Transcript: Student Session 7 | Aug 24, 1998

Lorraine and Stewart sit in the studio.

Lorraine is in her early thirties, with long slightly wavy red hair with bangs in a low ponytail. She wears an olive green blouse and small earrings.

Stewart is in his early forties, with short wavy brown hair and a trimmed beard. He wears glasses, a purple T-shirt and suspenders.

An assignment sheet appears on screen with two sets of Mayan numerals.

Stewart says WHAT I WOULD LIKE
YOU TO DO, OF COURSE,
IS TO FIND OUT WHAT
THE EQUIVALENT IS IN
OUR OWN BASE, THAT
IS, NORMAL NUMBERS,
AND ANSWER THOSE
TWO QUESTIONS.
THEN I EVENTUALLY ASKED
YOU TO TAKE OUR NUMBERS
AND FIND THE SYMBOLS
FOR MAYAN NUMBERS.
SO NICE LITTLE EXERCISE
TO DO WITH MAYAN NUMBERS.

He takes another sheet of paper with 3 sets of Egyptian hieroglyphs.

He says DOWN HERE AT THE BOTTOM,
WE HAVE EGYPTIAN
HIEROGLYPHS OR KIND
OF A DRAWING OF WHAT
HIEROGLYPHS LOOK LIKE.
IF YOU ACTUALLY
WERE IN A TOMB,
THEY WOULDN'T LOOK
EXACTLY LIKE THIS,
AND IT ACTUALLY WAS
VERY, VERY DIFFICULT
FOR A NUMBER OF YEARS
TO ACTUALLY INTERPRET
WHAT THEY MEANT.
BUT AFTER A
MATTER OF TIME,
ARCHAEOLOGISTS WERE
ACTUALLY ABLE TO READ
THESE NUMBERS AND THIS
IS A PRETTY GOOD IDEA
OF WHAT THEY KIND OF
MEANT IN THE FIRST PLACE.
SO WHAT I'M ASKING
YOU TO DO, AGAIN,
IS TO TAKE THESE THREE
SAMPLES OF NUMBERS,
LOOK AT THE RELATIONSHIP
BETWEEN THE SAMPLE
AND THE ACTUAL NUMBER
THAT'S WRITTEN IN BASE 10,
OUR NUMBER SYSTEM, AND
FIGURE OUT EXACTLY
HOW THESE NUMBERS
WERE WRITTEN.
AND WITH THAT
INFORMATION...
THEN YOU TAKE THESE
NUMBERS HERE,
AND IN FACT WORK OUT
WHAT THE NUMBERS ARE.

He grabs another sheet with 3 Math operations using hieroglyphs.

His says THIS IS AN ADD,
OBVIOUSLY.
IF I TAKE THE TOP ONE,
THERE'S A SUBTRACT.
NOW, I ADMIT, CHANCES ARE,
BACK IN EGYPTIAN TIMES,
THEY DIDN'T USE THE SAME
SYMBOL FOR SUBTRACTION
AND ADDITION, BUT
FOR OUR PURPOSES,
I THOUGHT THIS
WOULD WORK OUT WELL.
AND THE IDEA IS TO
GET THE ANSWER
AND TO WRITE IT
IN HIEROGLYPHS.
NOT IN OUR NUMBER SYSTEM,
BUT IN HIEROGLYPHS.
THE ONE AT THE BOTTOM,
I'VE SORT OF GIVEN YOU
QUITE A QUESTION HERE.
IT'S THIS NUMBER HERE,
SUBTRACT, BRACKETS,
THOSE ARE BRACKETS JUST
LIKE YOU WOULD SEE,
AND THIS DOT REPRESENTS
MULTIPLICATION.
WHAT DOES THAT BRING YOU
TO MIND AND SOMETHING
THAT STUDENTS HAVE
TO LEARN STARTING,
OH, QUITE EARLY, GRADE
6, 7, AND SO ON?
THERE'S A CONCEPT
HERE WITH BRACKETS.

Lorraine says ORDER OF OPERATION.

Stewart says ORDER OF OPERATIONS,
THAT'S RIGHT.
AND, YOU KNOW, THIS
WOULDN'T BE A BAD IDEA
IF WE COULD TAKE A
CALL AND ASK SOMEBODY
IF THEY KNOW WHAT THE
ORDER OF OPERATIONS IS,
BECAUSE I THINK WE NEED
TO KNOW IT FOR THIS.
WE'VE GOT SOMEBODY
ON THE LINE PERHAPS?

Lorraine says YES, LET'S TRY SOMEBODY
FROM COLLEGE AVENUE.
DAVID FROM
COLLEGE AVENUE.

Stewart says YEAH, IT'S ONE OF THOSE
THINGS THAT KEEPS
COMING UP IN MATHEMATICS
OVER AND OVER AGAIN.
ORDER OF OPERATIONS ARE
VERY, VERY IMPORTANT.

Lorraine says VERY IMPORTANT.

Stewart says AND IF WE CAN FIND
OUT AND GET A SENSE THAT
STUDENTS ARE BASICALLY
ONLINE WITH THIS,
IT WILL HELP OUT.
HI.

The caller says IT'S BEDMAS.

Stewart says IT'S BEDMAS.
I'M GOING UNDER
HERE ON THE BLUE
AND I'M GOING TO
PRINT BEDMAS.
CAN YOU TELL ME
WHAT THAT MEANS?
DO YOU REMEMBER
WHAT THIS ALL MEANS?

The caller says YEAH.

Stewart says WHAT DOES IT MEAN?

The caller says BRACKETS, FOR B.

Stewart says RIGHT.

The caller says AND THEN EXPONENTS,
AND THEN DIVISION.

Stewart says RIGHT.

The caller says THEN MULTIPLICATION.

Stewart says THIS IS THE ONE THAT
I ALWAYS HAVE TROUBLE
SPELLING, AS YOU
WILL SEE LATER.

The caller says YEAH.

Stewart says AND WHAT'S THIS ONE?

The caller says ADDITION.

Stewart says YEAH.
AND THE LAST ONE?

The caller says IS SUBTRACTION.

Stewart says THANK YOU VERY MUCH.

The caller says YOU'RE WELCOME.

