Transcript: Student Session 17 | Aug 24, 1998

(music plays)
A white screen appears with the title “TVO’s Virtual Classroom. Get Connected,” and a five-second timer at the bottom.

A woman in her late thirties and a man in his forties are sitting at a table. She has red hair tied back, and is wearing a white blouse under a black blazer. He has a brown full beard, wavy brown hair, and is wearing a light blue T-shirt and glasses.

Lorraine says GOOD AFTERNOON AND WELCOME
BACK TO THE VIRTUAL CLASSROOM
FOR SESSION 17 OF
YOUR MATH MYSTERY.
GOOD AFTERNOON, STEWART.

Stewart says YEAH, YOU KNOW, IT'S HARD TO
BELIEVE WE'RE ALREADY ON THIS
HIGH PRIME NUMBERED
SESSION NUMBER, 17.
HOLY CRUMB.
IT'S GREAT TO BE BACK.
GOOD TO BE HERE.

Lorraine says THAT'S RIGHT.
OUR AGENDA FOR
TODAY IS AS FOLLOWS

A blue slate appears with the title “Agenda.” Under the title a numbered list gradually appears “1. Exercise 1 and 2. 2. Special Math Lesson. 3. Destination.”

Stewart says I THINK THAT DESTINATION IS
GOING TO BE A LITTLE BIT OF
A CHALLENGE.
IT'LL BE INTERESTING TO SEE
WHAT EVERYBODY'S DONE WITH
THAT, AND I'M LOOKING FOR A
LOT OF RESPONSES SO THAT MAYBE
I CAN FIGURE OUT FOR MYSELF
WHAT YOU MIGHT DO WITH THIS.
I'M GOING TO START OFF
WITH EXERCISE NUMBER ONE,
QUESTION NUMBER ONE.
TAKE A LOOK AT THE GRAPHICS
HERE, AND THIS IS WHAT YOU
WOULD HAVE SEEN, OBVIOUSLY.
WE'RE GOING TO ZOOM IN ON
THIS LITTLE CHUNK RIGHT HERE,
WHICH IS THE MONTH, AND
THEN THE NUMBER OF PAIRS
OF RABBITS.

He shows a graphic with the months from 1 to 12, and the number of pairs: 1 in the first month, 2 in the second, 3 in the third and 5 in the fourth.

Stewart continues AND MY UNDERSTANDING IS YOU'VE
ACTUALLY BEEN DOING A LOT OF
WORK WITH THIS SEQUENCE.
SO MAYBE WHAT WE SHOULD DO IS
TAKE A CALL, AND JUST HAVE
SOMEBODY HELP ME
FILL THIS CHART OUT.

Lorraine says SOUNDS LIKE A GOOD IDEA.
YES, THEY DID VERY WELL WITH
THE FIBONACCI SEQUENCE THERE.
WE'RE NOTICING A FEW CALLS.
GREAT.
WE HAVE ONE, WE'RE CALLING
IN FROM JACK MINER,
AND IT'S JUNA.
HELLO?

Stewart says HI.

A man says HELLO.

Stewart asks CAN YOU HELP ME
FINISH OUT THIS CHART?

The man says YEAH.
EIGHT
OKAY.
Thirteen
Twenty-one
Thirty-four
Fifty-five
Eighty-nine
One hundred and forty-four
Two hundred and thirty-three

Stewart writes the numbers in the graphic.

Stewart says THAT'S JUST FINE.
SO WHAT'S THE RULE FOR
ACTUALLY GOING THROUGH THIS
JUST NUMERICALLY, WITHOUT
ACTUALLY DOING A BIG HUGE CHART?

The man says EACH NUMBER IS THE SUM OF
THE TWO PRECEDING NUMBERS.

Stewart says FANTASTIC.
IT'S VERY SIMPLE, ISN'T IT?
VERY STRAIGHTFORWARD.
BUT A VERY, VERY
IMPORTANT SEQUENCE.
AND YOU'VE ALREADY BEEN
TALKING A LOT ABOUT THAT.

Lorraine says THAT'S RIGHT, YES.

Stewart says WE'RE GOING TO MOVE FAIRLY
QUICKLY BECAUSE I KNEW WITH
THIS PARTICULAR ONE, YOU HAD
DONE A FAIR BIT OF WORK ON
THIS ON TUESDAY, SO I DIDN'T
REALLY WANT TO DWELL ON THIS
ONE TOO MUCH.
BUT I DO WANT TO SPEND
SOME TIME WITH NUMBER TWO.
THAT'S NOT BAD.
BECAUSE THAT ACTUALLY, IF WE
COME BACK JUST A LITTLE BIT
THERE, WE'LL SEE
THE TERM NUMBERS.

He shows an exercise with 2 equations: t1 = 12 + 12 = 2; t2 = 12 + 12 + 22 = 6; t3 = 12 + 12 + 22 +32 = 15; t4 = 12 + 12 + 22 +32 +52 = 40

Stewart continues NOW THE FIRST PROBLEM HERE
THAT I'M CONCERNED ABOUT,
AND MAYBE WE'LL TAKE A
CALL IF WE'VE GOT ONE.
I WOULD LIKE TO KNOW
THE EXPANDED FORM.
AND I'M USING A VERY IMPORTANT
MATHEMATICS TERM, THE
EXPANDED FORM OF
TERM FIVE AND SIX.
AND JUST TO GIVE SOME SENSE
OF WHAT THE EXPANDED FORM IS,
THIS PART IN HERE IS
THE EXPANDED FORM.
OR THIS PART HERE IS
THE EXPANDED FORM.
WHAT YOU HAVE OVER HERE, OF
COURSE, IS THE CONDENSED FORM,
ONCE YOU'VE ACTUALLY
DONE THE ADDING.
BUT WHAT I'D LIKE TO KNOW IS
HOW YOU GENERATE TERM FIVE
AND TERM SIX.
HAVE WE GOT SOMEBODY
ON THE LINE, PERCHANCE?

Stewart writes “t5 =.”

Lorraine says YES.
WE HAVE A FEW CALLS HERE.
WE'RE CALLING DREW
FROM JACK MINER.
HELLO?

Drew says HELLO?

Lorraine says HI.

Stewart says HI, DREW.
CAN YOU TELL ME WHAT THE
EXPANDED FORM OF TERM FIVE IS?

Drew says YES, IT'S
ONE SQUARED,
PLUS ONE SQUARED,
PLUS TWO SQUARED,
PLUS THREE SQUARED,
PLUS FIVE SQUARED,
PLUS EIGHT SQUARED.

Stewart asks NOW WHAT'S THE
RULE, BASICALLY?
WHAT'S SPECIAL
ABOUT THOSE NUMBERS?

Lorraine says LOOK AT THE BASES.

Stewart asks THE BASES OF THE NUMBERS.
WHAT ARE THEY?

Drew says FIBONACCI NUMBERS.

Stewart says RIGHT, EXACTLY.
NOW, SO THE GRAND TOTAL OF
THIS, ONCE YOU ADD THE EIGHT
SQUARED ON, WHAT IS THE
GRAND TOTAL, DO YOU KNOW?

Drew says 104.

Stewart says 104, RIGHT.
THAT'S EXCELLENT.
THANKS VERY MUCH.

Lorraine says THANKS FOR YOUR CALL.

Stewart says ARE YOU TRYING TO
CONNECT TO SOMEBODY ELSE?

Lorraine says YES, WE'RE CALLING JUSTIN.

Justin says HELLO?

Stewart says HI, JUSTIN.
I'LL GET YOU TO DO TERM
SIX FOR ME, SO WE'LL DO THE
EXPANDED FORM ONE MORE TIME.

Stewart writes t6 as Justin tells him.

Justin says OKAY.
ONE SQUARED,
PLUS ONE SQUARED,
PLUS TWO SQUARED,
PLUS THREE SQUARED,
PLUS FIVE SQUARED,
PLUS EIGHT SQUARED,
PLUS THIRTEEN SQUARED.

Stewart says OKAY, SO WE'RE GETTING
A MUCH BIGGER NUMBER.
WHAT IS THAT?

Justin says 273.

Stewart says EXCELLENT.
OKAY, NOW THE BIG QUESTION IS
IF I JUST HAD THESE NUMBERS,
AND I'M GOING TO REWRITE
THEM ON JUST A BLUE PIECE
OF PAPER HERE

He writes the results in a separate paper sheet.

Stewart continues NOW, WHAT I'M WONDERING IS
IS IF THERE IS SOME WAY OF
LOOKING AT THESE NUMBERS AND
FIGURING OUT A PATTERN THAT'S
BUILT INTO THESE NUMBERS SO
I DON'T HAVE TO DO, FOR EACH
SUBSEQUENT TERM, ONE SQUARED,
PLUS ONE SQUARED, PLUS TWO
SQUARED, PLUS THREE SQUARED,
PLUS FIVE SQUARED, I GUESS MY
FIRST QUESTION IS, DO
WE HAVE A CALL, PERHAPS?

Lorraine says WE DO.
WE HAVE BRANDY ON THE LINE.
HELLO.

Stewart says HI, BRANDY.
CAN YOU TELL ME, IS THERE
ANYTHING SPECIAL ABOUT THESE
NUMBERS, OR SOMETHING I CAN
DO TO BETTER UNDERSTAND IF
THERE'S A PATTERN?

