Transcript: Cave Stories | Mar 31, 1999

(music plays)
The opening slate pops up with a countdown timer from 7 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.

When the countdown finishes, Stewart appears on screen. He’s in his forties, has short, wavy, side-parted Brown hair, wears big glasses, and has a long, trimmed Brown beard, and mustache. He wears a teal shirt with black overalls and sits at his computer desk.

Stewart says GOOD MORNING AND WELCOME
TO THE VIRTUAL CLASSROOM.
IT'S BEEN A LOT EASIER GETTING
IN TODAY THAN IT'S BEEN FOR
THE LAST COUPLE OF WEEKS AND,
IN FACT, I MADE IT IN RECORD
TIME SO I FEEL QUITE
REFRESHED AND READY TO GO.
I'D LIKE TO THANK THE STUDENTS
FROM TRILLIUM FOR SENDING IN
A NICE EVALUATION.
I WILL CONTINUE TO ATTEMPT TO
WEAR SOME NEAT SHIRTS, AND
THANK YOU VERY MUCH FOR YOUR
SUGGESTIONS AND I'LL DO THE
VERY, VERY BEST I CAN TO DO
WHATEVER I CAN TO TAKE UP
THOSE SUGGESTIONS.
IN THE MEANTIME, ONE OF THE
THINGS THAT YOU DID SAY THAT
YOU LIKED IS THE BEGINNING
PROGRAM, OR BEGINNING PROBLEM,
I SHOULD SAY, AND HERE IT IS.

The question appears on screen with a title that reads “Roll a Penny.” The question reads “Penny ‘A’ is rolled around Penny ´B´ without slipping until it returns to its starting point. How many revolutions does Penny ´A´ make? Under the question the A coins are two loonies and Stewart tosses two heads up loonies next to B.

Stewart says THIS IS CALLED ROLL A PENNY,
AND I'M GOING TO USE LOONIES
FOR MY DEMONSTRATION.
HOW MANY TIMES DOES
THIS COIN SPIN?
HOW MANY REVOLUTIONS?
NOW, WHAT I'M GOING TO SUGGEST
YOU DO IS THAT IF YOU GOT A
COUPLE OF PENNIES IN YOUR
POCKET, OR YOUR PARTNER, THAT
YOU GET THEM OUT AND YOU
ACTUALLY TRY THE LITTLE
EXPERIMENT TO SEE
WHAT THE ANSWER IS.
YOU MIGHT EVEN GUESS
BEFOREHAND WHAT YOU THINK
IT MIGHT BE.
SO I'M GOING TO ACTUALLY GIVE
YOU ABOUT ONE MINUTE TO TRY
THIS LITTLE EXPERIMENT WITH
A COUPLE OF PENNIES, IF YOU
HAPPEN TO HAVE THEM, AND THEN
I'LL INVITE YOU TO PHONE IN
AND LET ME KNOW HOW MANY TIMES
THIS PENNY WILL SPIN AS YOU
ROLL IT AROUND
THE OUTSIDE OF B.
SO ONE MINUTE,
I'LL BE BACK.
OKAY, WE'RE BACK AND I SEE WE
HAVE SOME PHONE CALLS ALREADY.
AND HAVE WE GOT FLETCHER
OR TOM ON THE LINE?

Thomas says THIS IS THOMAS.

Stewart says HI, THOMAS.
OKAY, WHAT DO YOU THINK?
HOW MANY REVOLUTIONS
WILL THAT COIN MAKE?

Thomas says WELL, I THINK WHEN IT'S
SPINNING AROUND COIN B,
IT'LL SPIN TWICE BECAUSE WHEN
IT SPINS HALFWAY, IT'LL BE
UPRIGHT AGAIN.

Stewart says OKAY, FINE.
WHAT I'M GOING TO DO IS I'M
GOING TO TAKE A COUPLE MORE
ANSWERS AND SEE IF
THEY'RE THE SAME OR NOT,
BUT THAT'S A GOOD ANSWER.
IT SOUNDS LIKE IT'S
GOT SOME POTENTIAL.
AND LET'S GO TO MIKE
OR JOHN AT FLAMBOROUGH.
HELLO, MIKE OR JOHN?

John says THIS IS JOHN.

Stewart says HI, JOHN.
HOW MANY REVOLUTIONS
DO YOU THINK?

John says I AGREE WITH THOMAS, BECAUSE
ME AND MY PARTNER TOOK A FEW
PENNIES OUT OF OUR POCKET.

Stewart says YEAH.

John says AND TRIED IT, SO I
THINK IT'S TWO, TOO.

Stewart says OKAY, GREAT.
LET'S CONNECT TO
SOMEBODY FROM TRILLIUM.
I SEE...
OH, WE'RE GOING
TO GET SOMEBODY...
JOSH OR PHIL, AND
WHAT DO YOU THINK?

Josh says HELLO?

Stewart says WHAT DO YOU THINK?
HOW MANY REVOLUTIONS
WILL PENNY A MAKE?

Josh says ABOUT ONE AND A HALF.

Stewart says YOU THINK ONE AND A HALF.
OKAY, SO WE HAVE
TWO ANSWERS NOW.
AND WE'RE GOING TO GO TO
AN ANSWER FROM TRILLIUM,
AND WE'RE LOOKING TO
TALK TO CHRISTOPHER.

Christopher says HELLO?

Stewart says HI, CHRISTOPHER?

Christopher says HI.

Stewart says HOW MANY REVOLUTIONS
DO YOU THINK?

Christopher says SEVEN HUNDRED AND
TWENTY DEGREES, OR TWO.

Stewart says OR TWO.
OH, I LIKE THE ANSWER.
THANK YOU VERY MUCH, CHRIS,
AND WE'LL TAKE ONE MORE ANSWER
AND THEN WE'RE GOING TO
TRY THE EXPERIMENT ON AIR,
SEE IF I CAN DO IT.
AND WE'RE CONNECTING TO NEIL
OR SEAN, AND THIS'LL BE THE
LAST ONE.

Neil says THIS IS NEIL.

Stewart says HI, NEIL.
HOW MANY REVOLUTIONS?

Neil says I THINK IT MIGHT BE ONE
BECAUSE THE CIRCUMFERENCE OF
THE PENNIES, THE CIRCUMFERENCE
IS THE SAME AND IT TAKES THE
CIRCUMFERENCE OF ONE PENNY TO
ROTATE ALL THE WAY AROUND.

Stewart says YEAH, AND YOU KNOW,
INTUITIVELY SPEAKING, I HAVE
TO AGREE WITH YOU, BUT WE'RE
GOING TO TRY THE EXPERIMENT
AND SEE WHAT HAPPENS.
WE'VE GOT SOME REALLY GREAT
ANSWERS, AND I LOVE THE FACT
THAT YOU'RE EXPLAINING YOUR
THINKING AND HOW YOU THINK
IT'LL WORK.
I LIKE THAT ANSWER WITH
720 DEGREES AS WELL.
LET'S SEE.
NOW, I'M GOING TO
HOLD THIS ONE FIXED.

Stewart holds one penny fixed and then rotates the border of another penny around it to measure the circumference.

