Transcript: Student Session 22 | Aug 24, 1998

The opening slate pops up with a countdown timer from 5 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.

Lorraine and Stewart sit one next to the other in the studio. Lorraine is in her thirties, with short brown hair tied-up and bangs. She’s wearing a black jacket over a white shirt. He’s in his fifties, with a dark beard and wavy brown hair. He’s wearing glasses, a white T-shirt with a colourful geometrical drawing and patterned suspenders.

He says WELCOME TO SESSION NUMBER 22
OF THE VIRTUAL CLASSROOM,
THE MATH MYSTERY.
WE'RE GETTING REALLY
CLOSE TO THE END.
WHAT DO YOU SAY, LORRAINE?

Lorraine says WELL, SESSION 22,
IT'S HARD TO BELIEVE.
WE'RE ALREADY THERE.

He says OH YEAH, AND I THINK TODAY
IT'S GOING TO BE VERY
INTERESTING BECAUSE WHAT WE
ARE GOING TO TRY TO DO IS GET
YOU TO DO THE MATHEMATICS IN
THE LITTLE EXERCISE WITH US,
TOGETHER, AND WE'RE JUST
GOING TO SORT OF STRETCH IT
OUT AND GIVE YOU
ENOUGH TIME TO DO IT.
SO I HOPE YOU -- WE'VE GOT
AN AGENDA HERE, AND I THINK
WE'LL GO TO THAT RIGHT AWAY.

She says OKAY, AND FOR
YOUR AGENDA TODAY:

The slate changes to “Agenda. 1. Sphinx Problem. 2. Pythagorean Theorem. 3. Activity.”

He says NOW, IN TERMS OF THE SPHINX
PROBLEM, THE ONLY THING I WANT
TO CLARIFY, I THINK I
MISINTERPRETED A PHONE CALL
YESTERDAY AFTERNOON WHEN
SOMEBODY SAID IT WAS
IMPOSSIBLE TO DO THREE SPHINX.
AND I'M GOING TO GET A PEN
HERE AND JUST REMIND YOU WHAT
I MEANT BY A THREE SPHINX.
THAT'S WHERE YOU HAD THREE
BASICALLY ALONG THE BOTTOM.
AND I SAID IT WAS POSSIBLE
TO DO IT WITH ONLY FOUR.
I DIDN'T QUITE MEAN THAT.
WHAT I'M SAYING IS THAT THE
THREE SPHINX PROBLEM IS
POSSIBLE, BUT YOU ACTUALLY
NEED 12 SPHINXES TO DO IT.
THAT'S THE CLARIFICATION.
I'M GOING TO LEAVE THAT
PROBLEM FOR YOU TO DEAL WITH
BETWEEN NOW AND THURSDAY.
AND IF WE DO HAVE ANY
RESPONSES BY FAX, THEN IN FACT
WE WILL SHOW YOUR DIAGRAMS,
SEE THE CONSTRUCTION OF A
THREE SPHINX.
OKAY.
SO THAT'S ABOUT IT.
IF THERE'S ANY QUESTION,
DON'T HESITATE TO ASK US.
BUT THAT'S THE CLARIFICATION
I WANTED TO MAKE.
OKAY, WE'RE GOING FROM THE
SPHINX PROBLEM NOW TO THE
PYTHAGOREAN THEOREM.
AND WHAT I WOULD REALLY LIKE
TO DO IS INVITE A STUDENT TO
PHONE IN AND LET US KNOW WHAT
THE PYTHAGOREAN THEOREM IS
AND MAKE A STATEMENT OF IT.
I WILL MAYBE MAKE SOME NOTES,
AND THEN WE WILL, PERHAPS,
HAVE A SLATE OR SOMETHING
LIKE THAT TO MAKE SURE
THE WORDING IS QUITE RIGHT.
SO HAVE WE GOT
ANY PHONE CALLS?
ANYBODY CALLING IN YET?

She says YES, WE HAVE A FEW HERE.

He says GREAT.

She says AND WE'RE GOING TO
CONNECT WITH JACK MINER.

He says OH, GOOD.

She says MEGAN FROM JACK MINER.

He says HELLO, MEGAN,
ARE YOU THERE?

Megan says YEAH.
HELLO?
GIVE IT!
PLEASE!

He says HELLO?

Megan says HELLO.

He says HI, MEGAN.

Megan says HI.

He says CAN YOU TELL ME WHAT THE
PYTHAGOREAN THEOREM IS
ALL ABOUT?

Megan says I DON'T KNOW.
DOES ANYONE HERE KNOW?

He says PARDON?

Megan says NO, I'M JUST ASKING.
NO ONE HERE KNOWS.
SORRY.

Lorraine says THAT'S OKAY.
THANKS, MEGAN.

Megan says OKEY DOKE, BYE.

Lorraine LET'S TRY SOMEONE
FROM THE PINES.

He says OKAY, GREAT.
THE PYTHAGOREAN THEOREM IS
MAYBE THE MOST IMPORTANT
THEOREM YOU EVER LEARN ABOUT.
SO THIS IS ONE I'D
REALLY LIKE TO REINFORCE.
HAVE WE GOT A CONNECTION?

Lorraine says YES, SARAH FROM THE PINES.
HELLO?

Sarah says HI.
IT'S WHEN YOU HAVE A
TRIANGLE, AND YOU'RE GIVEN THE
LENGTH OF TWO SIDES AND YOU
TRY TO FIND OUT THE THIRD ONE
WITH WHAT YOU'VE BEEN GIVEN.

He says THAT'S RIGHT.
SO THE LENGTH OF
TWO SIDES OF A WHAT?

Sarah says TRIANGLE?

He asks ANY SPECIAL KIND OF TRIANGLE?

Sarah says A RIGHT ANGLE.

He says A RIGHT TRIANGLE.
OKAY, SO YOU SAID IN A RIGHT
TRIANGLE, AND I THINK THAT'S A
REALLY IMPORTANT POINT, THAT
IF YOU ARE GIVEN TWO SIDES,
SAY YOU KNOW THIS ONE HERE
AND THIS ONE THERE, YOU CAN
FIGURE OUT THIS ONE HERE.
THAT KIND OF THING?

Stewart draws a right triangle.

Sarah says YEAH.

He says CAN YOU SEE MY DIAGRAM?

Sarah says YEAH.

He says OKAY, WELL, LET'S
GO ONE STEP FURTHER.
HOW?

Stewart appears on a small window at the right bottom of the screen.

Sarah says WE LABEL THEM SO THAT THE
ANGLE ON THE LEFT WOULD BE A.

He says THIS ONE HERE?

Sarah says SURE.
THEN WE CALL THE TWO SIDES
IN THE RIGHT ANGLE B AND X
OR WHATEVER.

He says WHAT I'M GOING TO DO
IS I'LL USE A, B, C.
SO I'LL CALL THIS SIDE
OVER HERE LITTLE C.
SEE WHAT I'M DOING?
THIS ONE OVER HERE LITTLE A,
AND THIS ONE OVER HERE LITTLE B.
OKAY, GREAT.

Sarah says TO FIGURE OUT A, YOU'D PUT B
PLUS C EQUALS THE LENGTH OF A.

He says IT'S NOT JUST STRICTLY B PLUS
C EQUALS THE LENGTH OF A.
YOU'RE CLOSE.
YOU'VE GOT THE RIGHT IDEA.

Sarah says B SQUARED PLUS --

He says AH!
SO...

He writes reads “A square equals B square plus C square.”

He continues WE'LL GO TO A POWER POINT
AND THIS IS THE WAY
IT'S STATED FORMALLY.
IF YOU WANT TO MAKE A NOTE.
IF YOU DIDN'T KNOW THIS
BEFORE, I THINK IT'S IMPORTANT
FOR YOU TO WRITE THIS DOWN.
GO AHEAD.
WHAT'S OUR POWER POINT?

