Transcript: Counting on an Answer | 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, Mr. C 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 white T-shirt with black overalls and sits at his computer desk.

Mr. C says GOOD MORNING,
IT'S Mr. C. BACK
IN THE VIRTUAL
CLASSROOM.
WELCOME BACK ON A BRIGHT
AND SUNNY MONDAY MORNING,
WHICH IS REALLY A
NICE THING TO SAY.
THE FIRST THING I'M
GOING TO START WITH IS,
OF COURSE, THE RESULTS OF
THE PUZZLE THAT I GAVE YOU
LAST WEEK, WHICH WAS
CREATING THE SQUARE.
WE'LL TAKE A QUICK
LOOK AT WHAT
THE ORIGINAL PUZZLE
LOOKED LIKE.
THERE ARE THE FIVE PIECES,
AND I'VE ACTUALLY
GOT SOME OF THEM
HERE, AS YOU CAN SEE.

The piece of paper appears on screen. It is a rectangle drawn on lined graph paper with cut-outs of different shapes in the form of tessellations numbered 1 through 5. He shows the shapes cut out from the paper and then features students’ attempts at creating squares out of the cut out shapes.

Mr. C shows the papers and continues AND I WILL USE THEM
IN A MOMENT OR TWO.
BUT YOU KNOW WHAT?
I GOT A LOT
OF RESPONSES,
BOTH FROM TRILLIUM
AND ELGIN.
WHAT I WANT TO DO IS
VERY BRIEFLY SHOW
WHAT I GOT AND AT LEAST
SAY WHO SENT THEM IN.
AND THIS FIRST ONE CAME
FROM SAVANNA HARMON,
AND WE'RE GOING
TO TAKE A LOOK AT
A COUPLE OF
THESE LATER ON.
I THINK I'LL SAVE THIS
ONE TO TAKE A LOOK AT.
AND THEN I'VE
GOT SARAH MULLIN,
WHO SENT IN A
RESPONSE.
AND I'VE GOT
DARCY RUSHING.
AND I'VE GOT
JODIE MORRIS.
LET'S SEE IF I CAN GET
IT IN THE RIGHT SPOT.
AND I HAVE JALENE.
SO, WE'VE GOT A WHOLE
BUNCH OF RESPONSES.
THEN WE HAVE STACEY AND
JILLIAN FROM ELGIN AVENUE.
NOW, BASICALLY, THEY WERE
ALL FUNDAMENTALLY THE SAME.
LET'S LOOK AT THE
RESULTS FROM TRILLIUM.
WE HAVE SARAH BATEMAN.
SCOTT ROBERTSON.
JOSH.
AND ALEX DRURY.
NOW, WHAT I WANT TO DO
IS I WANT TO GO BACK
TO THAT VERY FIRST ONE.
AND I WANT TO TAKE
A QUICK LOOK AT IT.

Mr. C shows the piece of paper with the shapes cut out forming a square with each shape numbered.

Mr. C says THERE IT IS.
THE NUMBERS MAY
BE UPSIDE-DOWN,
BUT THAT DOESN'T
MATTER TOO MUCH.
WHAT I'M CURIOUS
ABOUT IS, IS THIS
A PERFECT
SQUARE OR NOT?
AND IT LOOKS
LIKE IT.
LET'S COUNT THE NUMBER
OF SQUARES ON EACH SIDE.
THERE'S ONE,
TWO, THREE, FOUR.
NOW, THESE ARE
COMPLETE SQUARES,
IF THEY WERE
DONE RIGHT.
BUT I THINK
THEY SHOULD BE.
SO, THERE'S
SIX THERE.
AND THERE'S CLEARLY SIX
HERE OF THE SAME SIZE.
SO, THAT'S LOOKING
PRETTY GOOD.
AND THERE'S CLEARLY
SIX ON THIS SIDE.
THE BOTTOM'S WHERE I GOT A
LITTLE BIT OF A PROBLEM.
I'VE GOT THREE.
BUT THEN, I'VE GOT THIS
LITTLE CHUNK IN HERE.

Mr. C points at the bottom right hand corner of the square where there is a triangle shape that has different shaped squares.

Mr. C says NOW, I WOULD SUGGEST TO
YOU THAT THIS IS REALLY,
REALLY CLOSE TO
EQUALLING THREE UNITS.
BUT NOTICE I ONLY HAVE
REALLY TWO PIECES IN HERE.
NOW, THE QUESTION
IS, IS THAT
EXACTLY THREE
UNITS OR NOT?
AND YOU KNOW, IT'S
PROBABLY NOT QUITE.
SO, THERE'S SOMETHING
THAT'S GONE ON IN HERE
THAT'S PROBABLY INVOLVED A
LITTLE BIT OF OVERLAPPING.
I WANT TO TAKE A
LOOK AT ANOTHER ONE.
I THINK I'LL TAKE A
LOOK AT ALEX DRURY'S,
JUST BECAUSE IT'S
SITTING CLOSE TO ME.
AND THIS ONE'S REALLY
QUITE DIFFERENT.
IF YOU NOTICE IN THIS
PARTICULAR CASE,
YOU DON'T HAVE
THE SQUARE SIZE
COMING OUT
TO THE EDGE.
WHAT YOU'LL HAVE ARE THE
TRIANGULAR PIECES, LIKE THIS.
AND THE DIAGONALS
COME OUT TO THE EDGE.
IT'S NOT REALLY CLEAR IN
HERE HOW THAT ALL WORKS OUT.
SO, WHAT I'M GOING TO DO
IS TO SET UP THIS PUZZLE.

Mr. C sets up a puzzle and says SET UP THESE PIECES.
SO, TODAY, REALLY,
I'M JUST...
VERY CAREFULLY
SETTING THAT UP.
SO, WHAT YOU SEE ON THIS
SIDE IS ONE DIAGONAL,
TWO, THREE, FOUR.
AND THIS LITTLE
PIECE UP AT THE TOP,
WHICH IS ACTUALLY
HALF OF A DIAGONAL.
THIS PIECE WILL FIT
PERFECTLY THERE,
BECAUSE THE THREE
SQUARES MATCH UP.
SO, THAT'S NO
REAL PROBLEM.
THIS PIECE WILL FIT
PERFECTLY THERE.
AND THIS PIECE -
LAST BUT NOT LEAST -
WILL FIT DOWN
IN THE CORNER.
NOW, LET'S
TAKE A LOOK.

Mr. C counts the lines on each side of the square and says ONE DIAGONAL, TWO
DIAGONALS, THREE DIAGONALS,
FOUR AND A BIT.
ONE DIAGONAL, TWO
DIAGONALS, THREE DIAGONALS,
FOUR AND A BIT.
ONE DIAGONAL, TWO
DIAGONALS, THREE DIAGONALS,
FOUR DIAGONALS,
AND A BIT.
AND LAST BUT NOT LEAST, ONE
DIAGONAL, TWO DIAGONALS,
THREE DIAGONALS,
FOUR AND A BIT.
THIS SOLUTION IS AN
ABSOLUTELY PERFECT SQUARE.
INTERESTINGLY ENOUGH, IF
YOU DO A LITTLE BIT MORE
MATHEMATICS WITH THIS AND
ACTUALLY GET TO THE POINT
WHERE YOU DO SOME
CALCULATIONS,
WHAT YOU'LL FIND IS THAT
THE ORIGINAL PIECES HAD,
I BELIEVE, AN AREA
OF 40 AND A HALF SQUARE UNITS.
AND IF YOU ACTUALLY GO
ABOUT THE BUSINESS OF
WORKING OUT THE SQUARE ROOT
OF THAT TO FIND OUT
THE LENGTH OF THE SIDE,
IT WILL WORK EXACTLY
TO THOSE FUNNY LITTLE PIECES
THAT I WAS TALKING ABOUT.
THERE'S SOME REALLY NICE
MATHEMATICS IN THERE THAT
MAYBE YOU'LL GET A CHANCE
TO DO LATER IN GRADE 6,
BUT CERTAINLY IN
GRADE 7 AND 8.
IT JUST SO HAPPENS THAT
THIS WEEK I HAVE ANOTHER
PERSON FROM THE MANITOULIN
ISLAND ON THE PHONE.
I BELIEVE THAT SAM
IS ON THE PHONE.
I UNDERSTAND, SAM,
THAT YOU LIVE ON
THE MANITOULIN ISLAND.
WHAT IS IT THAT
YOU DO UP THERE?