Stewart continues NOTICE THAT I HAVE A
MARK ON THIS TO INDICATE
WHERE IT STARTED.
NOW, LET'S SEE IF I
CAN DO THIS CAREFULLY.
WHOOPS.
SLIPPAGE IS A PROBLEM.
NOW, IF I HAD DONE THAT REALLY
CAREFULLY, I WOULD HAVE GOTTEN
HALFWAY AROUND AND THE FACE OF
THE QUEEN WOULD BE FACING IN
THE SAME DIRECTION, MEANING
IT'S MADE ONE REVOLUTION.
NOW, LET'S SEE IF I CAN
DO IT THE REST OF THE WAY.
IT'S HARD TO DO THIS ON
AIR WITHOUT SOME DEGREE
OF SLIPPAGE.
NOW, IF I'D DONE IT CAREFULLY,
YOU'LL FIND THAT IT'LL REVOLVE
ONE MORE TIME AS IT COMES BACK
UP THE BOTTOM SIDE, AND THE
ANSWER IS TWO DEFINITELY.
NOW, THE QUESTION IS, WHY
IS IT TWO AND NOT JUST ONE?
LIKE, I MEAN, THAT LAST
EXPLANATION MAKES SENSE TO ME.
THE CIRCUMFERENCE OF
THIS IS THE SAME AS THAT.
SO IT SEEMS TO MAKE SENSE TO
ME THAT IT SHOULD ONLY BE ONE,
BUT THE REALITY IS IT'S TWO.
ANYBODY WANT TO
COMMENT ON THAT?
IF YOU DON'T, WE CAN CERTAINLY
GO ON TO THE NEXT EXERCISE,
BUT WE DO HAVE A CALL.
[clinking coins]
MAYBE I'LL JUST LEAVE THESE
HERE IN CASE I NEED THEM.
AND I THINK IT'S PHIL
OR JOSH AT FLAMBOROUGH.
HI, PHIL OR JOSH?

Phil says IT'S PHIL.

Stewart says OKAY, PHIL, HAVE YOU GOT AN
EXPLANATION FOR WHY IT'S TWO?

Phil says BECAUSE I THINK YOU HAVE TO
ADD THE CIRCUMFERENCE OF THE
FIRST ONE AND THE
CIRCUMFERENCE OF THE SECOND
ONE TOGETHER.

Stewart says THAT SOUNDS LIKE
A FAIR ARGUMENT.
THAT SOUNDS FAIR COMPLETELY.
I'M GOING TO GO
ALONG WITH THAT.
I THINK THAT BASICALLY
YOU HAVE IT RIGHT.
YOU KNOW, EVEN I'M NOT SURE
HOW TO MAKE MY EXPLANATION,
BUT THAT SOUNDED REALLY GOOD
AND I'M GOING TO TAKE THAT AS
A GREAT ANSWER, AND LET'S
MOVE ON TO YOUR HOMEWORK.
NOW, YOUR HOMEWORK INVOLVED
TRIANGLES AND WHEN YOU'RE
DOING TRIANGLES, THERE WAS A
RULE THAT I TALKED ABOUT LAST
WEEK THAT IS REALLY CRITICAL
IN DOING THIS EXERCISE, AND
WHAT I'M GOING TO DO IS WE'RE
GOING TO SET UP RIGHT NOW AND
DO THIS QUESTION BE...
WHOOPS, I WANT
THAT
QUESTION.
THERE IT IS.
THERE'S QUESTION NUMBER ONE.
I WANT YOU TO ANSWER THIS
BEFORE WE ACTUALLY GO INTO
TAKING UP THE EXERCISE.
THIS IS A STATEMENT AND
THE ANSWER IS TRUE/FALSE.
IS THAT A TRUE OR
A FALSE STATEMENT?
PRESS ONE FOR TRUE
AND TWO FOR FALSE.

The question appears on screen and reads “The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.” The bar to the right shows the percentage of callers answering.

Stewart continues NOW, I'M GOING TO WAIT UNTIL THE
MAJORITY OF YOU HAVE ANSWERED.
THE SUM OF THE LENGTHS OF ANY
TWO SIDES OF A TRIANGLE IS
ALWAYS GREATER THAN THE
LENGTH OF THE THIRD SIDE.
[paper shuffling]
MOST OF YOU HAVE ANSWERED.
[paper shuffling]
I'LL WAIT UNTIL A
COUPLE MORE COME IN.
WE'LL TAKE A LOOK
AT YOUR RESULT.
I'M GOING TO ASK PEOPLE TO
PHONE IN AND MAKE THEIR
EXPLANATIONS IN A MOMENT.
OH, I SEE, WE'VE GOT
PRETTY MUCH 89 PERCENT.

The results appear on screen. The green bar shows 7 for true and the purple bar shows 10 for false.

Stewart says SO MOST OF YOU ACTUALLY
THOUGHT THIS STATEMENT WAS
FALSE, ALTHOUGH I MUST ADMIT
YOU'RE NOT SURE BECAUSE
WE'RE SORT OF HALF AND HALF,
OR PRETTY CLOSE TO IT.
SO WHAT WE'RE GOING TO DO IS I'M
GOING TO ASK YOU TO PHONE IN.
IF YOU ANSWERED FALSE, CAN
YOU PHONE IN AND JUST TALK
TO ME FOR A COUPLE OF MOMENTS
AND WE'LL GO FROM THERE?
OKAY, WE'VE GOT TOM OR
FLETCHER FROM FLAMBOROUGH.
AND IN A MOMENT OR TWO, WE'LL
HAVE A QUICK CHAT HERE.
OH, WE GOT SOME MORE CALLS
AND THIS IS WHAT I WANT.
THIS IS A REALLY IMPORTANT
CONCEPT, AND WE GOT TO NAIL
THIS ONE DOWN.
THAT STATEMENT IS ABSOLUTELY
TRUE OR ABSOLUTELY FALSE,
ONE OR THE OTHER.

Tom says HELLO?

Stewart says HELLO, TOM?

Tom says YUP.

Stewart says OKAY, NOW, DID YOU
ANSWER TRUE OR FALSE?

Tom says I ANSWERED FALSE.

Stewart says OKAY.
CAN YOU EXPLAIN WHY
YOU ANSWERED FALSE?

Tom says WELL, SAY YOU HAVE
A PERIMETER OF FOUR.
SOMETIMES IT CAN BE ONE
AND ONE, AND ONE PLUS ONE
EQUALS TWO, SO TWO BELOW.
SO IT'S NOT ALWAYS GREATER.
IT CAN BE EVEN SOMETIMES.

Stewart says OKAY, OKAY.
NOW, I'M GOING TO...
YOU SAID WITH A PERIMETER OF
FOUR, ONE POSSIBILITY IS A
SIDE OF ONE, A SIDE OF ONE AND
A SIDE OF TWO AND, OF COURSE,
ONE PLUS ONE EQUALS TWO,
WHICH IS EXACTLY EQUAL
TO THE OTHER TWO, RIGHT?

Tom says YEAH.

Stewart says OKAY.
NOW, LET'S TRY TO
CONSTRUCT THAT TRIANGLE.
NOW, I DON'T KNOW IF YOU'VE
DONE CONSTRUCTION OF TRIANGLES
YET WITH A COMPASS
AND A RULER.
HAVE YOU EVER DONE
ANYTHING LIKE THAT?

Tom says NO.