The slate changes to “The Pythagorean Theorem. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the square on the other two sides.”

He continues NOW, BELIEVE IT OR NOT, THAT'S
EXACTLY WHAT YOU JUST SAID.
AND I WANT TO GO BACK TO THE
GRAPHICS CAMERA AND ILLUSTRATE
THAT ONE A LITTLE
BIT MORE CLEARLY.
WHAT IT SAYS IS IF I WERE
TO DRAW A SQUARE ON THE
HYPOTENUSE -- NOW THE
HYPOTENUSE IS THE LONGEST SIDE
OF A RIGHT-ANGLE TRIANGLE.
IT'S THE SIDE OPPOSITE
THE RIGHT ANGLE.
SO THIS SIDE HERE, WHICH
WILL BE THE LONGEST SIDE.
SO IF I HAD A SQUARE, AND
FOUND THE AREA OF THAT, AND
REMEMBER WHAT WE CALLED THAT
WAS LITTLE A, TIMES LITTLE A,
AND THE AREA OF THIS IS
SQUARED, AND I WERE TO DRAW A
SQUARE ON THE OTHER TWO
SIDES, SOMETHING LIKE THIS.
AND THIS ONE WAS LITTLE B,
SO THAT'S LITTLE B, AND THAT
AREA OF THAT IS B SQUARED.
AND THIS ONE WAS
LITTLE C, SO LITTLE C.
AND THE AREA OF THAT
IS LITTLE C SQUARED.

He draws the figures as he explains them.

He continues THIS BIG SQUARE HAS THE SAME
AREA AS THE COMBINED AREAS OF
THESE TWO.
AND THAT THEOREM HAS
BEEN REALLY, REALLY
IMPORTANT HISTORICALLY.
IT'S A THEOREM, BELIEVE IT
OR NOT, YOU WILL USE OVER
AND OVER AGAIN.
SOMETIMES YOU WON'T EVEN KNOW
YOU ARE USING IT BECAUSE IT
WILL BE IN SOMETHING CALL
THE DISTANCE FORMULA, OR
SOMETHING LIKE THAT, BUT
THE REALITY IS IT'S THE
PYTHAGOREAN THEOREM.
SO I WANTED TO REALLY
MAKE THAT CLEAR.
BECAUSE IN TERMS OF ACTUALLY
DOING THE QUESTIONS FROM
EXERCISE NUMBER ONE, YOU
ACTUALLY HAVE TO USE THE
PYTHAGOREAN THEOREM.
SO I WANT TO LEAVE
THAT RIGHT NOW.
NOW THAT YOU'VE SEEN HOW TO
USE IT, I'M GOING TO ASK YOU
AT LEAST TWICE TO USE IT IN
SOLVING SOME OF THE PROBLEMS
IN EXERCISE NUMBER ONE.
WHAT I WOULD LIKE TO DO RIGHT
NOW IS GO TO QUESTION NUMBER
ONE, AND I'M GOING TO PUT IT
UNDER THE GRAPHICS AND READ IT
TO YOU.
SO WE'LL ZOOM IN A LITTLE BIT.
THAT'S IT.

He shows a piece of paper and reads
THE RATIO OF THE ALTITUDE OF
THE GREAT PYRAMID OF GIZA TO
THE LENGTH OF ONE SIDE OF THE
SQUARE BASE IS APPROXIMATELY
5 TO 8.
He continues NOTICE THAT THOSE NUMBERS
ARE SUBSEQUENT TERMS OF THE
FIBONACCI SEQUENCE?
He reads THE HEIGHT OF THIS PYRAMID
IS RECORDED AS 5,813 INCHES.
He continues WE WORK IN METRIC SO I
CONVERTED IT TO 147.65 METRES.
THE INTERESTING THING ABOUT
5,813, NOTICE THAT 5, 8, AND
13 ARE ALSO FIBONACCI NUMBERS.
IT DOESN'T QUITE WORK SO
NICELY IN THE METRIC SYSTEM.
WHAT I ASKED IS IF YOU KNOW
THE HEIGHT, AND YOU KNOW THE
RATIO, WHAT IS THE LENGTH
OF THE BASE OF THE PYRAMID?
AND I WILL INVITE STUDENTS TO
CALL IN NOW AND MAYBE GIVE US
AN ANSWER.
WE WON'T DO THAT ONE YET.
WHAT I WOULD LIKE TO KNOW
IS IF THE HEIGHT IS 147.65
METRES, AND THE RATIO OF THE
HEIGHT TO THE LENGTH OF ONE
SIDE OF THE SQUARE BASE IS 5
TO 8, WHAT IS, IN FACT, A GOOD
APPROXIMATION FOR THE
LENGTH OF THE BASE.
NO CALLS?

Lorraine says NO, NOT YET.

He continues WELL, I'LL USE THIS.
I MADE IT REALLY BIG, SO
MAYBE WE CAN ZOOM BACK
A LITTLE WEE BIT.
IN OTHER WORDS, WHAT
WE'RE SAYING IS:

He grabs a blue piece of paper that reads “8 to 5 equals base to height. Height is 148 metres. 8 to 5 equals base as compared to 148.”

He continues SO WHAT I WANT TO KNOW RIGHT
NOW IS THIS CHUNK RIGHT HERE.
AS YET NOBODY...

He draws an arrow under “base as compared to 148.”

He continues I'LL GIVE YOU A COUPLE OF
MOMENTS TO MAYBE WORK IT OUT
WITH YOUR CALCULATORS, BUT
WHAT NUMBER WOULD FIT IN HERE?
LOOKS LIKE WE HAVE A CALL.
THAT'S GREAT.

Lorraine says YES, WE HAVE
GABE FROM COLLEGE.

He says GREAT.

Gabe says HELLO?

Lorraine says HELLO.
IS THIS GABE?

Gabe says YEAH.

Lorraine says HI.

He says GREAT.
HAVE YOU DONE A CALCULATION
TO FIGURE OUT THE LENGTH
OF THE BASE?

Gabe says YEAH, I GOT 236.8 METRES.

He says EXCELLENT.
WELL DONE.
THANK YOU, GABE.
AND WHAT I'M GOING TO DO, I
THINK YOU MIGHT HAVE DONE
SOMETHING LIKE THIS.

Stewart grabs another blue piece of paper. It reads “148 divided by 5 times 8 equals B.”

He continues IS THAT MORE OR
LESS WHAT YOU DID?

Gabe says YEAH.

He says FANTASTIC.
YOU SHOULD ALL BE ABLE TO
HANDLE RATIOS LIKE THIS.
I PUT DOWN 237.
IS THAT OKAY WITH YOU, GABE?

Gabe says YEAH.

He says EXCELLENT.
SO WE'VE TAKEN CARE OF THE
FIRST PROBLEM, AND THAT'S HOW
YOU'D DO THE SOLUTION,
AND IT'S ALL DONE.
SO NOW WE CAN GO TO
THE SECOND PROBLEM.

Lorraine says THANKS, GABE.

