Transcript: NFA - Math Projects, Part 2 | May 31, 1999

(music plays)

The opening slate pops up with a countdown timer from 10 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.
On an abstract purple and pink background, the title changes to “Grade 3 Math Project with Stewart Craver.”

Mister C stands in the studio. He’s in his fifties, with a dark beard and wavy black hair. He’s wearing glasses, a black T-shirt with Einstein’s face and patterned suspenders.

Mister C says GOOD MORNING AND WELCOME
TO THE VIRTUAL CLASSROOM,
THE GRADE 3 PROJECTS,
THE ASSIGNMENT.
IT'S AN ABSOLUTELY GORGEOUS
MORNING HERE IN TORONTO.
I HOPE IT'S THE SAME
RIGHT ACROSS ONTARIO.
IT'D BE A GREAT DAY
TO GET OUTSIDE
AND DO SOME
MATHEMATICS.
WHAT I'M GOING TO DO TODAY
IS I'M GOING TO PRESENT
A PROBLEM AT THE BEGINNING,
THAT I'LL TAKE UP
NEAR THE END.
AND THEN I'M GOING TO GO
THROUGH FIVE POSTERS,
SAMPLES OF WORK, FROM THE
KIDS AT GEORGE WEBSTER SCHOOL,
WHERE WE PILOTED
THIS PROGRAM.
SO LET'S START WITH THE
PROBLEM, HERE IT IS:

A piece of paper reads “Why are these letters the same? B, C, D, E.”

He continues WHAT IS IT THAT'S
THE SAME ABOUT THEM?
AND I CAN ACTUALLY
PROVIDE, AT LEAST,
TWO ANSWERS.
I'M SURE THAT THERE ARE
OTHER ONES AS WELL,
BUT THERE ARE TWO
REALLY GOOD ANSWERS
AS TO WHY THEY
ARE THE SAME.

He appears in a small window at the right bottom of the screen.

He continues WHAT WE'LL DO, IS WE'LL
HOLD ONTO THOSE THOUGHTS
FOR A LITTLE WHILE
AND RIGHT AT THE END
OF THE PROGRAM, I'LL
PROVIDE A COUPLE OF IDEAS,
OF WAYS TO LOOK
AT THE ANSWERS
TO THAT LITTLE
PROBLEM.
OKAY, WE'RE SORT OF
BACK TO WHERE WE WERE
BEFORE AND WHAT WE'RE
GOING TO DO IS,
WE'RE GOING TO
LOOK AT POSTERS.
AND I'LL COMMENT ABOUT
WHAT'S IN THE POSTERS
THAT I'M REALLY
HAPPY ABOUT
AND THE KINDS OF
THINGS THAT,
PERHAPS, I WOULD LIKE
YOU TO ADD WHEN YOU GET
A CHANCE TO DO
A POSTER.
LET'S START WITH
THIS ONE RIGHT HERE.

He grabs a poster. It features colourful drawings of trees and buildings.