Stewart says OKAY, WHAT YOU DO,
THOUGH, IS YOU TAKE
THE LONGEST SIDE
USUALLY IS THE BASE.
YOU DON'T HAVE TO, BUT
IT'S A GOOD WAY TO DO IT.
AND WHAT YOU DO IS VERY
CAREFULLY DRAW SOMETHING
THAT'S TWO UNITS LONG, OKAY?
AGREED?

Tom says YEAH.

Stewart says NOW, WHAT I DO IS I
TAKE ONE OF THE SIDES.
THAT HAS A LENGTH
OF ONE, DOESN'T IT?

Tom says YEAH.

Stewart says AND YOU KNOW HOW
A COMPASS WORKS.
IT'S ONE OF THOSE THINGS WITH
A SHARP LITTLE THING THERE,
AND IT'S GOT A
PENCIL OVER HERE.
I'LL USE AN ARROW
AS A PENCIL, RIGHT?
AND IF I MAKE THAT DISTANCE
EXACTLY ONE UNIT, OKAY?

Tom says OKAY.

Stewart says AND I PUT THE POINT IN RIGHT
THERE AND I DRAW A CIRCLE, OR
PART OF A CIRCLE ANYWAY, IT'S
GOING TO BE ONE UNIT LONG, SO
IT'LL GO THROUGH THAT SPOT
RIGHT THERE PLUS SOME MORE,
OKAY?

Tom says OKAY.

Stewart says NOW, LET'S GO...
NOW, THE OTHER SIDE IS EXACTLY
ONE UNIT, TOO, SO DO I HAVE
TO CHANGE MY COMPASS?

Tom says DON'T KNOW.

Stewart says NO, IT'S THE SAME
UNIT, ISN'T IT?
I DON'T HAVE TO CHANGE THE
COMPASS AT ALL, BUT I CAN
START AT THE OTHER END
BECAUSE I'M GOING --
OBVIOUSLY, ONE SIDE STARTS
HERE AND THE OTHER ONE STARTS
ON THE OTHER SIDE, RIGHT?

Tom says YUP.

Stewart says SO WHEN I DRAW THAT ONE, I'M
GOING TO GO THROUGH THIS SPOT
AGAIN RIGHT THERE, AND THEN HAVE
A CIRCLE THAT GOES THIS WAY.
NOW, BOTH OF THOSE COMPASS
POINTS ENDED UP RIGHT
ON THE LINE.
SEE RIGHT THERE?

Tom says YEAH.

Stewart says SO DO YOU GET A TRIANGLE?

Tom says NO, IT'S A STRAIGHT LINE.

Stewart says RIGHT, EXACTLY.
SO THAT'S WHY IT'S GOT
TO BE GREATER THAN.

Tom says OKAY.

Stewart says IT CAN'T BE EQUAL TO.
BUT I'M GLAD YOU PHONED
BECAUSE THAT REALLY IS A GOOD
ANSWER -- AT LEAST GIVES ME
SOMETHING TO WORK WITH.
LET'S TALK TO PHIL OR
JOSH AND SEE IF THEY'VE GOT
ANOTHER OBSERVATION.
HELLO, PHIL?

Josh says NO, JOSH.

Stewart says I GUESSED WRONG.
YOU KNOW, A 50 50 CHANCE, I
HAD TO GO FOR IT ONCE ANYWAY.
OKAY, JOSH, WHAT WERE
YOU GOING TO SAY?

Josh says WELL, I PUT MY ANSWER
IN AS FALSE, TOO.

Stewart says YEAH.
DID YOU UNDERSTAND THE
EXPLANATION I JUST DID?

Josh says WELL, NO, BECAUSE
IF YOU USE SIX...

Stewart says YEAH.

Josh says FOR THE TRIANGLE, ALL
THE SIDES COULD BE EVEN.

Stewart says OH, OKAY, I GOTCHA.
NOW, STAY WITH ME.
I UNDERSTAND.
SO LET'S USE SIX, AND
ONE OF THE POSSIBILITIES
IS TWO, TWO, TWO, RIGHT?

Josh says YEAH.

Stewart says BUT REMEMBER WHAT
THE STATEMENT SAID.
IT'S IF I ADD TWO OF THEM,
IT'S GOT TO BE GREATER THAN
THE THIRD, AND IS
FOUR GREATER THAN TWO?

Josh says YES.

Stewart says SO THAT WORKS, DOESN'T IT,
AND IT DOESN'T MATTER WHICH
PAIR OF TWOS I ADD TOGETHER?
IT'S ALWAYS BIGGER
THAN THE OTHER ONE.
IT DOESN'T SAY THAT THE SIDES
CAN'T BE EQUAL IN LENGTH.
WHAT IT SAYS IS WHEN YOU ADD
TWO OF THEM, IT'S BIGGER
THAN THE THIRD.
YOU UNDERSTAND NOW?

Josh says YEAH.

Stewart says OKAY, GREAT.
SO THIS IS A TRIANGLE,
AND IT WORKS OKAY.
NOW, I'M GOING TO TAKE ONE
MORE QUESTION, AND I SEE THAT
NEIL OR SEAN AT --

Neil says HELLO?

Stewart says HI.
NEIL OR SEAN?

Neil says THIS IS NEIL.

Stewart says I WASN'T GOING TO
TAKE A GUESS THIS TIME.
ANYWAY, WHAT WAS YOUR COMMENT?

Neil says OH, I THOUGHT...
I WROTE FALSE BECAUSE YOU CAN
GET AN EQUILATERAL TRIANGLE.

Stewart says BUT NOW DO YOU UNDERSTAND THAT
EXPLANATION I JUST GAVE YOU?

Neil says YEAH.

Stewart says SUPER.
HEY, THAT'S WHERE
WE WANT TO BE.
NOW WE'RE GOING TO TAKE UP THE
EXERCISE, SO I'M GOING TO SKIP
OUT OF THAT.
YOU GUYS HAVE DONE A GREAT JOB
BECAUSE I THINK THAT CHAT IS
REALLY, REALLY IMPORTANT,
OTHERWISE YOU CAN'T DO THIS
EXERCISE WELL.
NOW, WE'LL TAKE SOME TIME AND
WE'LL DO THE FIRST SIX OR
SEVEN EXAMPLES, AND WE'LL MAKE
SURE THAT WE GET THEM ALL
RIGHT, AND THEN I MIGHT ASK
YOU ONE TO THINK ABOUT WITH
A QUESTION LATER ON.
SO LET'S GO FOR IT.
I'M GOING TO GO THROUGH...
THERE IT IS.
IT'S SITTING THERE RIGHT
IN FRONT OF MY EYES.

Stewart shows a chart with a title that reads “Triangle Investigation Results.” Under the title, the chart has two columns with titles that reads “Perimeter” and “Number of Triangles.”

Stewart continues WE'RE GOING TO GO THROUGH
COMPLETING THIS CHART, SO
PERIMETER FOUR, FIVE, SIX,
SEVEN, EIGHT AND NINE, AND
WHAT I WANT YOU TO DO, OF
COURSE, IS TO PHONE IN.
WE'LL START WITH FOUR AND TELL
ME HOW MANY TRIANGLES THERE
ARE, AND THE OTHER THING I
WANT YOU TO DO IS FOR ANY
TRIANGLES THAT EXIST, I WANT
YOU TO GIVE ME THE LENGTHS OF
THE SIDES SO WE CAN JOT THEM
OVER HERE ON THE SIDE AND MAKE
SURE THEY'RE ALL OKAY.
SO WE GOT SOMEBODY TO START.
WE SEE SOME PEOPLE PHONING IN.
THIS IS GOOD.
SO WE'LL BE TALKING TO TOM OR
FLETCHER IN A MOMENT OR TWO.
AND WE'RE GOING TO START
WITH A PERIMETER OF FOUR.
HI, FLETCHER OR TOM?