Stewart says AND IN FACT I'M GOING TO
READ THIS THE WAY THAT IF
YOU WERE TO READ IT AS
KIND OF THE WHOLE THING
TOGETHER, BRACKETS AND
EXPONENTS COMES FIRST.
DIVISION AND
MULTIPLICATION IN THE ORDER
IT APPEARS, AND THEN
ADDITION AND SUBTRACTION
IN THE ORDER IT APPEARS.
SO WHEN YOU'RE DOING THIS
QUESTION DOWN HERE
AT THE BOTTOM, YOU'VE
GOT SUBTRACTION.
YOU'VE ALSO GOT BRACKETS.
YOU GOT TO MAKE SURE
THAT YOU DO IT
IN THE RIGHT ORDER.
NOW, THIS QUESTION I'M NOT
INTENDING YOU READ IT
BUT WE'LL ZOOM
DOWN A LITTLE BIT
ON THE TOP OF
THIS QUESTION.
WHAT I'M ASKING YOU TO DO
IS TO ACTUALLY CREATE
YOUR OWN NUMBER SYSTEM.
AND IT'S GOT TO BE IN
A BASE OTHER THAN
2, 10, OR 20.
NOW WHAT I MEAN BY BASE
10 IS THE DECIMAL SYSTEM
WHICH YOU USE - WE
USE ALL THE TIME.
BASE 20, I'VE ALREADY
GIVEN YOU A SYSTEM IN BASE 20,
IT'S THE MAYAN SYSTEM.
SO I DIDN'T REALLY WANT
YOU TO DO REPEAT THAT.
AND BASE 2 IS
CALLED BINARY.
NOW, I DIDN'T WANT YOU TO
USE THAT ONE BECAUSE
IT ONLY INVOLVES TWO
SYMBOLS, ZERO AND ONE.
AND IN FACT SOME OF YOU
MAY ALREADY BE FAMILIAR
WITH BINARY IF YOU'VE
BEGUN TO UNDERSTAND THINGS
ABOUT COMPUTERS AND
BITS AND BYTES AND ALL
THAT KIND OF STUFF.
NOW, WHAT I'M PROPOSING
HERE IS THAT YOU INVENT
YOUR OWN NUMBER SYSTEM
WITH YOUR OWN SYMBOLS.

The task reads “Write the following 4 numbers using your system: 47, 1007, 183922, 7769003.”

Stewart says AND REMEMBER LAST WEEK
WE ACTUALLY HAD SOME
BUILDINGS OR PICTURES
OF BUILDINGS FAXED IN?
NOW, AT THE BOTTOM OF
THIS PAGE YOU'LL SEE
THAT I PUT A FAX NUMBER.
THAT'S NOT THE ONE
THAT'S FREE FOR NOTHING.
SO I THINK WE REALLY NEED
A FREE FOR NOTHING
FAX NUMBER.
HAVE WE GOT A PIECE OF
PAPER WITH IT ON IT?

Lorraine says YES.
WELL, LET'S
WRITE IT DOWN.
MAYBE IF YOU WANT TO
WRITE THIS DOWN,
1-888-

Stewart says AND WE'RE WAITING
FOR THE NUMBER.
WE'LL GIVE THIS NUMBER
AT THE END OF THE SHOW.
IT WAS JUST SET ASIDE A
MOMENT OR TWO AGO
AND WE'LL GET IT BACK,
BUT INSTEAD OF USING
THE NUMBER I SHOW
AT THE BOTTOM,
WHEN WE GET
THE 888 NUMBER,
THEN YOU DON'T HAVE TO
WORRY ABOUT PAYING.
I WOULD LOVE TO SEE THE
SAMPLES OF YOUR WORK
BEFORE THURSDAY.
AND LAST BUT NOT LEAST
IN THE ASSIGNMENT,
I CALL IT EXERCISE NO. 2,
IF YOU TAKE A LOOK
DOWN HERE AT THE BOTTOM,
WHAT YOU SEE IS
SOMETHING LIKE WHAT
YOU ARE WEARING,
LORRAINE.

Lorraine says A QUIPU.
MY BELT.

Stewart says SYMBOL REPRESENTATIONS OF
QUIPUS WITH THE BIG BELT
AT THE TOP AND THE
STRINGS COMING DOWN
WITH KNOTS ON THEM.
NOW, WATCH OUT.
WHAT I'VE DONE HERE
IS, THIS IS A NUMBER.
THAT'S A NUMBER.
THAT'S A NUMBER, AND
THAT'S A NUMBER.
SO THERE ARE FOUR
DIFFERENT NUMBERS THERE.
THE FIRST TWO ARE
SUBTRACTED IN BRACKETS
AND THEN IT'S TIMES
THIS NUMBER,
DIVIDED BY THIS NUMBER.
THIS QUIPU OVER HERE IS
THIS NUMBER DIVIDED
BY THIS NUMBER DIVIDED
BY THAT NUMBER.

Lorraine says REAT.

Stewart says NOW, IF I'M NOT MISTAKEN,
WE HAVE A QUESTION.
DO WE?

Lorraine says WE CERTAINLY DO.
AND IF WE SET IT UP HERE,
YOU'RE GOING TO REQUIRE
YOUR PHONES TO
ANSWER THIS QUESTION.
WHICH NUMBER SYSTEM
HAVE WE NOT ADDRESSED?

Stewart says NUMBER 1: BABYLONIAN;
NUMBER 2: MAYAN; NUMBER 3: EGYPTIAN OR
NUMBER 4: INCAN.

AND WHEN WE GET ABOUT
70 PERCENT OR SO THEN MAYBE
WE CAN PUT THE GRAPH UP.
OH, IT'S RISING QUICKLY.
ANYTIME YOU WANT TO
PUT THE GRAPH UP.

Lorraine says GREAT.
OKAY, IT'S JUST
GOING UP TO QUICKLY.
IT'S WONDERFUL.
ALL RIGHT, LET'S LOOK
AT OUR BAR GRAPH.

The results show 50 callers for option 1, 3 callers for option 2, 9 for option 3 and 6 for option 4.

Stewart says WELL, IT IS QUITE OBVIOUS
THAT EVERYBODY'S - MOST
EVERYBODY IS PAYING
REALLY CLOSE ATTENTION.
THE ONLY NUMBER SYSTEM
WE REALLY HAVEN'T DONE
IS BABYLONIAN.
YOU KNOW WHAT'S
INTERESTING ABOUT THAT,
IT'S BASE 60.
IT'S A TOTALLY
DIFFERENT BASE AS WELL,
SO MAYBE SOME OTHER TIME
WE CAN ADDRESS THAT.
NOW, IF I RECALL
CORRECTLY,
BACK ON THURSDAY, WE
ACTUALLY LEFT YOU
WITH A COUPLE OF SEQUENCES
TO FIND SOLUTIONS TO.
THIS WAS ONE OF THEM.

The sequence reads O, T, T, F, F, S, S, blank space, blank space.

Stewart says NOW, WHAT I'D LOVE TO HAVE
IS A FEW CALL-INS RIGHT NOW
TO TELL ME WHAT
THE TWO BLANKS ARE,
AND TO TELL ME WHY YOU
WOULD FILL THOSE
TWO BLANKS IN WITH THE
NUMBERS OR LETTERS,
I GUESS IN THIS CASE,
THAT YOU WOULD CHOOSE.

Lorraine says HELLO.
IT'S SOMEBODY
FROM FLAMBOROUGH.

The caller says HI.
I DON'T HAVE THEM.

Stewart says YOU DON'T HAVE AN ANSWER?

The caller says NO.

Stewart says OKAY, FAIR ENOUGH.

Lorraine says THANKS.

Stewart says LET'S GO TO
ANOTHER CALL, THEN.

Lorraine says SOMEONE FROM
COLLEGE AVENUE.

The caller says HELLO.

Lorraine says DID YOU COME UP WITH
AN ANSWER FOR THIS?

The caller says YES.
IT WOULD BE E AND N.

Stewart says WELL, YOU'VE GOT TO
EXPLAIN TO ME WHERE,
HOW AND WHY YOU GOT
THOSE TWO LETTERS.

The caller says OH, IT'S BECAUSE IT'S
1, 2, 3 --

Lorraine says VERY GOOD.