He continues YOU'LL SEE ALL THE FIVE
DIFFERENT COMPONENTS;
THAT IS, THERE WERE FIVE
DIFFERENT ACTIVITIES
THAT YOU HAD TO DO IN
THE WHOLE PROJECT.
AND THOSE FIVE ACTIVITIES
INCLUDED THE FIRST ONE,
WHICH WAS
ABOUT A FENCE.
AND AS YOU CAN
SEE HERE,
THAT THE STUDENTS
AT GEORGE WEBSTER,
THE ONE GROUP, DREW A
PICTURE OF THE FENCE
WITH TWO POSTS.
AND THE VERY FIRST
THING THAT THE STUDENTS
HAD TO DO WAS TO
ESTIMATE THE DISTANCE
BETWEEN THE TWO POSTS AND
THEN TO ACTUALLY MEASURE IT
AND PUT DOWN THEIR
EXACT MEASUREMENT
IN METRES AND
CENTIMETRES.
NOW, THIS IS A
GREAT DRAWING.
ONE OF THE THINGS
THAT I WOULD'VE LIKED
IS TO HAVE THE
STUDENTS ACTUALLY SHOW
THAT INFORMATION
ON HERE.
WHAT THEIR
ESTIMATES WERE,
WHAT THE ACTUAL
MEASUREMENT WAS.
BUT THERE WAS MORE TO
THAT PARTICULAR ONE
THAN JUST THE BETWEEN
THE TWO POSTS
AND I'LL COMMENT
ON THAT,
PERHAPS, WITH
ANOTHER ONE.
UP IN THIS CORNER, IS
THE SECOND ACTIVITY
THAT WE SET UP AND THAT
IS TO DO WITH WINDOWS.
AND THIS IS WINDOWS
IN A CLASSROOM.
SO THE IDEA WAS TO
DRAW A PICTURE
OF ALL THOSE WINDOWS.
THEN, TO FIND OUT HOW
MANY WINDOWS THERE WERE.
IF YOU LOOK AT THIS, IT'D
BE ONE, TWO, THREE,
FOUR ROWS OF WINDOWS.
ONE, TWO, THREE,
FOUR, FIVE, SIX,
SEVEN, EIGHT, NINE
COLUMNS OF WINDOWS.
I WONDER HOW MANY
THERE ARE IN TOTAL.
I THINK I CAN USE
MULTIPLICATION.
SO SAY, 4 TIMES 9.
AND 4 X 9 IS 36.
BUT THAT WASN'T ALL, THE
STUDENTS WERE SUPPOSED TO
AROUND THE SCHOOL,
WHICH THEY DID,
AND COUNT THE TOTAL
NUMBER OF CLASSROOMS.
SO, LET'S SAY
THERE WERE 10.
SO 10 X 36 IS 360.
BUT THEN ANOTHER
STUDENT WAS SUPPOSED TO
ALSO RECORD THE NUMBER
OF OTHER WINDOWS.
SAY THERE WERE
100 OTHER WINDOWS.
WELL, WHAT DO YOU DO
WITH THE QUANTITY 360
AND THE QUANTITY 100 IF YOU
WANT THE TOTAL WINDOWS?
IN THIS CASE, YOU ADD BECAUSE
YOU'VE GOT TWO TOTALS,
YOU WANT THE GRAND
TOTAL SO YOU WOULD
ADD THEM TOGETHER.

Pointing to the left bottom of the poster, he continues DOWN IN THIS CORNER,
IS AN INDICATION
THAT THEY DID DO SOME
WORK WITH A GARDEN.
THERE'S SOME
PLANTS IN HERE,
IT'S A LITTLE BIT
DIFFICULT TO MAKE OUT
THE INDIVIDUAL PLANTS
ON THE TV SCREEN.
AND OVER ON THIS ONE,
IS THE PLAYGROUND
WHERE THEY ACTUALLY
WORKED AT LOOKING FOR
DIFFERENT KINDS OF SHAPES
IN THE PLAYGROUND.
AND YOU CAN SEE A
FEW OF THEM IN HERE
LIKE THE SEMI-CIRCULAR
PIECE OVER HERE,
THE RECTANGLE
OVER HERE.
THIS IS THE MAP OF THE
SCHOOLYARD IN THE CENTRE.
I WILL COMMENT ON THIS
ONE A LITTLE BIT MORE
WITH ONE OF THE
OTHER POSTERS WHERE
THEY ACTUALLY PUT THE
KEY ELEMENT ON THERE.
REALLY NEAT LITTLE PICTURE
HERE THAT'S HARD TO SEE,
YOU IN FACT, HAVE A
TEACHER AND FOUR STUDENTS
WITH A TRUNDLE WHEEL.
VERY SMALL BUT
KIND OF CUTE.
THE SECOND POSTER I HAVE,
IT'S NICE AND BOLD.
IT'S EASY TO LOOK AT
AND IT'S PRETTY EASY
TO UNDERSTAND.
LIKEWISE, THEY DID, I
LIKE THE LABELLING HERE.
“A LENGTH OF FENCE.”
SO, THEY DREW THAT AND
YOU GET THAT SENSE
OF ALL KINDS OF RHOMBI -
RHOMBI, SINGLE IS RHOMBUS.
SO YOU CAN SEE THAT.
AGAIN, I KNOW THAT THESE
KIDS DID THE MEASUREMENT,
BUT I WOULD'VE REALLY
LIKED TO HAVE SEEN
THAT INFORMATION
ON THE POSTER.
HERE'S THEIR WINDOW
DIAGRAM IN THIS CORNER.
THEY FOUND ONE, TWO,
THREE, FOUR ROWS.
ONE, TWO, THREE,
FOUR, FIVE, SIX.
HOW MANY WINDOWS?
WHAT WOULD I DO?
HOW WOULD I
CALCULATE THAT?
MULTIPLICATION
IS THE IDEAL.
FOUR ROWS OF
SIX, 4 X 6 IS 24.
OVER IN THIS SIDE, ONE OF
THE OTHER ACTIVITIES
IN THE LAST ONE WAS, NOT
ONLY TO LOOK AT THE GARDENS,
BUT TO LOOK AT THE
TREES AND TO DO SOME
DATA ANALYSIS
OF THE TREES;
THAT IS, COUNT
ALL THE TREES.
YOU CAN SEE AN
INDICATION THAT THEY
PROBABLY DID THAT, BUT WE
DON'T HAVE THE DATA HERE.
UP HERE IS THEIR
PLAYGROUND PICTURE.
IT'S VERY NICE
AND SCHEMATIC,
SEMI-CIRCLE HERE,
RECTANGLE HERE,
MAYBE OVAL HERE,
CIRCLES HERE.
AND IT'S KIND OF AN
ANTI-GRAVITY PLAYGROUND.
IT PROBABLY SHOULD'VE BEEN
ROTATED 180 DEGREES.
BUT, THAT'S OKAY.
HERE'S THEIR PICTURE OF
THE MAP IN THE CENTRE.
BUT, ONE THING MISSING
FROM THERE AS WELL
AND WHEN WE GET TO
THE FOURTH POSTER,
YOU'LL SEE WHAT
THAT IS.
HERE'S THE
THIRD POSTER.
THERE'S NO DOUBT IN
MY MIND, WHATSOEVER,
THAT THESE KIDS PUT
IN A LOT OF WORK
TO TRY TO PRODUCE THE
BEST QUALITY THEY COULD.