He says THE SECOND PROBLEM ASKS YOU
TO CONSTRUCT THE GREAT PYRAMID
OF GIZA TO SCALE.
AND THIS IS THE NET.
AND BASICALLY, NOTICE I HAVE
A RIGHT-ANGLE TRIANGLE OVER
HERE ON THE CORNER, WITH THE
ALTITUDE, ONE-HALF THE LENGTH
OF THE BASE.
THE IMPORTANT THING HERE IS
WE NEED TO DISCOVER WHAT THE
SLANT HEIGHT IS SO WE
CAN ACTUALLY MAKE THIS.
NOW, ONE OF THE THINGS I'M
GOING TO COME BACK TO RIGHT
NOW, IF YOU TAKE A LOOK
UNDERNEATH HERE, IS THAT THE
SCALE IS 1 CENTIMETRE
EQUALS TEN METRES.
SO WHAT WE KNOW IS THAT WITH
YOUR PIECE OF CARDBOARD,
THE LENGTH OF THE BASE
IS 23.7 CENTIMETRES.
I'M GOING TO SUGGEST YOU MAKE
IT A NICE EVEN 24 CENTIMETRES
TO MAKE LIFE A LITTLE
WEE BIT EASIER.
NOW, THAT'S BASED ON THE
FACT WE TOOK THIS FIGURE AND
DIVIDED BY TEN, SO WE COULD
GET THE EQUIVALENT IN
CENTIMETRES FOR THE SCALE.
SO I'M SAYING THAT'S KIND
OF EQUAL TO 240 METRES.
SO WHAT WE HAVE RIGHT NOW IS
THAT THIS IS 24 CENTIMETRES,
AND THIS IS 24 CENTIMETRES
GOING UP HERE AS WELL.
OKAY?
SO YOU MAKE A SQUARE.
NOW, WHAT WE NEED TO KNOW IS
THIS LENGTH HERE SO WE GET
TRIANGLES OF THE RIGHT LENGTH.
REMEMBER, THIS IS AS ISOSCELES
TRIANGLE, AND THIS LENGTH HAS
GOT TO BE THE SAME AS THAT.
SO THIS VERTEX IS
RIGHT ABOVE THE MIDDLE.
WHAT WE DO KNOW
IS TWO THINGS.
WE KNOW THAT THE ALTITUDE
IS 148 METRES IN REALITY.
BUT ACCORDING TO OUR SCALE,
DIVIDE BY TEN, IT'S 14.8.
SO WE CAN CALL THAT
15 CENTIMETRES.
AND HALF THE LENGTH OF
BASE IS 12 CENTIMETRES.
AH, HOW AND WHAT DO WE USE TO
FIND OUT THAT LENGTH NOW THAT
WE KNOW THAT THIS IS 15
CENTIMETRES, AND THIS IS
12 CENTIMETRES?
WHAT THEOREM?

Lorraine says WE HAVE VICKI
FROM JACK MINER.
HELLO.
HELLO, VICKI?

He says HI, VICKI?

Kyle says HI.

Lorraine says OH, I DON'T THINK IT'S VICKI.

Kyle says HELLO?

Lorraine says HI, AND YOU ARE...?

Kyle says KYLE.

Stewart says HI, KYLE.
WHAT THEOREM DO WE USE TO
FIGURE OUT WHAT THAT MISSING
SIDE IS?

Kyle says SORRY, I CAN'T HEAR YOU.
WHAT DID YOU SAY?

Stewart says I SAID, WE KNOW THAT IN
THE RIGHT-ANGLE TRIANGLE
THAT THIS IS 15 CENTIMETRES,
AND THAT'S 12.
I WANT TO FIND OUT THE LENGTH
OF THIS OPPOSITE SIDE.
WHAT THEOREM DO I USE?

Kyle says I CAN'T REMEMBER
WHAT YOU HAVE TO DO.
IS IT SIX?

Stewart says OKAY, IT'S THE
PYTHAGOREAN THEOREM.
THAT WAS MY FIRST QUESTION.
WHAT THEOREM.
SO THE PYTHAGOREAN THEOREM.
IS THAT OKAY?

Kyle says I DON'T KNOW WHAT
YOU HAVE TO DO.

Stewart says OKAY.
HAVE WE GOT ANOTHER
CALL, PERHAPS?

Lorraine says YES.
LET'S TRY BRENDA AT THE PINES.
HELLO, BRENDA.

Brenda says HI.

Lorraine says HI.
CAN YOU HELP US OUT THERE?

Brenda says YEAH.

Lorraine says OKAY.

Brenda says YOU HAVE TO USE
PYTHAGOREAN THEOREM.

Lorraine says OKAY, EXCELLENT.

Stewart says RIGHT.
SO HOW WOULD WE USE THE
PYTHAGOREAN THEOREM
TO SOLVE THIS?

Brenda says WELL, THE ONE THAT'S 15
CENTIMETRES, WE COULD SAY
THAT'S A.

Stewart says YEAH.

Brenda says AND 12 IS B.

Stewart says YEAH.

Brenda says C WOULD EQUAL A SQUARED PLUS
B SQUARED, WHICH IS EQUAL TO
12 SQUARED PLUS 15 SQUARED.

Stewart says OKAY.
15 SQUARED IS 225,
I'LL HELP YOU ON THAT.
PLUS 144.
SO WHAT DOES THAT EQUAL?

Brenda says 369.

Stewart says RIGHT.
NOW, WHAT DO I DO WITH THIS?
NOW THAT I HAVE 369, IS THAT
THE LENGTH OF THE OTHER SIDE?

Brenda says YOU HAVE TO DIVIDE IT BY 10.

Stewart says NOT QUITE.
NOW, REMEMBER THE PYTHAGOREAN
THEOREM SAID A SQUARED PLUS
B SQUARED EQUALS C SQUARED.

Brenda says YOU HAVE TO FIND
THE SQUARE ROOT.

Stewart says SO THIS IS EQUAL
TO C SQUARED.

Brenda says YOU HAVE TO FIND
THE SQUARE ROOT.

Stewart says EXCELLENT.
THAT'S WHAT I WAS AFTER.
HAVE YOU GOT A
CALCULATOR HANDY?
CAN YOU FIND ME
A SQUARE ROOT?

Brenda says YEAH, JUST A MINUTE.

Stewart says EXCELLENT.
KIDS ARE WORKING WELL TODAY.

Brenda says 19.2.

Stewart says EXCELLENT.
AND THAT IS A REALLY IMPORTANT
MEASUREMENT IN TERMS OF
ACTUALLY MAKING
THE SCALE MODEL.
SO WHAT WE'RE GOING TO DO AT
THIS POINT, HOPEFULLY I CAN
PUT THIS BIG PIECE OF
CARDBOARD ON HERE BECAUSE WE
STARTED IT, AND THIS IS WHAT
WE ARE GOING TO ASK YOU TO DO
WHEN WE CUT AWAY FOR
ABOUT 12 MINUTES OR SO.
LET'S SEE IF WE CAN
GET ALL THIS ON HERE.
WE'RE GOING TO LOOK AT
THE GRAPHICS CAMERA.

Lorraine says OKAY, AND I'LL OPEN THAT OUT.

A zoom-out view homes out of a drawing. It features a square with four triangles attached to it. One of them is made up of two small triangles.

Stewart says OKAY.
SO THIS IS A NET.
ONE OF THE THINGS YOU'RE GOING
TO NOTICE IS THIS ONE OVER
HERE IS IN THE WRONG PLACE.
ONE OF THE REASONS IT'S IN THE
WRONG PLACE IS THIS CARDBOARD
ISN'T QUITE BIG ENOUGH
FOR ME TO DO IT.
SO WHAT I'M GOING TO DO
ACTUALLY IS I'M GOING TO CUT
THIS TRIANGLE OUT SEPARATELY,
AND I'M GOING TO USE SOME
MASKING TAPE TO TAPE
IT GOING THAT WAY.

He points to the top of the square.

He continues THEN THE REST OF THIS NET I
CAN CUT OUT, AND WE CAN FOLD
IT IN AND THEN TAPE THE EDGES.
BUT LET ME SHOW YOU, FIRST OF
ALL, WE'LL ZOOM IN A LITTLE
BIT UP IN THIS CORNER.

The camera focuses on the triangle made up of two smaller triangles.