Stewart says IN OTHER WORDS, THESE
REPRESENT THE FIRST
LETTERS OF THE NUMBERS.
NOW, THAT'S A
LITTLE BIT TRICKY.
AT FIRST SIGHT, MOST
PEOPLE DON'T SEE THAT.
VERY GOOD.
VERY GOOD.
WAS THAT BRAD?

Lorraine says YES.

Stewart says FANTASTIC, BRAD.
WELL, LET'S SEE.
I'VE GOT ANOTHER
ONE HERE.
THERE'S THE OTHER ONE.

Lorraine says OH, STEWART,
IT'S UPSIDE DOWN.

Stewart says OH, GEE, SORRY
ABOUT THAT.
YOU KNOW, I JUST SLIPPED
UP THERE, YOU KNOW.
THERE IT IS.
MAYBE WE SHOULD TAKE A
CALL AND SEE IF SOMEBODY
KNOWS WHAT THE SOLUTION
TO THIS ONE IS.

The sequence reads “1, 8, 11, 69, blank space, 96, 101, 111.”

Lorraine says LET'S TRY SOMEONE
HERE FROM FLAMBOROUGH.

Stewart says OKAY, LET'S SEE,
WE'LL STRAIGHTEN
THAT UP A LITTLE BIT.

The caller says HELLO.

Stewart says HELLO.
WHO'S SPEAKING,
CHRIS OR BLAKE?

The caller says CHRIS.

Stewart says HI, CHRIS.
HAVE YOU GOT A NUMBER
TO PUT IN THERE?

Chris says NO.

Stewart says NO?

Chris says NO.

Lorraine says HOW ABOUT BLAKE,
DOES HE HAVE ONE?

Chris says HE MIGHT.

Blake says NO.

Stewart says OKAY, WELL I GUESS WE
BETTER TRY SOMEBODY ELSE.

Lorraine says LET'S TRY ELISE OR
KATIE FROM FLAMBOROUGH.

The caller says HELLO.

Lorraine says HI.

Stewart says HAVE YOU GOT AN ANSWER
TO THIS SEQUENCE?

The caller says 81.

Stewart says 81.
CAN YOU EXPLAIN TO ME HOW
YOU GOT THE NUMBER 81?

The caller says I GUESSED.

Stewart says THAT'S NOT A BAD IDEA,
BUT IT'S STRICTLY A GUESS?
YOU DIDN'T ADD OR SUBTRACT
OR DO SOMETHING LIKE THAT?

The caller says NO.

Stewart says OKAY, FAIR ENOUGH.
HAVE WE GOT ANOTHER
ANSWER, PERHAPS?

Lorraine says OKAY, THANKS.

Stewart says TAKE ANOTHER CALL.

Lorraine says LET'S TRY CHRISTIE OF
LISA FROM FLAMBOROUGH.

Stewart says WELL, WHO'S ON
THE LINE?
IS IT LISA OR
CHRISTIE?
HELLO.

The caller says HI.

Stewart says HAVE YOU GOT AN
ANSWER FOR THIS ONE?

The caller says NO.

Stewart says YOU'RE NOT SURE.

The caller says WE DIDN'T GET
THAT SHEET.
WE WEREN'T
HERE ON THURSDAY.

Stewart says OH, OKAY, THAT
EXPLAINS THAT.
OKAY.
I WONDER IF THERE'S
SOMEBODY FROM JACK MINER
OR ONE OF THE SCHOOLS
WE HAVEN'T HEARD FROM,
MAYBE USBORNE, THAT MIGHT
HAVE AN ANSWER FOR US.

Lorraine says WELL, WE HAVE A COUPLE OF
CALLS HERE FROM COLLEGE.

Stewart says WELL, LET'S TAKE A CALL
FROM COLLEGE BUT IF
SOMEBODY FROM JACK MINER
OR USBORNE OR ANY ONE OF
THE SCHOOLS THAT WE
HAVEN'T TALKED TO YET,
I'D LOVE TO HAVE
YOU CALL IN.

The caller says HELLO.

Lorraine says HI.

Stewart says HELLO.

The caller says HI.

Lorraine says THIS IS PERRY.

Stewart says HI, PERRY.

Perry says HI.

Stewart says HAVE YOU GOT AN IDEA?

Perry says AH, WELL KIND OF.
I THINK IT'S LIKE 1, 8,
11, 69, HA HA, BLANK, 96,
101, 111, I THINK THE
BLANK IS A LITTLE BIT LIKE
79 OR SOMETHING.

Stewart says 79.

Perry says YEAH.

Stewart says IS THERE A
REASON FOR 79?

Perry says PARDON ME?

Stewart says HAVE YOU GOT A
REASON FOR 79?

Perry says AH, WAIT, NO,
I DON'T.

Stewart says YOU KNOW WHAT I'M
GOING TO DO, FOLKS.
I'M GOING TO
GIVE YOU A CLUE.
IT'S A VISUAL CLUE.
LEAVE IT ON THE
CAMERA HERE.
I'M GOING TO DO THIS A
COUPLE OF TIMES AND I WANT
YOU TO LOOK REALLY CLOSELY
AT WHAT YOU MIGHT BE
SEEING HERE THAT MIGHT
GIVE YOU A CLUE AS
TO WHAT'S GOING ON WITH
THIS PARTICULAR ONE.

Stewart turns the page upside down a couple of times.

Perry says 88?

Stewart says WHO SAID THAT?
THAT'S GREAT.

Lorraine says THAT'S PERRY.

Stewart says NOW, WHY DID YOU SAY 88?

Perry says BECAUSE ESTER SAID SO.

Stewart says AND WHY DID THEY SAY SO?

Perry says COULD YOU HOLD
ON A MINUTE?

Stewart says OKAY, WE CAN DO THAT.

Perry says BECAUSE SHE
LIKES THAT NUMBER.

Ester says IT KEEPS REPEATING
ITSELF, I THINK.

Stewart says IT KEEPS REPEATING
ITSELF BUT --

Ester says WELL, IT'S THE SAME
UPSIDE DOWN, I MEAN.

Lorraine says VERY GOOD.

Stewart says THIS SEQUENCE IS A SET OF
NUMBERS THAT ARE READABLE
UPSIDE DOWN AND
RIGHT SIDE UP.
THE ONLY PROBLEM WITH IT
IN THIS PARTICULAR FONT
IS YOU GET THIS LITTLE
THING ON THE ONE.
BUT IF YOU JUST DREW ONE
AS A STRAIGHT UP AND DOWN 1,
AND TURN IT
UPSIDE DOWN,
IT'S EXACTLY THE SAME.
AND WHEN YOU TURN
69 UPSIDE DOWN,
IT'S STILL 69, AND SO ON.

Lorraine says GREAT.
THANKS VERY MUCH.

Stewart says WE'VE GOT THE TOLL
FREE FAX NUMBER.
CAN WE PUT IT UP NOW?

Lorraine says CERTAINLY.

A slate pops up with the number 1-888-522-7141.

Stewart says THERE IT IS.
SOMETIMES THESE THINGS GET
LOST IN THE COMPUTER
AND THE LITTLE ELECTRONS
FINALLY GET THEMSELVES
TOGETHER AND
THERE THEY ARE.

Lorraine says AND FOR A
REFRESHER, WHAT IS IT
YOU ARE WANTING
THEM TO FAX?

