAN.
OKAY, OBJECT NUMBER 5,
I'VE GOT TO FIND IT.
OH, THIS ONE RIGHT HERE.
THIS IS A ROTATION,
90 DEGREES CLOCKWISE.
WHICH WAY IS CLOCKWISE?

Jillian says THE WAY A CLOCK GOES.

He says THE WAY A CLOCK GOES, SO
I GUESS IT'S THIS WAY.
SO, WHERE DID THIS
KIND OF END UP?

Jillian says LIKE, RIGHT BESIDE
IT, GOING DOWN.

He says EXCUSE ME, YOU
KNOW WHAT?
I MISREAD MY OWN
INSTRUCTION.
IT SAYS
COUNTERCLOCKWISE.
SO, IT MEANS WE'RE GOING
THE OTHER WAY, RIGHT?
SORRY ABOUT THAT.
WHERE DOES THIS
THING END UP?

Jillian says RIGHT BESIDE IT,
GOING THE SAME WAY.

He says TELL ME, DO YOU KNOW
HOW THE COORDINATE
SYSTEMS WORK, RIGHT?
THIS POINT RIGHT ON THE END OF
THIS LITTLE CURVY THING,
CAN YOU TELL ME
WHAT COORDINATES
THAT ENDED UP WITH?
WHERE'D IT GO?

Jillian says PARDON?

He says THIS POINT,
RIGHT ON THE END,
GOES SOMEWHERE UP HERE.
CAN YOU TELL ME WHAT
COORDINATES THAT IS?
IS IT LIKE ONE TO THE
RIGHT AND FOUR UP OR SO?

Jillian says YEAH.

He says YOU SEE WHAT I MEAN?
THIS ONE IS GOING TO MOVE
ONE OVER AND FOUR UP.
ARE YOU STILL WITH ME?

Jillian says YEP.

He says OKAY, SO THAT POINT WILL
GO ONE OVER AND FOUR UP.
YOU SEE WHAT I MEAN?

Jillian says YEAH.

He says NOW, CAN YOU TELL ME WHERE
THIS POINT ENDS UP GOING?

Jillian says UM...
UM...
ENDS UP GOING?

He says IT GOES ONE, TWO,
THREE - HOW MANY OVER?

Jillian says IT GOES...
OKAY, JUST A MINUTE.

He says THAT'S OKAY.
THIS IS A TOUGH
LITTLE QUESTION.

Jillian says THREE OVER?

He says THREE OVER AND
HOW MANY UP?

Jillian says UP FROM?

He says THIS LINE HERE?

Jillian says OH, FROM THERE?

He says SO, IT'D BE ONE,
TWO, THREE, FOUR...
HOW MUCH UP?

Jillian says UM...
FIVE?

He says OKAY, YOU'RE
CLOSE ACTUALLY.
AS IT TURNS OUT, IT'S
FOUR OVER AND FIVE UP.
THAT WAS CLOSE.
THANK YOU VERY MUCH,
THAT WAS WONDERFUL.
OKAY, WE'RE
GETTING THERE.
THREE MORE INSTRUCTIONS
AND WE'RE DONE.

He grabs a piece of paper that reads “Object number 6: Rotate 90 degrees clockwise. Object number 7: Reflect horizontally about line segment C. Object number 8: Translate 2 squares to the right and 13 squares up.”

He continues LET'S SEE, WHO ARE WE
CONNECTING TO NOW?
TRILLIUM AND
I THINK DEVON.
OBJECT NUMBER 6 IS 90 DEGREES
CLOCKWISE THIS TIME.
SO, I'D BETTER GET MY
CLOCKWISE STRAIGHT.
OKAY, DEVON,
ARE YOU THERE?
WE'RE STILL WAITING FOR
HIM TO COME, THAT'S OKAY.
OKAY, ARE YOU
THERE, DEVON?

Devon says YEAH.

He says SO, THE ONE WE'RE DOING
IS WE'RE ROTATING
THIS ONE ABOUT THAT
CENTRE 90 DEGREES.
NOW, THAT'S A
HORIZONTAL LINE.
IF YOU ROTATE 90 DEGREES,
WHAT DOES IT BECOME?

Devon says A STRAIGHT LINE.

He says UP AND DOWN, OR
LEFT AND RIGHT?

Devon says UP AND DOWN.

He says RIGHT ON, OKAY.
DOES IT GO THIS
WAY OR THAT WAY?
IN OTHER WORDS,
WHEN I END UP,
WHERE IS IT GOING TO
MORE OR LESS END UP?
TO THE RIGHT OF THE
CENTRE OR TO THE LEFT?

Devon says TO THE LEFT.

He says RIGHT ON.
SO, WE'VE GOT
IT VERTICALLY.
IS THIS MORE OR LESS
WHERE YOU'VE GOT IT,
SOMEWHERE IN HERE?
OR IS IT HIGHER UP?