He continues JUST SO YOU KNOW HOW TO
CONSTRUCT THE TRIANGLES, FIRST
OF ALL THE SQUARE IS 24
CENTIMETRES SQUARED, AND YOU
HAVE TO MAKE SURE YOU HAVE
NICE SQUARE CORNERS ALL THE
WAY AROUND.
AND IF YOU USE A PROTRACTOR
THAT MIGHT BE GOOD.
THERE ARE SEVERAL METHODS
FOR MAKING SURE THAT
THEY ARE SQUARE.
FIND THE MIDPOINT, WHICH WOULD
BE 12 CENTIMETRES THIS WAY,
AND 12 CENTIMETRES THERE.
AND WHAT YOU WANT TO DO AGAIN
IS TO DRAW A LINE WHICH IS
PERPENDICULAR TO THIS LINE
HERE, SO JUST A LINE LIKE THIS.
THE KEY THING HERE IS THAT
THIS IS 19.2 CENTIMETRES LONG.
SO YOU MEASURE FROM HERE
TO HERE, 19.2 CENTIMETRES.
ONCE YOU'VE GOT THAT, THEN YOU
JUST CONNECT THOSE, AND YOU
HAVE YOUR TRIANGLE.
IF YOU DO THAT ON ALL FOUR
SIDES, IN ESSENCE, AND FOLD IT
IN AND SO ON, YOU WILL
HAVE A SCALE MODEL OF
THE PYRAMID OF GIZA.
DO WE HAVE ANY
QUESTIONS OR ANYTHING?

Lorraine says NO.

He continues NO?
OKAY, SO I THINK AS LONG AS YOU
UNDERSTAND WHAT THE TASK IS,
GET SOME CARDBOARD, AND GROUPS
OF TWO OR THREE, DEPENDING
UPON HOW YOUR TEACHER HAS
ARRANGED IT TO BASICALLY BEGIN
TO PRODUCE A PYRAMID OF GIZA,
USING THE NET, AND ALL THE
CORRECT MEASUREMENTS, FOLD
IT IN AND TAPE THE EDGES.
AND WE'LL COME BACK IN
ABOUT 12 MINUTES OR SO.
ANYTHING TO ADD, LORRAINE?

Lorraine says NO.
IT'S A LOT OF FUN,
ACTUALLY, TO BUILD.

He says AND WHEN WE COME BACK, WE'RE
GOING TO FINISH THIS ONE
OURSELVES, WHAT DO YOU THINK?

Lorraine says THAT'S RIGHT.
SO IF YOU DO HAVE ANY
QUESTIONS IN THE MEANTIME
DURING OUR ACTIVITY, FEEL FREE
TO CALL BY PRESSING POUND NINE.
AND THE ACTIVITY BEING:

The slate changes to “Construct a pyramid model of the Great Pyramid of Gizeh.” A caption appears on screen. It reads “Back in 12 minutes.”

Lorraine says ENJOY.

After a few minutes, Lorraine says HELLO, AMBER?

Amber says HELLO.

Lorraine says HI.

Amber says HI.

Lorraine says DO YOU HAVE A QUESTION?

Amber says NO, SOME IDIOT IN MY
CLASS PUSHED MY NUMBER.

Lorraine says THANKS, AMBER.
HELLO, PING?
HELLO?
HELLO, COLLEGE AVENUE, I BELIEVE
WE HAVE PING CALLING IN?

Ping says HELLO?

Lorraine says HI.
DO YOU HAVE A QUESTION?

Pink says YEAH.
DOES THE SKYDOME HAVE
ANYTHING TO DO WITH THIS?

Lorraine says CAN YOU REPEAT THE QUESTION?

Ping says WHAT ARE THE MEASUREMENTS?

Stewart says WHAT ARE THE MEASUREMENTS?

Ping says YES.

Stewart says THE SQUARE IS 24 CENTIMETRES
BY 24 CENTIMETRES.
THE SQUARE IS 24 BY 24.
THESE TRIANGLES, THE VERTEX
UP HERE IS STRAIGHT OVER THE
CENTRE, SO 12, 12.
BUT THIS LENGTH HERE IS 19.2
CENTIMETRES, AND EACH ONE OF
THE TRIANGLES IS IDENTICAL.

Ping says OKAY, THANKS.
BYE.

Lorraine says BYE.

A woman says HELLO?

Lorraine says HELLO, SARAH?

The woman says SHE LEFT THE ROOM.
I THINK SHE WENT
TO THE WASHROOM.

Lorraine says PARDON ME?

The woman says I THINK SHE WENT
TO THE WASHROOM.
I'M SORRY, SHE JUST LEFT.

Lorraine says OKAY, THANKS.
DO YOU HAVE A QUESTION?
HELLO, GABE?

She appears on a small window at the right bottom of the screen.

Mike says NO, MIKE.

Lorraine says PARDON ME?

Mike says HELLO?

Lorraine says HI, DO YOU HAVE A QUESTION?

Mike says WILL WE BE ABLE TO READ
MORE INFORMATION ON EGYPT?

Stewart says TO GIVE US MORE
INFORMATION ABOUT EGYPT?

Mike says YES, BECAUSE YOU
DIDN'T LET US READ ALL OF
OUR INFORMATION YESTERDAY.

Stewart says WHAT HAPPENED WAS IS THERE
WAS A COMPUTER CRASH YESTERDAY
WHILE YOU WERE ON.
THAT WAS DEFINITELY
NOT PLANNED.

Mike says CAN WE READ THE
REST TODAY THEN?

Stewart says HOW MUCH MORE HAVE YOU GOT,
JUST TO GIVE US AN IDEA?

Mike says JUST EGYPTIAN ART
AND ARCHITECTURE.

Stewart says I DON'T SEE WHY NOT RIGHT
NEAR THE END OF THE PROGRAM.

Lorraine says SURE.

Mike says OH, WAIT.
MY COUSIN WANTS
TO TALK TO YOU.

Nadepa says HE'S COMING!

Mike says SORRY THAT WAS NADEPA.
HE'S KIND OF MESSED
IN THE BRAIN.
BYE.

Lorraine says AND WE HAVE ABOUT
ONE MINUTE TO GO.
WE'LL BE BACK THEN.

After a few minutes, Stewart says HI, WE'RE BACK.
AND RIGHT IN FRONT OF US, WE
HAVE COMPLETED OUR SCALE MODEL
OF THE PYRAMID OF GIZA.

Lorraine says THAT'S RIGHT.
WE'LL MOVE OUR
OTHER ONE AWAY.

Stewart says WHAT DO YOU THINK, LORRAINE?
LOOK PRETTY GOOD TO YOU?

Lorraine says CERTAINLY.
WE CAN EVEN SHOW IT UNDER
OUR GRAPHICS CAMERA.
ISN'T IT BEAUTIFUL?

Stewart says IT'S NOT TOO BAD AT ALL.

Lorraine says VERY PROUD.

Stewart says YEAH, WE FEEL PRETTY GOOD.
AND I HOPE YOU'VE HAD AN
OPPORTUNITY TO ACTUALLY
COMPLETE ONE YOURSELF, OR
SEVERAL IN YOUR CLASSES.
BUT IT'LL GIVE YOU SOME SENSE
OF WHAT THIS LOOKS LIKE
PROPORTIONALLY, AND
THAT'S KIND OF NICE.
WE ASKED ONE OTHER QUESTION
BECAUSE ONE OF THE THINGS THAT
I THINK, QUESTION NUMBER THREE
GETS AT THE WHOLE IDEA OF IF
I WANTED TO FIND THE VOLUME OF
THIS, WHAT FORMULA WOULD I USE?
AND YOU KNOW, OFF THE TOP OF
MY HEAD, I'M NOT 100 PERCENT
SURE WHAT FORMULA
I SHOULD USE.
SO WE'VE DEVISED A LITTLE
BIT OF AN EXPERIMENT.
I'M GOING TO BRING IN JUST AT
THIS POINT, PERHAPS WE CAN
MOVE THAT ONE OVER.

Lorraine says CERTAINLY.