Stewart says WHAT I WOULD LIKE YOU TO
FAX IN IS BASED ON -
I THINK IT WAS QUESTION NO. 3
IN EXERCISE NO. 1,
BUT NONETHELESS, IT'S
THE ONE THAT ASKS YOU
TO COME UP WITH YOUR OWN
NUMBER SYSTEM WITH YOUR
OWN SYMBOLS AND SO ON,
AND BE ABLE TO TAKE THOSE
NUMBERS AT THE TOP AND
WRITE THEM IN YOUR
OWN SYSTEM OF NUMBERS.
AND AS I SAY, ON THURSDAY,
WE'LL SHOW A NUMBER OF THEM.
I HOPE WE GET A
NUMBER OF FAXES.
WE GOT FOUR OR FIVE THE
LAST TIME SO WHY
NOT MORE THIS TIME?

Lorraine says YES, WE ENCOURAGE
ALL OF YOU.
GREAT.

Stewart says NOW, I'M GOING TO DO JUST
A REALLY, REALLY SHORT
LESSON THAT WILL HELP
YOU TO ACTUALLY DO SOME
OF THE MATERIAL TO
DO WITH BASES.
AND IT'S JUST A
DEFINITION OR TWO.
AT THE END OF THIS
I'M GOING TO ASK YOU,
IN ABOUT FIVE MINUTES,
IT WON'T TAKE VERY LONG,
TO BE PREPARED
TO PHONE IN,
AND PHONE IN SPECIFICALLY
WITH A RULE OR A PATTERN.

He shows a sheet of paper with 5 to the third exponent and the words “Powers,” “Exponent” and “Base.”

Stewart says SO I'LL START
BY SAYING THIS.
POWERS.
POWERS YOU WILL SEE IS
THE ENTIRE THING HERE.
WE HAVE 5 WITH A
LITTLE 3 AT THE TOP.
I THINK MOST OF YOU ARE
AWARE OF THIS AND SHOULD BE
FAMILIAR WITH THIS.
AND THE BIG NUMBER HERE ON
THE BOTTOM IS CALLED THE BASE.
THE LITTLE NUMBER WHICH
IS A SUPERSCRIPT
IS CALLED AN EXPONENT.
NOW, I'VE GOT TWO
EXAMPLES OF THIS.
WHAT DOES 5 TO THE
EXPONENT 3 OR 5 CUBE MEAN?
IT MEANS, TAKE THE NUMBER
5 AND MULTIPLY IT
BY ITSELF 3 TIMES.
5 TIMES 5 TIMES 5,
WHICH OF COURSE,
IF YOU WORKED
IT OUT, IS 125.
NOW I COULD REALLY PUT
LORRAINE ON THE SPOT HERE.
4 TO THE 5TH IS 4 TIMES 4
TIMES 4 TIMES 4 TIMES 4.
THERE ARE FIVE OF THEM.

Lorraine says SO 16 TIMES 16
TIMES 4, HOW'S THAT?

Stewart says 16 TIMES 16 TIMES 4?

Lorraine says OH, 1024.

Stewart says 1024.
I WASN'T GOING TO REALLY
MAKE HER DO THAT IN
HER HEAD, ALTHOUGH SHE
DID THOSE WONDERFUL
METRIC CONVERSIONS IN
HER HEAD, RIGHT?

Lorraine says THAT WAS MISSUS G.

Stewart says THAT'S TRUE,
I FORGOT THAT,
YOU'RE ABSOLUTELY RIGHT.
I'M GOING TO GIVE YOU
THE RULE FIRST,
AND NOTICE THERE'S
MY SPELLING MISTAKE.
I HAVE TO ADMIT TO IT.
MULTIPLICATION.

He shows a sheet of paper that reads “Multiplication. If the bases are the same you can add the exponents.”

Stewart says IF YOU'RE MULTIPLYING TWO
THINGS WITH THE SAME BASE -
IN OTHER WORDS, I WAS
TAKING 7 CUBE TIMES 7
TO THE 5TH, THEY HAVE
THE SAME BASE.
WHAT YOU CAN
DO IS, IN FACT,
ADD THE EXPONENTS
TO GET THE ANSWER.
SO THIS WOULD BE 7 TO 3
PLUS 5 IS EQUAL
TO 7 TO THE 8TH.
NOW, I'M GOING TO SHOW
YOU ONE MORE EXAMPLE LIKE THAT.
AND WHY IT WORKS.
FOR CUBE WE KNOW IS
4 TIMES 4 TIME 4,
THREE OF THEM, TIMES
THAT'S THAT TIMES,
4 TO THE 4TH.
4 TIMES 4 TIMES 4 TIMES 4.
WELL, HOW MANY HAVE WE
GOT ALL TIMES TOGETHER?
1, 2, 3, 4, 5, 6, 7,
WHICH IS THE ANSWER,
4 TO THE 7TH.
OR COULD HAVE
BEEN JUST AS EASY,
SKIP THIS ENTIRE STEP
AND JUST SAY, OH,
4 TO THE EXPONENT
3 PLUS 4.
AND THAT EQUALS
4 TO THE 7TH,
SO THAT'S YOUR ANSWER.
THE KEY THING IS, YOU
CANNOT DO THAT UNLESS
THE BASE IS THE SAME.
NOW, VERY LAST SLATE HERE
AND I'M GOING TO ASK YOU
TO CALL IN AFTER THIS ONE.
DIVISION.
I HAVE AN EXAMPLE HERE, 4 TO
THE 4TH DIVIDED BY 4 SQUARED.
YOU CAN WRITE THIS AS A
FRACTION 4 TIMES 4 TIMES 4
TIMES 4 DIVIDED
BY 4 TIMES 4.
WE CAN DIVIDE 4
EVENLY TO THIS IN
THE ONE IN TOP AND BOTTOM,
WHICH IS NO PROBLEM.
WE CAN DIVIDE 4, AND
THIS IS CALLED CANCELLING.

He crosses out two of the factors in the numerator and the two factors in the denominator and writes down numbers one instead.

Stewart says AND OF COURSE 1
TIMES 1 IS JUST 1,
SO THAT'S NO PROBLEM.
AND 4 TIMES 4, WHICH
IS 1 TIMES 1, NO PROBLEM.
THAT EQUALS 4 SQUARED.
WHAT I WOULD LIKE YOU TO
DO AT THIS POINT IS
TO PHONE IN AND TELL ME WHAT
THE RULE IS FOR DIVISION
WITH ALL THE LITTLE
BITS AND PIECES
AND I'LL WRITE
IT DOWN HERE.

Lorraine says WE'RE CALLING JACK
MINER PUBLIC SCHOOL.
JAY.

Stewart says OH, JACK MINER, GOOD.

The caller says HELLO.

Lorraine says HI.

Stewart says HELLO, HOW ARE YOU
DOING, IS IT JAY?

The caller says YES.

Stewart says CAN YOU TELL ME
WHAT THE RULE IS?

Jay says IF YOU'RE DIVIDING AND
THE BASES ARE THE SAME,
SUBTRACT THE EXPONENTS.

Lorraine says EXCELLENT.