Sam says WELL, Mr. C, I GET
MY KICKS SPELUNKIN'
ALL OVER THE ISLAND.

Mr. C says SPELUNKING!
WHAT'S THAT?

Sam says OH, I GUESS YOU SAY
CITY SLICKERS WOULDN'T
KNOW WHAT THAT IS.
SPELUNKING IS ANOTHER
TERM FOR CAVE SEARCHING.

Mr. C says WHY ON EARTH WOULD YOU
WANT TO SPEND YOUR TIME
UNDER THE EARTH,
WHERE IT'S DAMP, DANK,
AND IT MUST BE MUSTY.

Sam says IT'S NOT THAT
BAD, Mr. C.
MY MAIN INTEREST IS TO
DO GEOLOGICAL STUDIES
FOR THE GOVERNMENT.
ON THE OTHER HAND, I REALLY
ENJOY THE CHALLENGE
OF GOING UNDERGROUND.
IT'S CERTAINLY NOT
A WALK IN THE PARK,
IF YOU GET THE PUN.

Mr. C says OH, THAT'S TRUE.
I DIDN'T MEAN TO SUGGEST
THAT IT WAS EASY.
WHAT DO YOU SEE WHEN
YOU GO UNDERGROUND?

Sam says WELL, Mr. C, YOU'VE
GOT THESE THINGS CALLED
STALACTITES AND
STALAGMITES.
AND THEY'RE DEEP BLACK PITS
IN UNDERGROUND STREAMS.
ONCE IN A WHILE, YOU
EVEN COME ACROSS ANCIENT
AND INDIAN ARROWHEADS.

Mr. C says OH, YOU WOULDN'T HAPPEN
TO HAVE SOME PICTURES THAT
MIGHT SHOW OFF A CAVE?

Sam says AS A MATTER OF FACT, I DO.
WANT ME TO RUN IT?

Mr. C says OH, ABSOLUTELY, GO AHEAD.

A clip of a large plant covered mountain with a group of students entering a cave appears on screen.

Mr. C continues OH, THAT'S AN
INTERESTING CAVE.
IT DOESN'T LOOK LIKE THE
MANITOULIN ISLAND THOUGH.
YOU KNOW SOMETHING, I JUST
HAVE A LITTLE NOTE HERE
THAT SAYS THAT THIS CAVE
IS ACTUALLY IN CHINA.
DURING THE SUMMER, I
ACTUALLY HAD A CHANCE TO GO
IN A CAVE MYSELF, IN
NEW MEXICO, CARLSBAD.
AND IT WAS JUST AMAZING.
AH, STALAGMITES
AND STALACTITES.

The clip changes to the inside of the cave where pointy rock sculptures jut out from the ceiling and the cave ground.

Mr. C continues THAT'S INTERESTING.
THE FORMATIONS ARE
VERY STRANGE INDEED.
I THINK THERE COULD BE SOME
WONDERFUL MATHEMATICS
ONE COULD DO IN A
CAVE LIKE THIS,
PERHAPS EVEN FRACTALS.

Back to Mr. C, he says THANK YOU FOR
JOINING US TODAY.
I HOPE YOU ENJOYED YOUR
LITTLE BIT OF TIME WITH US.

Sam says I SURE DID, Mr. C.
NOW, IF YOU'LL EXCUSE ME,
I GOT SOME ITCHIN'
FOR SOME SPELUNKIN'.

Mr. C says OKAY, WE'LL TALK
TO YOU AGAIN.
BYE-BYE.
IT BRINGS US SORT OF BACK
TO THE EXERCISE THAT WE DID
THIS WEEK, WHICH HAVE
IMAGES THAT KIND
OF LOOK LIKE CAVES.
AND THAT'S ONE OF THE
REASONS WHY I WANTED
TO TALK TO A SPELUNKER
JUST TO SORT OF MAKE IT
A LITTLE BIT OF A
THEME FOR TODAY.
SO, LET'S TAKE A
LOOK AT SEQUENCE NUMBER 1.

A worksheet appears on screen with 5 numbered objects that looks like potatoes with gray engravings on the side. The title of the sheet reads “Sequence Number One, the first drawing represents a whole number less than 10.”

Mr. C says SO, THIS IS FROM
YOUR HOMEWORK.
AND I JUST SORT OF
RE-SET IT UP ON HERE.
AND THIS IS WHAT THE
SEQUENCE LOOKS LIKE.
AND THE ONLY THING THAT I
GAVE YOU WAS THE CLUE
THAT THIS FIRST CAVE
WITH THIS ONE OBJECT...
OH, BY THE WAY, MAYBE
YOU CAN PHONE IN IF
YOU KNOW SOMETHING.
WHAT'S THE DIFFERENCE
BETWEEN A STALACTITE
AND A STALAGMITE?
I'M NOT SURE WHICH
ONE IS WHICH.
AND I THINK THAT ON
THIS SET OF DRAWINGS,
I'M JUST USING ONE KIND.
CAN SOMEBODY PHONE IN
AND LET ME KNOW WHAT
A STALACTITE IS AND
WHAT A STALAGMITE IS,
AND WHAT AM I
USING HERE?
IT SEEMS THAT WE HAVE
A CALL FROM TRILLIUM.
HELLO, IS
IT CHRIS?

Chris says HELLO.

Mr. C says HI, IS IT CHRIS?

Chris says YEAH.

Mr. C says OKAY, CHRIS,
WHAT'S A STALAGMITE
AND WHAT'S A STALACTITE?

Chris says STALACTITE HANGS AND A
STALAGMITE IS ON THE FLOOR.

Mr. C says IT COMES UP FROM
THE FLOOR, RIGHT.
NOW, CAN YOU TELL ME HOW
IS IT THAT YOU REMEMBER
WHICH ONE IS WHICH?
BECAUSE I ALWAYS HAD
DIFFICULTY REMEMBERING
THAT THE STALACTITE'S
THE ONE UP HERE AND THE
STALAGMITE'S THE
ONE ON THE BOTTOM.
HAVE YOU GOT A
MEMORY TRICK?

Chris says STALACTITES -
WHOOPS - HANG TIGHT.

Mr. C says HANG TIGHT, OKAY.
ACTUALLY, MY LITTLE MEMORY
TRICK THAT I SOMETIMES
REMEMBER IS: STALACTITE
HAS A C IN IT,
WHICH STANDS FOR CEILING.
THERE'S ANOTHER
WAY OF REMEMBERING.
SO, I'M USING
STALACTITES HERE, RIGHT?

Chris says RIGHT.

Mr. C says OKAY, THANKS A
LOT, CHRIS.
OKAY, SO I'VE SET UP A
SEQUENCE THAT'S BASED ON
A SERIES OF DRAWINGS.
AND ALL I'VE TOLD YOU IS
THAT THE FIRST DRAWING
REPRESENTS A WHOLE
NUMBER LESS THAN 10.
SO, WHAT I'M CURIOUS ABOUT
IS WHAT DO YOU THINK
THIS SEQUENCE IS?
DO YOU HAVE
ANY IDEAS?
SO, AGAIN, I WOULD LIKE
RESPONSES FROM YOU
TO LET ME KNOW WHAT
YOU MIGHT HAVE FOUND
WHEN YOU DID
THIS ONE.
AND IT LOOKS LIKE
WE'RE CONNECTING
TO ALEX FROM TRILLIUM.

Alex says HELLO?

Mr. C says GOOD MORNING, ALEX.

Alex says GOOD MORNING.

Mr. C says OKAY, WHAT DO YOU
THINK THE SEQUENCE IS?

Alex says THE LONG ONES ARE THREE
AND THE SHORT ONES ARE ONE.