Stewart says WE'RE NOT GOING TO USE THAT
ONE BECAUSE IT'S ACTUALLY
VERY, VERY LARGE.
I'M GOING TO STAND UP NOW, AND
I'M GOING TO BRING IN THIS
LITTLE PIECE RIGHT HERE.
MAYBE WE CAN LOOK AT IT
FROM THE GRAPHICS CAMERA
POINT OF VIEW.

Lorraine says CERTAINLY.

Stewart says THERE IT IS.
IT'S NOT NEARLY AS BIG AS THE
OTHER ONE, AND ACTUALLY IF
YOU REALLY WERE STARING...

Lorraine says IF WE WERE TO COMPARE.

Stewart says YOU CAN SEE THIS ONE
IS QUITE A BIT LARGER.
NOW, THE AMOUNT OF SUGAR I
WOULD NEED FOR THAT WOULD BE A
LOT MORE THAN THE SUGAR I
WOULD NEED FOR THIS ONE.
SO WE'VE DECIDED
TO USE THIS ONE.
NOW, ONE OF THE THINGS THAT
I WANT TO DO IS, FIRST OF ALL,
DETERMINE THE IMPORTANT
DIMENSIONS OF THIS
PARTICULAR PYRAMID.
AND I MIGHT ASK FOR
YOUR HELP A LITTLE BIT.
HERE'S WHAT WE KNOW.
WE'LL GO TO THE
GRAPHICS CAMERA.
HERE'S WHAT WE DO KNOW.
WE KNOW THAT THE SQUARE OF
THE BASE IS 19 CENTIMETRES
BY 19 CENTIMETRES, OKAY?

He draws a square and continues
THE OTHER THING THAT WE
KNOW, AND WE CAN DO THIS BY
MEASUREMENT IS -- THIS
IS NOT A SCALE MODEL.
IT'S NOT INTENDED TO BE.
BUT WHAT WE DO KNOW IS
THAT THE SLANT HEIGHT IS
14 CENTIMETRES.
MEANING HALFWAY ALONG
HERE IS 9.5 CENTIMETRE.
WHOOPS, I SAID
THE SLANT HEIGHT.
14 CENTIMETRES IS
THE SLANT HEIGHT.
WE CAN DO THAT STRICTLY
BY MEASUREMENT.
THIS IS 9.5 CENTIMETRES HERE.
NOW, I WANT TO KNOW HOW LONG
THIS SIDE OF THE TRIANGLE IS.
THIS ONE OVER HERE.
I'LL CALL IT X.
AND I WOULD CERTAINLY BE
INTERESTED IF ANYBODY IS
INTERESTED IN HELPING ME, LET
ME KNOW WHAT WE USE TO FIND
OUT WHAT THE MISSING SIDE IS.
BECAUSE WHAT WE ARE
ACTUALLY FINDING --
OH, I'M GOING TO REDRAW.
IT'S ONE OF THOSE DAYS.
LET'S USE THIS ONE OVER HERE.
THIS IS BETTER.

Lorraine says THIS WAS THE SIZE OF IT.

Stewart says THERE WE ARE.

A boy says HELLO?

Stewart says THERE'S THE PIECE.
I'M GOING TO SLIDE IT KIND OF
OVER A LITTLE BIT HERE SO WE
CAN GET A PROPER LOOK AT IT.

Lorraine says HELLO.

The boy says HI.

Lorraine and Stewart say HI.

Stewart says OKAY, NOW I'M GOING TO
GO BACK TO MY DIAGRAM.
JUST BEAR WITH ME
FOR A MOMENT OR TWO.

The boy says SURE.

Stewart says I HAVE A TRIANGLE.
AND I THINK WHEN I DO IT THIS
WAY I'M GOING TO BE A LOT
SAFER THAN THE OTHER ONE.
IT'S A RIGHT-ANGLE TRIANGLE.
WE KNOW THE SLANT HEIGHT
IS 14 CENTIMETRES.
WE KNOW THIS SECTION ALONG
HERE IS 9.5 CENTIMETRES.
WHAT I WANT TO KNOW
IS THIS HEIGHT HERE?
WHAT THEOREM WOULD I USE?

The boy says WHICH TRIANGLE ARE YOU USING?
BECAUSE FOR SLANT
HEIGHT, I HAVE 19.2.

Stewart says WHAT I WAS SAYING AT THE
BEGINNING IS, YES, YOU'RE
RIGHT, 19.2 CENTIMETRES IS
THE SLANT HEIGHT OF THIS ONE,
WHICH IS THE SCALE MODEL.
BUT FOR DOING THE
EXPERIMENT, WE ACTUALLY
MADE UP A SMALLER ONE.
AND WE HAVE TO GET THE
DIMENSIONS OF THIS SMALLER
ONE BECAUSE I DON'T HAVE
ENOUGH SUGAR TO FILL THIS.

The boy says OH, OKAY.

Stewart says SO I'M GOING TO ASK
THE QUESTION AGAIN.
WHAT THEOREM AM I GOING TO
USE TO FIND THIS HEIGHT HERE,
WHICH IS WHAT I REALLY WANT.

The boy says WELL, YOU'D USE
PYTHAGOREAN THEOREM.

Stewart says EXACTLY.
NOW, CAN YOU HELP ME.
WHAT IS THE CALCULATION THIS
TIME, AND BE REALLY CAREFUL
BECAUSE THIS IS A SLIGHTLY
DIFFERENT ARRANGEMENT THAN
THE OTHER ONE.

The boy says WOULD YOU DO 9.5 SQUARED?

Stewart says PLUS WHAT SQUARED?

The boy says THEN YOU'D FIND THE SQUARE
ROOT, OR WHATEVER THAT IS,
THEN YOU'D SUBTRACT
THAT FROM 14 SQUARED.

Stewart says EXCELLENT, OKAY.
YOU'VE SAID IT CORRECTLY.
WHAT YOU ARE ACTUALLY TELLING
ME IS THAT YOU WOULD ADD THIS
SQUARED AND THAT SQUARED,
THE ONE I DON'T KNOW,
EQUALS 14 SQUARED.
THEN YOU SAID SUBTRACT.
SO IN OTHER WORDS...

On a new piece of paper he writes “X squared equals 14 squared subtracts 9.5 squared.”

Stewart continues NOW, CAN YOU DO A CALCULATION
FOR ME WITH A CALCULATOR?
FIRST OF ALL, BEFORE YOU TAKE
A SQUARE ROOT, FIND OUT WHAT
THAT DIFFERENCE IS.

The boy says I'VE GOT TO GET
A CALCULATOR.

Stewart says THAT'S FINE.
GO RIGHT AHEAD.
VERY GOOD.

The boy says OKAY, HOLD ON.

Stewart says YEAH, NO PROBLEM.

The boy says WE'RE EVEN GETTING A
COMPUTERIZED CALCULATOR.

Stewart says HEY, THEY'RE EVEN
BETTER, AREN'T THEY?

Lorraine says THAT'S RIGHT.

The boy says OKAY, 14 SQUARED...

Lorraine says PARDON?

The boy says WE'RE JUST WORKING IT OUT.

Stewart says IT'S JUST HAPPENING.
THAT'S GOOD.
THAT WAS VERY, VERY GOOD
TO RECOGNIZE IT'S NOT THE
STRAIGHT ADD AND TAKE THE
SQUARE ROOT BUT SUBTRACT
AND TAKE THE SQUARE ROOT
BECAUSE IT'S A DIFFERENT SIDE
IN THE TRIANGLE.

Lorraine says OBVIOUSLY THEY'RE
COMFORTABLE WITH THE THEOREM.

Stewart says THE THEOREM, IF YOU BEGIN TO
UNDERSTAND HOW TO WORK WITH
WHICHEVER SIDE IS MISSING,
THEN YOU'RE IN GREAT SHAPE.