He continues drawing lines following the students’ instructions.

Devon says I GUESS SO.

He says I THINK ACTUALLY IT'S
PROBABLY HIGHER UP,
IN HERE SOMEWHERE.
WHEN YOU ROTATE 90 DEGREES,
ACTUALLY THIS SHOULD
CROSS THIS LINE.
I KIND OF MISSED ON
MY FIRST MOVE THERE.
DOES THAT MAKE SENSE TO
YOU: IT TURNS TO THE LEFT,
AND IT'S A VERTICAL LINE?

Devon says YEAH.

He says OKAY, SUPER.
WE'LL TAKE ONE MORE
CALL AND I THINK
WE CAN BASICALLY
WRAP IT UP.
AND I THINK WE'RE
GOING TO GO TO ELGIN.
AND NICK OR
GERVAIS, I THINK.
SOMETIMES IT'S HARD
FOR ME TO READ THAT.
OKAY, IS IT
NICK OR GERVAIS?

Gervais says GERVAIS.

He says OKAY, LET'S
SEE, WE GOT NUMBER 7.
WHERE DOES THIS
ONE END UP GOING?
REMEMBER THAT WE WERE
REFLECTING IT HORIZONTALLY
ABOUT THAT LINE C.

Gervais says THAT ONE WOULD GO OVER
LINE C, IT WOULD GO TO...

He says THIS SPOT?

Gervais says YEAH.

He says NOW, I ALREADY
DREW THAT IN,
BUT THAT WAS MY
ORIGINAL MISTAKE.
IT LEAVES YOU WITH
ONE MORE INSTRUCTION.
IT'S BASICALLY NUMBER 8 HERE.
AND NUMBER 8 SAYS: TRANSLATE
TWO SQUARES TO THE RIGHT,
AND 13 SQUARES UP.
WHERE DOES IT END UP?

Gervais says ABOUT...
CAN YOU...
WHAT?
PUT UP YOUR
MARKER, LIKE, MORE.
IN THE TOP RIGHT CORNER.

He says TELL ME WHERE
I SHOULD BE.
TELL ME WHEN TO
STOP MY MARKER.

Gervais says A LITTLE BIT MORE.
OVER TO THE RIGHT,
A LITTLE BIT MORE.
STOP RIGHT THERE, OKAY.

He says THAT'S ONE POINT.
WHERE ELSE?

After a moment, Gervais says GO IN LIKE A HALF CIRCLE.
MAKE LIKE A...

He says LIKE THAT?

Gervais says YEAH.

He says OKAY, I THINK YOU'VE
DONE A GOOD JOB,
EXCEPT YOU WENT TOO
FAR TO THE RIGHT.
I THINK IT'S RIGHT THERE.
YOU'RE REALLY
CLOSE THOUGH.
YOU WENT UP ENOUGH,
BUT YOU WENT TOO FAR
TO THE RIGHT.
SO, WHAT DID WE END UP WITH
AS OUR FINAL SOLUTION?

Gervais says OKAY, BYE.

The lines drawn create a number. It is number 12.

He says BYE-BYE, THANK
YOU VERY MUCH.
I THINK YOU'VE DONE
A WONDERFUL JOB.
THIS IS ONE OF THE
THINGS THAT, OF COURSE,
I REALLY ENCOURAGE, IS
THAT YOU REALLY WORK HARD
WITH TRANSFORMATIONS.
AND THE MORE YOU GET USED
TO DOING INSTRUCTIONS
AND SO ON, THE
BETTER IT IS.
NOW, I MUST ADMIT THAT
I DID GET ONE MORE FAX
THIS MORNING.
AND HERE IT IS.
AND WE HAVE THE
INSTRUCTIONS UP AT THE TOP.
NOW, WHAT I'M GOING TO TRY
TO DO IS I'M GOING TO TRY
TO FOLLOW THE INSTRUCTIONS
AND SEE IF I GET WHATEVER
FIGURE THIS PERSON
HAS CREATED.
THIS CAME FROM TRILLIUM
SCHOOL AS WELL,
AND I THINK
IT WAS ALEX.
SO, I'M GOING TO DO WHAT
THE INSTRUCTIONS SAY,
AND SEE IF I CAN GET AN
OBJECT OF SOME SORT.
NOW, REMEMBER, I JUST SAW
THIS THIS MORNING
FOR THE VERY FIRST TIME,
ABOUT 10 MINUTES
BEFORE I CAME ON AIR.
SO, I HAVE NO IDEA
WHAT IT SHOULD DO.

He reads “REFLECT HORIZONTALLY ABOUT
THE LINE SEGMENT A
AND TRANSLATE
VERTICALLY SEVEN DOWN.”