Mr. C says OKAY, I'M GOING TO...
DRAWING NUMBER 1 IS THREE.
IS THAT CORRECT?

Alex says YEAH.

Mr. C says AND THEN DRAWING NUMBER 2
REPRESENTS A TOTAL OF?

Alex says FOUR.

Mr. C says RIGHT.
KEEP GOING, YOU MIGHT
AS WELL TAKE ME...

Alex says FIVE.
AND THE NEXT ONE, SIX.
SEVEN.

Mr. C says AND SO ON.
CAN YOU TELL ME WHAT THE
RULE FOR THE PATTERN IS?

Alex says ADD ONE.

Mr. C writes and says ADD ONE.
THERE'S ONE OTHER
THING I WOULD LIKE YOU
TO TELL ME
ABOUT THE RULE.
THAT'S CORRECT,
IT'S ADD ONE.
BUT I ALWAYS LIKE TO
KNOW WHEN I TALK ABOUT
SOME KIND OF SEQUENCE,
IS WHERE IT STARTS.
SO, IT'D BE: ADD
ONE AND START WITH?

Alex says START WITH THREE.

Mr. C says YEAH, START WITH THREE.
IF YOU KNOW THOSE TWO
FACTS, BASICALLY,
ABOUT THIS KIND
OF SEQUENCE,
YOU WILL ALWAYS HAVE ENOUGH
TO DEFINE WHAT IT IS.
THANK YOU VERY
MUCH, ALEX.

Alex says OKAY, BYE.

Mr. C says NOW, IN THE
INTEREST IN SCIENCE,
I'M GOING TO DO BACK
TO THIS DRAWING AGAIN.
ALEX WAS RIGHT.
BUT I WONDER IF SOMEBODY
HAD A DIFFERENT ANSWER
THAT MIGHT ALSO BE RIGHT.
REMEMBER THAT I ONLY SAID
THAT THE FIRST DRAWING
REPRESENTS A WHOLE
NUMBER LESS THAN 10.
MAYBE THERE IS
ANOTHER ANSWER.
OKAY, SADIE OR
DARCY FROM ELGIN.

Darcy says IT'S DARCY.

Mr. C says HI, DARCY.

Darcy says HI.

Mr. C says HOW'S THE WEATHER
DOWN YOUR WAY TODAY?

Darcy says GOOD.

Mr. C says OKAY, GOOD.
DO YOU HAVE AN IDEA
ABOUT ANOTHER SEQUENCE
THAT JUST MIGHT
WORK FOR THIS?

Darcy says YEAH, I GOT THE LONG
ONES ARE SIX AND
THE SHORT ONES ARE TWO.

Mr. C says OKAY, LET'S DO THAT
FOR THE SECOND ONE
I'VE GOT UP HERE.
YOU SAY THAT THE FIRST
ONE IS 6, RIGHT?

Darcy says YEP.

Mr. C says AND THEN WHAT'S
DRAWING NUMBER 2?

Darcy says 8.

Mr. C says THEN DRAWING NUMBER 3?

Darcy says 10.

Mr. C says THEN DRAWING NUMBER 4?

Darcy says 12.

Mr. C says AND...?

Darcy says 14.

Mr. C says OKAY, NOW DESCRIBE
THE PATTERN AGAIN.

Darcy says START WITH SIX
AND COUNT BY TWOS.

Mr. C says YOU GOT IT.
YOU GOT THE IDEA: START
WITH SIX AND COUNT BY TWOS.
THANK YOU VERY MUCH.
NOW, YOU SEE, I'M EVEN
SUGGESTING BY THE FACT THAT
ON THAT CHART I'VE GOT
ANOTHER POSSIBLE ANSWER.
HAS SOMEBODY GOT YET
A THIRD POSSIBILITY?
YOU SEE, IT'S NOT ALWAYS
TRUE THAT WHEN YOU GIVE
SOME KIND OF PATTERN THAT
THERE'S ONLY ONE ANSWER.
IN THIS PARTICULAR CASE,
I KIND OF DESIGNED IT
SO THERE WOULD BE MORE
THAN ONE ANSWER.
ANDREW OR KATIE: WHO
AM I SPEAKING TO?

Katie says KATIE.

Mr. C says HI, KATIE.
WHAT'S ANOTHER
POSSIBILITY?

Katie says I REALLY DON'T KNOW.
I JUST CALLED IN
FOR THE ONE BEFORE.

Mr. C says OH, OKAY.
SO, YOU KNEW ABOUT
THE SIX AND THEN
THE DIFFERENCES OF TWO.

Katie says YEAH.

Mr. C says OKAY, MAYBE I'LL GO
TO ANOTHER CALLER.
THANK YOU VERY MUCH.
OKAY, AND WE'RE
CONNECTING TO TRILLIUM.
CHRIS.
HI, CHRIS.

Andrew says HELLO, THIS
IS ANDREW.

Mr. C says OH, SORRY
ABOUT THAT.
ANDREW, DID YOU HAVE
ANOTHER SOLUTION?

Andrew says I WAS PHONING
FOR THE OTHER ONE,
BUT I MIGHT
HAVE A SOLUTION.

Mr. C says WHAT IS THAT?
WHAT DO YOU THINK?

Andrew says 4 AND 12.

Mr. C says 4 AND 12.
SO, THE FIRST ONE...
OKAY, YOU'RE SAYING
THE FIRST ONE IS 12
AND THEN 4 IS
AFTER THAT?

Andrew says YES.

Mr. C says ACTUALLY, THE ONLY PROBLEM
WITH THAT IS THAT 12
IS NOT A NUMBER
LESS THAN 10.
ALTHOUGH, FUNDAMENTALLY,
12 AND 4s WOULD WORK,
IF I WAS DOING ANY WHOLE
NUMBER AS A STARTER, RIGHT?
12 AND 4 WOULD WORK.
WHAT ABOUT A NUMBER
THAT'S JUST LESS THAN 10
THAT MIGHT ALSO WORK?
THINK ABOUT IT
FOR A SECOND.
WE'VE GOT 3, WE'VE
GOT 6 AS A STARTER.
WHAT MIGHT BE
THE NEXT STARTER?
KNOWING THAT 12
WOULD ACTUALLY WORK,
THERE'S A NUMBER IN
BETWEEN THAT ALSO WORKS.

Andrew says 9?

Mr. C says RIGHT.
AND WHAT WOULD THE
DIFFERENCES BE?
INSTEAD OF A DIFFERENCE OF
ONE OR A DIFFERENCE OF TWO,
WHAT WOULD THE DIFFERENCE
BE IN THIS CASE?
9 AND?

Andrew says 4?

Mr. C says NO, IT'D BE
12 AND 4.
SO, 9 AND?

Andrew says 3.

Mr. C says RIGHT ON.
SO, IT'D BE 9, 12,
15, 18, 21, RIGHT?
SO, HOW WOULD YOU
DESCRIBE THIS SEQUENCE
IF I ASKED YOU TO
STATE THE RULE?

Andrew says START WITH 9
AND ADD 3.

Mr. C says RIGHT ON, THANK
YOU VERY MUCH!
WELL DONE, GROUP.
COUNT BY THREES.
NOW, AS YOU MOVE ALONG
IN YOUR MATHEMATICS,
ONE OF THE THINGS THAT YOU
WILL BEGIN TO DISCUSS,
FIRST TERM IS
ALWAYS IMPORTANT,
SO THAT “START
WITH” IS IMPORTANT.
THOSE DIFFERENCES
ONES, TWOS,
OR THREES - ARE CALLED
COMMON DIFFERENCES.
AND SOMEDAY, YOU'LL
ACTUALLY DO SOME MORE
FORMAL MATHEMATICS AND
ACTUALLY REFER TO IT
AS COMMON DIFFERENCES.
OKAY, LET'S GO
TO THIS ONE.

Another worksheet appears on screen with five numbered, deformed square-like drawings. Each has a consecutively larger black blog within each square. The title reads “Sequence Number 2, the first drawing represents the number 2.”