Lorraine says IT'S A TOUGH QUESTION.

Stewart says IT
IS A TOUGH QUESTION.

Brandy says THE DIFFERENCE BETWEEN THE
NUMBERS ARE FIBONACCI NUMBERS.

Stewart says THE DIFFERENCE
BETWEEN THIS AND THIS?

He points at t1 = 2 and t2 = 6

Brandy says YES.

Stewart says ACTUALLY, THE DIFFERENCE IS
NOT FIBONACCI NUMBERS BUT...?

Brandy says SQUARED.

Stewart says SQUARED NUMBERS,
THAT'S CORRECT.
NOW, THAT'S TRUE, AND I'M NOT
SURPRISED AT THAT BECAUSE
OF THE WAY THE WHOLE
SEQUENCE WAS GENERATED.
IS THERE SOMETHING ELSE
YOU MIGHT BE ABLE TO DO
WITH A NUMBER?
I'M JUST GOING TO SET THAT
ONE ASIDE FOR A MOMENT.
IF I HAVE THE NUMBER SIX,
WHAT'S ANOTHER WAY OF WRITING
THE NUMBER SIX?

Brandy says TWO SQUARED.
NO, NO.

Stewart says TWO TIMES...?

Brandy says THREE.

Stewart says SURE.
LET'S TAKE THE NUMBER 15.
LET'S JUST CARRY THIS FURTHER.

Brandy says FIVE TIMES THREE.

Stewart says I'M GOING TO WRITE
IT THE OTHER WAY.
LET'S TAKE THE NUMBER 40 AND
SEE IF THERE'S SOMETHING GOING
ON HERE.

Brandy says TEN TIMES FOUR.

Stewart says TEN TIMES FOUR IS ONE
POSSIBILITY, TRY ANOTHER ONE.

Brandy says FIVE TIMES EIGHT.

Stewart says SURE.
ARE YOU BEGINNING TO SEE
WHERE I'M GOING ON THIS?
LET'S GO BACK TO TWO.
IT'S THE SAME AS WHAT?

Brandy says ONE TIMES ONE.

Stewart says ONE TIMES...?

Brandy says TWO.

Stewart says THANK YOU.
I KNOW YOU'RE ON
THE SPOT HERE.
I'M MAKING IT TOUGH.
104 MAY NOT BE SO OBVIOUS.
BUT IF YOU CAN FIND TWO
NUMBERS TO MULTIPLY, TAKE A
LOOK AT WHAT'S HAPPENING.
LOOK AT THESE NUMBERS.

Lorraine says THANKS FOR YOUR CALL, BRANDY.

Stewart asks HAVE WE BEEN DISCONNECTED?

Lorraine says ACTUALLY I'M CONNECTING
NOW WITH DEREK.

Stewart says OKAY, WITH DEREK.

Lorraine says THANKS SO MUCH, BRANDY.
HELLO, DEREK.

Derek says HI.

Stewart says NOW, YOU CAN SEE WHAT I'VE
GOT ON THE GRAPHICS CAMERA
RIGHT NOW, RIGHT?

Derek says YEAH.

Stewart says NOW, WHEN I MULTIPLY THESE
PAIRS OF NUMBERS TOGETHER,
DO YOU SEE SOMETHING THAT'S
KIND OF INTERESTING AGAIN?
LOOK AT THE PAIRS OF NUMBERS.

Derek says JUST A MINUTE.
EIGHT TIMES 13.

Stewart says EXACTLY.
NOW, LET'S JUST
GUESS WHAT 273 IS.
THAT ONE IS EIGHT TIMES 13.
WITHOUT THINKING TOO MUCH,
CAN YOU PROPOSE THE NEXT?

Derek says 13 TIMES 21.

Stewart says RIGHT.
IN OTHER WORDS, WHAT ARE
THESE NUMBERS AS WELL?
WHAT'S THE NAME OF
THAT ITALIAN GUY?

Derek says FIBONACCI.

Stewart says YEAH, THEY'RE FIBONACCI
NUMBERS AS WELL.
SO IN OTHER WORDS, THE
TOTALS HERE ARE ACTUALLY
COMBINATIONS OF
FIBONACCI NUMBERS.
NOW, WHAT I'M GOING TO TRY AND
REMIND YOU IS WHEN WE CREATE
A PATTERN, THIS WAS TERM ONE,
THIS WAS TWO, THIS WAS TERM
THREE, AND SO ON.
THIS IS TERM FIVE, TERM SIX.
AND WHAT WE TRY TO DO IS
SOMEHOW OR OTHER CONNECT
THIS TERM NUMBER
WITH THESE NUMBERS.

He highlights the 6 in t6, and 13 x 21.

Stewart continues NOW, THAT'S NOT AN EASY JOB
SO I'M GOING TO HELP YOU
A LITTLE BIT, OKAY?

Lorraine says THANKS, DEREK.

Stewart says WHAT I'M GOING TO DO IS SORT
OF SWITCH GEARS A LITTLE BIT.
THIS WAS A VERY
DIFFICULT QUESTION.
I REALIZE THAT IT WAS, BUT ON
THE OTHER SIDE OF THE COIN,
ONE OF THE THINGS I'M TRYING
TO GET ACROSS TO YOU, IN TERMS
OF DOING MATH, ESPECIALLY WITH
NUMBERS, IS YOU CAN LOOK AT
THE NUMBERS IN MANY, MANY,
MANY DIFFERENT WAYS.
THAT IS TO SAY, IF YOU'VE GOT
A NUMBER LIKE SIX AND 15 AND
40 AND SO ON, SOMETIMES YOU
JUST DON'T LOOK AT THE NUMBER
ITSELF, AND SOMETIMES YOU
DON'T LOOK AT THE DIFFERENCES
BETWEEN THEM, BUT YOU ACTUALLY
FACTOR THEM, WHICH SIMPLY
MEANS FIND TWO THINGS,
PERHAPS, THAT MULTIPLY
TO GIVE THE NUMBER.
AND WHEN YOU DO THAT, THEN
YOU MIGHT BEGIN TO SEE A
DIFFERENT PATTERN, OR A PATTERN
EMERGE FROM SOMETHING THAT TO BE
QUITE HONEST, 6, 15, 40,
104, 273, THERE JUST DOESN'T
SEEM TO BE A PATTERN TO IT.
SO WHAT I'M GOING TO REMIND
YOU RIGHT NOW IS THIS.
I'VE GOT FIBONACCI ONE,
WHICH IS THE NUMBER ONE.
AND FIBONACCI TWO, WHICH
IS THE NUMBER ONE AGAIN.
REMEMBER, YOU HAVE TO HAVE
TWO OF THOSE TO GET STARTED.
FIBONACCI THREE IS TWO.
FIBONACCI FOUR IS THREE,
FIBONACCI FIVE IS FIVE,
AND ONE MORE, FIBONACCI
SIX IS EIGHT.

He writes the numbers in a new sheet of paper.

Lorraine says AND WE DO HAVE
ANDREW ON THE LINE,
SO HE MAY BE ABLE
TO HELP YOU.

Stewart says I'M GOING TO PUT OVER HERE,
I'M GOING TO BRING ANDREW ON
AFTER I PUT THE
INFORMATION ON.
TERM ONE HERE WAS
ONE TIMES TWO.
NOW, WHAT WE'RE TRYING TO DO
IS RELATE THESE NUMBERS TO
FIBONACCI NUMBERS BECAUSE
YOU KNOW THEY ARE RELATED.
ANDREW, ARE YOU STILL THERE?

Andrew says I'M STILL HERE.

Stewart says OKAY.
NOW, WHAT WE'RE INTERESTED IN
TRYING TO FIGURE OUT IS HOW
CAN I RELATE THIS NUMBER HERE,
SOMEHOW, USING THESE TWO
NUMBERS, TO THESE GUYS HERE?

Andrew asks SO YOU WANT ME TO
RELATE WHAT TO WHAT?

Stewart says SEE THIS NUMBER FOUR,
IS THE FOURTH TERM.
IN THE FOURTH TERM, I'VE
GOT TWO FIBONACCI NUMBERS.
WHICH TWO ARE THEY?

Andrew says FIVE AND EIGHT.

Stewart says FIVE AND EIGHT, BUT WHAT'S
THEIR DESIGNATION OVER HERE?

Andrew says F 5 TIMES F 6.

Stewart says THAT'S THE KIND OF
THING I'M LOOKING FOR.
SO IN THE FOURTH TERM,
THIS IS F 5, THAT'S F 6.
LET'S TAKE A LOOK
AT THE THIRD TERM.
RIGHT.
SO IN OTHER WORDS, NOTICE THIS
IS ONE MORE, AND THAT ONE IS
TWO MORE THAN THIS.
SEE THAT?

Andrew says YES.

Stewart says OKAY, I THINK IT'S TIME FOR
AN AREL QUESTION REALLY.

Lorraine says ALL RIGHT.

Andrew says BYE-BYE.

Stewart says BYE.

Lorraine says THANKS, ANDREW.

Stewart says WE HAVE BASICALLY
WALKED THROUGH THAT.
AND WE HAVE THREE
ANSWERS TO A PROBLEM.

Lorraine says ALL RIGHT.
AND THE QUESTION BEING, WHICH
OF THESE FORMULA REPRESENTS
THE NTH TERM IN EXERCISE
ONE, NUMBER TWO?