He continues NOW, THERE'S THE LINE A.
WE HAVE AN OBJECT HERE.
IT'S GOING TO BE
TRANSLATED ONE, TWO,
THREE, FOUR,
FIVE, SIX, SEVEN.
SO, I THINK THAT THAT WILL
END UP RIGHT ABOUT THERE,
THAT BIG OBJECT.
SO, THAT'S NUMBER 1.

He draws a red horizontal line.

He reads” ROTATE 40 CLOCKWISE. .”

He continues NOW, I PRESUME
THAT'S DEGREES;
SO NUMBER 2 IS GOING
TO GO CLOCKWISE.
CLOCKWISE IS DOWN
IN THIS DIRECTION.
SO, IT SEEMS TO ME IT'S
NOT GOING TO MOVE TOO MUCH;
IT'S GOING TO BE
SOMEWHERE IN THERE.
SO, THAT'S OBJECT NUMBER 2.

He reads “REFLECT VERTICALLY ABOUT
THE LINE SEGMENT B.”

He continues THAT'S NUMBER 3.
LINE SEGMENT B
IS RIGHT THERE.
I REFLECT IT, SO IT'S
GOING TO BE DOWN
IN HERE SOMEWHERE.
OH, I HAVE A SENSE
OF WHAT THIS ONE IS.

He reads “TRANSLATE HORIZONTAL
LEFT EIGHT. .”

He continues THAT'S NUMBER 4.
NOW, I HAVE A FEELING THAT
LEFT IS NOT THE DIRECTION,
BECAUSE THAT WOULD PUT
ME OVER HERE SOMEWHERE.

He reads “REFLECT VERTICALLY ABOUT
THE LINE SEGMENT C. .”

He continues NOW, THAT'S NUMBER 5.
VERTICALLY, LINE SEGMENT
C: WHEN THAT REFLECTS,
THIS POINT WILL GO THERE.
THIS POINT WILL GO -
ONE, TWO, THREE, FOUR...
AND IT WILL
LOOK LIKE THIS.

He reads “AND TRANSLATE LEFT NINE. .”

He continues NOW, I THINK THAT THE
INSTRUCTION FOR THESE
TWO SHOULD HAVE BEEN RIGHT,
BOTH THIS ONE AND THAT ONE.
SO, IF I TAKE
THIS RIGHT NINE,
IT WOULD BE DOWN
IN HERE SOMEWHERE.
IF I TAKE THIS ONE
TO THE RIGHT EIGHT,
IT'LL GO IN
HERE SOMEWHERE.
THAT LEAVES THIS ONE HERE.
AND I'M NOT SURE, BUT YOU
KNOW WHAT I SEE HERE IS
THE NUMERAL FIVE.
IF, ALEX, YOU WOULD LIKE
TO PHONE IN AND LET ME KNOW
IF THAT'S THE CORRECT
ANSWER, THAT, IN FACT,
YOU HAVE A FIVE DOWN
IN THIS TERRITORY,
I'D LOVE TO HEAR
FROM YOU.
I SEE ALEX, HE'S
ON THE LINE.
AND WE ARE CONNECTING.
WHOOPS, PROBLEM THERE
WITH THE INK BLEEDING.
THERE, I'M BACK.
AND WE'RE CONNECTING...
OKAY, WE ARE MAKING
AND CONNECTING.
IT'S JEFF FROM USBORNE;
DO YOU HAVE A QUESTION?
HELLO, JEFF?

Jeff says I DON'T HAVE A
QUESTION ANYMORE,
YOU ALREADY
ANSWERED IT.

He says OKAY, THAT'S FINE.
NO PROBLEM THERE.
OKAY, I'M GOING TO NOT
TAKE ANY MORE CALLS
AT THIS INSTANT.
I DO HAVE A SHORT LESSON
HERE TODAY THAT I WANT
TO TALK ABOUT BECAUSE
IT LEADS INTO WHAT
YOU'RE DOING THIS WEEK.
TEACHERS, I WANT TO
MAKE A REAL POINT THAT
I'M GOING TO BE SENDING
SOMETHING OUT TO YOU TODAY
THAT MIGHT HELP YOU
DO THE EXPERIMENTS.
SO, I THINK THAT, IN THE
LITTLE IN-SERVICE THAT
I DO AT NOONTIME, IF YOU
GET A CHANCE TO LOOK
AT THE TAPE, I WILL TALK A
LITTLE BIT MORE ABOUT WHAT
I AM SENDING OUT TO YOU,
TO GIVE YOU A LITTLE BIT
OF A HAND ANYWAY.
ANYWAY, HERE'S WHERE
WE'RE GOING TO START.
PROBABILITY EXPERIMENTS:

A blue sheet of paper reads “What is probability?”