Mr. C says NOW, I'M GOING TO DO
THE APPROACH THIS TIME.
THEN I'M GOING TO ASK
YOU A QUESTION FIRST.
SO, LET'S TAKE
A LOOK AT IT.
THERE IT IS.
SEE, I'M BEING A LITTLE BIT
SNEAKY HERE BECAUSE THERE
WERE ONLY FIVE TERMS IN THE
SEQUENCE THAT WERE GIVEN.
SO, I'M ASKING YOU WHAT
THE SIXTH TERM MIGHT BE.

A question appears on screen and reads “Question Number one, the sixth term in the second sequence has a value of 8, 16, 32, or 64.”

Mr. C continues SO, TAKE A LOOK AT WHAT YOU
HAVE, WHAT YOUR ANSWER IS,
AND SEE IF THERE IS A
NUMBER THERE THAT MAKES
SENSE TO YOU, AS TO WHAT
THE SIXTH TERM MIGHT BE.
THEN WE'LL TAKE A LOOK AT
YOUR ANSWERS AND WE'LL
TALK ABOUT THE SEQUENCE
FOR A MOMENT OR TWO,
AND HOW YOU BASICALLY
FIGURED IT OUT.
I SEE THAT A LOT OF PEOPLE
ARE ANSWERING THIS.
IT'S REALLY,
REALLY GOOD.
I'D LIKE TO SEE AT
LEAST 75 PERCENT OF YOU.
OH, WE'RE GOING
REALLY WELL NOW.
AND I SEE THE ANSWERS
AS THEY'RE GROWING.
NOT BAD; A COUPLE
MORE PEOPLE.
AND THEN I'LL TAKE
A LOOK AT THE GRAPH.
THAT'LL DO IT.
THAT'S GREAT.

The graph appears on screen. From left to right, the votes per corresponding answer are the following: 0 votes for number 1, 2 votes for number 2, 2 votes for number 3, and 21 votes for number 4.

Mr. C continues THE VAST MAJORITY SAY THAT
THE CORRECT ANSWER IS NUMBER 4.

Back to the worksheet, Mr. C says LET'S CHECK IT OUT.
HERE'S THE SEQUENCE.
WHAT'S THE RULE
FOR THE SEQUENCE,
AND HOW DID YOU
DISCOVER IT?
SO, WHAT'S THE RULE
FOR THE SEQUENCE,
AND HOW DID YOU
DISCOVER IT?
WE'VE GOT A CALL, AND IT
LOOKS LIKE FROM ELGIN.
I THINK WE'RE TRYING
TO CONNECT TO EITHER
JESSIE OR SAVANNA.
WHAT IS THE RULE, AND
HOW DID YOU DISCOVER IT?
HELLO!

Jessie says HELLO?

Mr. C says JESSIE OR SAVANNA?

Jessie says IT'S JESSIE.

Mr. C says HI, JESSIE.
SO, WHAT IS THE RULE HERE,
AND THEN I WANT TO PROBE
A LITTLE BIT MORE
AND FIND OUT HOW YOU
KIND OF DISCOVERED IT.

Jessie says YOU JUST DOUBLE
EACH NUMBER.

Mr. C says OKAY, SOUNDS LIKE
A PERFECT RULE,
AND I AGREE WITH YOU.
NOW, HOW DID YOU KNOW IT
WAS DOUBLE EACH NUMBER?
WHAT WAS THE CLUE THAT
TOLD YOU THAT YOU SHOULD
DOUBLE EACH TIME?

Jessie says UM...
BECAUSE, LIKE, TWO
AND TWO IS FOUR,
AND FOUR AND FOUR IS
EIGHT, I DON'T KNOW.

Mr. C says WHEN YOU LOOK AT THE
ACTUAL DIAGRAMS THOUGH,
WHAT WAS THE CLUE IN THE
PICTURES THAT TOLD YOU THAT
YOU SHOULD BE DOUBLING?

Jessie says THEY KEPT GETTING
TWICE AS BIG.

Mr. C says EXACTLY.
NOW, WHEN YOU SAY TWICE AS
BIG, YOU MEAN AREA, RIGHT?

Jessie says YES.

Mr. C says THIS AREA HERE, THIS
ONE'S DOUBLE THAT ONE.
AND THEN WHEN YOU LOOK AT
IT AND COMPARE THIS ONE
TO THAT ONE, THIS ONE
APPEARS TO BE DOUBLE.
RIGHT?

Jessie says RIGHT.

Mr. C says OKAY, VERY GOOD.
THAT'S EXACTLY WHAT
I WANTED TO HEAR.
NOW, I CAN FILL OUT THAT
SEQUENCE IN A MOMENT
OR TWO, AND I WILL.
ONE OF THE THINGS I WANTED
TO TELL YOU IS ABOUT HOW
I ACTUALLY DO ONE OF THESE
THINGS ON THE COMPUTER.
BECAUSE, IN A SENSE, WHAT
I'M DOING ON THE COMPUTER
IS GETTING VERY CLOSE
TO EXACT ANSWERS.
WHAT I'M ASKING THE
COMPUTER TO DO IS WHEN
I DRAW THE FIRST OBJECT,
ALL I DO IS I GO IN
AND I TAKE THAT
OBJECT AND I COPY IT.
BUT THEN I ASK FOR
A TRANSFORMATION,
TO DOUBLE THE WIDTH
OR DOUBLE THE HEIGHT,
JUST ONE AT A TIME.
AND WHEN YOU DOUBLE ANY
DIMENSION EXACTLY ONCE,
THE WHOLE AREA DOUBLES.
SO, IF WE GO BACK
TO THE DIAGRAM,
WHAT I DID HERE IS I COPIED
THAT DIAGRAM OVER TO HERE.
AND THEN I ASKED IT
TO DOUBLE THE HEIGHT.
AND THAT GAVE YOU
DEFINITELY A DOUBLE AREA.
NOW, I COPIED THIS
ONE OVER TO HERE,
AND THIS TIME I
DOUBLED THE WIDTH.
THEN I COPIED
THIS ONE HERE,
AND I DOUBLED
THE HEIGHT.
WHAT'S HAPPENING EACH
TIME IS I'M GETTING
A VERY TRUE PICTURE OF
DOUBLE THE AREA EACH TIME.
AND THAT'S ONE OF THE
REASONS THAT YOU DO USE
MATHEMATICS: IF YOU'RE
CREATING A SERIES
OF PICTURES, WHERE THAT'S
AN IMPORTANT IDEA,
THE AREA IS
DOUBLING EACH TIME,
IF YOU USE A LITTLE BIT OF
MATHEMATICAL KNOWLEDGE,
IT'S VERY EASY TO DO.
SO, HERE'S OUR QUICK
DRAWING NUMBER 1.
YOU GUYS BASICALLY
KNEW THIS.
AND YOU WERE
ABSOLUTELY RIGHT.
THE SIXTH PICTURE WOULD
HAVE REPRESENTED 64,
SO YOU DID A NICE JOB.
I WOULD LIKE SOMEBODY TO
PHONE IN AND STATE FOR ME
EXACTLY WHAT THE RULE
FOR THE PATTERN IS.
THIS IS REALLY
IMPORTANT.
I WANT TO GO OVER THIS
OVER AND OVER AGAIN.
WHAT IS THE RULE
FOR THE PATTERN?
SO, IF YOU GIVE ME A
QUICK CALL AND TELL ME
WHAT THE RULE IS.
AND I THINK WE'RE
CONNECTING TO ELGIN AGAIN,
WHICH IS GREAT.
GOT SOME OTHER
CALLS COMING.
HELLO?
NOT QUITE THERE YET.
HELLO?

Savanna says HELLO?

Mr. C says HI, IS IT JESSIE OR
SAVANNA THIS TIME?

Savanna says SAVANNA.

Mr. C says HI, SAVANNA.
WHAT'S THE RULE
FOR THE PATTERN?

Savanna says YOU JUST DOUBLE IT
EVERY SINGLE TIME
YOU DOUBLE THE NUMBER.

Mr. C says OKAY, WHAT WAS THE
OTHER THING I WANT
WHEN YOU STATE A RULE?