Stewart says PERFECT.
WHAT I WANTED YOU TO SAY
WAS DEFINITELY THE BASES
ARE THE SAME AND THEN
YOU SAY SUBTRACT,
THEN YOU SUBTRACT
THE EXPONENTS.
THANK YOU VERY MUCH.
THAT'S GREAT.
GLAD TO HEAR FROM
JACK MINER, TOO.

Lorraine says AND NOW, LET'S HEAR
FROM COLLEGE AVENUE.

Stewart says AND WHO HAVE WE
GOT ON THE LINE?

Lorraine says I BELIEVE SEAN.

Stewart says HI, SEAN.
ARE YOU THERE?

Lorraine says SEAN FROM COLLEGE AVENUE,
IF YOU CAN LIFT UP
YOUR PHONE, PLEASE.

Stewart says IS THAT SEAN?

Sean says HELLO.

Lorraine says HI.

Stewart says HI, SEAN.

Sean says HELLO.

Stewart says DID YOU COME TO THE
CONCLUSION THAT YOU HAD
THE SAME RULE?

Sean says IT'S THE SAME - YES.

Lorraine says OKAY.

Stewart says GOOD GOING, BUT THE KEY
IS THAT THE BASES
HAVE TO BE THE SAME.

Sean says YEAH.

Stewart says AND THEN YOU DO WHAT
WITH THE EXPONENTS?

Sean says YOU DIVIDE TO SUBTRACT.

Stewart says YOU SUBTRACT
THE EXPONENTS.

Sean says YEAH.

Lorraine says AND NOW IT MIGHT BE A
GOOD IDEA TO WRITE
THIS DOWN SO THAT FOR
TOMORROW'S LESSON IT WILL
BE THAT MUCH EASIER.

Stewart says I THINK THAT'S GOING TO
BE A NICE LEAD IN UNTIL
TOMORROW, RIGHT?

Lorraine says GREAT, THANKS.

Stewart says OKAY, GREAT.
SO WE'RE DOING PRETTY
WELL WITH THAT.
I GUESS WE'VE GOT A COUPLE
OTHER ITEMS OF BUSINESS
TO TAKE CARE OF.
ONE OF THEM IS JUST A
REMINDER AND WE GOT
TO TAKE SOME PHONE
CALLS, AS WELL.
BUT ONE REMINDER IS THAT
IF YOU NEED TO USE
A LITTLE BIT MORE PRACTICE,
THEN DON'T FORGET,
IF YOU'VE GOT PLATO
INSTALLED IN YOUR SCHOOL,
THEN WHAT YOU SHOULD BE
DOING IS ASKING YOUR
TEACHER TO LET YOU
GET ON THE MACHINE,
AND ONE OF THE THINGS THAT
YOU'D PROBABLY BE LOOKING
FOR IN THE MANUAL IS
ANYTHING TO DO WITH BASES,
POWERS, OR EXPONENTS.
AND YOU WILL WORK YOUR
WAY INTO THAT PARTICULAR
PROGRAM AND PRACTISE
MULTIPLICATION AND
DIVISION FIRST
AND FOREMOST.
I THINK THAT THAT WOULD
BE A REASONABLE THING.

Lorraine says GREAT IDEA.
YES, I BELIEVE
AT THIS POINT,
IF YOU HAVE ANY QUESTIONS
ABOUT LAST WEEK'S LESSONS
OR TODAY'S, PLEASE FEEL
FREE TO CALL IN RIGHT
NOW AT POUND 9 AND WE CAN
ANSWER YOUR QUESTION.

Stewart says SURE.
WE CAN TAKE QUESTIONS
ABOUT ANYTHING, I THINK,
VIRTUALLY.

Lorraine says AND WE'RE CALLING
SOMEONE FROM JACK MINER.

Stewart says GREAT.

Lorraine says HI, DO YOU HAVE A
QUESTION FOR US?

The caller says HELLO?

Lorraine says HI, DO YOU
HAVE A QUESTION?

The caller says YEAH.
ON EXERCISE 1, 1B, WHY DID
THEY USE THE NUMBERS
THAT THEY USED,
LIKE 144,000?

Stewart says OH, OKAY.
DOWN HERE AT
THE BOTTOM.

Lorraine says GIVE ME AND WE'LL
SHOW WHICH ONE.

Stewart says I KNOW WHERE YOU'RE
ZOOMING INTO.
IT'S RIGHT DOWN HERE.
THE MAYAN SYSTEM IS A
MOST UNUSUAL SYSTEM.
I THINK WHAT I'M
GOING TO DO IS THIS,
I'LL DO A QUICK
EXPLANATION WITHOUT
GIVING AWAY THE
WHOLE THING.
THEY START WITH
SOME UNITS.
NOW, IN OUR SYSTEM, WE
ALSO HAVE UNITS, RIGHT?

The caller says YES.

Stewart says BUT THEN WE GO
TO 10s, RIGHT?
SO IN OUR SYSTEM
WE HAVE 10s.
BUT THEY WENT
TO 20s INSTEAD.
NOW, I'M NOT SURE EXACTLY
WHY THEY DECIDED ON 20s.
BUT THEY DECIDED ON 20s.
NOW, WE WENT 10 TIMES
10 TO GET 100, RIGHT?
SO WE WENT TO 100s
AFTER THAT, RIGHT?
NOT A BIG SURPRISE.
WHY DIDN'T THESE GUYS GO
TO 20 TIMES 20 TO GET 400
IS WHAT YOU'RE
ASKING, I THINK.
THE ANSWER TO THAT WAS
AN INTERESTING ONE.
THEY WERE AWARE THAT THE
EARTH WENT AROUND
THE SUN IN
ABOUT 365 DAYS.
SO WHAT THEY DECIDED IS,
IS THAT THEY'D MAKE
18 MONTHS IN THE
CALENDAR.
EVERY MONTH WOULD
BE 20 DAYS LONG.
SO INSTEAD OF GOING TO
400, THEY WENT TO 360.
BUT WHAT'S
WRONG WITH THAT?
WELL, THE PROBLEM
WITH THAT IS,
YOU STILL HAVE FIVE
DAYS LEFT OVER.
SO WHAT THEY DID WAS,
IN THEIR NUMBER SYSTEM,
THEY MADE IT SO IT'S SORT
OF LIKE THEIR CALENDAR.
IT GOES TO 360.
BUT WHAT THEY DID IN THE
ACTUAL CALENDAR IS TOOK
18 MONTHS OF 20 AND ADDED
5 RELIGIOUS HOLIDAYS.
THEY WEREN'T REGULAR
DAYS OF THE MONTH.
THEY WERE ADD-ONS.
SO YOU ENDED UP WITH A TOTAL
OF 365 DAYS IN THE YEAR.
MIND YOU THEY DIDN'T SORT
TAKE INTO ACCOUNT THAT
EXTRA QUARTER OF LEAP
YEARS AND SO NOT.
I'M NOT QUITE SURE
HOW THEY HANDLED IT,
BUT I DO KNOW THE MAYANS
WERE VERY SOPHISTICATED
ABOUT THE CALENDAR.
THEY WERE VERY GOOD.
DOES THAT HELP
EXPLAIN THAT?

The caller says YEAH.

Stewart says OKAY, GREAT.

The caller says BYE.

Stewart says SO HAVE WE GOT
ANY MORE QUESTIONS?