He continues THAT'S WHAT THE TOPIC
IS FOR THE COMING WEEK.
I WANT TO ASK YOU,
WHAT IS PROBABILITY?
SO, I'D LOVE TO HAVE
SOMEBODY PHONE IN,
GIVE ME A CALL, AND
TELL ME WHAT YOU THINK
PROBABILITY IS.
IT'S A BIG TOPIC.
IN FACT, IT IS NOW IN THE
CURRICULUM ALL THE WAY
FROM GRADE ONE ALL
THE WAY TO GRADE 12,
AND OBVIOUSLY BEYOND.
SO, I WOULD LOVE TO HEAR
WHAT YOU HAVE TO SAY
ABOUT WHAT IT IS.
AND I THINK WE'RE
MAKING A CONNECTION
TO DAVID AT TRILLIUM.

Andrew says HELLO.

He says IS IT DAVID?

Andrew says NO, IT'S ANDREW.

He says THAT'S FINE,
SORRY ABOUT THAT.
OKAY, ANDREW, WHAT
IS PROBABILITY?

Andrew says I THINK IT IS GUESSING,
WHATEVER IT IS.

He says WHAT KIND OF GUESSING?
IS IT JUST
RANDOM GUESSING?

Andrew says NO, YOU SAY IT'S
PROBABLY THIS.
YOU JUST TAKE WHAT YOU
HAVE AND JUST GUESS.

He says OKAY, FAIR ENOUGH,
GOOD ANSWER.
LET'S GO TO
ANOTHER CALLER,
THANK YOU VERY MUCH.
I THINK THAT WAS
ANDREW, SORRY.
OKAY, WE'RE GOING
TO TRILLIUM AGAIN,
AND IT'S SARAH?

Sarah says HELLO?

He says HI, SARAH.

Sarah says HI.

He says OKAY, WHAT DO YOU
THINK PROBABILITY IS?

Sarah says MATH PROBLEMS.

He says IT HAS TO DO
WITH MATHEMATICS.
IT'S ONE OF THE NEWER
KINDS OF MATHEMATICS,
BELIEVE IT OR NOT.
IT WAS INVENTED MORE
OR LESS IN THE 1700s,
AND THAT'S NEW
FOR MATHEMATICS.
BUT IT'S
DEFINITELY MATH.
CAN YOU TELL ME
SOMETHING ELSE?

Sarah says IT'S ABOUT HISTORY.

He says IT'S GOT A
HISTORICAL CONTEXT.
WHEN DO YOU USE
PROBABILITY?

Sarah says UM...
I DON'T KNOW.

He says OKAY, I'M GOING TO
GO TO ANOTHER CALLER.
MAYBE WE CAN CONNECT TO
SOMEBODY FROM ELGIN.
AND WHO AM I
TALKING TO NOW?
OH, THERE YOU ARE.

Alyssa says HELLO?

He says HI, WHO IS IT?

Alyssa says ALYSSA.

He says OKAY, ALYSSA, WHAT
IS PROBABILITY?

Alyssa says THE CHANCES OF
IT OCCURRING?

He says CHANCES OF IT
OCCURRING - WHAT IS IT?
CHANCES OF WHAT
OCCURRING?

Alyssa says AN ESTIMATE.

He says OKAY, CAN YOU GIVE ME
AN EXAMPLE OF WHERE
YOU USE PROBABILITY?

Alyssa says LIKE HOW MANY TIMES THAT
IF YOU FLIPPED A COIN,
LIKE HOW MANY TIMES THAT
HEADS WOULD COME UP?

He says EXCELLENT,
FLIPPING A COIN,
THAT'S THE KIND OF
THING I'M LOOKING FOR.
LET'S TAKE ONE
MORE CALLER,
AND THANK YOU
VERY MUCH, ALYSSA.
AND THEN I'M GOING
TO GO TO THE NEXT
LOGICAL STEP ON THIS.
AND I THINK WE'RE
GOING TO USBORNE.
IT SHOULD BE EITHER
RANDY OR IAN, I BELIEVE.

Ian says HELLO?

He says HELLO, RANDY OR IAN?

Ian says IAN.

He says OKAY, WHAT IS
PROBABILITY?

Ian says A QUESTION?

He says IT CAN BE INVOLVED
IN A QUESTION.
IF I WANT TO
SOLVE A PROBLEM,
I CAN POSE IT
AS A QUESTION.
LIKE, FOR INSTANCE, WHAT
IS THE PROBABILITY
OF SOMETHING
HAPPENING, RIGHT?
I'VE ACTUALLY GOT
ANOTHER QUESTION HERE,
WHICH FOLLOWS FROM IT.

A blue sheet of paper reads “Where do people use probability?”

Ian says IN MATH?

He says IN MATH CLASS, YES.
BUT WHEN YOU'RE
NOT IN MATH CLASS,
DO PEOPLE
ACTUALLY USE THIS?

Ian says YEAH, A LITTLE.