He shows a sheet of paper with “1) F4 + F5 ; F4 x F5 ; Fn+1 x Fn+2” where F1 = 1 ; F2 = 1 ; F3 = 2 ; F4 = 3.

Stewart says IN OTHER WORDS, THE EXERCISE
WE WERE JUST WORKING WITH,
WHICH ONE OF THESE IS THE
FORMULA FOR THE NTH TERM?
IN THE MEANTIME, LET'S SEE IF
WE CAN GET A WHOLE BUNCH OF
RESPONSES HERE.
HOW WE DOING?

Lorraine says WE HAVE APPROXIMATELY
30 PERCENT.
THEY ARE SLOWLY
LOOKING AT IT.

Stewart says TAKE A LOOK AT THIS.
NOW, REMEMBER WHAT I'VE
JUST BEEN TALKING ABOUT.

Lorraine says WHICH OF THESE FORMULAS
REPRESENTS THE FORMULA
FOR THE NTH TERM?

Stewart says REMEMBER, TERM N EQUALS
ONE OF THOSE THINGS.

Stewart writes “Tn = ?”

Stewart asks HOW ARE WE DOING?

Lorraine says WE HAVE ABOUT
ALMOST 50 PERCENT.

Stewart says OKAY.
ARE WE GOING TO BE ABLE
TO PUT THE GRAPH UP?

Lorraine says WE'RE GETTING MORE HERE.
IT'S STARTING TO HAPPEN.

Stewart says OKAY.

Lorraine says GIVING THEM A FEW MINUTES.
MAYBE THEY'RE FINDING THEIR
EXERCISE ONE NUMBER TWO.
OKAY, WE HAVE 75 PERCENT, 76.
80 PERCENT?
ALMOST.
AND ONE MORE PERCENT
TO GET OUR 80.

Stewart says YEAH, SOMEBODY
KICK IN ALREADY.
LET'S TAKE A LOOK
AT THE ANSWERS.

Lorraine says GREAT.
HERE WE GO.

Stewart says WHAT WE HAVE IS ABOUT AS
EVEN AS I'VE SEEN SO FAR.
SO I GUESS

Lorraine says WE CAN'T GET MORE
EVEN THAN THAT.
THEREFORE, LET'S GO HERE
TO OUR GRAPHICS CAMERA.
AND THE ANSWER BEING?

Stewart says REMEMBER, TERM N, ANY TERM
NUMBER, LIKE 21 OR SOMETHING
LIKE THAT, NOTICE, I'M GOING
TO COME BACK TO THIS ONE.
TERM THREE IS F 4 TIMES F 5.
SO THAT SHOULD HAVE TOLD YOU
THAT TIMES WAS ONE OF THE
THINGS YOU WERE LOOKING FOR.
SO THAT WOULD
ELIMINATE THAT ANSWER.

Lorraine says THAT'S RIGHT.

Stewart says HOWEVER, IF WE'RE LOOKING AT
TERM N, IT'S GOT TO HAVE AN N
INVOLVED IN IT, AND WHAT WE
SAID WITH THIS ONE, IF YOU
COMPARED THIS NUMBER TO THESE
TWO, THIS ONE IS ONE MORE,
AND THIS ONE IS TWO MORE.
SO THE WAY YOU WRITE
THIS ACTUALLY IS
THIS IS SOMETHING I KNOW IS A
LITTLE BIT OF A STRETCH, BUT
ON THE OTHER SIDE OF THE COIN,
THE MORE MATHEMATICS YOU DO,
AND THE MORE COMFORTABLE YOU
GET WITH THIS KIND OF A FORMAT
WRITING, I'LL ABSOLUTELY
GUARANTEE TO YOU YOU'LL DO
MUCH BETTER IN
MATHEMATICS LATER ON.

Lorraine says THAT'S RIGHT.
AND FIBONACCI OBVIOUSLY
THOUGHT IN THOSE TERMS.

Stewart says FIBONACCI, THERE ARE SO MANY
THINGS, LORRAINE, I KNOW YOU
WERE DOING SOME STUFF ON
TUESDAY, BUT THAT'S JUST
SCRATCHING THE SURFACE OF
FIBONACCI, WHICH IS REALLY
KIND OF NEAT.
LET'S GO TO THIS QUESTION,
WHICH IS KIND OF MY FUN
QUESTION FOR THE DAY.
AND THIS ONE HAS TO DO WITH
WHY, YOU'VE GOT 64 SQUARE
UNITS HERE, AND YOU REARRANGE
THEM, AND YOU GET 65.
AND BOY, WOULD I EVER LOVE TO
HEAR AN ANSWER, MAYBE FROM
SOMEBODY AT HOMELANDS, OR
PERHAPS USBORNE, HEAR FROM
ANOTHER SCHOOL.
BE KIND OF NEAT TO FIND
OUT WHY YOU THINK.
WHY DID THIS HAPPEN?

Lorraine says WELL, I'M GOING TO CONNECT,
I'M GOING TO SURPRISE SOMEONE
FROM USBORNE CENTRAL.
AND SEE WHAT THEY HAVE FOR
EXERCISE ONE NUMBER THREE.
IT'S EITHER
CHRISTIAN OR CARRIE.

Stewart says WE'LL BE CONNECTED
PRETTY SOON.
THIS IS A VERY
INTERESTING QUESTION.
ACTUALLY, I'VE GOT A
NICE BIG DIAGRAM HERE.

He shows a square composed of two rectangles which at the same time are composed of two rectangle triangles and two rectangle parallelograms respectively.

Lorraine says HELLO?

A woman says WE JUST GOT HERE, SO WE
JUST HAVE TO CATCH UP.

Lorraine says DO YOU HAVE YOUR EXERCISE ONE
NUMBER THREE IN FRONT OF YOU?

A woman says NO.

Lorraine says NOT YET?
OKAY, WE'LL GET BACK TO YOU.
LET'S TRY SPENCER.

Stewart asks WHERE'S HE FROM?

Lorraine says HELLO?

Spencer says HELLO?

Lorraine says HI.
WHAT DO YOU HAVE FOR YOUR
EXERCISE ONE NUMBER THREE?

Spencer says OUR SCHOOL DOESN'T
HAVE THE PAGE.

Stewart says OKAY.
SOMEHOW THAT MUST HAVE
GOT MISSED IN PHOTOCOPY.

Lorraine says OKAY, THANKS.
WE'LL SHOW YOU HERE ON THE
CAMERA TO HELP YOU OUT THERE,
SPENCER, THANKS.

Stewart says ACTUALLY, MAYBE, IF WE DON'T
GET AN ANSWER SHORTLY, I'LL
DEMONSTRATE THIS ONE BECAUSE
THIS IS ONE, ACTUALLY, THE
NEAT THING ABOUT THIS ONE,
THIS IS ONE YOU COULD REMEMBER
HOW THIS WORKS, THEN MAYBE
TRICK SOMEBODY ELSE.
THAT'S KIND OF FUN.
LIKE YOUR PARENTS.

Lorraine says MATH HUMOUR.

Stewart says YEAH, LITTLE BIT
OF MATH HUMOUR HERE.
THE WAY THIS WORKS, WE START
WITH A SQUARE, WHICH IS EIGHT
UNITS BY EIGHT UNITS,
SO IT'S 64 SQUARE UNITS.
THEN WHAT WE DO IS, THREE
UNITS DOWN, SO THAT'S THREE
UNITS DOWN, WE DRAW A LINE
STRAIGHT ACROSS AND DIVIDE
THAT RECTANGLE
WITH A DIAGONAL.
DOWN BELOW, WE CREATE
TWO TRAPEZOIDS.
THIS SPOT HERE IS FIVE UNITS
ACROSS, AND THE BOTTOM POINT
HERE IS THREE UNITS FROM HERE.
DRAW A LINE.
WHAT YOU DO WITH THAT IS YOU
CUT THAT VERY CAREFULLY INTO
FOUR PIECES, AND YOU PASTE
IT BACK TOGETHER LIKE THIS
AT THE BOTTOM.
THE TWO TRAPEZOIDS HERE,
AND THE TWO TRIANGLES.
PERHAPS WE'VE
GOT SOMEBODY --

Lorraine says FROM USBORNE CENTRAL.
HELLO?

A woman says HELLO.

Stewart asks DID YOU GET THIS QUESTION?
ACTUALLY GET A COPY OF IT?

The woman says NO, WE DIDN'T
GET THAT QUESTION.

Stewart says OKAY.
DO YOU KNOW WHY -- I'M GOING
TO ASK YOU, JUST IN CASE AS
YOU ARE FOLLOWING ME ALONG,
YOU NOTICE WHEN I MAKE IT INTO
THE BIG RECTANGLE I HAVE
65 UNITS SQUARED, RIGHT?
IT'S FIVE UNITS BY 13.
HAVE YOU ANY IDEA WHY I COULD
CREATE ONE MORE SQUARE UNIT
GOING FROM HERE TO HERE?

The woman says NO.

Stewart says YOU'RE NOT SURE ABOUT THAT.
OKAY, WELL I THINK I'M GOING
TO HAVE TO DEMONSTRATE.
WHAT DO YOU THINK?

Lorraine says SURE.
THANKS FOR YOUR CALL.