Tom says THIS IS TOM.

Stewart says OKAY, TOM.
PERIMETER OF FOUR,
HOW MANY TRIANGLES?

Tom says WELL, ACTUALLY, I THINK
THAT'S IMPOSSIBLE.

Stewart says THANK YOU, WHICH
MEANS ZERO, RIGHT?

Tom says YEAH.

Stewart says YOUR ANSWER'S RIGHT.
THANK YOU VERY MUCH.

Tom says THANK YOU.
BYE.

Stewart says LET'S GO ON TO FIVE.
WE'RE GOING ON TO A
PERIMETER OF FIVE.
HOW MANY TRIANGLES CAN WE GET
WITH A PERIMETER OF FIVE?
AND WE'RE GOING TO BE
GOING TO JENNY OR ASHLEY.

Jenny says HELLO?

Stewart says HELLO.
WHO AM I SPEAKING TO?

Jenny says IT'S JENNY.

Stewart says OKAY.
MY GUESSING ABILITY TODAY
IS PRETTY AWFUL, SO I...
OKAY, JENNY, HOW MANY
TRIANGLES WITH FIVE?

Jenny says I ONLY GOT ONE TRIANGLE.

Stewart says CAN YOU TELL ME WHAT THE
LENGTHS OF THE SIDES ARE?

Jenny says ONE SIDE WAS TWO, THE OTHER
SIDE IS TWO AND THEN THE OTHER
SIDE WAS ONE.

Stewart says RIGHT ON.
THANK YOU VERY MUCH.
THAT'S EXACTLY RIGHT.

Jenny says BYE.

Stewart says LET'S GO ON TO TOTAL OF SIX,
AND I THINK WE HAVE TRILLIUM
COMING ON AND CHRISTOPHER.

Christopher says HI.
I GOT ONE FOR SIX.

Stewart says OKAY.
LET'S CHECK IT OUT.
WHAT'S THE ONE THAT YOU GOT?
WHAT ARE THE LENGTHS OF
THE SIDES FOR THAT ONE?

Christopher says ALL TWOS.

Stewart says AND I THINK YOU'RE
RIGHT ON THE BUZZER.
THANK YOU VERY MUCH.
THANKS, CHRIS.
LET'S GO ON TO SEVEN.
AND WE'RE CONNECTING
TO NICOLE OR SARAH.

Nicole says HI.

Stewart says HI.
IS IT NICOLE OR SARAH?

Nicole says NICOLE.

Stewart says OKAY, NICOLE, HOW MANY
TRIANGLES DID WE GET WITH
A PERIMETER OF SEVEN?

Nicole says I GOT TWO.

Stewart says YOU GOT TWO.
GIVE ME WHAT...
WHAT ARE THE LENGTHS OF
THE SIDES FOR THE TWO?

Nicole says TWO, TWO AND THREE.

Stewart says THAT'S A GOOD ONE.

Nicole says AND THREE, THREE AND ONE.

Stewart says I THINK THAT'S RIGHT, UNLESS
ANYBODY OUT THERE DISAGREES.

Nicole says OKAY.

Stewart says I THINK THAT'S A GOOD ANSWER.
THANK YOU VERY MUCH.
LET'S GO ON TO
PERIMETER EIGHT.
YOU GUYS ARE
JUST DOING GREAT.
MIKE OR JOHN.

John says THIS IS JOHN.

Stewart says HI, JOHN.
HOW MANY WITH EIGHT?

John says I GOT TWO.

Stewart says YOU GOT TWO.

John says OR FOR NUMBER EIGHT...
YEAH, I GOT TWO.

Stewart says OKAY.
NOW, WHAT ARE THE
LENGTHS OF THE SIDES?

John says THREE, THREE AND TWO.

Stewart says THREE, THREE AND TWO.

John says AND TWO, TWO AND FOUR.

Stewart says OKAY.
LET'S CHECK OUT
TWO, TWO AND FOUR.

John says OR, SORRY, NO,
THAT WON'T WORK.

Stewart says THAT ONE WON'T...
YEAH, WHY WON'T IT WORK?

John says BECAUSE THE TWO SIDES ARE
SMALLER THAN THE OTHER NUMBER.

Stewart says YEAH, TWO PLUS TWO IS THE
SAME AS, BUT IT'S GOT TO BE
GREATER, SO WHOOP.
SO THAT MEANS ONLY ONE?

John says OKAY.

Stewart says OKAY.
ANYBODY DISAGREE WITH THAT?
YOU GET...
NEXT PERSON I CONNECT TO,
LET'S SEE, WE'RE GOING TO
ASHLEY OR JENNY.

Jenny says HELLO?

Stewart says HELLO.
IS IT ASHLEY OR JENNY?

Jenny says IT'S JENNY AGAIN.

Stewart says OKAY, JENNY.
I'M GOING TO GO BACK
TO EIGHT FOR A MOMENT.
DO YOU AGREE WITH ONE OR TWO?

Jenny says I AGREE WITH ONE.

Stewart says RIGHT ON, OKAY.
LET'S GO TO NINE.
[phone disconnects]
OH, WE'RE GOING TO GO TO
SOMEBODY ELSE TO DO NINE.
WE'RE GOING TO
TAMARA OR ASHTON.

Tamara says TAMARA.

Stewart says HI, TAMARA.
HOW MANY WITH NINE?

Tamara says TWO.

Stewart says TWO.
CAN YOU TELL ME WHAT THE
LENGTHS OF THE SIDES ARE?

Tamara says FOUR AND FOUR AND TWO.

Stewart says FOUR AND FOUR AND...?

Tamara says TWO.

Stewart says I THINK ONE, RIGHT?

Tamara says OH, YEAH.

Stewart says NO PROBLEM.
OKAY, WHAT ELSE?

Tamara says AND THREE, THREE AND THREE.

Stewart says OKAY.
THERE AREN'T ANY OTHERS?

Tamara says NO.

Stewart says OKAY.
I'M GOING TO HAVE A
DOUBLE CHECK ON THAT.
WE'LL TAKE THE NEXT CALL AND
SEE IF THEY GET THE SAME ANSWER.
IT'S GOING TO BE
TOM OR FLETCHER.

Tom says HELLO?

Stewart says HI.
IS IT TOM?

Tom says YEAH, IT'S TOM.

Stewart says OKAY.
PERIMETER OF NINE, DID YOU
GET TWO AS YOUR ANSWER?

Tom says YUP, I DID.

Stewart says OKAY, SO YOU DON'T HAVE ANY
OTHER POSSIBLE SIDE LENGTHS?

Tom says I DON'T HAVE ANY OTHERS.
I GOT TWO, THAT'S ALL.

Stewart says OKAY.
THIS ONE, I ACTUALLY
THINK THERE IS ONE MORE.
I ACTUALLY THINK
THIS IS THREE.
CAN ANYBODY TELL
ME WHAT IT IS?
AND MIKE OR ANDREW ARE GOING
TO JUMP IN HERE TO HELP ME OUT.
HELLO, MIKE OR ANDREW?