He says WHERE MIGHT
THEY USE IT?
WHERE MIGHT THEY THINK
ABOUT PROBABILITY?

Ian says IN A CASINO?

He says AH-HA, OKAY.
I'M GOING TO PUT DOWN A
FEW OF THESE POINTS -
SO, AT A CASINO.
NOW, THAT IS A
COMMON ANSWER,
YOU'RE ABSOLUTELY RIGHT.
SO, THAT'S ONE PLACE.
HAVE YOU GOT ONE
MORE SUGGESTION?
IF NOT, I'LL GO
TO ANOTHER CALLER.

Ian says A LOTTERY?

He says OKAY, THANK YOU, IAN.
AND WE'LL GO TO
ANOTHER CALLER.
SO, THERE ARE
TWO PLACES.
AND WE'RE GOING
BACK TO TRILLIUM,
AND I THINK
IT'S CHRIS.
HELLO, CHRIS.
GOT YOUR PHONE?

Chris says HELLO?

He says HI, CHRIS.
CAN YOU GIVE ME ONE
MORE PLACE WHERE
YOU MIGHT USE
PROBABILITY?

Chris makes a pause and says WEATHER.

He says YOU WANT TO BET, I WAS
LOOKING FOR THAT ONE.
WEATHER FORECASTERS
USE IT ALL THE TIME.
ANY OTHER SUGGESTIONS?

Chris says NO.

He says OKAY.
NOW, I'M GOING TO TELL
YOU ABOUT A COUPLE
OTHERS MYSELF, JUST TO
ADD INTO THE MIX.
AND I MIGHT TAKE
ANOTHER CALL HERE,
BUT I'VE GOT TO WATCH
MY TIME AS WELL.
ONE IS SAFETY.
QUITE OFTEN, LIKE FOR
INSTANCE IF YOU GET ON
AN AIRPLANE OR WHATEVER, ONE
OF THE THINGS THAT SOME PEOPLE
WANT TO KNOW IS HOW
SAFE IS IT TO BE ON
AN AIRPLANE, TO
TRAVEL BY AIRPLANE?
IS IT SAFER TO TRAVEL ON
AN AIRPLANE THAN IN A CAR?
AND THOSE CONCEPTS
INVOLVE PROBABILITY.
THERE'S ONE EXAMPLE.
I'LL GIVE YOU A REALLY
GOOD EXAMPLE THAT IS
IN THE REALM OF SAFETY.
I'VE HAD THE HONOUR TO
ACTUALLY GO TO NASA
AND VISIT ASTRONAUTS AND SO
ON IN HUNTSVILLE, ALABAMA.
AND ONE OF THE THINGS
THAT, AS AN ASTRONAUT,
I WOULD LIKE TO KNOW WHAT
THE PROBABILITY IS
THAT I WILL HAVE
A SAFE VOYAGE?
THAT IS, I'LL BE BLASTED
OFF IN THE SHUTTLE AND
I'LL COME BACK IN
ONE PIECE, ALIVE.
AND IT'S VERY, VERY
INTERESTING TO NOTE
THAT IT DEPENDS
UPON WHO YOU TALK TO.
THIS IS NOT A
SIMPLE QUESTION.
WHAT YOU'LL FIND IS
THAT SOME PEOPLE
WILL SAY IT'S 99 percent SAFE.
SO, THERE'S A ONE IN A 100
CHANCE THERE'S A PROBLEM.
I CAN LIVE WITH THAT.
I'D BE THRILLED TO GET A
CHANCE TO GO ON A SHUTTLE;
I COULD LIVE WITH THAT.
HOWEVER, OTHER PEOPLE HAVE
SAID IT'S ONLY 90 percent SAFE.
WHAT THAT SAYS IS THE
SHUTTLE'S GOING
TO BLOW UP ON AVERAGE
ONE IN EVERY 10 TIMES.
YOU KNOW, I'M NOT SO SURE
THAT I WOULD WANT TO GO
ON A SHUTTLE TRIP
IF, IN FACT,
THE PROBABILITY
WAS 90 percent.
I VALUE MY LIFE.
BUT THEN THERE
ARE OTHERS, EVEN,
THAT SAY THAT IT
IS 99.999 percent SAFE.
WHEN YOU GET
TO THAT RANGE,
THEN IT'S HIGHLY UNLIKELY
THAT THERE WILL BE A PROBLEM.
I'M NOT QUITE SURE I
BELIEVE THAT ONE EITHER.
BUT HOW DO THEY ACTUALLY
FIGURE OUT THESE
PROBABILITIES?
IN THE CASE OF NASA,
THEY TRY TO FIGURE THEM OUT
BY DOING A WHOLE
SERIES OF EXPERIMENTS.
IT'S THE ONLY WAY
THEY CAN DO IT.
AND THAT'S ONE OF THE
THINGS THAT I'M GOING TO
BE ASKING YOU TO DO OVER
THE COURSE OF THE NEXT WEEK.
NOW, I'M GOING TO QUICKLY
GO THROUGH SOME QUESTIONS,
AND ONE ORAL QUESTION,
AND THEN SIGN OFF.
LET'S GO TO THIS
QUESTION FIRST OF ALL,
AND YOU CAN PHONE
IN WITH AN ANSWER.