The poster reads “Math to be marked Ash! Rose! Windows. Sam!Danile.”

He continues STARTING DOWN HERE WITH
THE LENGTH OF FENCE,
WHAT YOU SEE IS SEVERAL
SEGMENTS WHICH INDICATES
THE PART WHERE THEY HAD
TO GET THE ESTIMATE
FOR A WHOLE LENGTH
OF THE SIDE OF A FENCE
ON A SCHOOLYARD.
AND EVENTUALLY MEASURE
IT WITH A EITHER
A TRUNDLE WHEEL
OR A PACER.
THEIR PLAYGROUND IS
UP HERE AND AGAIN,
YOU CAN SEE THOSE
SHAPES THAT YOU SAW
ON THE OTHER ONE.
RECTANGLE,
SEMI-CIRCLE, UM,
YOU GET A CURVE
IN HERE.
THERE'S A
TRIANGLE IN HERE.
WINDOWS - ONE,
TWO, THREE.
ONE, TWO, THREE,
FOUR, FIVE.
SO THE TOTAL NUMBER OF
WINDOWS IN THIS
PARTICULAR SETUP IS
3 X 5 IS 15.
WHAT I REALLY LIKE
IN THEIR DIAGRAM
IS THE GARDEN.
THE GARDEN IS
IN WHAT SHAPE?
THIS SIDE IS PARALLEL
TO THIS; THESE ARE NOT.
THIS IS A TRAPEZOID.
AND IN THE TRAPEZOID, YOU
FIND THE DIFFERENT PLANTS.
AND THERE ARE FOUR
HERE IN THIS ROW,
THERE ARE FIVE IN THIS
ROW AND THERE ARE
ANOTHER FIVE HERE.
SO, YOU GET A TOTAL OF
5 PLUS 5 IS 10 PLUS 4 IS 14.
AGAIN, A NICE JOB OF
COLOURING THE MAP.
BUT ONE THING IS
STILL MISSING.
HERE'S THE
FOURTH ONE.

The fourth map reads “Mathematics adventure. Shapes in the playground. Our trail.”