Stewart says I VERY CAREFULLY, THERE WE
ARE, WE'LL GET A PRETTY GOOD
LOOK AT IT HERE.
I TOOK MY PIECES
AND I CUT THEM.
SO THERE'S YOUR TRIANGLE,
AND OTHER TRIANGLE, AND THE
TRAPEZOID AND THE TRAPEZOID.
IF YOU DO IT REALLY CAREFULLY,
I THINK YOU CAN ACTUALLY SEE
IT QUITE WELL IN
THE GRAPHICS CAMERA.
NOTICE IN HERE, IF IT TURNS
OUT, IF YOU DO THIS AS A
PERFECT RECTANGLE,
YOU GET A GAP IN HERE.
AND GUESS WHAT THE AREA
OF THAT GAP JUST MIGHT BE?

Lorraine says ONE PERFECT SQUARE.

Stewart says THAT'S FIVE BY 13.
SO IT'S A TOTAL OF
65 SQUARE UNITS.
BUT THE EXTRA ONE, ACTUALLY,
IS A LITTLE WEE GAP IN BETWEEN
THE UPPER AND LOWER PORTION.
SO IF YOU DO THIS CAREFULLY ON
A PIECE OF GRID PAPER, THEN
PERHAPS YOU CAN ACTUALLY TRY
IT ON YOUR PARENTS AND SEE
IF THEY CAN FIGURE IT OUT.
WHICH IS KIND OF FUN.
GOT A CALL?

Lorraine says YES.
JENNIFER.
HELLO?
HI, JENNIFER.

Jennifer says HI.

Lorraine asks DO YOU HAVE A QUESTION?

Stewart asks DO YOU HAVE A
COMMENT OR QUESTION?

Jennifer says NO.
WE FORGOT TO
CANCEL, SORRY.

Lorraine asks THAT'S OKAY.
DID YOU UNDERSTAND
THE EXERCISE?

THERE'S SOMEBODY ELSE WHO
WANTS TO ASK A QUESTION.

Stewart says SURE, THAT'S FINE.

Stacie says HI, THIS IS STACIE.
YESTERDAY I ASKED YOU ABOUT
THE FULL MOON, ABOUT THE MOON.

Lorraine says OH, YES, YES.

Stewart says THIS IS SOMETHING
I DON'T KNOW ABOUT.

Stacie says IT IS NOT IN SEQUENCE.

Lorraine says IT'S NOT.
YES, I ACTUALLY ASKED
A FEW FRIENDS, AS WELL.
WE WERE GOING THROUGH THAT.
SO THAT WAS AN
EXCELLENT QUESTION.
THANKS.

Stacie says YOU'RE WELCOME.

APPRECIATE THAT.

Stewart says YOU'LL HAVE TO TELL ME ABOUT
THIS FULL MOON QUESTION.

Lorraine says IT'S EXCELLENT.
THEY HAD SOME GREAT IDEAS.
WE WERE PRETENDING WE WERE THE
MATHEMATICIANS ALL AROUND THE
WORLD, AND WE WERE COMING UP
WITH OUR FIBONACCI NUMBERS
THAT WE COULD SEE AROUND US.

Stewart says I SEE, OKAY.

Lorraine says SHE HAD SOME GREAT IDEAS.

Stewart says LET'S TAKE CARE OF
THE NEXT QUESTION.
LAST BUT NOT LEAST, WE'LL
GET TO THE DESTINATION,
I THINK.

Lorraine says OKAY.

Stewart says NOW, THIS PARTICULAR ONE IS
JUST A QUESTION OF FINDING ALL
THE DIFFERENT ROUTES.
AND THE ONLY THING THAT I'M
GOING TO DO HERE IS, I THINK
TAKING PHONE CALLS TO TELL ME
WHAT TO DO HERE WOULD BE A
LITTLE BIT DIFFICULT, ALTHOUGH
WE MIGHT GET SOME COMMENTS.
I'M GOING TO JUST VERY, VERY
QUICKLY, PUT THE DESTINATION
FOR EACH ONE OF THESE IN THIS

I KNOW I'VE GOT TO GET UP
TO THAT CORNER.

He shows an exercise with five sets of five hexagons in a beehive pattern. There is a bee in the first hexagon of each set.
He paints a dot in the last hexagon of each set.

Lorraine says MIND YOU, THEY COULD CALL IN
AND TALK ABOUT SOUTH EAST,
WEST, AND GIVE US
SOME DIRECTION.

Stewart says SURE THEY COULD.

Lorraine says YOU COULD GET US STARTED, AND
THEN WE'LL TAKE A FEW CALLS
TO ADD ON.

Stewart says WELL, ONE WAY IS CLEARLY
TO GO STRAIGHT ACROSS.
SO THAT'S ONE.
THAT'S PRETTY STRAIGHTFORWARD.
AGAIN, I THINK ONE OF THE
IMPORTANT THINGS IN DOING A
QUESTION LIKE THIS IS THAT, IN
FACT, YOU WANT TO HAVE KIND
OF A SEQUENTIAL WAY OF DOING
IT SO THAT YOU DON'T MISS ANY.
THERE'S A REAL METHOD IN
THE WAY YOU ARE DOING IT.
HAVE WE GOT SOMEBODY CALLING
IN THAT MIGHT BE ABLE TO HELP
US OUT?

Lorraine says YES, WE HAVE A FEW CALLS.
IN THE MEANTIME, WE
CAN ATTEMPT ANOTHER.

Stewart says I'M GOING TO GO STRAIGHT ONE
MORE TIME, BUT I DID HAVE THE
OPTION TO GO DOWN AND
THEN FINISH THAT OUT.
SO THAT DOESN'T
BREAK THE RULES.

Lorraine says WE HAVE STEVE FROM HOMELAND.

Stewart says HI, STEVE.
CAN YOU SORT OF GIVE ME A
ROUTE I CAN TAKE TO GET THIS
BEE FROM HERE TO HERE WITHOUT
DOING ONE OF THESE OTHERS
THAT I'VE ALREADY DONE?

Steve says YOU COULD GO DOWN THEN
UP AND DOWN THEN UP AGAIN.

Stewart says LIKE THIS?
GIVE ME ANOTHER ONE.
WOULD YOU MIND
GIVING ME ONE MORE?

Steve says DOWN THEN ACROSS
THEN UP AGAIN.

Stewart says EXCELLENT.
YOU MIGHT AS WELL
FINISH IT OFF WITH ME.

Steve says OKAY, DOWN, UP
AND THEN ACROSS.

Stewart says RIGHT.
AND OF COURSE WHAT YOU ARE
FINDING HERE IS THIS IS
ANOTHER FIBONACCI
SEQUENCE, ISN'T IT?
BECAUSE THE TOTAL NUMBER OF
WAYS OF DOING THIS IS FIVE.
WELL, HEY, THAT
WORKED VERY WELL.
LET'S TRY IT FOR
THE LAST GROUP HERE.

He shows another exercise, but this one has eight sets of six hexagons.

Lorraine says OKAY, ANOTHER CALL.
IT'S ALICIA.

Stewart says HI.

Alicia says HELLO?

Lorraine says HI, ALICIA.

Stewart says CAN YOU GIVE ME THE
FIRST FOUR POSSIBILITIES,
THEN WE'LL GO FROM THERE?

Alicia says YOU CAN GO DOWN THEN
BACK UP, THEN DOWN AGAIN,
AND THEN BACK UP.
THEN DOWN AGAIN.

Stewart says GIVE ME ANOTHER ONE.

Alicia says YOU CAN GO DOWN
AND STRAIGHT ACROSS.
YOU CAN GO STRAIGHT ACROSS.

Stewart says THEN DOWN AT THE END?

Alicia says YEAH.

Stewart says OKAY, FINE.
SO I GOT THAT ONE.

Lorraine says GREAT.
AND WE'RE GOING TO
CHECK ONE MORE CALL.
THANKS, ALICIA.
THOSE LOOK INTERESTING PATHS.
THE FIRST ONE BEING QUITE.

Stewart says THIS ONE IS THE
COMPLICATED ONE.
THAT'S THE LONGEST POSSIBLE
ROUTE YOU COULD TAKE, I THINK.
AND THESE ARE THE
TWO MOST EFFICIENT.

Lorraine says HELLO?
MAURA?

Stewart says HELLO, ARE YOU CONNECTED?

Lorraine says MAURA FROM HOMELAND.
LET'S TRY ONE MORE HERE.
TRY SHARIF FROM HOMELAND.
HI, CAN YOU GIVE US
A ROUTE FOR THE BEE?

Sharif says YOU COULD GO
STRAIGHT, DOWN, UP.

Stewart says IN OTHER WORDS, BACK
DOWN AGAIN, RIGHT?

Sharif says YEAH.

Stewart says OKAY, GIVE ME ANOTHER ONE.

Sharif says YOU GO DOWN FOR THE FIRST
ONE, AND THEN STRAIGHT,
THEN UP.

Stewart says THEN FINISH.
HOW ABOUT ONE MORE?
AND THEN WHOEVER HAS GOT THE
LAST TWO IS GOING TO HAVE A
REALLY TOUGH TIME BECAUSE
THEY'VE GOT TO FIGURE OUT
WHAT'S NOT THERE.
OKAY, ONE MORE.

Sharif says DOWN, UP, DOWN, THEN IN.