Savanna says START WITH TWO.

Mr. C says YES, THAT'S WHAT
I WANT EVERY TIME.
START WITH TWO.
AND DOUBLE EACH TIME.
THANK YOU VERY MUCH.

Savanna says BYE!

Mr. C says BYE-BYE.
NOW, WHAT I'M GOING TO
DO ON THE NEXT SHEET -
ASSUMING THAT I'VE GOT
EVERYTHING RIGHT
IN ORDER, AND I DO.

A table appears on screen with three columns that read “Drawing Number, Sequence number one, and sequence number 2.” Mr. C fills out the table.

Mr. C says THIS IS GOOD.
WE'RE GOING TO LOOK AT
THOSE TWO SEQUENCES.
NOW, FOR SEQUENCE NUMBER 1, I'M
GOING TO JUST CHOOSE
ONE OF THE THREE
POSSIBILITIES.
AND I'M GOING TO PUT IN
THE FIRST FIVE TERMS.
I'LL PICK THIS ONE.
AND IN SEQUENCE NUMBER 2,
WE DID START WITH TWO.
NOW, WHAT I WANT EVERYBODY
TO DO IS TO TRY.
I'M GOING TO GIVE YOU A
FEW SECONDS TO DO THIS.
FACT IS I'LL GO AWAY
FOR ABOUT 30 SECONDS.
AND WHAT I'D LIKE YOU TO
DO IS CALCULATE WHAT THIS
VALUE WOULD BE IF IT WAS THE
EIGHTH TERM IN THE SEQUENCE.
LIKEWISE WITH THIS ONE.
YOU MIGHT NEED A CALCULATOR
WHEN YOU'RE DOING SEQUENCE NUMBER 2.
ALSO, SEE IF YOU CAN DO
IT FOR THE 14TH DRAWING.
AND THEN I'LL TALK ABOUT
WHAT'S GOING ON HERE
AT THE BOTTOM IN A
MOMENT OR TWO.
SO, THE 14TH DRAWING,
SEQUENCE NUMBER 1 AND
SEQUENCE NUMBER 2, THE
EIGHTH ONE.
AND I'M GOING TO STEP BACK
FOR 30 SECONDS AND GIVE
YOU 30 SECONDS TO DO
SOME QUICK CALCULATIONS.
I'LL BE RIGHT BACK.
OKAY, I THINK
WE'RE BACK NOW.
SO, I'LL TAKE
YOUR PHONE CALLS.
WE'VE GOT SOMEBODY
LINED UP ALREADY,
AND IT'S SADIE
OR DARCY.

Sadie says HELLO?

Mr. C says HI, IS IT SADIE
OR DARCY?

Sadie says IT'S SADIE.

Mr. C says HI, SADIE.
HOW ABOUT SEQUENCE NUMBER 1,
DRAWING NUMBER 8?
WHAT WOULD THAT BE?

Sadie says 32.

Mr. C says 32?
ARE YOU SURE?

Sadie says OH, 31.

Mr. C says I THINK 30.
IS THAT CORRECT?

Sadie says YEAH.

Mr. C says OKAY, YOU WANT TO
TRY ANOTHER ONE?
I'LL LET YOU DO
THIS ONE OVER HERE.
HAVE YOU GOT AN ANSWER
FOR SEQUENCE NUMBER 2?
SOMETHING THAT I'VE
PRACTICED AS AN ADULT
CERTAINLY, BUT
MAYBE EVEN AS A KID,
DOUBLING IS SOMETHING THAT
I LOVE DOING IN MY HEAD.
SO, ACTUALLY, WHEN
I DO THIS 14TH ONE,
I'M GOING TO CHECK
WHATEVER YOU DO IN MY HEAD
AND SEE HOW GOOD I AM.
BUT I LOVE DOING THAT
KIND OF THING IN MY HEAD.
OKAY, HAVE YOU
GOT AN ANSWER YET?

Sadie says 64?

Mr. C says 64 IS THE 6TH ONE.
YOU'VE GOT TO DOUBLE
AGAIN AND DOUBLE AGAIN.
WHAT'S 64 TIMES 2?

Sadie says 96?

Mr. C says 64 TIMES 2.
HAVE YOU GOT A
CALCULATOR THERE,
OR ARE YOU JUST TRYING
TO DO IT IN YOUR HEAD?

Sadie says I'M DOING IT
IN MY HEAD.

Mr. C says OKAY.
I'LL TELL YOU THE
TRICK ON DOING IT.
64 TIMES 2; IF YOU
DOUBLE 60 IT'S 120.
PLUS DOUBLE 4, WHICH
IS 8 - IS 128.
THEN YOU HAVE
TO DO IT AGAIN.
IF YOU DOUBLE
120, IT'S 240.
IF YOU DOUBLE 8,
IT'S 16.
SO, THE NEXT
ONE IS 256.
SO, I HELPED YOU OUT
A LITTLE BIT ON THAT.
BUT YOU UNDERSTAND HOW
TO GET THAT, RIGHT?

Sadie says YEAH.

Mr. C says OKAY, LET'S GO TO THE
PHONE LINES ONCE AGAIN.
AND THIS TIME, I'M LOOKING
FOR THOSE ANSWERS FOR 14,
WHICH I MUST ADMIT WILL
BE GETTING A LITTLE
BIT MORE CHALLENGING.

Joshua says HELLO?

Mr. C says HI, JOSHUA?

Joshua says YEAH.

Mr. C says OKAY, 14.
THE 14TH ONE
AND SEQUENCE NUMBER 1.
WHAT WOULD YOU
PUT IN THERE?

Joshua says 16?

Mr. C says 16?
DOES THAT FOLLOW
THE SEQUENCE?

Joshua says DOES IT FOLLOW
THE SEQUENCE?

Mr. C says 12, 15, 18, 21, 30.
IT'S GOT TO BE QUITE
A BIT BIGGER, RIGHT?

Joshua says YEAH.

Mr. C says DO YOU WANT TO THINK
ABOUT IT A LITTLE BIT,
OR WOULD YOU LIKE ME
TO TAKE ANOTHER CALL?

Joshua says WOULD IT BE...

Mr. C says OKAY, I'M GOING TO
TAKE ANOTHER CALL.
THANK YOU VERY
MUCH, JOSHUA.
AND WE'RE GOING
TO GO TO ELGIN,
AND THIS TIME EITHER
BRITTANY OR JILLIAN.
HELLO?
OH, THERE YA ARE.

Jillian says HELLO?

Mr. C says HI, IS IT BRITTANY
OR JILLIAN?

Jillian says IT'S JILLIAN.

Mr. C says OKAY, HI, JILLIAN.
DO YOU KNOW WHAT GOES
IN THIS BLANK HERE
FOR THE 14TH DRAWING?

Jillian says UM...
NO.

Mr. C says HOW DO YOU ACTUALLY
FIGURE OUT...
LIKE, WHEN YOU
MOVED FROM 21 TO 30,
AND YOU MOVED
FROM 5 TO 8,
WHAT ACTUALLY
HAPPENED THERE?

Jillian says YOU ADDED 9.

Mr. C says YOU ADDED 9,
WHICH WAS BASICALLY...
NOTICE THAT THE
DIFFERENCE IS 3 HERE,
AND THE COMMON
DIFFERENCE IS 3.
SO, WHAT IT IS IS
3 TIMES 3, ISN'T IT?

Jillian says YEAH.

Mr. C says OKAY, NOW WHAT'S THE
DIFFERENCE BETWEEN
HERE AND HERE?

Jillian says UM...

Mr. C says BETWEEN 14 AND 8?

Jillian says 6.

Mr. C says RIGHT.
AND THE COMMON
DIFFERENCE IS 3.
WHAT WOULD YOU DO WITH
THOSE TWO NUMBERS?

Jillian says YOU TAKE 3 TIMES 6?

Mr. C says RIGHT, WHICH IS?
3 TIMES 6 IS?

Jillian says UM...
18?

Mr. C says RIGHT.
AND YOU ADD IT TO WHATEVER
THIS NUMBER IS HERE.
SO, YOU END UP WITH?
48.
OKAY?