He continues AGAIN, IF YOU TAKE A
LOOK UP IN THIS CORNER,
YOU CAN SEE THEY HAVE
SEVERAL SECTIONS
OF FENCE WHICH
INDICATES THAT THEY
WERE LOOKING AT THE
TOTAL LENGTH OF FENCE.
OVER HERE IN
THEIR PLAYGROUND,
YOU CAN CERTAINLY
SEE THE CIRCLES,
YOU CAN SEE
PARALLELOGRAMS,
YOU CAN SEE A
TRIANGLE HERE,
A RECTANGLE OVER HERE,
A SEMI-CIRCLE THERE.
SO, THEY'VE ACTUALLY SHOWN
A NUMBER OF THE SHAPES.
I WOULD'VE REALLY LIKED
TO HAVE SEEN THE NAMES
OF THE SHAPES LABELLED
AROUND THE OUTSIDE
OF THAT DIAGRAM.
THEIR WINDOW ARRAY IS ONE,
TWO, THREE, FOUR, FIVE, SIX.
ONE, TWO, THREE.
3 TIMES 6 IS 18.
BUT HERE'S THE PART
I'M THRILLED ABOUT.
ALL THE KIDS DID THIS,
THEY JUST DIDN'T PUT IT
ON THEIR POSTER.
THIS IS THE TRAIL THAT
THESE KIDS MAPPED OUT,
THAT THEY THOUGHT WAS
ONE KILOMETRE LONG.
AND IT'S REALLY IMPORTANT
FOR KIDS TO FEEL
WHAT A KILOMETRE IS.
THAT WAS THE
PURPOSE OF THIS.
THIS WAS SORT OF THE
BIG TASK AT THE END
IS TO GET THAT FEEL OF
WHAT A KILOMETRE IS.
WHEN I WAS YOUNG, I
ACTUALLY MARCHED
WHEN I WAS PROBABLY
IN HIGH SCHOOL,
THE MILES FOR MILLIONS
WHICH WAS 26 MILES.
BUT 26 MILES IS
ABOUT 40 KILOMETRES.
AND I'LL TELL YOU,
YOU REALLY GOT A FEEL
FOR THAT KIND OF A
LENGTH WHEN YOU DID IT
SEVERAL YEARS RUNNING.
IT TELLS YOU HOW LONG
A KILOMETRE REALLY IS.
NOW, GOING BACK TO
THIS PARTICULAR PIECE,
THEY STARTED UP HERE AND
FOLLOWED ALONG THE FENCE
AND YOU CAN FOLLOW MY
FINGER AND THEN ALONG
THE SIDEWALK AND THEY DOUBLED
BACK, ROUND THE SCHOOL,
THROUGH THE PORTABLES AND
THEN AROUND THE SCHOOL
AND SO ON.
NOW, YOU'LL SEE
THEM ACTUALLY
WITH THEIR TRUNDLE
WHEEL IN THE VIDEO.
AND WHAT YOU'LL SEE,
IS THAT, IN FACT,
THEY GOT TO ABOUT
RIGHT THERE
AND THEY HIT
ONE KILOMETRE.
THAT WAS PHENOMENAL
BECAUSE YOU CAN SEE THAT,
THEY ONLY MISSED
THEIR GUESS
BY A LITTLE WEE
SECTION UP HERE.
THOSE STUDENTS JUST DID A
FANTASTIC JOB OF FIGURING OUT,
IN ADVANCE, WHAT THEY
THOUGHT A KILOMETRE WAS.
AND THEN THEY WENT OUT AND
FELT WHAT A KILOMETRE IS.
YOU'LL SEE THAT IN THE
VIDEO THAT WE'LL SHOW
IN TWO WEEKS' TIME,
ONE MORE TIME.
SO THAT YOU GET
TO SEE THOSE KIDS
ACTUALLY BEING
EXTREMELY SUCCESSFUL.
AND WE HAVE ONE MORE
POSTER TO SHOW.
AND HERE IT IS.
I KIND OF SAVED THIS
ONE FOR THE LAST
FOR ONE REASON ANYWAY.
THEIR WINDOWS ARE VERY,
VERY GOOD AS WELL.
ONE, TWO, THREE,
FOUR ROWS.
ONE, TWO, THREE,
FOUR, FIVE, SIX.
6 TIMES 4 IS 24.
I LIKE THE
DETAIL HERE.
He reads “BE BIKE SMART,
WEAR A HELMET.”