Andrew says THIS IS ANDREW.

Stewart says OKAY.
ANDREW, DO YOU THINK YOU
KNOW WHAT THE THIRD ONE IS
FOR A TOTAL OF NINE?

Andrew says FOUR -- NO.

Stewart says YEAH, THAT'S ONE OF THEM.

Andrew says YEAH.

Stewart says WHAT'S ANOTHER WAY...
WHAT ARE WAYS THAT
YOU CAN ADD TO FIVE?
FOUR AND ONE EQUALS FIVE, BUT
WHAT'S ANOTHER WAY OF ADDING
TO FIVE?
FOUR PLUS ONE IS FIVE.
WHAT'S ANOTHER WAY
OF GETTING FIVE?

Andrew says THREE PLUS TWO.

Stewart says THAT ONE WORKS.
OKAY?

Andrew says OKAY.

Stewart says SO THAT'S THE THIRD ONE
THAT WE WERE MISSING BEFORE.
SO I'M GOING TO GO ON TO THE
NEXT SIZE ANYWAY BECAUSE...
OH, HERE ARE OUR --
THERE'S MY ANSWERS,
JUST SO WE COULD CHECK.
ZERO, ONE, ONE, TWO, ONE,
THREE, AND YOU CAN SEE ALL THE
ANSWERS ARE THERE.
SO FAR, SO GOOD.
LET'S DO THE NEXT TWO, 10 AND
11, SEE IF WE CAN HANDLE THEM,
AND THEN WE'RE GOING TO ASK
THE 64,000 DOLLAR QUESTION --
IS THERE A PATTERN?
SO WE'LL GO TO 10 NOW AND I
THINK WE'RE GOING TO NICOLE
OR SARAH.
AND WHO AM I SPEAKING
TO THIS TIME?

Sarah says SARAH.

Stewart says HI, SARAH.
PERIMETER OF 10, HOW MANY?

Sarah says ONE.

Stewart says ONE.
OKAY, WHAT IS IT?

Sarah says FOUR, FOUR AND TWO.

Stewart says OKAY, THAT'S CERTAINLY.
NOW, ARE YOU SURE THAT
THERE AREN'T ANY OTHERS?

Sarah says I DON'T KNOW.

Stewart says TRY A THREE AT THE BEGINNING
AND SEE WHAT HAPPENS HERE.

Sarah says THREE, THREE AND FOUR.

Stewart says THAT WORKS.

Sarah says AND FOUR, FOUR AND TWO.

Stewart says YUP, YOU'VE...
THAT'S ALL THERE ARE.
LIKE, YOU WERE JUST
MISSING THE ONE.

Sarah says TWO, TWO AND SIX.
OH, WAIT, THAT WON'T WORK.

Stewart says THAT WON'T WORK,
RIGHT ON.
YOU'RE THINKING.
THAT'S DOING GOOD.
I THINK WE'VE GOT THEM NOW.
THERE ARE ONLY TWO.
THANK YOU VERY MUCH.
AND WE'RE GOING TO GO
ON TO PERIMETER 11.
CORY OR CHRIS.

Cory says HELLO?

Stewart says HI, CORY?

Cory says HI.

Stewart says I WAS RIGHT THIS TIME, EH?

Cory says UH-HUH.

Stewart says I GOT LUCKY.
[laughing]
OKAY, CORY, HOW MANY
TRIANGLES DO YOU GET WITH 11?

Cory says I GOT THREE.

Stewart says YOU GOT THREE.
LET'S GO THROUGH THE LIST
AND SEE IF WE GOT THEM ALL.
WHAT ARE THE LENGTHS
OF THE SIDES?

Cory says ONE'S FIVE AND
THREE AND THREE.

Stewart says ONE, FIVE AND FIVE, RIGHT?

Cory says MM-HMM.

Stewart says AND THEN WHAT'S THE NEXT ONE?

Cory says SEVEN.
NO, NO THAT WON'T WORK.

Stewart says THAT WON'T WORK, RIGHT.

Cory says THAT'S THE ONLY ONE I'VE GOT
BECAUSE THE REST OF MINE
ARE WRONG.

Stewart says OKAY, AND...

Cory says FOUR, THREE, THREE AND FIVE.

Stewart says THREE, THREE AND
FIVE, YES, THAT WORKS.

Cory says OKAY.

Stewart says SO WE GOT TWO.
THERE ARE MORE.

Cory says AND TWO, FIVE AND FOUR.

Stewart says YEAH, THAT WORKS.
TWO, FOUR, FIVE, I'M GOING TO
JUST WRITE THEM IN THE ORDER.
AND THERE IS
ACTUALLY ONE MORE.
IT MIGHT BE ON YOUR LIST.
GOING TO GIVE YOU A CLUE.
IT HAS A FOUR IN IT.

Cory says FOUR, FOUR AND THREE?

Stewart says BINGO!
RIGHT ON.
SO THAT ONE WORKS
TOO, DOESN'T IT?
SO WE GET UP TO FOUR, RIGHT?

Cory says UH-HUH.

Stewart says NOW, LET'S CHECK
SOME OF OUR ANSWERS.
LET'S SEE.
THERE WERE TWO HERE, FOUR HERE
AND IF WE GO A LITTLE BIT
FARTHER, YOU WOULD HAVE GOTTEN
THREE HERE AND FIVE HERE AND
SO ON AND SO ON.
NOW, I'M GOING TO
ASK THE BIG QUESTION.
IS THERE A PATTERN?
AND WHAT I'M GOING TO DO TO
SORT OF GET THE JUICES ROLLING
A LITTLE BIT, IS I'M GOING TO
SKIP ALL THE WAY THROUGH HERE
AND THERE IS A RECORDING.
THIS IS TOO SMALL TO LOOK
AT SO I'VE JUST WRITTEN THE
NUMBERS HERE.
HERE'S THE NUMBER SEQUENCE,
STARTING HERE AT THE TOP.
NOW, MY QUESTION IS DO YOU
SEE A PATTERN WHEN YOU LOOK
AT THOSE NUMBERS?
PHONE IN AND LET ME KNOW WHAT
YOU THINK, AND I SEE THAT
WE'RE CONNECTING TO
RACHEL OR JACQUELINE.
IS IT RACHEL OR JACQUELINE?

Jackie says THIS IS JACKIE.

Stewart says HI, JACKIE.
DO YOU SEE A PATTERN?
AND IF SO, TELL
ME HOW YOU DO IT.

Jackie says I SAY I DON'T SEE A PATTERN.

Stewart says YOU DON'T SEE A
PATTERN AT ALL, EH?

Jackie says NO.

Stewart says IT'S A KIND OF
CONFUSING SET OF NUMBERS.
NOW, I'LL ASK YOU ONE
OTHER LITTLE QUESTION.
I BASICALLY AGREE
WITH YOU, JACKIE.
THIS IS FOR A
PERIMETER OF FOUR.
THIS ONE'S FOR A
PERIMETER OF FIVE.
THIS IS FOR A
PERIMETER OF SIX.
IS THERE ANY GENERAL
OBSERVATION YOU CAN MAKE ABOUT
THE EVEN AND THE ODD
NUMBERED PERIMETERS?