Lorraine says YES, WE DO.
WE'LL TRY SOMEONE HERE
FROM COLLEGE AVENUE, PERRY.

Perry says HI.

Lorraine says HI, YOU HAVE A
QUESTION FOR US, PERRY?

Perry says PARDON ME?

Lorraine says DO YOU HAVE A
QUESTION FOR US?

Stewart says NO.
I THINK I PRESSED POUND 9
INSTEAD OF POUND 0 SO.

Lorraine says DO YOU UNDERSTAND WHAT'S
REQUIRED FOR YOU FOR THURSDAY?

Perry says PARDON ME?

Lorraine says DO YOU UNDERSTAND
THE EXERCISES?

Perry says YEAH.

Lorraine says GREAT.

Stewart says OH, SAINT JOHN.

Lorraine says CERTAINLY.
WE HAVE SOMEONE FROM
SAINT JOHN BREBEUF.

Stewart says AND WE'RE JUST
CONNECTING.

Lorraine says EITHER MARK OR
SHEILA.

Stewart says OKAY.

The caller says HELLO.

Lorraine says HI.

Stewart says HI, WHO IS THIS,
MARK OR SHEILA?

The caller says JACOB.

Lorraine says OH, JACOB.

Stewart says THAT'S OKAY.
HI, JACOB.
HAVE YOU GOT A
QUESTION FOR US?

Jacob says YES.
HOW DO YOU WORK THE
INCA'S NUMBER SYSTEM?

Stewart says OKAY.
I'LL GIVE YOU A
BRIEF IDEA ANYWAY.

Stewart draws a quipu.

He says UP HERE IS A BELT.
WE DON'T COUNT THAT BUT
YOU'VE GOT TO HAVE THE BELT.
AND THEY HAD STRINGS THAT
JUST CAME DOWN LIKE THIS.

Jacob says YES.

Stewart says AND WHAT THEY DID IT,
THEY PUT KNOTS IN THE
STRING AND KIND OF
BUNCHED THEM TOGETHER.
SO THEY MIGHT HAVE HAD
THREE DOWN THERE AND THEN
THEY MIGHT HAVE HAD TWO UP
HERE AND A COUPLE
MORE UP HERE.

Jacob says OKAY.

Stewart says NOW, THIS IS KIND
OF LIKE THEIR UNITS.
THAT'S DOWN AT THE BOTTOM.
AND THIS IS KIND
OF LIKE THEIR 10s.
IN OTHER WORDS, THEY
LEFT SPACES IN BETWEEN.
AND THEY WORKED IN
THE DECIMAL SYSTEM,
WHICH MAKES IT KIND OF
LIKE OUR SYSTEM ANYWAY.

Jacob says OKAY.

Stewart says AND THAT WILL HELP YOU
UNDERSTAND THAT THE WHOLE
WAY OF READING
THOSE KNOTS.
NOW, THE ONLY CATCH IS
WHAT HAPPENS WHEN
YOU GO FROM 10s TO 1000s.
WELL, THIS SPACE
WILL BE EXTRA LONG,
SO YOU'VE GOT TO REALLY
WATCH THE SPACING.
SO IF YOU WENT
FROM 10s TO 1000s,
THEN THIS WILL BE
A BIG SPACE, OKAY?

Jacob says ALL RIGHT, THANK YOU.

Lorraine says THANKS.

Stewart says NO PROBLEM.
GREAT QUESTIONS TODAY.

Lorraine says YES, AND WE
HAVE, I BELIEVE,
BRAD FROM
COLLEGE AVENUE.

Brad says HELLO.

Lorraine says HI.
YES.

Brad says I HAVE A QUESTION.
WHAT DO THE BIG
CIRCLES MEAN?

Stewart says WHERE?

Brad says ON THE INCAS.

Stewart says WHICH CIRCLES?
I'VE GOT TO SORT
OF TAKE A LOOK
AT IT TO SEE
WHAT YOU MEAN.

Brad says OKAY.

Stewart says YOU MEAN AT THE TOP?
YOU MEAN UP HERE?

Brad says THE MIDDLE PART
BY THE LINK.

Lorraine says YOU MEAN THOSE?

Brad says YEAH, THOSE THINGS.

Stewart says THESE THINGS UP HERE
I'M POINTING TO, RIGHT?

Brad says YES.

Stewart says THOSE ARE JUST
BIGGER KNOTS.
NOW, AS IT TURNS OUT, ONE
OF THE WAYS THAT THE INCAS
DISTINGUISHED ONE PLACE
VALUE FROM ANOTHER IS
TO MAKE THE KNOTS EITHER
SMALLER OR BIGGER.
SO IN THIS CASE, IT'S JUST
ANOTHER PLACE VALUE
AND IT'S A SLIGHTLY
DIFFERENT KNOT.
IT'S JUST A LITTLE BIT
BIGGER THAN THE OTHER ONES.
BUT THEY'RE ALL KNOTS.
EVERY ONE OF
THESE ARE KNOTS.
THIS, THAT'S A KNOT,
THAT'S A KNOT, AND SO ON.

Brad says OH, YEAH, AND WHAT
DOES THE CIRCLE MEAN?
DOES THAT MEAN
MULTIPLICATION?

Stewart says THIS ONE RIGHT HERE?

Brad says YEAH.

Stewart says THAT'S MULTIPLICATION,
YOU'RE RIGHT.
YUP.

Brad says ALL RIGHT.

Lorraine says GREAT, THANKS VERY MUCH.
AND SOMEONE
FROM JACK MINER.

Stewart says OKAY, GOOD.

Lorraine says VANESSA.

Stewart says HELLO, VANESSA.

Vanessa says HELLO.

Stewart says HOW ARE YOU DOING?

Vanessa says FINE.

Stewart says ASK ME A QUESTION.
GO FOR IT.

Vanessa says IN EXERCISE 1, NOUMBER 3,
I WAS WONDERING,
WHEN YOU INVENT YOUR
OWN NUMBER SYSTEM,
DOES IT MATTER LIKE
WHAT SHAPE YOU USE
OR?

Stewart says NO.
ACTUALLY, THAT'S THE FUN
OF IT BECAUSE NOT ONLY
DO I WANT YOU TO DECIDE
ON A DIFFERENT BASE,
BUT I ALSO WANT YOU TO
MAKE UP YOUR OWN SYMBOLS.
YOU CAN MAKE THEM
LIKE HIEROGLYPHS
IF YOU LIKE THAT SYSTEM.
YOU CAN MAKE THEM UP
SOMETHING LIKE THE MAYAN
NUMBERS IF YOU LIKE THAT.
YEAH, NO, MAKE UP
YOUR OWN SYSTEM.
THAT'S WHAT THE
FUN'S GOING TO BE.

Vanessa says AND LIKE HOW FAR DO
YOU HAVE TO WRITE THEM?

Stewart says YOU HAVE TO BE ABLE TO HANDLE
THE PLACE VALUE SUFFICIENT
TO CHANGE - SEE THE NUMBERS
I PUT AT THE TOP?
I'LL HAVE TO TAKE A LOOK
AT IT NOW THAT YOU'VE
ASKED ME THE QUESTION.
YOU'VE GOT TO BE ABLE TO
FIND A SYSTEM - AND I'LL
WRITE THIS BIG - THAT
WILL IN FACT WRITE
THE NUMBER 7,769,003.
SO IN OTHER WORDS,
WHATEVER SYSTEM
YOU CREATE HAS TO BE ABLE
TO HANDLE THAT NUMBER.