Lorraine says AND SOMETIMES IT'S EASIER IF
THE STUDENTS THINK OF THIS
AS A, FOR THE ONES THAT MIGHT
FIND IT A LITTLE MORE
DIFFICULT, AND THEN
THIS BECOMING B.

Lorraine modifies the equation “9.5 squared plus x squared equals 14 squared.” Where it says “x squared ,” she writes “b squared.”

Stewart says I LIKE MESSING AROUND WITH
LETTERS, YOU KNOW HOW IT IS.
HAVE YOU GOT A NUMBER YET?

The boy says YES, I DO.
IT'S 195.75.

Stewart says I THINK IT'S
105.75, ISN'T IT?

The boy says WE HAVE 195.75.

Stewart says DOUBLE CHECK IT BECAUSE
14 SQUARED IS 196.
AND 9.5 SQUARED.
SO I THINK IT MAY JUST
BE A PUNCHING ERROR.
IS 90.25.
SO IT'S GOT TO
BE CLOSE TO 105.

The boy says OKAY.

Stewart says NOW, WHAT'S THE SQUARE
ROOT OF THIS, 105.75,
APPROXIMATELY?
JUST ONE DECIMAL.

The boy says I DON'T KNOW.

Stewart says OKAY, I'LL HELP YOU OUT.
I'VE GOT A CALCULATOR HERE.
I'LL GET MY CALCULATOR, AND
I'LL TAKE THE SQUARE ROOT
OF 105.75.
AND I GET 10.28,
WHICH IS ABOUT 10.3.

The boy says OH, OKAY.

Stewart says IS THAT GOOD?

The boy says ALL RIGHT, YEAH,
THAT SOUNDS GOOD.

Stewart says SO WHAT WE HAVE NOW IS THE
HEIGHT OF THIS PYRAMID IS
10.3 CENTIMETRES.
NOW, I THINK WHAT WE'VE
GOT TO DO IS DEMONSTRATE
HOW WE DID THIS.
NOTICE THAT WE HAVE
THE TOP OF THIS OPEN.
DON'T OPEN IT UP TOO MUCH.
BUT WHAT WE'RE GOING TO DO
HERE IS WE SET UP THIS FUNNEL
SCENARIO, AND WE HAVE SOME
SUGAR, MAYBE WE CAN PUT A
LITTLE WEE BIT IN.
YEAH.
AND WHAT WE DID IS WE
BASICALLY FILLED THIS THING
RIGHT UP TO THE TOP WITH
SUGAR, AS CLOSE AS WE COULD
GET TO THE TOP WITHIN REASON.
IT WOULD SPILL OUT A BIT.
IF WE MISS A LITTLE BIT AT THE
TOP, IT WON'T BE ENOUGH TO
MAKE A DIFFERENCE.
SO YOU WOULD FILL IT UP.
NOW, WHAT WE'RE GOING TO DO
NOW IS FIND OUT HOW MUCH SUGAR
IS IN THERE AND USE, WHAT
DO YOU CALL THESE THINGS,
LORRAINE?

Lorraine says YES, LOVELY CYLINDER HERE.

Stewart says GRADUATED CYLINDERS.
THERE WE ARE.

Lorraine says THIS IS WHERE IT GETS FUN.

Stewart turns the pyramid upside down and the sugar pours into a cylinder.

Stewart says NOW, I DON'T KNOW HOW MUCH IS
GOING TO BE IN HERE BUT, YOU
KNOW, WE BETTER BE READY WITH
ANOTHER ONE IN CASE THERE IS
MORE SUGAR THAN WE THINK.
IT'S FILLING FAIRLY RAPIDLY.
THAT'S GOOD.
WITH A LITTLE BIT OF LUCK
WE'LL BE FINE ON THIS.
WE'RE ALREADY UP TO 600 MLS.
UH-OH.
GOTTA BE READY,
GOTTA BE READY.
THERE.

As Stewart holds the pyramid, Lorraine changes the cylinder.

He continues NOW, WE'LL HAVE TO TOP IT UP
A LITTLE BIT, BUT I THINK,
YEAH, SO WE'RE
DOING PRETTY WELL.
THAT WAS PRETTY GOOD.
OH, WE REALLY PUT
MORE SUGAR IN THERE.

Lorraine says WELL, WE'VE GOT
QUITE A BIT TO ADD.

Stewart says WE'VE GOT A BIT TO
ADD THERE, THAT'S GOOD.
LET'S SEE.
WE'RE GOING TO TOP
THAT UP TO A THOUSAND.
CAN YOU SHAKE THAT AROUND?
WE'VE GOT A LITTLE
BIT MORE TO ADD THERE.
OKAY, SHAKE IT AROUND.
OKAY, THAT'S GOOD.
SO THERE'S THE AMOUNT OF
SUGAR WE FOUND IN THERE.
IF WE ACTUALLY READ THE TWO
AMOUNTS, THERE'S 1000 IN HERE,
AND THIS IS VERY,
VERY CLOSE TO 380.
SO WE FOUND THE VOLUME OF
THIS IN MILLILITRES ANYWAY.
AND I'M GOING TO MOVE
THAT TO THE SIDE.
WE HAVE 1380 MILLILITRES.
I'M GOING TO CALL IT --

He writes reads “1380.”

Stewart continues NORMALLY, WITH WATER,
1 MILLILITRE EQUALS 1 CC, AND
I THINK FOR THE PURPOSE OF
OUR LITTLE EXPERIMENT, WE'RE
GOING TO ACTUALLY STICK
WITH THAT IDEA.
SO IT'S CUBIC CENTIMETRES,
CENTIMETRES CUBED.
NOW, THE INTERESTING SIDE OF
THIS IS, IF WE TAKE THIS,
I'M GOING TO COME
BACK TO THIS AGAIN.
IF THIS WAS A BOX, A
RECTANGULAR PRISM BOX, AND IT
HAD THE SAME HEIGHT AS THE
HEIGHT, AND THAT'S WHY I
WANTED TO CALCULATE THAT, WE
HAD THE SAME HEIGHT AS THIS,
WITH THE SAME BASE, WHAT
WOULD THE VOLUME BE?
WELL, THE VOLUME WOULD BE
LENGTH TIMES WIDTH TIMES HEIGHT.
SO IF I PUT THAT IN A BOX SO
THE HEIGHT WOULD JUST FIT IN,
THEN I'D GET A BOX:

He writes “Length times width times height equals 19 times 19 times 10.3.”

He continues WHAT WE'RE GOING TO DO IS
COMPARE THE VOLUME OF THIS BOX
TO THE VOLUME OF THE SUGAR
THAT WE FOUND AND SEE IF
THERE'S SOMETHING INTERESTING.
SO I'M GOING TO GET
MY CALCULATOR AGAIN
AND CALCULATE THAT.
SO 19 SQUARED, TIMES 10.3.
AND I GET 3,718 -- I'LL
MAKE IT NICE AND ROUND.
3,720 CENTIMETRES CUBED.
I'M CURIOUS TO KNOW WHAT
FRACTION THIS IS OF THAT.
SO I WILL TAKE 1380 AND I'M
GOING TO DIVIDE BY 3,720.
LET'S SEE WHAT WE GET.
OKAY.
AH, YES.

He writes “point 37.”

He continues NOW, THAT FRACTION, REMEMBER,
THIS IS A VERY, VERY, VERY
ROUGH MEASUREMENT.
IN FACT, I'D BE SURPRISED IF
WE WERE REALLY, REALLY CLOSE.
WHAT I DO KNOW IS THE FRACTION
WE WERE ACTUALLY LOOKING
FOR WAS....3 REPEATED, AND THE ANSWER
TO THAT IS ONE-THIRD.
THIS IS VERY CLOSE.
AND IN FACT, GIVEN THE
ACCURACY WITH WHICH WE WERE
MEASURING AND SO ON, I FIGURE
THAT IS EXCEPTIONALLY CLOSE.
NOW, WHAT I'M GOING TO PROPOSE
TO YOU THEN IS THE VOLUME OF
A PYRAMID IS
CALCULATED THIS WAY:

On a new piece of blue paper he writes “Volume of a pyramid.”