Jackie says OH, THE ODD NUMBERS
ARE... I DON'T KNOW.

Stewart says LET'S JUST TAKE A LOOK.
IF YOU TAKE THESE IN PAIRS,
THAT ODD-NUMBERED ONE AND THAT
EVEN-NUMBERED ONE, THEN YOU
TAKE A LOOK AT THESE TWO, THEN
YOU LOOK AT THESE TWO, THEN
YOU LOOK AT THESE TWO, THEN
YOU LOOK AT THESE TWO.
WHAT'S SORT OF HAPPENING TO
THE ODD-NUMBERED ONES AS
COMPARED TO THE
EVEN-NUMBERED ONES?

Jackie says THE ODD-NUMBERED
ONES ARE HIGHER.

Stewart says THEY'RE HIGHER,
THAT'S RIGHT.
THAT'S ONE OBSERVATION, AND
THERE'S ONE OTHER THAT'S
KIND OF IN THE SAME...
IT'S THE SAME IDEA AS BEING
HIGHER, BUT IF YOU LOOK AT
THE NUMBERS SEPARATELY, LET'S
TAKE THE EVEN-NUMBERED ONES
AND PUT THEM OUT SEPARATELY,
ZERO, ONE, ONE, TWO,
THE NEXT ONE'S
THREE, THEN FOUR.
NOW, LET'S PUT THE
ODD-NUMBERED ONES BESIDE THEM,
THEIR VALUES.
NOW, WHAT ELSE CAN YOU SEE?
THEY ARE HIGHER IN EVERY CASE,
I AGREE, BUT WHAT ELSE IS
SORT OF HAPPENING?
LOOK AT THE DIFFERENCES.
THERE'S A DIFFERENCE OF ONE,
ONE, TWO, TWO, TWO, THREE.

Jackie says OH, THERE'S A
DIFFERENCE OF TWO.

Stewart says OR MORE.
ACTUALLY, WHAT'S HAPPENING AND
WHAT I WAS TRYING TO GET AT IS
THIS ONE'S GROWING FASTER.

Jackie says OH.

Stewart says YOU SEE, IT'S
GETTING BIGGER FASTER.

Jackie says OH, OKAY.

Stewart says OKAY.
YOU'VE DONE A NICE JOB.
THIS IS NOT A HARD ONE.
THE ODDS ARE GROWING FASTER.
NOW, TO BE QUITE HONEST,
THAT'S ALL I CAN EXPECT, IS...
I'LL TAKE ONE OR TWO MORE
COMMENTS BEFORE I GO ON
TO MY LAST EXERCISE.
BUT THESE ARE THE KINDS OF
OBSERVATIONS YOU CAN MAKE.
HELLO.
IS IT NEIL?

Neil says YES.

Stewart says HI, NEIL.
NOW, WHAT OBSERVATIONS
MIGHT YOU HAVE?

Neil says I THOUGHT IT WAS ROUND TO THE
NEAREST MULTIPLE OF THREE AND
THEN DIVIDE BY THREE, BUT
NOW I THINK IT'S WRONG.

Stewart says YEAH, THE...
THAT MIGHT WORK FOR
A WHILE, MIGHT IT?
HAVE YOU CHECKED IT OUT FOR
SOME NUMBERS AND IT WORKED,
BUT THEN IT QUIT WORKING?

Neil says YEAH.

Stewart says YEAH.
THIS HAPPENS WITH SOME UNUSUAL
SEQUENCES, AND THIS ONE IS
DEFINITELY IN THE
WORLD OF UNUSUAL.

Neil says WELL, I WROTE IT DIFFERENT AT
HOME AND IT WORKED AT HOME, SO.

Stewart says OKAY, THAT'S FINE.
THAT'S PART OF THE TRICK OF
MAKING SURE THAT YOU'VE GOT
THE RIGHT DATA AS WELL, MAKING
SURE THE NUMBERS ARE RIGHT,
RIGHT?

Neil says YEP.

Stewart says YOU'VE DONE A
GOOD JOB, THOUGH.
THANK YOU VERY MUCH.
AND I SEE WE HAVE SOMEBODY
ELSE AT FLAMBOROUGH, EITHER
MIKE OR JOHN, THAT
MIGHT HAVE A COMMENT.

Mike says HELLO?

Stewart says HI, IS IT MIKE OR JOHN?

Mike says MIKE.

Stewart says HI, MIKE.
DID YOU HAVE AN OBSERVATION
THAT YOU CAN ADD TO THE POOL?

Mike says I THOUGHT THE... WHAT?

Stewart says HAVE YOU GOT AN OBSERVATION?

Mike says I THOUGHT THE ODD
ONES WERE THE HIGHEST.

Stewart says DEFINITELY.
THERE'S NO DOUBT THE ODD
NUMBERED PERIMETERS HAVE MORE
TRIANGLES THAN THE EVEN
NUMBERED ONES, AND THE
QUESTION MIGHT BE
SORT OF WONDER WHY.
BUT IT WORKS OUT
THAT WAY FOR SURE.
SO YOU NOTICED
THAT ALREADY, EH?

Mike says MM-HMM.

Stewart says FANTASTIC.
WELL, THANKS, EVERYBODY.
THIS IS NOT AN EASY EXERCISE.
I MEAN, YOU HAVE TO
BE REALLY ACCURATE.
YOU MUST UNDERSTAND A
REALLY IMPORTANT IDEA ABOUT
TRIANGLES, THAT IS WHAT WE
CALL THE TRIANGLE INEQUALITY.
IF YOU ADD THE SUM OF ANY
TWO SIDES, IT WILL ALWAYS BE
GREATER THAN THE THIRD SIDE.
AND BELIEVE YOU ME, THAT IDEA
WILL BE USED BY YOU IN HIGHER
MATHEMATICS IN GRADE 12 AND 13.
WELL, ACTUALLY, YOU'RE NOT
GOING TO HAVE A GRADE 13 YEAR,
BUT IN GRADE 11 AND 12, YOU'LL
ENCOUNTER IT, AND BELIEVE IT
OR NOT, YOU'LL EVEN ENCOUNTER
THIS KIND OF IDEA BEING USED
IN UNIVERSITY MATHEMATICS.
IT'S A CRITICAL IDEA TO
REMEMBER AND IT'S A GOOD TIME
TO START THAT
REMEMBERING PROCESS.
THE OTHER THING IS, IS THIS
PARTICULAR SEQUENCE DOESN'T
HAVE A RULE THAT I KNOW OF.
I ALSO KNOW THAT
MATHEMATICIANS ARE WORKING
REALLY HARD TO SEE IF
THEY CAN FIND THE RULE.
MY POINT HERE IS THAT NOT
EVERYTHING YOU DO WILL ALWAYS
HAVE A PATTERN.
YOU MIGHT HAVE SOME GENERAL
OBSERVATIONS YOU CAN MAKE,
LIKE THEY'RE GROWING, AND
THAT'S IMPORTANT, BUT YOU
MIGHT NOT ALWAYS
HAVE A NEAT PATTERN.
SO THAT'S AN INTERESTING
LITTLE NOTE ON THE SIDE.
YOUR LESSON FOR NEXT WEEK
IS NOT A TERRIBLY LONG ONE.
IT SHOULDN'T TAKE YOU TOO LONG
TO DO, BUT IT WILL REQUIRE A
LITTLE BIT OF THINKING AND
WHAT I WANT TO DO IS KIND OF
WARM YOU UP TO DOING THAT...
THE KIND OF THINKING THAT WE
NEED TO DO FOR NEST WEEK, AND
HERE'S WHAT WE'RE GOING TO DO.
IT'S IN THE CATEGORY OF
PATTERNING AND ALGEBRA.