He continues HERE IS THEIR
PLAYGROUND AND, AGAIN,
YOU CAN SEE MOST OF THOSE
SHAPES I WAS TALKING ABOUT
WITH THE OTHER ONES.
ALTHOUGH, IT'S NOT QUITE
AS BOLD AND OBVIOUS HERE.
THIS IS ONE SECTION
OF FENCE OVER HERE
AND THERE'S THEIR MAP.
UNFORTUNATELY, AGAIN, WE
DON'T HAVE THE FULL TRAIL
SHOWN ON THERE WHICH
WOULD GIVE ME A SENSE
OF WHAT THEY THOUGHT
ONE KILOMETRE WAS.
NOW HERE'S THE FUN PART
UP HERE IN THIS CORNER.
THESE KIDS JUST HAD A
BLAST WHEN WE FILMED THEM
FOR THE TVO SEGMENTS
THAT YOU GET TO SEE,
THAT YOU SAW LAST WEEK AND
THAT YOU'LL GET TO SEE
IN TWO WEEKS' TIME AGAIN.
THEY HAD A WONDERFUL
TIME AND IN A SENSE,
THEY ARE HONOURING
THEIR OPPORTUNITY
TO BE ON TVO BY
DRAWING UP HERE,
NOTICE THE TVO
T-SHIRT AND TVO UP HERE
AND THEY'RE
WALKING A KILOMETRE.
SO THIS WAS PRETTY
EXCITING AND I KNOW
WHEN I SHOWED THEM THE FILM
ABOUT FOUR OR FIVE DAYS AGO,
THEY WERE
ABSOLUTELY THRILLED
TO BE PART OF
THE PROGRAM.
NOW, BEFORE I WRAP UP,
I'M GOING TO GO BACK
TO MY LITTLE
PROBLEM HERE.
AND WE'LL ZOOM IN ON
IT AND WE'LL MOVE IT
AND THERE WE ARE.
SO THERE'S
OUR PROBLEM.
WHAT IS THE SAME
ABOUT THESE LETTERS?
THE FIRST THING
THAT STRUCK ME,
I WAS READING THEM.
B, C, D, E.
AND YOU KNOW WHAT?
THEY ALL SOUND
THE SAME.
THEY HAVE THE
E SOUND.
B, C, D, E.
BUT THAT'S NOT WHAT
I WAS QUITE AFTER.
THERE'S ONE MORE
MATHEMATICAL IDEA.
NOTICE THIS.
IF I DRAW A HORIZONTAL
LINE LIKE THIS RIGHT
IN THE CENTRE OF EACH ONE,
WE HAVE A HORIZONTAL LINE
OF SYMMETRY IN EACH ONE.
MEANING, THE UPPER PART
OF THE B FOLDS ONTO THE
BOTTOM PART EXACTLY.
OR, THE BOTTOM
PART OF THE C
FOLDS ON THE UPPER
PART OF THE C EXACTLY.
IT DOESN'T MATTER
WHICH WAY YOU GO.
THE SAME WITH THE D AND
THE SAME WITH THE E.
THEY'RE ALL KINDS
OF SETS OF LETTERS
THAT HAVE DIFFERENT
CHARACTERISTICS.
THE CHARACTERISTICS OF
SYMMETRY ARE SOMETHING
THAT YOU CAN LOOK
FOR WHEN YOU START
LOOKING AT LETTERS.
BECAUSE DIFFERENT LETTERS
HAVE DIFFERENT KINDS
OF SYMMETRY AND IT'S KIND
OF FUN TO FIGURE OUT
WHICH ONES HAVE WHICH.
SO, THAT'S SOMETHING THAT
YOU CAN THINK ABOUT
AS YOU LOOK AT
YOUR ALPHABET.
NOW, WHAT I'D LIKE TO
SAY IS, VERY QUICKLY,
IF YOU GET AN OPPORTUNITY
WITH YOUR CLASS
TO GO OUTSIDE AND DO
THESE MEASUREMENTS,
REMEMBER RECORD
EVERYTHING CAREFULLY,
MAKE SURE THAT IF
YOU DO A POSTER,
THAT YOU PUT ALL THAT
INFORMATION ON THE POSTER
AND I HOPE THAT YOU HAVE
A WONDERFUL DAY BEING
OUTSIDE AND DOING SOME
REALLY GOOD MATHEMATICS.
WE ARE COMING BACK IN
TWO WEEKS AND IT'LL BE,
AGAIN, A RELATIVELY
SHORT PROGRAM.
WHAT WE WILL SHOW YOU
IS THE WHOLE LESSON
WE DID THE WILLIAM BURGESS
KIDS, WITH THEIR TEACHER
MISTRESS TISCHLER AND SHOW, RIGHT
FROM THE INSTRUCTIONS,
RIGHT THROUGH THE
ACTIVITIES,
THE FIRST FOUR ACTIVITIES,
TO FEELING THE KILOMETRE.
WHAT THE WHOLE PIECE SORT
OF FELT LIKE AND HOW IT
PROGRESSED FROM ONE
STAGE TO THE NEXT.
I HOPE YOU HAVE A GREAT
TIME AND I HOPE
THAT YOU GET AN
OPPORTUNITY TO GO OUT
AND ACTUALLY DO
SOME MEASUREMENTS.
AND I HOPE THE
WEATHER IS GREAT.
SO, WE'LL SEE YOU
IN A COUPLE WEEKS.
UNTIL THEN, SO
LONG FROM TORONTO.

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Watch: NFA - Math Projects, Part 2