Stewart says OKAY, I THINK THAT'S
A DIFFERENT ONE TOO.
VERY GOOD.

Lorraine says THANKS VERY MUCH
FOR YOUR CALL.
LET'S TRY... JENNIFER
HERE FROM JACK MINER.

Stewart says LET'S SEE WHAT'S MISSING.
I'VE GOT TO BE CAREFUL MYSELF
AND SEE WHAT'S MISSING.

Lorraine says I SEE ONE.
OKAY.

Stewart says THIS IS GOING TO BE TRICKY.

Lorraine says HELLO?
HI.
WE HAVE KRISTEN OR CARRIE
FROM USBORNE CENTRAL.
YOU ARE?

Carrie says CARRIE.

Lorraine says HI, CARRIE.
AND WHAT DID YOU COME UP
WITH FOR THE LAST TWO?

Carrie says YOU GO DOWN, THEN UP,
ACROSS, AND THEN DOWN AGAIN.

Stewart says I DON'T THINK
WE'VE GOT THAT ONE.
AND ONE MORE?

Carrie says ACROSS, DOWN, AND ACROSS.

Stewart says I THINK THAT'S
DIFFERENT, AS WELL.
AND WE HAVEN'T
MISSED ANY, HAVE WE?

Carrie says PARDON?

Stewart says I DON'T THINK WE MISSED ANY.
WE'VE GOT THEM ALL
NOW, I THINK, RIGHT?

Carrie says YUP.

Stewart says SO WE'VE GOT A
TOTAL OF EIGHT.
AND ONCE AGAIN IT COMES
BACK TO BEING FIBONACCI.
NOW, THE INTERESTING SIDE OF
IT IS I POSED THIS PROBLEM
JUST ABOUT FIVE OR SIX
DAYS AGO WITH A UNIVERSITY
PROFESSOR, WHO IS A VERY GOOD
FRIEND OF MINE, PROFESSOR BARBO.
AND HE SAID ONE OF THE
CHALLENGES HE WOULD GIVE KIDS
AT THIS POINT IS TO PROVE WHY
THIS BEEHIVE PROBLEM WORKS IN
THE FIBONACCI SEQUENCE?
IN OTHER WORDS, IS THERE SOME
WAY OF ILLUSTRATING THIS
GEOMETRICALLY TO PROVE IT?
SO I'M GOING TO KIND
OF LEAVE THAT WITH YOU.
AND IF YOU ARE INTERESTED,
YOU CAN ALWAYS SEND ME SOME
INFORMATION BY FAX TO THE
NORMAL TVO FAX NUMBER, AND I'D
BE VERY HAPPY TO RESPOND TO
YOU IF YOU THOUGHT IT WOULD BE
KIND OF FUN TO PROVE THAT THE
NEXT ONE AFTER THIS WOULD
DEFINITELY BE 13, AND THE
ONE AFTER THAT WOULD BE 21.

Lorraine says TO FOLLOW THE SEQUENCE.

Stewart says IN OTHER WORDS YOU GO FROM
SIX CELLS TO SEVEN CELLS,
AND IT WOULD BE 13, AND SO ON.
SO I THINK THAT'S
A NEAT QUESTION.
WELL, THAT TAKES US TO,
ACTUALLY, THE VERY BOTTOM OF
THIS PAGE, TO BE QUITE HONEST.
I THINK JEWELS IS
PLAYING TRICKS WITH US.
AT THE BOTTOM, I'VE GOT
FIBONACCI NUMBERS, F 3, F 8
AND SO ON.
WHAT I NEED IS A CALL FROM
SOMEBODY WHO WOULD BE WILLING
TO TELL ME WHAT EACH ONE OF
THESE FIVE DIFFERENT NUMBERS
WOULD BE, AND THAT'S OUR
STARTING POINT FOR THE PROBLEM.

He shows an exercise that reads “If the Fibonacci numbers are designated: Fibonacci #1 = F1 = 1; Fibonacci #2 = F2 = 1; Fibonacci #3 = F3 = 2; Fibonacci #4 = F4 = 3 and so on, the coordinates of your next destination is a combination of two of the following: F3 +12.F3 ; -(F8 +F9 + F3); F1 + F6 + F10 ; -(F12 – F5); F11 – F13.”

Lorraine says OKAY.
WE HAVE A FEW CALLING IN.
WE HAVE SPENCER.
SO WE'RE LOOKING FOR
MAYBE COORDINATES.

Stewart says PROBABLY, COORDINATES.
BUT WE'VE GOT FIVE OF THEM,
AND THAT'S WHAT THE PROBLEM IS.

Lorraine says OKAY, HELLO?

Spencer says HELLO?

Lorraine says HI, CAN YOU GIVE US --

Stewart says WHAT'S THE VALUE FOR
THIS VERY FIRST ONE?

Spencer says TWO.

Stewart says F 3 IS EQUAL TO
TWO, THAT'S CORRECT.
SO WHAT'S THE TOTAL FOR THIS.

Spencer says POSITIVE 26.

Stewart says RIGHT, EXCELLENT.
YOU WANT TO CARRY
ME ONE FURTHER?

Spencer says NEGATIVE 57.

Stewart says GOOD.
PERHAPS WE CAN TAKE ONE MORE
CALL AND TRY AND FILL IN THE
LAST THREE BLANKS.
THANKS VERY MUCH, SPENCER.

Lorraine says WE'RE CALLING KRISTEN, I
BELIEVE, FROM USBORNE
CENTRAL AGAIN.
HELLO?

Kristen says HELLO.

Stewart asks CAN YOU TELL ME WHAT THIS
TOTAL VALUE WILL BE?

Kristen says POSITIVE 64.

Stewart says GOOD.
HOW ABOUT THIS ONE?

Kristen says NEGATIVE 139.

Stewart says EXCELLENT.
AND LAST, BUT CERTAINLY
NOT LEAST, THIS ONE?

Kristen says NEGATIVE 144.

Stewart says WELL DONE.
WELL, NOW WE'VE GOT SOME
NUMBERS, WHAT I NEED IS SOME
ADVICE ABOUT WHAT I SHOULD BE
DOING WITH THESE NUMBERS TO
FIGURE OUT WHERE OUR
NEXT DESTINATION IS.

Lorraine says OKAY.
AND WE DO HAVE
A LOT OF CALLS.
GREAT.
AND WE'RE CALLING
MAURA FROM HOMELAND.
SO NOW WE HAVE THOSE
FIVE NUMBERS UP ABOVE.
AND WE'LL PUT THEM THERE.
JUST READY TO PUT
THEM IN COORDINATES.
HELLO?

Stewart says HELLO, ARE YOU THERE?

Lorraine says LET'S TRY, MAYBE
STEVE FROM HOMELANDS.
OKAY, WELL, THERE WE GO, LET'S
TRY A FEW HERE FROM USBORNE
CENTRAL, ADAM OR AMANDA.
ONE OR THE OTHER.
WE'RE CONNECTING RIGHT NOW.
THERE'S QUITE A FEW
POSSIBILITIES IF WE HAVE
FIVE NUMBERS.

Amanda says HELLO?

Stewart says HELLO.
WHAT DO YOU THINK WE SHOULD
BE DOING NEXT WITH THESE
FIVE NUMBERS?
WHAT DID YOU DO?

Amanda says NOTHING, REALLY, BUT I KNOW
WHAT THE NEXT DESTINATION IS.

Stewart says WELL, IF YOU WOULDN'T MIND
MY HOLDING YOU ON THAT.
HOW DID YOU ACTUALLY DISCOVER
THAT, WITHOUT TELLING ME
WHERE IT IS?
HOW DID YOU DISCOVER WHAT
THE NEXT DESTINATION WAS?

Amanda says WE PUT PAIRS TOGETHER AND DID
THE LONGITUDE AND LATITUDE
ON THE ATLAS, AND
THAT'S HOW WE GOT IT.

Stewart says EXCELLENT.
SO I'M GOING TO HOLD YOU ON
THE LINE FOR JUST A MOMENT.
SO IN OTHER WORDS, YOU
HAD PAIRS LIKE THAT.

Stewart shows a sheet of paper with several sets of coordinates: (26, -57) ; (26, 64) ; (26, -139) ; (26, -144) ; (-57, 26) ; (-57, 64) ; (-57, -139) ; (-57, -144) ; (64, 26) ; (64, -57) ; (64, -139) ; (64, -144) ; (-139, 26) ; (-139, -57) ; (-139, 64) ; (-139, -144) ; (-144, 26) ; (-144, -57) ; (-144, 64) ; (-144, -139)

Stewart says NOW, THE ONLY THING THAT
I'VE DONE HERE IS I'VE NOT
INCLUDED PAIRS
THAT ARE THE SAME.
IN OTHER WORDS, 26, 26.
DID YOU DO
SOMETHING LIKE THIS?

Lorraine says AMANDA?

Amanda says NEGATIVE 139 AND 64.

Stewart says IS WHAT YOU EVENTUALLY
CAME OUT TO, EH?

Lorraine says SO THIS ONE RIGHT HERE.

Stewart says I'M JUST TAKING A
LOOK AT SOMETHING.

Amanda says HANG ON.