Stewart puts a piece of paper on screen under a title that reads “patterning and algebra.” Underneath, the instructions read “Using Trial and Error to find a ´Rule.´.”

Stewart continues YOU CAN USE TRIAL AND ERROR,
BUT WHAT WE'RE LOOKING
FOR IS A RULE.
I GUESS THIS IS OMEGA.
IT DOESN'T MATTER WHAT THE
SYMBOL IS, BUT WHAT I'M
GETTING AT HERE IS IF YOU TAKE
THE NUMBER FIVE AND THREE AND
YOU DO SOMETHING
TO IT, YOU GET 16.
IF YOU TAKE THE SAME RULE,
EXACTLY THE SAME RULE, THESE
TWO NUMBERS, PUT THEM
INTO THAT RULE MACHINE,
YOU GET THIS ANSWER.
LIKEWISE WITH THESE TWO
NUMBERS, YOU GET THIS ANSWER.
SO MY QUESTION IS, IF I TAKE
THESE TWO NUMBERS, WHAT'S THE
ANSWER USING THE SAME RULE?
NOW, WHEN YOU DO PHONE IN,
WHICH I DON'T WANT QUITE YET,
I WANT YOU TO PHONE IN AND
TELL ME NOT ONLY WHAT THE
ANSWER IS BUT
WHAT THE RULE IS.
I'M GOING TO GIVE YOU 30
SECONDS TO THINK ABOUT IT
BEFORE I START TAKING PHONE
CALLS, SO I'M GOING TO
BASICALLY GO SILENT FOR 30
SECONDS AND I'LL BE BACK.
SEE YOU THEN.
HELLO.
WE'RE MAKING A CONNECTION
RIGHT NOW TO FLAMBOROUGH
SCHOOL, AND I THINK WE'RE GOING
TO GO TO AMANDA OR ASHLEY.

Amanda says HI, IT'S AMANDA.

Stewart says HI, AMANDA.
WHAT'S THE ANSWER FOR
THE QUESTION MARK HERE,
DO YOU KNOW?

Amanda says YES, 33.

Stewart says OKAY, EXPLAIN YOUR RULE.

Amanda says THE RULE IS YOU TIMES THE
TWO NUMBERS TOGETHER --
YOU MULTIPLY THE TWO NUMBERS
TOGETHER AND THEN ADD ONE.

Stewart says OH, THAT WORKS FOR THIS?
GOOD.
YOU HAVE GOT THE
RULE FOR THIS ONE.
THANK YOU VERY MUCH.

Amanda says THANK YOU –

Stewart turns the page and says OKAY.
WE'RE GOING TO GO THROUGH THE
SAME PROCESS AGAIN FOR THIS ONE.
SEVEN DELTA FOUR, WHATEVER
THAT IS, IS NINE.
FOUR DELTA THREE IS FIVE,
EIGHT DELTA NINE IS 15, TWO
DELTA SIX, I'M GOING TO GO
SILENT AGAIN FOR 30 SECONDS.
WE'LL BE BACK TO TAKE YOUR
ANSWERS IN 30 SECONDS.
OKAY, WE'RE READY.
OKAY, WE'RE CONNECTING
TO MARK OR TRAVIS.
HI.

Travis says IT'S TRAVIS AT FLAMBOROUGH.

Stewart says IT'S TRAVIS AT
FLAMBOROUGH, OKAY.
WHAT'S DELTA MEAN, AND WHAT
IS THIS ANSWER RIGHT HERE?

Travis says ME AND MY PARTNER
FIGURED OUT THAT YOU ADD
THE TWO NUMBERS TOGETHER.

Stewart says YEAH.

Travis says AND SUBTRACT TWO.

Stewart says SO THIS ANSWER WOULD BE SIX?

Travis says YEAH.

Stewart says OKAY, LET'S CHECK IT OUT.
YOU'RE BATTING 100 PERCENT.
WHAT DO YOU THINK?

Travis says YEAH.

Stewart says RIGHT ON.
NOW, THE LAST ONE
I GIVE EVERYBODY...
YOU'VE DONE A GREAT JOB.
THANK YOU VERY MUCH.
OKAY.
THE LAST ONE I GIVE YOU IS
MAYBE A LITTLE BIT TRICKIER,
BUT YOU CERTAINLY HAVE THE
IDEA OF ESTABLISHING A RULE
AND THEN IT'S GOT TO WORK
FOR EVERY ONE OF THEM.
SO HERE WE GO.
[paper shuffling]

Stewart turns the page and continues I'VE GIVEN YOU FOUR
POSSIBILITIES THIS TIME,
AND I WANT YOU TO SEE IF YOU
CAN FIND THE RULE ON THIS ONE.
AND I'M GOING TO GIVE YOU 45
SECONDS TO THINK ABOUT THIS
ONE BEFORE YOU PHONE IN.
IT'S JUST A LITTLE BIT
TRICKIER THAN THE OTHER TWO.
AND WE'RE CONNECTING.
IS IT MIKE OR JOHN?

John says THIS IS JOHN.

Stewart says HI, JOHN, AND WHAT'S THE
ANSWER TO THE LAST ONE?

John says I'M NOT SURE ABOUT THIS.
I JUST GOT...
I HAD A SPLIT SECOND DECISION.

Stewart says WHAT'S YOUR SPLIT
SECOND DECISION?

John says AND IF YOU SUBTRACT
EIGHT FROM...
OR IF YOU SUBTRACT
SIX FROM EIGHT...

Stewart says YEAH.

John says IT GIVES YOU TWO AND
IT'S A MULTIPLE OF 12.

Stewart says OKAY.

John says AND IF YOU, LIKE,
SUBTRACT ONE FROM SEVEN,
THAT'S A MULTIPLE OF SIX.

Stewart says BOY, I LIKE IT.
LET'S CHECK IT OUT AND
SEE IF YOU'RE RIGHT.
SO EIGHT MINUS SIX,
WHICH IS TWO, TIMES SIX.
OH, I DON'T THINK YOU SAID
THAT TO ME, BUT I THINK YOU
SORT OF SAID IT.
WE GOT 12, RIGHT?

John says YEAH.

Stewart says AND THEN SEVEN MINUS ONE
TIMES ONE IS EQUAL TO?

John says SIX.

Stewart says OKAY.
NINE MINUS FOUR
TIMES FOUR IS?

John says TWENTY.

Stewart says OKAY, SO WHAT'S THE
ANSWER DOWN HERE?

John says LET'S SEE... NINE.