Jillian says OKAY.

Mr. C says THANK YOU VERY MUCH.
NOW, I'M GOING TO
SAVE YOU THE TROUBLE,
UNLESS YOU HAVE
A CALCULATOR.
NOW, WE'LL CONNECT TO
ALEX AND SEE IF
HE'S BEEN WORKING
WITH A CALCULATOR.
THIS IS ALEX
AT TRILLIUM.

Alex says HELLO?

Mr. C says HI, ALEX.
DO YOU KNOW WHAT
THIS BLANK IS HERE?
IN OTHER WORDS, THE 14TH
TERM IN THIS DOUBLING ONE.

Alex says IS IT...
515?

Mr. C says NO, IT'S GOING TO BE
A LOT MORE THAN THAT.
BECAUSE IF I DOUBLE...

Alex says I JUST GOT IT WRONG.
16,384?

Mr. C says I LIKE THAT ANSWER.
THAT'S A RIGHT ANSWER.
SO, IN OTHER WORDS, IT GETS
REALLY BIG REALLY FAST,
DOESN'T IT?
THANK YOU VERY
MUCH, ALEX.
NOW, I'M JUST GOING TO
SHOW THIS LAST STAGE,
JUST BECAUSE I'VE GOT A
LITTLE BIT MORE MATERIAL
TO GO THROUGH BEFORE
THE END OF THE SHOW,
AND I DEFINITELY
WANT TO HIT IT.
BUT WHAT WE EVENTUALLY
DO AS MATHEMATICIANS
IS TRY TO GENERALIZE.
AND THE IDEA IS TO SET
UP A LITTLE EQUATION
SO THAT WHEN I WANT TO
KNOW THE ANSWER TO, SAY,
THE 3RD TERM
OR THE 14TH TERM,
ALL I GOT TO DO IS PUT
THAT NUMBER INTO A
LITTLE FORMULA AND
FIGURE IT OUT.
WHAT YOU WILL FIND IS THAT
THIS FORMULA WILL BE...
IF WE WERE TO ACTUALLY
SIMPLIFY THAT A LITTLE BIT,
IT WOULD BE...
NOW, THAT'S NOT ON THE
GRADE 6 CURRICULUM.
BUT TAKE A LOOK AT HOW
EASY IT IS TO FIGURE OUT
THESE DIFFERENT NUMBERS.
FOR INSTANCE, THE 5th
TERM IS 3 TIMES 5
IS 15 PLUS 6 IS 21.
THIS ONE: 3 TIMES 8
IS 24 PLUS 6 IS 30.
IN OTHER WORDS, EVENTUALLY
IN PATTERNING AND ALGEBRA,
THE KIND OF THING
WE WANT TO GET TO,
ARE LITTLE FORMULAS
LIKE THAT.
AND IT MAKES OUR
LIFE A LOT EASIER.
SO, I'M JUST SORT OF
HIGHLIGHTING THAT.
THE BIG DEAL FOR YOU IS
TO RECOGNIZE SEQUENCES
AND BE ABLE TO EXTEND
THEM SOMEWHAT.
NOW, THAT LEAVES ME
WITH THE LAST ONE,
WHICH I CALLED A SEQUENCE
BUT REALLY ISN'T A SEQUENCE.
AND THERE IT IS.

A worksheet appears on screen with four square-like shapes and several shaded blobs within the shape. Next to the shapes a title and instructions read “Sequence number 3, if drawing number 1 equals 9, and if drawing number 2 equals 16, and if drawing number 3 equals 10, then drawing number 4 equals.”

Mr. C continues WHAT I'VE DONE IS I'VE
SAID THIS DRAWING,
THESE THINGS REPRESENT
A TOTAL OF 9.
THESE THINGS REPRESENT
A TOTAL OF 16.
THESE THINGS REPRESENT
A TOTAL OF 10.
IF I TAKE ONE
OF EACH OF THEM,
WHAT'S THE GRAND
TOTAL?
IF YOU'VE GOT AN
ANSWER, GIVE ME A CALL.
AND IT LOOKS LIKE WE'RE
GOING TO CONNECT
TO EITHER ANDREW
OR KATIE AT ELGIN.
SO, THEY MUST
HAVE AN ANSWER.
AND WHAT I WANT YOU TO
DO IS SORTA TELL ME
HOW YOU FIGURED IT OUT.
THERE ARE A COUPLE OF
REALLY BIG CLUES HERE
THAT MIGHT HELP OUT.

Katie says HELLO?

Mr. C says HI, IS IT KATIE?

Katie says YEAH.

Mr. C says HI, KATIE.
DID YOU GET AN ANSWER
FOR DRAWING NUMBER 4,
AND IF SO, WHAT IS IT?

Katie says IT'S 8.

Mr. C says OKAY, I'M NOT GOING
TO WRITE IT IN,
IT'S MY ONLY COPY.
BUT YOU DID SAY 8.
ACTUALLY, WHAT
I'LL DO IS THIS.
THERE IT IS; THERE'S
MY ANSWER: 8.
YOU'RE CORRECT.
HOW DID YOU
FIGURE THAT OUT?

Katie says BECAUSE I JUST FIGURED
OUT WHAT EACH OF
THE NUMBERS EQUALLED.
LIKE NUMBER 1, THE ONE EQUALS 5
AND THE ONES
AT THE
TOP EQUALLED 2.
AND THERE'S ONE
THAT EQUALLED ONE.

Mr. C says RIGHT.
AND DID YOU KIND OF
DO A TRIAL AND ERROR
APPROACH TO IT?
TRIED DIFFERENT NUMBERS
LIKE ONES AND TWOS
AND THREES AND STUFF?

Katie says YEAH.

Mr. C says EXCELLENT.
THAT'S EXACTLY WHAT I
WOULD EXPECT YOU TO DO,
IS TO TRY SOME
TRIALS AND ERRORS.
THE ONE THAT PROBABLY IS
THE BIGGEST CLUE IS THIS
ONE DOWN HERE, WHERE
YOU GOT FOUR OF THESE
AND TWO OF THESE.
NOW, THERE ARE REALLY
ONLY TWO POSSIBILITIES.
IF THESE WERE EACH
ONE - REMEMBER,
THEY'RE WHOLE NUMBERS -
THEN THESE
WOULD BE EACH 3.
AND IF YOU WENT BACK
AND YOU SAY, OH,
THOSE ARE EACH ONE,
THEN THIS MUST BE A 7.
AND YOU'LL FIND
THAT, OF COURSE,
IT DOESN'T WORK
WITH THAT ONE.
THAT ONLY LEAVES
TRYING TWOS AND ONES.
IN WHICH CASE, YOU GO
BACK AND YOU FIND OUT
THAT THIS IS A 5,
AND 5, 5, 5,
AND A ONE WILL WORK.
SO, THE IDEA IS
YOU TRY ONE AND YOU
PLAY AROUND, RIGHT?
GREAT.
NOW, I SEE SOME
HANDS ARE STILL UP.
PERHAPS THERE'S A QUESTION,
AND I'D BE WILLING TO TAKE
AT LEAST ONE QUESTION
BEFORE I GO ON TO
TODAY'S RELATIVELY
QUICK LESSON.
HELLO, CHRISTOPHER.

Christopher says I WAS GOING TO
TALK ABOUT THIS ONE,
THE ONE YOU JUST DID.

Mr. C says YEAH, WHAT DID YOU
DO TO FIND THE ANSWER?

Christopher says THE SAME THING.

Mr. C says THE SAME THING, JUST SORT
OF PLAYED AROUND WITH
THE NUMBERS UNTIL THEY ALL
WORKED OUT PERFECTLY, RIGHT?

Christopher says YEP.

Mr. C says EXCELLENT, THAT'S THE KIND
OF THING I WANT TO HEAR.
YOU DID A REALLY NICE JOB.
I THINK WE'LL TAKE ONE
MORE CALL, JUST TO SEE.
THIS IS TRISHA OR
ALYSSA FROM ELGIN.
HELLO.
PICK UP YOUR PHONE.