Stewart says OKAY.
WHAT I WANT YOU TO DO HERE IS
YOU HAVE A LIST LIKE THIS.
CAN YOU TELL ME WHICH ONES
OF THESE PAIRS CANNOT
POSSIBLY WORK?
IF YOU WERE TRYING TO MAKE
THIS AN EASIER PROBLEM, WHICH
ONES CAN YOU THROW OUT WITHOUT
ACTUALLY LOOKING IN THE ATLAS?

Amanda says THE OCEANS.

Stewart says YOU CAN CERTAINLY, BUT THERE
ARE ONES YOU CAN EVEN THROW
OUT BEFORE YOU THINK ABOUT
OCEANS, WHICH IS TRUE.
A WHOLE BUNCH OF
THESE ARE IN OCEANS.
WHICH ONES OF THESE PAIRS OF
COORDINATES JUST CANNOT WORK.

Amanda says THE NEGATIVES.

Stewart says NO, NEGATIVES ARE OKAY
BECAUSE REMEMBER WE WENT LEFT
AND RIGHT ON THE AXIS.
BUT REMEMBER, LATITUDE AND
LONGITUDE, IS THERE SOMETHING
SPECIAL ABOUT LATITUDE?
WHAT'S THE BIGGEST NUMBER
YOU CAN HAVE IN LATITUDE?

Amanda says PARDON?

Stewart says WHAT'S THE BIGGEST NUMBER
OR VALUE THAT YOU CAN HAVE
FOR LATITUDE?

Amanda says 90.

Stewart says RIGHT.
NOW, WHICH OF THESE
COORDINATES IS LATITUDE?
THE FIRST COORDINATE OR
THE SECOND COORDINATE?

Amanda says PARDON?

Stewart says WHICH OF THESE TWO
COORDINATES, ONE IS LATITUDE,
AND ONE IS LONGITUDE.
WHICH ONE IS WHICH?

Amanda says THE FIRST ONE IS LATITUDE.

Stewart says RIGHT, EXACTLY.
SO IF THIS FIRST NUMBER IS
BIGGER THAN 90, OR LESS
THAN NEGATIVE 90, WHAT
CAN YOU DO WITH IT?

Amanda says GET RID OF IT.

Stewart says THAT'S RIGHT.
SO ANYTHING LIKE THIS YOU CAN
THROW OUT RIGHT AWAY WITHOUT
DOING ANY WORK.
THAT ONE, THAT ONE,
THAT ONE, THAT ONE.
OH, A WHOLE BUNCH OF THEM.
LOOK HOW MANY WE GOT RID OF.
THEN WE CAN GO TO THE ATLAS.

Lorraine says YUP.
AMANDA?

Amanda says YES.

Lorraine asks WHAT WERE YOU GOING TO SAY?

Amanda says CAN I TELL YOU
WHERE WE ARE GOING?

Lorraine says OKAY, WE'LL KEEP YOU ON THE
LINE IF YOU DON'T MIND
HANGING ON.
WE JUST WANT ONE MORE LITTLE
STEP AND THEN YOU CAN SAY IT.

Stewart says YOU CAN SAY IT.
WE'RE GOING TO LET YOU DO IT.
WHAT YOU END UP
WITH IS SOMETHING THAT --

Lorraine says AS AMANDA MENTIONED, ALL
THESE WITH THE OCEANS.

Stewart says OCEANS, AND THE MIDDLE OF
FINLAND, ACTUALLY, TO BE QUITE
HONEST, I'LL PAIRED IT DOWN
BECAUSE I GOT RID OF THE OCEANS.
NOW, AMANDA, WHICH ONE
OF THESE PLACES IS IT?
IS SHE THERE?

He shows four coordinates that read “(26, 64) The Middle of Finland. (64, 26) The Middle of Pakistan. (-139, 64) Dawson City, Yukon. (-144, 64) The Middle of Alaska.”

Amanda says PARDON?

Stewart says ARE YOU STILL THERE?
TELL ME WHERE WE ARE GOING.

Amanda says DAWSON CITY, YUKON.

Stewart says WHY DID YOU CONCLUDE IT
WAS DAWSON, NOT PAKISTAN,
FINLAND, OR ALASKA?

Amanda says BECAUSE THEY ARE IN
THE MIDDLE OF NOWHERE.

Stewart says THE OTHER ONES ARE IN THE
MIDDLE OF NOWHERE, THAT'S TRUE.
AND I THINK THAT'S A
PERFECTLY GOOD CONCLUSION.

Lorraine says OKAY, GREAT.
THANK YOU VERY MUCH.
YOU DID VERY WELL.

Stewart says WELL, WE KNOW WE'RE
GOING TO DAWSON CITY.
WHAT'S SPECIAL ABOUT
DAWSON CITY, I DON'T KNOW.
I THINK WE'RE
GOING TO FIND OUT.

Lorraine says I KNOW ONE THING --

Stewart says NOT YET.

Lorraine says I KNOW ONE THING.

Stewart says YOU KNOW SOMETHING ABOUT
DAWSON CITY, I BELIEVE WE ARE
GOING TO HAVE COLLEGE
AVENUE CALL IN ABOUT DOING...?

Lorraine says THAT'S RIGHT.
COLLEGE AVENUE IS DEFINITELY
THE NEXT SCHOOL TO SHARE
WITH US INFORMATION
ABOUT DAWSON CITY.
SO COLLEGE AVENUE, WE'RE
GOING TO BE WAITING FOR THE
INFORMATION ON MONDAY TO
HEAR ABOUT DAWSON CITY.
AND THANKS, AMANDA,
FOR BRINGING THAT UP.

Stewart says SOMETHING ELSE I'D LIKE
TO ADD, THIS IS A NOTE TO
TEACHERS I'M GOING TO SEND
OUT TOMORROW AFTERNOON, FROM
HERE, A SINGLE PAGE FAX AS A
CLARIFICATION TO DO WITH THE
MATHEMATICS ASSIGNMENT
FOR NEXT WEEK.
SO JUST BE ON THE ALERT I'LL
BE SENDING A FAX OUT PROBABLY
SHORTLY AFTER I ARRIVE HERE AT
WORK AT ABOUT 11:30 TOMORROW
MORNING OR SO THAT WILL
CLARIFY THE VERY FIRST QUESTION.
IT TURNS OUT IT'S A VERY LARGE
QUESTION, AND I'M GOING TO
PROPOSE THAT YOU DO IT
MORE AS A CLASS PROJECT,
AS AN INDIVIDUAL PROJECT.

Lorraine says EXCELLENT.

Stewart says SO I'LL SEND
SOMETHING OUT TOMORROW.
ANYWAY, WE HAVE A
LITTLE MATH LESSON HERE.
IT'S A MATH CHALLENGE,
TO BE MORE EXACT.
I LIKE LEAVING YOU WITH A
CHALLENGE OVER THE WEEKEND,
SO HERE'S WHAT
WE'RE GOING TO DO.
HERE'S THE QUESTION

He shows a question “The following 8 x 8 chess board has diagonally opposite squares missing. Can you tile the chessboard with dominoes? If so, show such a tiling. If not, explain why not.”

Stewart says YOU CAN SEE IT'S A CHESSBOARD
OR CHECKERBOARD, WHATEVER
YOU WANT TO CALL IT.
THESE TWO SQUARES, YOU'VE
GOT TO PRETEND THEY ARE
TOTALLY MISSING.
THEN, IF YOU'VE GOT SOME
DOMINOS AT HOME, THE QUESTION
IS, I CAN PUT THAT DOMINO ON
THERE, AND PUT ANOTHER, SAY,
DOMINO HERE, AND IT'S HARD
TO SEE THAT BECAUSE IT GOES
RIGHT THROUGH, I DIDN'T
REALIZE THAT, BUT THAT'S OKAY.
THE QUESTION REALLY IS -- IS
IT POSSIBLE TO GET A SET OF
DOMINOS AND COVER EVERY SINGLE
ONE OF THE REMAINING SQUARES
WITHOUT OVERLAPPING THE
DOMINO, OR LETTING THE DOMINO
STICK OUT ON THE EDGE?
IN OTHER WORDS, JUST GETTING
A SET OF DOMINOS, AND CAN YOU
COVER THIS ENTIRE THING
WITHOUT OVERLAPPING A DOMINO,
OR WITHOUT IT GOING
OVER THE EDGE?
NOW, REMEMBER, THESE TWO PIECES
ARE MISSING, AND OF COURSE
THE DOMINOS WILL NOT
COVER THOSE PIECES.

Lorraine says AND IT'S EIGHT BY EIGHT.

Stewart says IT'S AN EIGHT BY
EIGHT CHECKERBOARD.

Lorraine says THEY SHOULD WRITE
DOWN THIS QUESTION.

Stewart says YES.

Lorraine says OKAY.
SO IT SAYS, AND WE CAN HAVE YOU
ANSWER THIS FOR US ON MONDAY.

Stewart says IT'S A NEAT LITTLE QUESTION.
AND ACTUALLY THE ONE THING WE
CERTAINLY WANT TO DO THERE IS
TO GET AN EXPLANATION
AS TO WHY IT WORKS,
OR WHY IT DOESN'T WORK.
SO WE'LL BE LOOKING FOR
THOSE ANSWERS ON MONDAY.

Lorraine says AND WE'LL TAKE ONE CALL
HERE FROM JACK MINER.
HELLO, JENNIFER?

Jennifer says YEAH.