He shows a blue sheet of paper that reads “If you roll a six-sided die, what is the chance that you will roll: a) A 5? b) An even number? c) A prime number?”

He continues ACTUALLY, WHOEVER
PHONES IN,
I'M GOING TO GET THEM
TO ANSWER ALL
THREE QUESTIONS FOR ME.
YOU'VE GOT A
SIX-SIDED DIE;
THERE'S AN EXAMPLE
OF ONE RIGHT THERE.

He puts a red dice on the page and continues
WHAT IS THE CHANCE
I'LL ROLL A FIVE?
WE'RE CONNECTING TO
USBORNE, AND I THINK ERIC.
IN A MOMENT OR TWO, WE
SHOULD BE ALL CONNECTED.
ROLLING A FIVE; THE NEXT
ONE AFTER THAT WILL BE
AN EVEN NUMBER, AND
THEN A PRIME NUMBER,
WHICH REQUIRES YOU TO KNOW
WHAT A PRIME NUMBER IS.
THERE HE IS.
HELLO, ERIC?

Eric says YEAH?

He says OKAY, WHAT'S THE
PROBABILITY OF GETTING
A FIVE IF YOU ROLL
A SIX-SIDED DIE?

Eric says ONE IN SIX?

He says RIGHT, THERE ARE SIX
SIDES: ONE, TWO, THREE,
FOUR, FIVE, SIX.
I DIDN'T POINT
THEM ALL OUT.
AND THERE'S ONLY ONE FIVE
ON THIS PARTICULAR DIE.
AS YOU CAN SEE,
IT'S A STANDARD DIE,
SO THE PROBABILITY IS,
INDEED, ONE IN SIX.
AND I'M JUST GOING
TO RECORD THAT.
OKAY, GREAT.
WHAT'S THE PROBABILITY OF
GETTING AN EVEN NUMBER?
YOU'RE STILL WITH ME.
HOW MANY EVEN NUMBERS
ARE THERE ON THE DIE?

Eric says THREE IN SIX.

He says THREE IN SIX, THAT'S
EXACTLY HOW YOU DO IT.
THERE'S ONE, THERE'S TWO,
THERE'S THREE OVER SIX.
THREE IN SIX, WHICH
IS EQUAL TO ONE HALF.
VERY GOOD.
HOW ABOUT THIS LAST ONE:
WHAT'S THE CHANCE OF
GETTING A PRIME NUMBER?
DO YOU KNOW WHAT
A PRIME NUMBER IS?

Eric says THREE IN SIX.

He says YOU'RE ABSOLUTELY RIGHT.
IT'S THIS ONE AGAIN,
BECAUSE THE PRIME NUMBERS
ARE TWO, THREE, AND FIVE.
AND THAT'S ALL THERE ARE
IN THE FIRST SIX NUMBERS.
SO, THERE ARE THREE
OF THEM IN SIX.
THANK YOU VERY, VERY MUCH;
YOU DID A GREAT JOB, ERIC.
LET'S DO THIS ONE.
IF YOU FLIP A COIN,
WHAT'S THE CHANCE
YOU'LL GET A HEAD?

Another piece of paper reads “If you flip a coin, what is the chance that you get: a) A head? b) A tail? c) A head or a tail?”

He continues AND WE'LL TAKE
SARAH AT TRILLIUM.
HELLO, SARAH.

Dan says HELLO?

He says HELLO, SARAH.

Dan says THIS IS DAN.

He says OKAY, YOU SEE, MY
COMPUTER SCREEN SAYS SARAH,
SO IF IT'S DAN I'LL
GO WITH IT.
WHAT'S THE CHANCE
OF GETTING A HEAD
WHEN YOU FLIP A COIN?

Dan says UH...

He says HOW MANY SIDES
TO A COIN?

Dan says ONE OUT OF TWO.

He says ONE OUT OF TWO.
WHAT'S THE CHANCE
OF GETTING A TAIL?

Dan says ONE OUT OF TWO.

He says WHAT'S THE CHANCE OF
GETTING A HEAD OR A TAIL?

Dan says ONE OUT OF TWO?

He says NO.
SEE, I WAS SETTIN'
YOU UP FOR THIS ONE,
BECAUSE THE FIRST TWO
ARE STRAIGHTFORWARD.
WHAT'S THE CHANCE OF
GETTING EITHER
A HEAD OR A TAIL?

Dan says 100 percent?