He continues AFTER THIS, WE HAVE TWO AREL
QUESTIONS WE ARE GOING TO
TRY YOU OUT WITH.
AND WE'LL GO FROM THERE.

He continues writing “Area of the base times the height times one third. One third times length times width times height.”

He continues WHEN YOU ARE DEALING WITH A
SQUARE BASE PYRAMID, YOU CAN
USE THAT TO FIND THE VOLUME.
THEREFORE, WE CAN FIND THE
VOLUME ALSO OF THE GREAT
PYRAMID OF GIZA.
VERY QUICKLY, THAT WOULD BE:

He writes “One third 237 times 237 the height 148.”

He continues I'M GOING TO DO A QUICK
CALCULATION ON THAT.

He writes “2,771,004 metres cubed.”

He continues THAT IS HUGE.
NOW, WE'VE GOT TWO
AREL QUESTIONS.
ONE OF THE AREL QUESTIONS --
IS IT ABOUT THE
PYRAMIDS THEMSELVES?

Lorraine says CERTAINLY IS.

The slate changes to “Question 1. What did the Egyptians use to make the corners of Pyramids square? 1. Protractor. 2. Sextant. 3. 3, 4, 5 triangle.” A gray bar graph reads “0 per cent.”

The bar graph changes to blue as numbers go up from “6 per cent” to “30 per cent.”

Stewart says HOW MANY?
30 PERCENT.
COME ON, WE CAN GET
A LOT MORE ANSWERS.
LET'S GET A FEW
MORE PERCENT ANYWAY.
A LOT OF PEOPLE SEEM
TO BE GETTING IT RIGHT.
I'M PLEASED ABOUT THAT.
32 PERCENT.
AH, THERE WE COME.
A LOT OF PEOPLE CAME
IN RIGHT ABOUT THERE.
NOW, LET'S PUT
THE GRAPH UP ON THE...
NOW, AS IT TURNS OUT, SOME
PEOPLE THOUGHT THE SEXTANT,
AND A NUMBER OF PEOPLE ARE
THINKING THE 3, 4, 5 TRIANGLE.
THE PROTRACTOR DIDN'T
EXIST AT THE TIME.
SO YOU CAN
ELIMINATE THAT ONE.
THE SEXTANT EXISTED,
PERHAPS BUT WAS NOT
THE INSTRUMENT.
IN FACT, IT'S A
3, 4, 5 TRIANGLE.

A three-bar graph appears. A green bar reads “8,” a purple bar reads “14” and a blue bar reads “11.”

He continues 3, 4, 5, IT'S CALLED
A PYTHAGOREAN TRIPLE.

He draws a right triangle and continues
IT MEANS THIS LENGTH WAS
THREE, THIS LENGTH IS FOUR,
THAT LENGTH IS FIVE.
AND YOU'LL SEE THAT:

He writes “3 squared plus 4 squared equals 25 equals 5 squared.”

He continues SO WHAT THEY DID IS THEY GOT
A PIECE OF ROPE, WHICH WAS
MARKED IN EQUAL LENGTHS.
THE FACT IS, IT'LL BE A
BIG LONG PIECE OF ROPE.
IT'LL BE THREE SPOTS THERE FOR
THE THREE, THEN ANOTHER FOUR...
THEN YOU WOULD FIND
ANOTHER FIVE ACTUALLY.
IF YOU WERE TO PUT A CORNER
HERE, A CORNER HERE, AND
STRETCH IT AROUND TO THE
CORNER HERE, YOU WOULD GET AN
EXACT RIGHT-ANGLE TRIANGLE.
AND THAT'S HOW THEY
DID IT ACTUALLY.
IT'S A MOST INTERESTING
WAY OF DOING IT.
THAT'S ONE OF OUR QUESTIONS.
WE HAVE, ACTUALLY, A
SECOND QUESTION, AS WELL,
WHICH I THINK IS REALLY
APPROPRIATE AT THIS MOMENT.
HERE WE ARE.

The question changes to “Which of the Pyramids has the greatest volume? 1. Number 1. 2. Number 2. 3. Same.” A gray bar graph reads “0 per cent.”

He continues NOW, I WANT YOU TO
TAKE A REALLY CLOSE LOOK.
WE'RE GOING TO LOOK AT
THIS FROM THE FRONT.
WE HAVE TWO PYRAMIDS.
NOW, THEY ARE
BOTH SQUARE BASED.
Talking to Lorraine, he continues YOU CAN HOLD THAT UP.
SHOW THE BOTTOM.
THEY ARE BOTH SQUARE BASED.
BUT THEY ARE A LITTLE BIT
DIFFERENT BECAUSE THIS ONE THE
VERTEX IS SORT OF STRAIGHT
OVER A CORNER, AND THIS ONE
THE VERTEX IS WAY OVER THERE.
NOW, THE QUESTION IS, GO
BACK TO THE QUESTION, HERE'S
NUMBER ONE, THIS IS NUMBER
TWO, WHICH ONE OF THESE HAS
THE BIGGEST VOLUME?
NOW I WOULD REALLY LIKE TO
INVITE PEOPLE TO PHONE IN.
EXCELLENT, EXCELLENT.

The bar graph changes to blue as numbers go up from “8 per cent” to “43 per cent.”

He continues OKAY, LET'S SHOW THE GRAPH.
AND I WOULD LIKE TO INVITE
ANYBODY THAT ANSWERED NUMBER
THREE TO PHONE IN AND EXPLAIN
WHY YOU CHOSE THE SAME.

A three-bar graph appears. A green bar reads 48,” a purple bar reads “5” and a blue bar reads “19.”

Lorraine says AND THEY MAY WANT TO
LOOK AT IT ONE MORE TIME.
REMEMBER THE BASES ARE --

He says THE BASES.
THAT WOULD BE GOOD.

Lorraine says ALRIGHT.
WELL, WE HAVE QUITE A FEW
NAMES HERE THAT HAVE
ANSWERED THREE.
HERE WE GO.
WE'RE CALLING AARON
FROM THE PINES.

Stewart says OH, GREAT.

Lorraine says HELLO?

Aaron says HI.

Lorraine says AND YOU CHOSE NUMBER
THREE FOR AN ANSWER.
WHY IS THAT?

Aaron says BECAUSE THE BASES
ARE THE SAME.

Stewart says OKAY, THAT'S TRUE.
YOU ARE ABSOLUTELY RIGHT.
BUT ONE OTHER THING HAS TO BE
THE SAME TOO, AND WHAT IS IT?
TAKE A LOOK RIGHT
IN FRONT OF ME.
WHAT'S THE SAME ALSO?

Aaron says THEIR HEIGHT.

Stewart says EXACTLY.
EVEN THOUGH THEY ARE SO
TREMENDOUSLY DIFFERENT IN
SHAPE, YOU CAN SEE THIS ONE IS
WAY STRETCHED OUT COMPARED TO
THAT, IF THE BASES ARE THE
SAME, AND THE HEIGHTS ARE THE
SAME, THEN THEY ARE THE SAME.
EXCELLENT.
THAT IS JUST SUPER.
ABSOLUTELY GREAT.

Lorraine says THANK YOU.

Stewart says NOW I HAVE ONE MORE QUESTION
IN THE EXERCISE TO PROPOSE.
I DON'T KNOW IF ANYBODY HAS
INTERNET ACCESSIBILITY HERE IN
THE CLASS, AND PERHAPS WE
HAVE TO LEAVE THIS ONE
UNTIL THURSDAY.
IT'S NOT A BIG QUESTION.
THE QUESTION IS, WHICH
HAS THE BIGGER VOLUME?
THAT IS, THE SKYDOME OR
THE GREAT PYRAMID OF GIZA?
AND MAYBE WE CAN TAKE A CALL
IF SOMEBODY WOULD LIKE TO LET
US KNOW WHAT THEY THINK.
OR IF THEY'VE ACTUALLY CHECKED
THE INTERNET TO SEE WHAT THE
COMPARISON IS.
OH, WE'VE GOT SOMEBODY
FROM SAINT JOHN.