Lorraine says HI.
DID YOU HAVE A QUESTION?

Jennifer says YEAH.
FOR THE FIRST PAGE, NUMBER
FOUR, ABOUT THE BEES,
CAN YOU PUT THAT
BACK ON, PLEASE?

Lorraine says SURE.
IT'S RIGHT HERE.

Stewart says YUP, OKAY, WE
GOT IT, I THINK.

Lorraine says ONE MOMENT.
THIS ONE HERE?

Jennifer says YEAH.
THANK YOU.

Lorraine says DID YOU WANT A
LITTLE MORE THAN THAT?

Jennifer says NO, I JUST DIDN'T
GET IT THE FIRST TIME.
OKAY, THANKS.

Lorraine says DO YOU HAVE A QUESTION AS
FAR AS WHAT YOU ARE SEEING?

Jennifer says NO.

Stewart says OKAY, GREAT.
NO PROBLEM.
HAPPY TO DO
THAT FOR YOU.

Lorraine says YES.
THANKS FOR YOUR
CALL, JENNIFER.
OKAY, WE'LL LEAVE THIS ON FOR
ANOTHER 30 SECONDS TO GIVE
YOU A CHANCE TO WRITE IT OUT.
HELLO, JACK MINER?
OR HELLO ANDREW
FROM JACK MINER.

Andrew says HELLO?

Lorraine says HI.
DID YOU HAVE A QUESTION?

Andrew says YEAH.
FOR THE FIBONACCI NUMBERS ON
EXERCISE ONE, TWO, FOR THE
LAST TERM SEVEN, COULD
YOU SHOW THAT ONE AGAIN?

Lorraine says OKAY, LET'S GET
THAT ONE AGAIN.
SO EXERCISE, AND WHERE IS IT?
EXERCISE ONE, WHICH QUESTION?

Andrew says NUMBER TWO.

Lorraine says OKAY, I'LL GET TO THAT.
EXERCISE ONE, NUMBER TWO.
OF COURSE, I DON'T
HAVE IT RIGHT AT HAND.
OH, HERE IT IS.
OKAY, IF YOU ARE
TALKING ABOUT THIS PAGE?

Andrew says YES, THAT'S THE ONE.

Lorraine says AND WHAT ARE YOU QUESTIONING?

Andrew says TERM NUMBER SEVEN.
WHAT WAS THE ANSWER FOR IT?

Lorraine says OKAY, WELL, CAN
YOU HELP US OUT?
IF WE ARE KEEPING THAT SAME
PATTERN THAT WE'VE DONE HERE,
WHAT WOULD YOU ADD TO THIS
LINE TO MAKE IT TERM SEVEN?

Andrew says I DON'T HAVE A CLUE.

Lorraine says WELL, WHAT ARE YOU NOTICING
WITH TERM FIVE AND TERM SIX?

Andrew says THE FIRST ONE IS 1 SQUARED.

Lorraine says YES, THEY BOTH HAVE ONE
SQUARED, AND THIS ONE IS ONE
SQUARED, AS WELL.
WHAT ELSE ARE YOU NOTICING?
NOW, EIGHT SQUARED STOPPED
FOR THIS PARTICULAR TERM,
THEN THEY ADDED THE NEXT
FIBONACCI NUMBER, WHICH IS?

Andrew says 13 SQUARED.

Lorraine says THAT'S RIGHT.
SO I HAVE TO ADD THAT TO HERE,
BUT TO MAKE IT TERM SEVEN,
I HAVE TO ADD THE NEXT FIBONACCI
NUMBER, WHICH WOULD BE?

Andrew says 21 SQUARED.

Lorraine says THAT'S RIGHT.
AND THAT'S IT.
THEN YOU HAVE YOUR WHOLE
NUMBER WHEN YOU PUT IT TOGETHER.
OKAY?

Andrew says OKAY.

Lorraine says THANKS, BYE.
AND I'M SURE AT THIS POINT
YOU'VE HAD A CHANCE TO FINISH
THE QUESTION HERE, IF
NOT, WE CAN PUT IT UP LATER.
AND I WOULD LIKE A QUICK
REMINDER HERE WHEN WE SEE THE
PINEAPPLE, AS WELL, AS THE
ARTICHOKE, WHAT'S FIBONACCI
ABOUT THAT?
DO YOU REMEMBER?

She shows to the camera a pineapple and an artichoke.

Lorraine says HELLO?
HI, DUSTIN?

Dustin says HELLO?

Lorraine says HI, WHAT CAN YOU TELL US?
DO YOU REMEMBER WHAT'S
FIBONACCI ABOUT A PINEAPPLE?

Dustin says THE DIAGONAL LINES.

Lorraine says THAT'S RIGHT.
AND HOW MANY ARE THERE?

Dustin says EIGHT.

Lorraine says THAT'S RIGHT.
THERE HAPPEN TO BE EIGHT,
WHICH IS A FIBONACCI NUMBER.
HOW ABOUT THE ARTICHOKE?

Dustin says THE DIAGONAL THING AGAIN.

Lorraine says THAT'S RIGHT, THE SPIRAL.
HOW MANY?

Dustin says FOUR?
FIVE?

Lorraine says THAT'S RIGHT.
THERE'S FIVE.
IF YOU SEE THERE ARE FIVE
ACTUAL ROWS, WHICH IS
A FIBONACCI NUMBER.
GREAT, THANKS VERY MUCH.

Dustin says YOU'RE WELCOME.

Lorraine says HEY, THERE'S
Mr. C AND Mrs. G.
WHAT ON EARTH IS THAT
THING BESIDE Mr. C?

Stewart is standing beside a plant in a pot. He is wearing a dark blue cap.

Stewart says WELL, Mrs. G, NOW DON'T YOU
BELIEVE ME WHEN I SAID
WE WOULD FEAST ON
HOME GROWN PASTA?

Lorraine is wearing a blue cap.

Lorraine says WELL, Mr. C, I GOTTA HAND IT
TO YOU THIS TIME, THAT'S GOT
TO BE THE MOST BEAUTIFUL
TREE I'VE EVER SEEN.
AND IT CERTAINLY HAS
GROWN QUITE QUICKLY.
MUST HAVE HAD SOME
KIND OF SEEDS THERE.

Stewart says WELL, I TOLD YOU I WAS GOING
TO GET VALUE FOR MY MONEY.

Lorraine says REALLY?
WELL, IF YOU USE THIS VALUE BY
STILL COOKING ME A SPAGHETTI
DINNER LIKE YOU PROMISED
ME, THAT WOULD BE GREAT.
UNLESS, OF COURSE, YOU COOK LIKE
YOU DO MODELS FOR AIRPLANES.

Stewart says I'LL HAVE YOU KNOW, Mrs. G.,
I MAKE ZEE BEST PASTA.
MOLTO BENE.

Lorraine says MOLTO BENE?
NO, NO, I LIKE MY
PIZZA AL DENTE.
JUST JOKING, Mr. C.
ANYWAY, I MEANT TO ASK YOU,
HOW ARE RENE AND ISAAC?
ANYMORE NEWS?

Stewart says NO, I HAVEN'T HEARD
ANYTHING LATELY AT ALL.
IN FACT, NO NEW
SUSPECTS SINCE MONDAY.
BUT YOU KNOW, I THINK THIS
WOULD BE A GOOD TIME TO REVIEW
SOME OF THE FACTS.

Lorraine says OH, GREAT IDEA.
WHY DON'T WE START
WITH OUR SUSPECTS.
WE'VE GOT SPIKE.
HE'S THE OLDER
BROTHER, CORRECT?

Stewart says THAT'S RIGHT.

The camera shows four photos attached to a map of the world.

Lorraine says THERE HE IS.
WE SEE HIM A BIT
TO THE FAR LEFT.
WE HAVE BEATRICE, SHE'S THE
COMPUTER NERD WHO IS IN GRADE
EIGHT, I BELIEVE.
THEN THERE'S GRAMMIE
FROM BRAMPTON.
AND, FINALLY, Ms. PENELOPE.

Stewart attaches a label with a name to each of the photos.

Stewart says YES, SHE'S THE SOCIAL
STUDIES TEACHER, I THINK?

Lorraine says THAT'S RIGHT.
I HOPE WE'RE PUTTING ALL THIS
INFORMATION IN OUR JOURNALS,
THAT WOULD BE A GOOD
IDEA, WOULDN'T IT?

Stewart says RIGHT.

Lorraine says THEN, THE AREAS, BUT THE
FUNNY THING IS, WE HAVE QUITE
A FEW SUSPECTS BUT NONE OF THEM,
TO ME, LOOK LIKE VILLAINS.
WHAT DO YOU THINK?

Stewart says YEAH, SPIKE, HE'S A
LITTLE BIT WILD LOOKING.
BUT YOU'RE RIGHT, I JUST
DON'T GET THAT SENSE.

Lorraine says IT'S DIFFICULT TO SAY.
NOW, THE PLACES WE'VE
BEEN TO, OBVIOUSLY,
JUMBOTRON, TORONTO.
AND THEN JEWELS HAD US
GO TO ATHENS, GREECE.
MACHU PICCHU, PERU.
NAGANO, JAPAN.
OH, WHAT WONDERFUL AREAS.
CAPE CANAVERAL, IN FLORIDA.
FLORENCE, ITALY.