He says YOU GOT IT, THANK
YOU VERY MUCH.
THAT'S ANOTHER WAY OF
SAYING PROBABILITY, TOO;
IT'S BY SAYING
A PERCENT.
OKAY, NOW, I'M GOING
TO DO AN ORAL QUESTION
AT THIS POINT INSTEAD.
THERE WE ARE.
THERE'S THE QUESTION.

A caption appears on screen under the title “Question Number 1.” It reads “Which of the following is most likely to happen? 1: Winning Lotto 649. 2: Being hit by lighting in 1999. 3: The Leafs win the 1999 Stanley Cup.” A gray bar graph reads “0 per cent.”

He continues OH, INTERESTING
RESULTS.
A COUPLE MORE
PUNCHING IN THERE,
AND I'M GOING TO COME
UP WITH THE GRAPH.

The bar graph changes to blue as numbers go up from “3 per cent” to 82 per cent.”

He continues THIS IS ACTUALLY
QUITE AMAZING.

A three-bar graph appears. A green bar reads “10,” a purple bar reads “10” and a blue bar reads “13.”

He continues OKAY, WHAT YOU'VE
SAID TO ME
IS THAT YOU'RE
NOT SURE.
NOW, I WILL TALK ABOUT THE
THREE SITUATIONS REALLY,
REALLY, REALLY BRIEFLY.
SO, WE'LL GO BACK
TO THE QUESTION.
THERE IT IS.
JUST FOR YOUR INTEREST,
WINNING 649 IS PROBABLY
THE LEAST LIKELY
THING TO HAPPEN.
THERE'S ABOUT A ONE
IN 13 MILLION CHANCE.
INTERESTINGLY ENOUGH, NUMBER 2:
NOT ONLY BEING HIT
BY LIGHTNING IS MORE LIKELY,
IT'S EVEN MORE LIKELY
TO BE KILLED
BY LIGHTNING.
IF I SAID, TO BE
KILLED BY LIGHTNING
IN CANADA, THAT'S CLOSE
TO LIKE WINNING 649,
BUT MANY, MANY PEOPLE -
A SURPRISING NUMBER
OF PEOPLE - GET HIT BY
LIGHTNING IN CANADA:
IN BOATING ACCIDENTS AND
ON GOLF COURSES AND SO ON.
NOW, NUMBER 3: I GUESS THAT
DEPENDS UPON WHETHER
YOU'RE A DIE-HARD
LEAF FAN OR NOT.
TO BE QUITE HONEST,
I THINK THEY'VE GOT
A REASONABLE CHANCE.
IF YOU SEE THE PROBABILITY
OF THE ODDS THAT
THE LEAFS WILL WIN
THE 1999 STANLEY CUP.
I BET YOU THAT THIS YEAR
THAT THE ODDS MAKERS
ARE GOING TO MAKE IT
AROUND ONE IN 15,
MAYBE ONE IN 20.
SO, YOU KNOW SOMETHING,
IT IS MORE LIKELY THAT
THE LEAFS WILL WIN THE
STANLEY CUP IN 1999
THAN EITHER OF THOSE
OTHER SITUATIONS.
WHAT YOU'LL BE DOING NEXT
WEEK - AND I'LL BRIEFLY
MENTION THIS AND THEN
MAYBE TAKE ONE OR TWO
QUICK CALLS AT THE END
IS YOU'LL BE DOING
PROBABILITY EXPERIMENTS
WITH COINS, STONES,
AND COWRIE SHELLS.
ONE OF THE THINGS THAT
I WAS SAYING TO YOUR
TEACHERS, THESE
ARE COWRIE SHELLS.
AND WHAT I'M GOING TO DO
IS I'M GOING TO SEND YOU
A SMALL PACKAGE OF THESE
OUT TO YOU SOMETIME TODAY.
NOW, THAT'S SOMETHING YOU
DON'T HAVE TO GET YOURSELF.
COINS ARE NO REAL PROBLEM.
STONES, I MAY HAVE CREATED
A LITTLE BIT OF A PROBLEM.
BUT WHAT YOU'RE LOOKING
FOR ARE FLAT STONES
THAT ARE LIKE ROUNDED
AND FLAT STONES,
SOMETHING LIKE THIS.

He places a few cowrie shells, coins and stones over a piece of paper.

He continues AND WHAT I'M LOOKING FOR
YOU TO DO IS BASICALLY
DO EXPERIMENTS WITH
ALL THREE THINGS
AND ANSWER A FEW QUESTIONS.
NOW, BEFORE I SIGN OFF,
DO YOU HAVE ANY QUESTIONS
THAT I CAN
FIELD RIGHT NOW?
AND WE'RE CONNECTING
TO EITHER LINDSAY
OR SARAH AT ELGIN.
NOW, REMEMBER, I'LL ONLY
BE ABLE TO TAKE ONE
OR TWO QUICK CALLS.
After a moment, he continues YES, THERE WE ARE.
HELLO.