Lorraine says HELLO?

Jacob says HI.

Stewart says HI.
DO YOU HAVE EITHER KNOWLEDGE
OR AN OPINION ABOUT WHICH IS
BIGGER, THE PYRAMID OF
GIZA OR THE SKYDOME?

Jacob says I'M PRETTY WELL SURE THAT
THE GREAT PYRAMID OF GIZA IS
BIGGER THAN THE SKYDOME
AND HAS MORE VOLUME.

Stewart says ACTUALLY, YOUR FEELING
IS A VERY GOOD ONE.
AND, IN FACT, IT IS CORRECT.
WHAT I WOULD INVITE YOU TO
DO, IF YOU GET A CHANCE --
HAVE YOU GOT ACCESSIBILITY
TO THE INTERNET YOURSELF?

Jacob says I GET ABOUT TEN MINUTES
BEFORE MY DAD KICKS ME OFF.

Lorraine laughs.

Stewart says WELL, TEN MINUTES
WOULD DO IT.
THE SKYDOME HAS A WEBSITE,
AND IT WAS ONE OF THE ONES WE
LISTED REALLY, REALLY EARLY IN
THE FIRST WEEK OF THE PROGRAM.
JUST LOOK THEM UP.
THE VOLUME OF THE SKYDOME
IS LISTED AS ONE OF
THEIR STATISTICS.
AND WHAT YOU'RE COMPARING IT TO,
REMEMBER, WE WORKED IT OUT AS:

He shows the piece of paper that reads “2,771,004 metres cubed.”

Stewart continues SO WOULD YOU BE WILLING
TO CHECK THAT OUT FOR US
FOR THURSDAY?

Jacob says SURE.

Lorraine says GREAT.

Jacob says DO YOU HAVE THE
ADDRESS OF THE WEBSITE?

Stewart says AND YOUR NAME IS AGAIN?

Jacob says JACOB.

Stewart says JACOB.

Jacob says DO YOU HAVE THE
WEBSITE ADDRESS?

Stewart says WE'LL BE LOOKING FOR A
PHONE CALL FROM YOU, JACOB?

Jacob says DO YOU HAVE THE ADDRESS?

Stewart says WE MAY HAVE TO GET
BACK TO YOU AFTERWARD.
WE'VE GOT THE WEBSITE
ADDRESSES UPSTAIRS.

Jacob says OKAY, SO BEFORE
THE SHOW IS DONE?

Stewart says WHEN THE SHOW IS DONE,
ACTUALLY -- YOU'RE AT WHICH
SCHOOL AGAIN?

Lorraine says St. JOHN BREBEUF SO
WE CAN MAYBE SEND IT.
WE'LL BROADCAST IT ON
THE SATELLITE FOR YOU.
ON THE SCREEN.

Stewart says SUPER.

Lorraine says GREAT.
THANKS, JACOB.

FOR YOUR HOMEWORK, IF
YOU CAN WRITE THIS DOWN:
WE HAVE TO SOLVE OUR MATH
MYSTERY ON THURSDAY.

The caption changes to “Homework. Sphinx problem. Math Mistery Journals. Outline of Story.”

Stewart says WE HAVE TO SOLVE THE
MYSTERY, YOU WANNA BET.

Stewart says GREAT.
WE JUST HAD A CALL DURING THE
BREAK, AND I THINK WE COULD
TAKE A LITTLE BIT MORE
INFORMATION ABOUT EGYPT
BEFORE WE CLOSE OFF.
COLLEGE AVENUE, WE'LL
ASK YOU TO PHONE IN.
WE WILL ASK YOU TO BE FAIRLY
BRIEF BECAUSE WE ONLY HAVE ONE
OR TWO MINUTES BEFORE
WE HAVE TO SIGN OFF.

Lorraine says THAT'S RIGHT.
THEREFORE, WE'LL START
WITH GABE FROM COLLEGE.

Gabe says HI.

Stewart says HI.
YOU HAD A LITTLE BIT MORE
INFORMATION ABOUT EGYPT.

Gabe says OKAY, BEFORE I READ THE
INFORMATION, OUR TEACHER
WANTED TO FAX IN A SHEET
WITH EGYPTIAN HIEROGLYPHICS.

Stewart says RIGHT.

Gabe says SO COULD YOU SHOW THAT ON
THURSDAY IF YOU GET IT?
HELLO?

Lorraine says YES, YES.

Gabe says OKAY, THANKS.
I'M READING ABOUT --
OKAY, WAIT.

Lorraine says WE'RE HAVING A LITTLE BIT
OF DIFFICULTY HEARING YOU.

Gabe says I'M READING ABOUT EGYPTIAN
ART AND ARCHITECTURE.

Lorraine says OKAY, GREAT.
TALK A LITTLE BIT LOUDER.

Gabe says EGYPTIAN ART AND ARCHITECTURE.
THE BUILDINGS, PAINTINGS,
SCULPTURES...

Stewart says TALK SLOWLY.
PEOPLE WILL NOT BE ABLE TO
UNDERSTAND YOU, INCLUDING ME.

Gabe continues MEDITERRANEAN EXTENDING
WITH FEW INTERRUPTIONS
FROM ABOUT 3000 BC
THROUGH THE 4th CENTURY AD.
THE NATURE OF THE COUNTRY
FERTILIZED AND UNITED
BY THE NILE AND ITS
SEMI-ISOLATION FROM
THE OUTSIDE CULTURAL
INFLUENCES, PRODUCED AN
ARTISTIC STYLE THAT CHANGED
LITTLE DURING ITS LONG PERIOD.
ART IN ALL ITS FORMS
WAS DEVOTED VISIBLY
TO THE SERVICE OF THE
KINGs, THE PHARAOHs,
WHO WAS CONSIDERED
A GOD ON EARTH
TO STATE AND RELIGION.
FROM EARLY TIMES THE
BELIEF IN LIFE AFTER DEATH
DEDICATED THAT THE DEAD BE
BURIED WITH MATERIAL GOODS
TO ENSURE WELL-BEING
FOR ETERNITY.

Stewart says GREAT.
OKAY THANKS VERY MUCH.
WE'VE GOT TO SIGN OFF, SO
WE'LL SEE YOU ON THURSDAY
FOR THE VERY LAST PROGRAM.

Lorraine says YES.
AND I UNDERSTAND
THURSDAY'S SESSION --

Stewart says OH, HECK, WE'RE NOT
GOING TO BE THERE.
IT'S GOING TO Mr. C.

Lorraine says IT'S OUR LAST.

Stewart says MISTER C AND MISSUS G.
WELL, I GUESS THEY'RE
GOING TO HAVE TO TAKE CARE
OF THE MATH QUESTIONS.

Lorraine says THAT'S RIGHT.

Stewart says MISTER I'LL LET THEM KNOW.

Lorraine says AND ANOTHER THING IS TO
LET THE FACILITATOR FROM
COLLEGE AVENUE, IF YOU
COULD CALL THE HELP LINE,
WE'D APPRECIATE THAT.
THANKS.
AND WE'LL SEE YOU -- ACTUALLY,
WE WON'T SEE YOU THURSDAY,
BUT ALL THE BEST.

Stewart says MISTER C AND MISSUS G.
Lorraine says BYE-BYE.

The slate 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!”

The PowerPoint presentation finishes and a mouse closes windows.

The caption changes to “Skydome website: www.skydome.com.”

Watch: Student Session 22