Vanessa says OH, OKAY.

Stewart says OKAY?
NOW, IF YOU MAKE A BASE
THAT'S BIGGER THAN 10 AND
LESS THAN 20, IT WILL
BE EASY TO HANDLE THAT NUMBER.
IF YOU MAKE A BASE LIKE 3,
THEN YOU'VE GOT TO HAVE A
LOT OF SYMBOLS, OKAY?

Vanessa says OH, OKAY.

Lorraine says OKAY, THANKS.

Stewart says HOW ARE WE DOING?

Lorraine says WELL TRY ONE
PERSON FROM USBORNE,
SEE IF THEY HAVE
ANY QUESTIONS.

Stewart says OKAY, GREAT.
ARE WE ALL CONNECTED?
OH, NOT QUITE YET.
JUST ABOUT.

Lorraine says IT'S MEGAN OR
JORDAN FROM USBORNE.

Stewart says HELLO.

Lorraine says HI.

The caller says WHAT DOES ALL THIS MATH
HAVE TO DO WITH THE
MYSTERY?

Lorraine says OOH.

Stewart says WELL, THAT'S A GOOD
QUESTION AND I THINK PART
OF WHAT - YOU'RE GOING
TO ANSWER THAT QUESTION,
I THINK, FOR ALL
INTENTS AND PURPOSES.
AS WE MOVE ALONG, PERHAPS
WE'RE FINDING A PATTERN.
AND YOU KNOW SOMETHING,
THAT'S A REALLY GOOD POINT.
ONE OF THE THINGS
WE'LL BE DOING IS,
WE'LL BE PUTTING A NUMBER
OF LITTLE FLAGS ON THE MAP
AND PERHAPS THE DIFFERENT
LOCATIONS THAT WE HAVE
TO VISIT FORM A PATTERN
THAT MIGHT HELP US SOLVE
WHO'S DOING THIS.
AND IN FACT, I THINK BY
THE MIDDLE OF NEXT WEEK
OR SHORTLY THEREAFTER, WE'RE
GOING TO GET SOME MORE
INFORMATION UP HERE ON THE
MAP AND PERHAPS IT'S GOING
TO BE MORE APPARENT
HOW THESE DIFFERENT
LOCATIONS MIGHT HELP
SOLVE THE MYSTERY.
THERE IS A CONNECTION.
YOU'RE JUST GOING TO
HAVE TO KEEP WORKING
AT IT TO FIND IT.

Lorraine says JUST LIKE RENE AND I DID.

Stewart says YOU WANNA BET, SO SOPHIA.
DON'T FORGET SOPHIA.

Lorraine says THAT'S RIGHT,
SOPHIA, THE SISTER.
GREAT.
THANKS.
DID THAT ANSWER
YOUR QUESTION?
AND WE'RE OFF THERE.
LET'S TRY ONE
MORE FROM COLLEGE.

Stewart says ONE MORE CALL.
SOUNDS GOOD.

Lorraine says HI, IS THIS BRAD?

The caller says HELLO?

Lorraine says HI, BRAD?

Brad says HI.
I WAS TOLD THAT I HAD TO
INVENT A NUMBER SYSTEM
IN LESS THAN A DAY.
OKAY, IT TOOK THESE
PEOPLE YEARS TO DO THIS.
WHY DO I HAVE
A DAY TO DO IT?

Stewart says BECAUSE YOU HAVE THE
ADVANTAGE OF KNOWING
A LOT MORE MATHEMATICS
THAN THOSE PEOPLE KNEW
AT THE TIME, AND IN FACT,
INVENTING THIS SYSTEM
IS PROBABLY FAR EASIER
THAN YOU IMAGINE.
IT'S A QUESTION OF
CHOOSING A BASE
AND THEN MAKING UP
YOUR OWN SYMBOLS.

Lorraine says WHEREAS BEFORE, THEY
DIDN'T HAVE THAT.

Stewart says NO, THEY DIDN'T HAVE THE
ADVANTAGE OF THE KIND OF
KNOWLEDGE THAT YOU HAVE.
YOU'RE STANDING ON THE
SHOULDERS OF GIANTS.
YOU HAVE TONS OF
INFORMATION THAT
THEY NEVER HAD.

Lorraine says GREAT.
THANK YOU, AND LET'S TRY
ONE MORE FROM USBORNE.
AND FROM THERE,
WE'LL WRAP UP.

Stewart says HELLO, WHO HAVE WE
GOT ON BOARD NOW?

The caller says AMANDA.

Stewart says HI, AMANDA.
WHAT WOULD YOU
LIKE TO KNOW?

Amanda says I WAS JUST WONDERING WHAT
THAT THING THAT LOOKS LIKE
AN EYE, LIKE WHAT
NUMBER IS THAT?

Stewart says THAT'S ACTUALLY
LIKE A ZERO.
IF YOU NOTICE THE
FIRST CHART I STARTED
AT ONE AND RAN TO 19.
SO THE MAYANS HAD TO HAVE
SOMETHING THAT REPRESENTED
ZERO, SO IT'S LIKE A ZERO.

Amanda says OKAY, AND THAT ONE ON THE
SHEET WHERE IT HAS ALL
THE DIFFERENT SYMBOLS
AND EVERYTHING?

Stewart says WHICH ONE?

Amanda says IT SAYS EXERCISE 1 ON
IT AND IT HAS 1B
CONTINUED AT THE TOP.

Stewart says YEAH.

Lorraine says LIKE THIS?

Stewart says THIS ONE?

Amanda says NO, IT HAS THE NUMBER
293,911 ON THE TOP OF IT.

Stewart says 293, OKAY, JUST A MOMENT.

Lorraine says THERE IT IS.

Stewart says YUP.
YES?

They show an assignment sheet that with Mayan and Arabic numbers on it.

Amanda says HOW DID THEY GET
LIKE THAT 144,000?

Stewart says YOU SEE, THIS IS A REALLY
GOOD QUESTION AND I'M MORE
THAN HAPPY TO STOP AND
TRY TO EXPLAIN TO YOU.
WHAT IF I MAKE UP ANOTHER
NUMBER AND SORT
OF SHOW YOU A LITTLE BIT?

Amanda says OKAY.

Stewart says WITHOUT GOING ALL THE
WAY TO THE SYMBOLS.
I'M GOING TO TAKE A
NUMBER LIKE 172,241.
AND THE WAY YOU
BASICALLY DO THIS,
YOU KNOW THAT IN
THE MAYAN SYSTEM,
IF YOU GO BACK TO THE
PREVIOUS PAGE - I'M GOING
TO PUT A LITTLE THING
OVER HERE ON THE SIDE -
YOU HAVE UNITS.
YOU HAVE 20s.
YOU'VE GOT 360s.
YOU GOT 7200s, AND 144000s.

Lorraine says AND HE'S TALKING ABOUT
THIS SECTION RIGHT HERE.

Lorraine shows the section on the corresponding page.

Stewart says RIGHT HERE, SEE
THOSE AT THE BOTTOM?

Amanda says OH, OKAY.