Stewart attaches labels with each location and it’s coordinates to the map.

Lorraine says AND TODAY, WE
JUST FOUND OUT --

Stewart says WE FOUND OUT WE
ARE GOING TO?

Lorraine says LORRAINE AND STEWART WERE
SAYING IT WAS AMANDA THAT
MENTIONED... DAWSON CITY.

Stewart says WAY UP HERE.

Lorraine says EXCELLENT.

Stewart says WE'LL HAVE TO GET A
LABEL FOR THAT NOW.
NOW THAT WE KNOW
THAT IT'S THERE.

Lorraine says THAT'S RIGHT.
YOU KNOW, DON'T WE HAVE OUR
MAP FROM BRAMPTON AS WELL.
SO MAYBE WE SHOULD
REVIEW THAT.

Stewart says LET'S REVIEW THAT AS WELL.
I DON'T KNOW THAT WE'VE GOT
ALL THE LOCATIONS ON HERE YET.

Lorraine says WELL, I DON'T SEE
THE POST OFFICE.

Stewart says THE POST OFFICE?
OH, THAT'S DOWN HERE
ON THE MAIN STREET.
SO THAT'S ACTUALLY
WAY DOWN HERE.
I'LL TRY TO -- POST OFFICE.

Lorraine says MAYBE YOUR STUDENTS COULD BE
WRITING THIS DOWN, AS WELL.
IT MIGHT BE SOMEWHAT HELPFUL.
AND WE HAVE A HIGH
SCHOOL, MARK GARNEAU.

Stewart is writing on a drawn map titled “Brampton.”

Stewart says HIGH SCHOOL IS RIGHT ACROSS
FROM THE LIBRARY, IN FACT.
AND THAT'S OVER HERE.
SO THIS IS MARK GARNEAU
COLLEGIATE INSTITUTE.

Lorraine says AND BEATRICE.

Stewart says SHE LIVES NEAR
THE KIDS, ACTUALLY.
JUST OVER HERE.

Lorraine says THAT'S THE GRADE EIGHT
COMPUTER NERD, CORRECT.

Stewart says SO THAT'S BEATRICE.
SHE LIVES OVER HERE
SOMEWHERE, YEAH.

Lorraine says OKAY.
AND THEN THERE'S GRAMMIE.

Stewart says GRAMMIE LIVES NEARBY,
AS IT TURNS OUT.
GRAMMIE LIVES JUST DOWN HERE.
ACROSS FROM THE POST OFFICE,
CLOSE TO THE SCHOOL AND SO ON.

Lorraine says OKAY.
THIS IS LOOKING INTERESTING.
SO THEY CERTAINLY
ALL CAN BE SUSPECTS.
OH, I KNOW, Ms. PENELOPE.
SHE'S THE SOCIAL STUDIES --

Stewart says SHE LIVES OUT IN BRAMPTON,
BUT SHE'S OUT ON THE
OUTSKIRTS SOMEWHERE.
SO I'M JUST GOING TO HAVE TO
PUT HER HOUSE KIND OF UP HERE.
BUT SHE
IS
IN BRAMPTON.
SO Ms. PENELOPE.
WE'VE GOT A CALL.

Lorraine says WE MIGHT HAVE SOME OF OUR
STUDENTS HERE THAT CAN HELP
US OUT.
WE HAVE SPENCER FROM JACK MINER
SEEMS TO WANT TO TALK TO US.
HELLO?

Spencer says HELLO?

Lorraine says HI, DID YOU WANT
TO SAY SOMETHING?
HELP US OUT, AS FAR
AS THE SUSPECTS?

Spencer asks SAY SOMETHING ABOUT WHAT?

Stewart says GIVE US A COMMENT OR QUESTION
ABOUT THE SUSPECTS OR THE
LOCATIONS OR WHATEVER?

Spencer says I WANTED TO ASK A QUESTION
ABOUT DAWSON CITY.

Lorraine says OKAY.

Spencer says I THOUGHT, IN LATITUDE,
WASN'T ALLOWED TO GO OVER 90.
HOW WAS IT 139?

Stewart says I THINK I GOT SOME
FIGURES FLIPPED THERE.

Lorraine says WE WERE BEING DYSLEXIC.

Stewart says I THINK SOMETHING
GOT FLIPPED THERE.
BUT AS IT TURNS OUT, I
KIND OF NOTICED THAT
AS I WAS GOING THROUGH.
I PROBABLY WAS CROSSING --

Lorraine says IT'S THE SECOND NUMBER
THAT'S THE LATITUDE.

Stewart says SO I ACTUALLY FLIPPED IT WHEN
I DID IT, AND DIDN'T REALIZE
IT UNTIL AFTERWARDS.
SO I WAS CROSSING
OUT THE WRONG ONES.

Lorraine says THANKS FOR YOUR CALL.

Stewart says DOES THAT ANSWER
YOUR QUESTION?

Spencer says YES.

Lorraine says THANKS FOR YOUR CALL.
AND LET'S TRY ONE
MORE CALL HERE.
VANESSA, MAYBE, HAS SOMETHING
TO SHARE WITH US AS FAR AS --
WE'LL HAVE TO LET STEWART AND
LORRAINE KNOW THAT AS FAR AS...

Stewart says THEY GOT ALL MESSED UP.
IT'S NOT OUR FAULT.

Lorraine says HELLO?

Vanessa says HELLO?

Lorraine says VANESSA, YOU WANTED
TO MENTION SOMETHING?

Vanessa says YEAH.
I WAS THINKING, FOR THE
SUSPECTS, MAYBE THEY ARE
ALL INVOLVED.

Stewart says ESPECIALLY BECAUSE --
WHY ARE YOU THINKING THAT?

Lorraine asks WHY ARE YOU SAYING THAT?
'COS I LIKE YOUR IDEA.

Vanessa says THEY ALL KNOW SOMETHING
ABOUT THOSE PLACES.

Lorraine says OKAY.
AND THEY ALL LIVE SO
CLOSE TO ONE ANOTHER, TOO.
GREAT.
WE SHOULD ADD THAT
TO OUR JOURNALS.
THANKS VERY MUCH, VANESSA.

Stewart says YOU KNOW, THAT'S SOMETHING
LIKE AN AGATHA CHRISTIE
I SAW ONE TIME.
SHE WAS A GREAT
MYSTERY WRITER.
AND IT SEEMS TO ME THERE WAS
ONE OF THOSE MYSTERIES
THEY WERE ALL INVOLVED
SOMEHOW OR OTHER.
THAT'S KIND OF A NEAT IDEA.

Lorraine says TEN LITTLE INDIANS.

Stewart says NO, I THINK IT WAS
THE
MURDER ON THE ORIENT EXPRESS.

Lorraine says THAT'S SUCH A
FAMOUS ONE, TOO, YES.
HELLO, ALICIA?
HI.
DID YOU WANT TO
MENTION SOMETHING?

Alicia says I THINK THAT Mr. C
IS A SUSPECT.

Lorraine says SOMEONE'S MENTIONED
THAT BEFORE?
ARE YOU A SUSPECT, Mr. C?

Alicia says HE HAS THE EXACT SAME HAT.

Stewart says WELL, I UNDERSTAND THE HAT,
BUT YOU KNOW THAT MAY HAVE
BEEN SIMPLY COINCIDENTAL.
IF I'M NOT MISTAKEN, THAT
FIRST EMAIL WAS SENT --

Alicia says OKAY, ANYWAY, HE
HAD THE SAME HAT.

Stewart says THAT'S TRUE.
I REALIZE THAT.
BUT I DO HAVE AN ALIBI BECAUSE
IT'S IMPORTANT TO ESTABLISH
ALIBI, DON'T YOU THINK?

Lorraine says DEFINITELY
.
Stewart says AND IF I RECALL YOU AND I WERE
IN THE STUDIO WHEN THE FIRST
EMAILS WERE BEING SENT.
WEREN'T WE IN REHEARSAL?

Lorraine says WELL, I DEFINITELY CAN CHECK
MY NOTES HERE IF WE WERE.
ON THAT DATE... ACTUALLY,
YES, WE WERE TOGETHER.

Stewart says SO I THINK I'VE GOT AN
ALIBI, TO BE QUITE HONEST.

Lorraine says WELL, WE'LL HAVE TO KEEP
THAT IN MIND, THOUGH.
AND WE DO HAVE ANDREW FOR
OUR LAST CALLER TODAY.
HELLO.

Andrew says HELLO?

Lorraine says HI.
DID YOU WANT TO
MAKE A COMMENT?

Andrew says NO.

Lorraine says YOU DON'T, OKAY.

Stewart says MAYBE THAT'S A GOOD NOTE
TO FINISH UP TODAY ON.

Lorraine says WELL, THANKS VERY MUCH.
AND MAKE SURE YOU DO PUT ALL
THOSE WONDERFUL COMMENTS FROM
THE STUDENTS, AS FAR
AS THE MATH MYSTERY.
AND WE'LL SEE YOU ON MONDAY.
AND COLLEGE AVENUE, ENJOY
FINDING OUT ABOUT DAWSON CITY.
BYE-BYE.

Stewart says BYE-BYE.

A blue slate appears on screen. It reads “Please remember to log off! Pick up handset. Press #7. Press 1 to confirm. Hang up handset. See you next time!”

Watch: Student Session 17