Alyssa says HELLO?

Mr. C says HELLO, IS IT
TRISHA OR ALYSSA?

Alyssa says ALYSSA.

Mr. C says HAVE YOU GOT A
QUESTION OR A COMMENT?

Alyssa says I HAVE A QUESTION.
FOR SEQUENCE NUMBER 2,
I GOT 1,536.
AND YOU GOT 16,384.
HOW DID YOU GET THAT?

Mr. C says OKAY, I'LL DO A
DOUBLE CHECK HERE.
WHAT I KNOW IS THIS.
THAT'S ACTUALLY
THE 10TH TERM.
SO, IF I DOUBLED
THIS TWICE...
THEN I HAVE TO DOUBLE
IT FOUR MORE TIMES.
SO, I'M JUST DOING
A QUICK CHECK.
I WAS TAKING IT AT FAITH
THAT HE WAS IN THE
RIGHT BALLPARK.
I'M PRETTY SURE THAT
THAT'S WHAT WAS THERE.
IN OTHER WORDS, IT'S
JUST A QUESTION
OF DOUBLING EACH TIME.
IF YOU DOUBLE SIX TIMES,
IT'D BE DOUBLE THAT -
512, THEN 1,024.
DOUBLE AGAIN IS 2,048,
THEN 4,096, THEN 8,192,
AND LAST BUT NOT
LEAST, 16,384.
AS YOU CAN SEE, I'M
BASICALLY DOING
THAT IN MY HEAD.
BUT THAT'S SOMETHING
I PRACTICE DOING.
YOU GOTTA PRACTICE
TO GET GOOD.
ANYWAY, DOES THAT
ANSWER YOUR QUESTION?
OKAY, I'M GOING TO
GO ON TO THE LESSON.
THERE ARE A COUPLE THINGS
I WANT TO POINT OUT.
FIRST OF ALL, THIS IS ONE
I'M GOING TO INVITE YOU
TO FAX YOUR SOLUTIONS.
ONE OF THE THINGS THAT
YOU'LL FIND HERE IS THAT
YOUR SOLUTION SHOULD
BE QUITE DIFFERENT
FROM ONE ANOTHER IN
THIS PARTICULAR CASE.
CONSIDER THIS TO
BE YOUR BEGINNING
PUZZLE FOR NEXT WEEK.

The worksheet appears on screen and Mr. C explains it aloud.

He says THE SCALE IS 1 CENTIMETRE
EQUALS 10 METRES -
THAT IS USEFUL
IN A SENSE.
AND THEN YOU'VE GOT
THESE SIX SPOTS HERE.
AND YOU GOT FOUR PEOPLE
TO WATCH THOSE SIX SPOTS.
THE IDEA IS TO PLACE FOUR
X's ON HERE SO THAT
THE SPIES ARE AS CLOSE
AS POSSIBLE TO EACH
ONE OF THOSE
DIFFERENT SPOTS.
SO, WHERE WOULD YOU PLACE
YOURSELF STRATEGICALLY
TO BE ABLE TO WATCH THE
SPOTS MOST EFFECTIVELY?
AGAIN, YOU CAN FAX
ME YOUR SOLUTIONS.
AT THE END OF THE PROGRAM,
I THINK WE HAVE A...
OH, WE'VE GOT A POWERPOINT,
AND THERE IT IS.
THERE'S THE FAX NUMBER,
WHICH WE'RE USING THIS ONE
NOW BECAUSE IT IS TOLL FREE
AND YOU WON'T HAVE ANY
LONG DISTANCE CHARGES.

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

Back to Mr. C, he says AND I'LL BE VERY INTERESTED
TO SEE YOUR SOLUTIONS.
AND IF YOU ACTUALLY
WRITE A LITTLE BIT OF
AN EXPLANATION, THAT
WOULD BE USEFUL AS WELL.
WHY IS IT SO?
NOW, I'M GOING TO
BRIEFLY GO THROUGH WHAT
YOU DO TO DO THIS
NEXT INVESTIGATION.
THIS IS WHAT YOU SEE
IN YOUR ASSIGNMENT.
BUT THIS IS WHAT
I'M TALKING ABOUT.
SO, WE'LL GO BACK TO
THE FRONT CAMERA
AND TAKE A LOOK
AT IT FROM...
SO, WHAT I HAVE
IS A CONTAINER.