Stewart says SO WHAT I'M LOOKING AT,
I SEE THIS NUMBER HERE,
AND I SAY, HMM, I LOOK AT
THE BIGGEST ONE POSSIBLE.
AND I SAY TO MYSELF, DOES
THAT - CAN I DIVIDE
THAT INTO THIS AND HAVE A
REMAINDER ABOVE AND BEYOND?
IN OTHER WORDS, IS THIS
NUMBER BIGGER THAN THAT?
AND IT IS.

He points 172,241 as being bigger than 144,000.

He continues SO IF I WERE TO TAKE THIS
NUMBER AND DIVIDE BY
144,000, NOW I DON'T CARE
ABOUT THE DECIMAL PART.
WHAT HAPPENED THERE IS
IF I DIVIDE INTO THAT,
I GET 1 PLUS A
REMAINDER, RIGHT?

Amanda says MM-HMM.

OKAY, SO I'M GOING TO
MAKE A RECORD OF THAT.
I'M GOING TO TAKE
ONE OF THOSE 144,000,
IF IT WAS TWO, IT
WAS BE 288, WHATEVER,
AND SUBTRACT IT.
AND WHAT I HAVE
HERE IS 28,241.
WELL, OBVIOUSLY THERE
ARE NO MORE 144,000s
BUT ARE
THERE 7,200s?

Amanda says YES.

Stewart says OKAY, SO I'M GOING TO
LOOK AT THAT AND I'M GOING
TO DIVIDE INTO THAT.
THE BIGGEST WHOLE
NUMBER I CAN GET.
THE BIGGEST ONE.
WELL, I THINK IT'S 3.
SO I'M GOING TO
MULTIPLY THAT BY 3
AND WHAT I WOULD
GET IS THIS.

He writes down 21600.

Stewart says AND I WOULD
SUBTRACT AND GET 41.
I WOULD GET 6
AND I GET 6.
OH, THAT'S SMALLER THAN
7,200, SO I'M OKAY.
I WAS RIGHT ABOUT 3.
SEE WHAT I'M DOING?

He writes down 6 641.

Amanda says PARDON?

Stewart says THIS NUMBER IS
SMALLER THAN 7,200,
SO 3 WAS RIGHT.
IF THIS NUMBER WAS
BIGGER THAN 7,200,
I MIGHT HAVE
TO GO TO 4.
SEE WHAT I'M DOING?

Amanda says OH, OKAY.

Stewart says OKAY.
NOW I'M GOING
TO GO TO 360s.
DO I GET ANY OF
THOSE IN THERE?

He points at 6 and 641.

Amanda says SURE.

Stewart says SURE I DO.
DO YOU WANT TO
GUESS HOW MANY?
I'D SAY ABOUT
9 OF THEM.
I MAY BE WRONG,
BUT I'LL TRY.
9 TIMES 0, 54.
9 TIMES 3 IS 27 OR -
DID I MAKE A MISTAKE?
OH, I'VE GOT TO REMEMBER.
YOU KNOW WHAT'S WRONG?
I'M THINKING DECIMAL
SYSTEM RIGHT NOW.
I COULD HAVE ALL
THE WAY UP TO 20.
SO I THINK I
BETTER USE 19.
I GOT TO DO SOME
HEAVY DUTY WORK HERE.
I DON'T HAVE MY
CALCULATOR WITH ME.

Lorraine says MAYBE THEY DO AND
THEY CAN HELP US OUT.

Stewart says 6 8.
OKAY, IT'S GOING TO 18.
I'M GOING TO DO THIS AS
EFFICIENTLY AS I CAN.

Amanda says EXCUSE ME.

Lorraine says YES?

Amanda says I WAS WONDERING HOW YOU
GOT LIKE THE 1 AND THE 20
AND 360 AND THOSE NUMBERS.

Stewart says OH, OKAY.
WELL, LET ME FINISH THIS
ANYWAY AND THEN I'LL COME
BACK AND RESPOND TO THAT.
360 OFF OF THAT.
IS THAT RIGHT?
6580.
OKAY.
SO WHEN YOU
SUBTRACT THIS TIME,
YOU GET 61 AND
THAT'S IT.
DO YOU GET ANY 20s?
THE ANSWER IS YES.
AND THERE ARE 3 OF THEM
AND THEN YOU HAVE A 1.
SO THE MAYAN NUMBER
THAT YOU END UP WITH HAS-
1 BY 144,000, IT HAS 3 BY
7200, HAS 18 360 IN IT, AND HAS
3 20S AND IT HAS ONE 1

Lorraine says IS THIS MAKING
SENSE TO YOU?
AND THEN YOU WOULD TRANSLATE
THAT INTO SYMBOLS.
WHY DID THEY CHOOSE BASE
20 IS WHAT YOU'RE ASKING.
WHY THESE NUMBERS?

Amanda says YEAH.
WHERE DID THOSE COME FROM?

Stewart says WELL, I WAS EXPLAINING
THAT THEY - FOR SOME
REASON THEY DECIDED THEY
LIKED THE NUMBER 20.
I HATE TO SAY IT THAT
WAY, BUT YOU KNOW THAT
COULD BE THE NUMBER OF
FINGERS ON A HAND
PLUS THE NUMBER OF
TOES ON YOUR FEET?
BELIEVE IT OR NOT, THEY
MAY HAVE DECIDED
IN THAT MANNER.

Amanda says OKAY.

Stewart says AND THEN WHEN
THEY WENT TO 360,
THE REASON THEY
DID THAT IS,
THEY WANTED 18
MONTHS IN THE YEAR.
SO THAT YOU GET 360 DAYS
WHICH IS JUST A LITTLE BIT
LESS THAN A NORMAL YEAR.
AND THEN THEY WENT BACK
TO BASE 20 AGAIN AND
MULTIPLIED BY 20, AND THEY
CONTINUED DOING THAT
FROM THERE ON.
IT'S A VERY
STRANGE SYSTEM.
AND VERY INTERESTING, TOO.

Amanda says WHAT'S THE NEXT NUMBER
GOING TO BE, THEN?

Stewart says I MULTIPLY THAT BY 20, SO
WE GET 4 ZEROS AT THE END
AND WE HAVE 2,880,000.

Lorraine says THEN MULTIPLY IT AGAIN.

Stewart says THEN MULTIPLY AGAIN
BY 20 AND SO ON.
THE ONLY TIME THEY DON'T
MULTIPLY BY 20 IS RIGHT THERE.
AND THAT'S BECAUSE THEY
WANTED TO MAKE THE YEAR FIT.

He points at the number 360.

Amanda says OKAY.

Stewart says WELL, THANK
YOU VERY MUCH.
I THINK THAT WAS A
PHENOMENAL QUESTION.
GOOD WAY TO END.

Lorraine says GREAT.
WELL, THANK YOU VERY MUCH
FOR ALL YOUR PARTICIPATION.
YOU DID VERY WELL TODAY.
AND TOMORROW'S LESSON WILL
JUST BE MAINLY ON THE
BASE 10 AND WE'RE LOOKING
FORWARD TO SEEING YOU THEN.

Stewart says FANTASTIC AND WE'LL
SEE YOU ON THURSDAY.
BYE BYE.

Lorraine says BYE.

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Watch: Student Session 7