Stewart says RIGHT ON.
NICE PIECE OF WORK, JOHN.
THANK YOU VERY MUCH.
NOW, THAT BASICALLY COVERS THE
THREE EXAMPLES THAT I WANTED TO.
THE EXERCISE NEXT WEEK
INVOLVES THIS PATTERNING
ALGEBRA KIND OF THING.
I'VE DRAWN IT IN KIND OF AN
UNUSUAL WAY SO YOU'LL HAVE TO
THINK ABOUT WHAT IT MEANS, AND
I'LL BE VERY INTERESTED TO SEE
WHAT YOUR RESPONSES
ARE NEXT WEEK.
NOW, BEFORE I TAKE SOME
QUESTIONS AT THE END, I'VE GOT
ONE MORE PROBLEM THAT I'M
GOING TO FAX OUT TO EACH OF
THE SCHOOLS THAT I WOULD LIKE
YOU TO THINK ABOUT FOR THE
WEEK, AND YOU CAN FAX ME A
RESPONSE BEFORE NEXT MONDAY
AND I'D BE WILLING
TO PUT IT ON AIR.
AND HERE'S THE PROBLEM:
I'M GOING TO FAX OUT BASICALLY
THIS PICTURE WITH THESE NUMBERS.

Stewart puts a diagram of squares on screen with a title that reads “Perfect Square.” Underneath the title, there is a tessellation shape with numbered pieces one through five.

Stewart explains the chart and says I'LL PROBABLY EVEN FAX THIS
ONE OUT JUST EXACTLY AS YOU
SEE IT, AND WHAT YOU
NEED TO DO IS THIS:
THERE ARE FIVE SECTIONS HERE,
ONE, TWO, THREE, FOUR, FIVE,
AND YOU CUT OUT
THESE FIVE PIECES.
SO YOU GET KIND OF A SQUIGGLE
PIECE HERE, A SQUARE, A HOUSE
PIECE, A SMALL TRIANGLE
AND A BIGGER TRIANGLE.
THESE TRIANGLES IN THE CORNERS
YOU CAN THROW OUT, FORGET THEM.
AND WHAT YOU'RE TRYING TO DO
IS TAKE THESE FIVE PIECES AND
FIT THEM BACK TOGETHER
TO GET A PERFECT SQUARE.
TO GET A PERFECT SQUARE.
STATEMENT OF THE PROBLEM'S
PRETTY STRAIGHTFORWARD,
AND IT DOES WORK.
SO I'LL BE FAXING A COPY OF
THAT OUT SO THAT YOU CAN HAND
THEM OUT TO THE STUDENTS, AND
THE STUDENTS, YOU CAN CUT THEM
OUT AND SEE IF YOU
CAN FIGURE THIS OUT.
IF YOU GET A SOLUTION, YOU CAN
FAX IT BACK TO ME, AND WE DO
HAVE A FAX NUMBER RIGHT THERE.

A blue screen appears with a clip art silhouette of a man with a light bulb hovering over his head. A caption reads “FAX Number 1-888-522-7141.”

Stewart continues THIS PARTICULAR FAX NUMBER IS
TOLL FREE, SO YOU CAN FAX YOUR
RESPONSES TO 1-888-522-7141.
AND WE'LL PUT THAT FAX NUMBER
RIGHT AT THE END OF THE
PROGRAM SO THAT IF YOU DIDN'T
GET A CHANCE TO COPY IT DOWN,
YOU CAN.
NOW, I'M MORE THAN
HAPPY TO TAKE...
PROBABLY A LITTLE BIT MORE
EFFICIENT THAN I WAS THIS
MORNING, SO I HAVE A MOMENT OR
TWO TO TAKE SOME QUESTIONS.
DO YOU HAVE ANY QUESTIONS THAT
I CAN ANSWER BEFORE THE END
OF THE SESSION?
OKAY, WE'VE GOT A CALL.
IT'S COMING FROM EITHER MARK
OR TRAVIS, BY THE LOOKS OF IT.
IT'S GOOD TO SEE
FLAMBOROUGH BACK.
I THINK YOU HAD SOME
DIFFICULTY WITH THE SNOWSTORM,
IF I'M NOT MISTAKEN.
AND A MOMENT OR TWO.
THERE WE ARE.
OKAY.
WE HAVE ONE MORE PERSON WE'RE
GOING TO TRY TO CONNECT TO.
THAT LAST ONE DIDN'T
QUITE WORK OUT.
ALWAYS HAVE CHALLENGES WITH
THE SATELLITES, I THINK.
SO WE'RE GOING TO SPEAK
TO EITHER PHIL OR JOSH.
HELLO, PHIL OR JOSH?

Josh says JOSH.

Stewart says HI, JOSH.
HAVE YOU GOT A QUESTION?

Josh says YEAH.
FOR THE CHRISTMAS PRESENT ONE
THAT YOU TOLD US ABOUT RIGHT
BEFORE CHRISTMAS?

Stewart says OH, RIGHT, AND THAT'S TO DO
WITH THE CUTTING IT INTO CUBES?

Josh says YEAH.

Stewart says OKAY, YOU DIDN'T GET A CHANCE
TO SEE THE ANSWER TO THAT?

Josh says NO.

Stewart says I DON'T HAVE THE SLATE WITH
ME, BUT I CAN DEFINITELY TELL
YOU THE ANSWER.

Josh says I KNOW WHAT THE ANSWER IS.

Stewart says TELL ME THE ANSWER.

Josh says YOU CUT IT THREE
TIMES ON THE TOP.

Stewart says YES.

Josh says THREE TIMES ALONG THE SIDE.

Stewart says YEAH.

Josh says AND THREE TIMES
ALONG THE OTHER SIDE.

Stewart says ACTUALLY, I THINK YOU'RE
BASICALLY RIGHT, BUT I THINK
IT'S TWICE, TWICE
AND TWICE, ISN'T IT?
I CAN DO A QUICK DRAWING HERE
WITHOUT GETTING TOO FANCY.
WE HAD A BIG CUBE LIKE THIS
AND WE WERE TRYING TO MAKE 27,
AND IF I'M LOOKING DOWN
ANYWHERE, I KNOW THAT I HAVE
TO DO...
YOU HAVE TO CUT
TWICE LIKE THAT.

Josh says MM-HMM.

Stewart says AND TWICE LIKE THAT AND THEN
TWICE MORE GOING ACROSS,
YOU'LL GET THE 27, RIGHT?

Josh says YEAH.

Stewart says NOW, THE QUESTION WAS CAN
YOU DO IT IN LESS THAN SIX?
DO YOU THINK SO?

Josh says I DON'T THINK SO.

Stewart says YOU CANNOT, AND THAT'S THE
CORRECT ANSWER, AND THE REASON
FOR THAT IS THE CUBE THAT'S
RIGHT IN THE CENTRE HAS SIX
FACES ON IT, AND TO MAKE
SOMETHING WITH SIX FACES,
YOU NEED AT LEAST SIX CUTS.
OKAY?

Josh says OKAY.

Stewart says OKAY, THANK YOU VERY MUCH FOR
BRINGING THAT ONE BACK UP.
I'M GLAD YOU ASKED.
OKAY.
I THINK THAT WE'VE COME TO THE
END OF THE SHOW, AND WE'LL SEE
YOU THE SAME TIME
AND THE SAME PLACE.
LOOK FORWARD TO
SEEING YOUR RESPONSES.
BYE-BYE.
COULD I ASK USBORNE, IF YOU'RE
ON AIR RIGHT NOW, TO PHONE THE
HELP DESK, PLEASE.

A blue screen appears with a clip art silhouette of a man with a light bulb hovering over his head. A caption reads “FAX Number 1-888-522-7141.”

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