Mr. C holds a measuring cup and red and white beans and says EACH TEAM IS GOING TO
HAVE TO HAVE A CONTAINER.
TO BE QUITE HONEST, IF
YOU'RE USING THE KINDS
OF BEANS THAT I'M
USING HERE...
I WENT OUT AND BOUGHT
SOME WHITE BEANS
AND SOME RED BEANS.
IF YOU'RE USING THESE
BEANS, THEY'RE PRETTY BIG.
AND IN FACT, THIS CONTAINER
OF WHAT I'M USING HERE
IS PROBABLY A
LITTLE BIT SMALL.
YOU PROBABLY NEED SOMETHING
A LITTLE BIT BIGGER THAN THIS.
HOWEVER, FOR MY
DEMONSTRATION,
IT'LL PROBABLY WORK FINE.
THIS IS KIND OF A
PROBABILITY EXPERIMENT
THAT WAS REALLY
VERY USEFUL.
WHAT WE'RE DOING HERE IS
SIMULATING THE KIND OF
EXPERIMENT THAT NATURALISTS
USED ALL THE TIME
TO FIGURE OUT HOW MANY ANIMALS
THERE ARE IN THE WILD,
LIKE FOR INSTANCE IF
THEY'RE TRYING TO FIGURE OUT
HOW MANY MUSKRATS THERE
ARE IN ALGONQUIN PARK.
THEY ACTUALLY MIGHT
USE A TECHNIQUE
THAT'S SOMETHING LIKE THIS.
OR IF THEY'RE TRYING TO
FIGURE OUT HOW MANY BROWN TROUT
THERE ARE IN A
CERTAIN LAKE IN NORTHERN
ONTARIO, THEY COULD ALSO
USE A TECHNIQUE LIKE THIS.
BUT THIS IS A SIMULATION,
AND I LIKE DOING
SIMULATIONS BECAUSE IT
GIVES YOU A SENSE
OF WHAT REALITY IS.
NOW, IF YOU GET A CONTAINER
A LITTLE BIT LARGER
THAN THIS, THEN IF YOU'RE
USING THIS TYPE OF BEAN,
IT WILL WORK OUT
JUST FINE.
WHAT I'VE SUGGESTED
INITIALLY IS THAT YOU
COUNT OUT 100 RED BEANS.
WHICH I DID, AND I PUT THEM
DOWN IN THE BOTTOM ALREADY.
AND THEN WHAT I DID IS I
FILLED IN THE WHITE BEANS
TO COME UP TO
1 FOURTH FULL.
NOW, THE VERY FIRST
INSTRUCTION SAYS
THAT WE SHOULD START
AT 1 EIGHTH FULL.
WITH 100 RED BEANS, I'M
ALREADY BEYOND 1 EIGHTH FULL
IN THIS CONTAINER.
THAT'S WHY YOU'D NEED
A SLIGHTLY BIGGER ONE.
SO, LET'S GO THROUGH
AGAIN WHAT THE STEPS ARE.
BASICALLY, I COUNTED
OUT 100 RED ONES
AND I DUMPED THEM
IN THE BUCKET.
THEN I FILLED IN THE WHITE
ONES UP TO WHATEVER LEVEL
I WAS SUPPOSED TO.
AND YOU GOT FIVE
DIFFERENT LEVELS.
SO, I FILLED IT
UP TO 1 FOURTH.
THEN I TAKE A WOODEN
STIRRING SPOON, AND,
TO BE QUITE HONEST,
YOU REALLY SHOULD
MIX THIS QUITE A BIT.
BECAUSE WHAT I WANT IS A
RANDOM DISPERSION
OF THE RED AND
THE WHITE BEANS.
THAT'S REALLY,
REALLY IMPORTANT,
OR THIS EXPERIMENT
DOESN'T REALLY WORK.
SO, GIVE IT A
REALLY GOOD MIX.
SO, THAT'S WHAT I HAVE
NOW: A REAL MIXTURE
OF RED AND WHITE BEANS.
AND IF WE LOOK FROM
ABOVE, YOU CAN SEE THAT
THEY'RE GETTING PRETTY
WELL MIXED NOW.
THEN YOU TAKE A
MEASURING CUP.
NOW, I SUGGESTED
A HALF A CUP,
BUT YOU KNOW SOMETHING,
EVEN A QUARTER CUP
OR A THIRD CUP WILL
PROBABLY DO FINE.
AND WHAT YOU DO IS YOU
GET A SCOOP OF BEANS.
UP TO APPROXIMATELY
THE TOP.
SO, YOU DO IT THE
SAME WAY EACH TIME.
WHAT YOU DO ONCE YOU
HAVE THE BEANS...
DUMP THEM OUT.
AND WHAT YOU WANT TO DO
IS YOU GOTTA COUNT BOTH
THE RED AND THE WHITE BEANS
THAT YOU HAVE HERE.
NOW, I'M GOING TO TAKE
THESE AND ACTUALLY I'M
NOT GOING TO COUNT THEM
IN THIS PARTICULAR CASE.
SO, I'M GOING TO GO THROUGH
NOW BASICALLY THE STEPS.
YOU'VE ALREADY DONE THE
BUSINESS TO DO WITH PUTTING
THE BEANS INTO THE BUCKET.
YOU'VE MIXED THEM UP,
YOU'VE PULLED OUT A SAMPLE.
THIS IS A SMALL GROUP
ACTIVITY THAT I MENTIONED HERE.
I'M NOT GOING TO GO
THROUGH EACH INSTRUCTION;
YOU HAVE THEM ALREADY.
BUT THE IMPORTANT PART HERE
AND THIS IS JUST A COPY
OF THE CHART RIGHT OUT
OF YOUR BOOK - IS THAT
FOR EACH ONE OF THE
INDIVIDUAL SECTIONS,
YOU DO THE
EXPERIMENT SIX TIMES.
SO, IN OTHER WORDS, THIS
IS ONE EIGHTH FULL, THIS IS ONE QUARTER,
THIS IS THREE EIGHTHS, THIS
IS ONE HALFFULL,
AND THIS IS FIVE EIGHTHS,
SO, YOU ACTUALLY
REPEAT THE EXPERIMENT
A NUMBER OF TIMES.
AND WHAT YOU HAVE HERE IS
A COUNT OF THE RED BEANS
AND THE WHITE BEANS.
YOU ADD THEM UP
IN THIS COLUMN.
AND THEN YOU WORK OUT THE
PERCENTAGE OR THE DECIMAL
WHEN YOU TAKE THE NUMBER
OF WHITE BEANS COMPARED
TO THE NUMBER OF
RED BEANS.
OH, EXCUSE ME, I SHOULD
SAY AGAIN THE NUMBER
OF WHITE BEANS COMPARED TO
THE NUMBER OF TOTAL BEANS.
SO, IN OTHER WORDS, IN THIS
EXAMPLE HERE THERE WERE
108 REDS, THERE
WERE 36 WHITES.
THE TOTAL WAS 144, AND
THE PERCENTAGE I GOT -
OR THE DECIMAL EQUIVALENT
WAS WHITE BEANS,
36 OVER 144 TO GET POINT 25.
SO, YOU CAN SEE THIS
IS SELF-EXPLANATORY
IN THE CHART THAT
YOU'VE RECEIVED.
BUT WHAT YOU WANT
IS AN AVERAGE FOR
THE PERCENTAGES
AT THE END.
SO, I'LL JUST TAKE HALF
A MOMENT TO REMIND
YOU WHAT AN AVERAGE IS.
REMEMBER THAT IF YOU HAVE
THREE, FOUR NUMBERS, SAY...
AND I WANT THE
AVERAGE, WHAT DO I DO?
SO, GIVE ME A QUICK CALL
AND LET ME KNOW WHAT
YOU DO TO GET AN AVERAGE.
AND WE'RE ALMOST
WRAPPED UP HERE.
VERY CLOSE TO THE END.
ANYBODY WANT TO TELL
ME WHAT AN AVERAGE IS,
OR HOW YOU CALCULATE IT
IF YOU HAVE FOUR NUMBERS?
AND THERE'S ALEX.
AND WE'LL BE CONNECTED
IN JUST A MOMENT OR TWO
AND HE CAN TELL ME WHAT
TO DO TO GET AN AVERAGE.
THERE ARE THE
FOUR NUMBERS.
AND WE'LL BE CONNECTED
IN HALF A SECOND HERE.
NOT A REALLY
DIFFICULT PROBLEM.
HELLO, ALEX.
SO, HOW DO YOU WORK OUT AN
AVERAGE OF FOUR NUMBERS?

Alex says YOU TAKE THE TWO
MIDDLE NUMBERS.

Mr. C says OH, YOU'RE WORKING
TO A MEDIAN.
REMEMBER WHAT I
WANT IS A MEAN.

Alex says YOU ADD ALL
THE NUMBERS.

Mr. C says ADD ALL THE
NUMBERS.
AND THEN WHAT DO I
DO ONCE I ADD THEM?

Alex says DIVIDE BY FOUR.

Mr. C says DIVIDE BY THE
NUMBER OF NUMBERS.
OKAY, THAT'S RIGHT.
AND YOU'LL GET AN
AVERAGE; IN THIS CASE,
YOU GET A DECIMAL
APPROXIMATION.
IT'S 14 POINT 75.
OKAY?

Alex says OKAY.

Mr. C says THANK YOU VERY MUCH.
THAT'S JUST A
QUICK REMINDER.
SO, I'VE GOT TWO MORE
THINGS TO SAY TO YOU
REALLY QUICKLY, AND THEN
I'LL OPEN FOR QUESTIONS.
ONE THING IS THAT YOU'LL
BE RECEIVING A FAX
FROM ME SOMETIME TODAY.
REMEMBER THAT I SAID
THAT THE MYSTERY,
THAT THERE WAS A FINAL
CULMINATING LITTLE PIECE
THAT YOU HAVE TO DO.
AND YOU WILL SEE THAT
YOU'LL GET AN ASSIGNMENT
THAT LOOKS LIKE THIS.
IT WILL LIST THE NUMBER OF
CHALLENGES FROM CERTAIN
CHAPTERS, AND THERE ARE
ANSWERS THAT YOU HAVE
TO DIG OUT OF
YOUR HOMEWORK.
AND YOU USE THEM TO
FILL IN THESE BOXES.
THIS IS TO COMPLETE
THE CHALLENGE.
AND THEN DOWN AT
THE BOTTOM HERE,
IT TELLS YOU WHAT TO DO
WITH THAT INFORMATION
THAT YOU'VE GATHERED.
I'LL TALK MORE ABOUT
THIS NEXT WEEK BECAUSE
IT'S CLOSER TO THE ACTUAL
TIME WHEN I WANT YOU
TO DO SOMETHING IF
YOU GET A CHANCE.
SO, LOOK OUT FOR THAT,
IN TERMS OF A FAX
COMING TO YOUR SCHOOL.
AT THIS POINT, I CAN ASK
YOU FOR ANY QUESTIONS
TO CLARIFY WHAT YOU'RE
DOING WITH THE EXPERIMENT.
YES, WE DO HAVE A
QUESTION FROM ELGIN.
AND THAT'S
PRETTY MUCH IT.
I'VE COVERED ALL
THE MATERIAL.
SO, LET'S SEE,
WHO HAVE WE GOT?
NO, WE DON'T SEEM TO
HAVE ANY PHONE CALLS.
SO, I'M LOOKING FORWARD TO
SEEING YOU AGAIN NEXT WEEK,
SAME TIME, SAME PLACE.
BYE-BYE.

A blue slate appears on screen. It shows a text that reads “Please remember to log off! Pick up handset. Press number sign then seven. Press 1 to confirm. Hang up headset. See you next time!”

Watch: Counting on an Answer