A girl says HI, ISN'T ONE
A PRIME NUMBER?

He says PARDON?

The girl says ISN'T ONE A
PRIME NUMBER?

He says WHAT IS A
PRIME NUMBER?

The girl says NO, ISN'T ONE
A PRIME NUMBER?

He says OH, OKAY, I DIDN'T
QUITE HEAR YOU, SORRY.
ONE IS NOT A PRIME NUMBER,
EVEN THOUGH IT SEEMS
TO FIT THE DEFINITION.
IN OTHER WORDS - WHAT'S
YOUR DEFINITION?

The girl says UM...
WHAT'S THE
DEFINITION?

He says IT'S A NUMBER
THAT CAN ONLY BE...
DIVIDED BY...?

The girl says ONE?

He says AND ITSELF.
SO, THE NUMBER THREE CAN
BE DIVIDED BY ONE AND
THREE, RIGHT, BUT
NOTHING ELSE, RIGHT?
NOW, IT SOUNDS LIKE ONE
WOULD BE IN THAT CATEGORY,
BUT MATHEMATICIANS
SEPARATE ONE AS
A VERY SPECIAL CATEGORY
CALLED A UNIT.
AND BY DEFINITION, IT IS
NOT A PRIME NUMBER, OKAY?

The girl says OKAY, THANK YOU.

He says NO PROBLEM.
WE'LL TAKE ONE
MORE QUESTION.
THAT WAS A GREAT
QUESTION, BECAUSE THAT
COMES UP IN CONVERSATION
ONCE IN A WHILE.
HELLO, ERIC?
PICK UP YOUR PHONE, IF
YOU HAVEN'T ALREADY,
AT USBORNE.

Eric says HELLO?

He says HELLO, ERIC.

Eric says HI.

He says OKAY, HAVE YOU
GOT A QUESTION?

Eric says YEAH.
DO YOU HAVE TO USE
RED AND BLUE STONES?

He says NO, WHAT I SAID WITH THE
STONES IS THAT YOU PUT
A MARK ON EITHER SIDE SO
IT'S DISTINGUISHABLE.
WITH THESE STONES I
ACTUALLY HAVE HERE,
NOTICE THAT I HAPPENED
TO BUY THEM THIS WAY.
BUT THEY HAVE A DESIGN
ON ONE SIDE AND
NOTHING ON THE OTHER.
SO, WHEN I FLIP IT, IT'LL
EITHER BE BLANK OR THE OTHER.
SO, WHAT YOU'RE LOOKING
FOR IS STONES THAT
ARE SOMETHING LIKE THIS
THAT YOU CAN DISTINGUISH
ONE SIDE FROM THE
OTHER, OKAY?

Eric says YEP.

He says OKAY, ONE MORE CALL AND
THAT'S REALLY ALL I CAN TAKE.
GIVEN THAT I'VE GOT
ANOTHER SHOW TO DO
IN ABOUT 12 MINUTES.
OKAY, IT'S ELGIN AVENUE.
WHO AM I SPEAKING TO?

Savanna says I'M SAVANNA.

He says OKAY, SAVANNA,
WHAT'S YOUR QUESTION?
[laughter]

Savanna says WHAT, I CAN'T
HEAR YOU.

He says WHAT IS YOUR
QUESTION?

Savanna says WE WERE GOING TO ASK IF
ONE WAS A PRIME NUMBER,
BUT I GUESS IT WAS
ALREADY ANSWERED.

He says WE SOLVED
THAT PROBLEM.
I HOPE YOU
UNDERSTOOD MY ANSWER.

Savanna says YES, ALL RIGHT, BYE.

He says OKAY, I THINK
AT THIS POINT...
WE'RE CONNECTING
TO ONE MORE.
LET'S SEE WHAT
WE CAN DO HERE.
WE'LL TRY TO
SQUEEZE IT IN.
ELGIN, HELLO,
IS IT...
WHO AM I SPEAKING TO?

Sadie says SADIE.

He says OKAY.

Sadie says MY QUESTION WAS
ALREADY ANSWERED.

He says OKAY, SUPER.
I THINK WE'RE GETTING
TO THE POINT
WHERE THE QUESTIONS ARE
FUNDAMENTALLY THE SAME,
SO I THINK IT'S THE
APPROPRIATE TIME
FOR ME TO SIGN OFF.
I'M LOOKING FORWARD TO
YOUR RESULTS NEXT WEEK,
SO WE'LL SEE
YOU SAME TIME,
SAME PLACE NEXT WEEK.

The caption changes to “Please remember to log off! Pick up handset. Press number sign 7. Press 1 to confirm. Hang up handset. See you next time!”

Watch: Coins, Stones and Shells