Transcript: Student Session 11 | Sep 15, 1998

A blue slate appears. It reads “Exponents are one way to write large numbers using fewer symbols. It was only in the 16 hundreds that people began to use exponents to write large numbers.”

A second slate appears. It reads “Positive exponents” as a title.
Below the title it reads “we see, 10 to the fourth power.
We think 10 times 10 times 10 times 10.

Lorraine reads from it. She says AN EXAMPLE OF THIS,
WE SEE A NUMBER OR A
PARTICULAR EXPONENT.
AND WE THINK WHEN
WE SEE THIS IS;
TEN TIMES TEN TIMES TEN TIMES TEN.
WHICH IS EQUAL TO TEN THOUSAND
AND WE SAY TEN TO THE FOURTH IS EQUAL TO TEN THOUSAND OR TEN TO THE POWER OF FOUR IS EQUAL TO TEN THOUSAND.
SO THERE ARE TWO
WAYS OF SAYING IT.
I'M SURE SOME OF YOU HAVE
USED OTHER WAYS OF EXPRESSING
EXPONENTS, BUT WE'RE GOING TO
USE THIS PARTICULAR METHOD SO
WE'RE ALL COMMUNICATING
IN THE SAME LANGUAGE.
THIS WAY WE UNDERSTAND
ONE ANOTHER.
I WOULD LIKE YOU TO LOOK AT
THIS NUMBER, AND CALL ME BY
PRESSING POUND NINE AND TELL
ME WHAT IT IS WE THINK WHEN
WE SEE THIS EXPONENT.

A blue slate appears. It reads “Positive exponents” as a title and then reads; we see 2 to the power of 3.

She continues AND I HAVE SOMEONE FROM
JACK MINER WHO IS CALLING.
AND IT'S WARREN.
AND THE REST OF YOU CAN BE
THINKING WHAT IT IS WE THINK,
AS WELL AS WHAT WOULD WE SAY
WHEN WE SEE THIS EXPONENT.
HELLO, HI, WARREN.

Warren says HELLO.

Lorraine says HI.
WHAT IS IT WE WOULD THINK
WHEN WE SEE THIS EXPONENT
ON THE SCREEN?

He says I WOULD THINK TWO TO
THE EXPONENT THREE.

She says YES, BUT HOW WOULD IT
LOOK,

He says TWO TIMES THREE.

She says NO, TRY AGAIN.

He asks WHAT?

She says LOOK AT THE SCREEN.
WHAT IS IT?
WE THINK WHAT?

The screen reads “We think 2 times 2 times 2.”

He says WE THINK 2 TIMES 2 TIMES 2.

Lorraine says YEAH, VERY GOOD.
IT'S NOT TWO TIMES THREE.
TRY NOT TO GET
THOSE TWO MIXED UP.
AND DO YOU KNOW
WHAT THE ANSWER IS?

He answers IT IS EIGHT.

She says VERY GOOD.
WHAT WOULD YOU SAY
WHEN WE SEE THE NUMBER?
YOU MENTIONED IT EARLIER.

He says TWO TO THE EXPONENT THREE.

She says OKAY.
THAT'S NOT ONE OF THE
METHODS WE'RE GOING TO USE.

He explains TWO TO THE POWER OF THREE.

Lorraine says THAT'S RIGHT.
AND WHAT'S ANOTHER ONE?

He answers I DON'T KNOW.

She suggests WHAT'S A FANCY WAY WHEN YOU
SEE THREE AS AN EXPONENT?

He answers TWO CUBED.

She says YEAH, VERY GOOD.
SO WE'LL REMEMBER THAT
METHOD, THANKS, WARREN.
AND THIS WAY, WE WILL BE
COMMUNICATING, OBVIOUSLY,
THE SAME WAY.
WE'RE GOING TO BE DOING
A LITTLE ACTIVITY.
WHAT I'D LIKE FROM YOU
IS TO TAKE TWO PAGES.
DOESN'T HAVE TO BE BLUE,
DOESN'T NECESSARILY HAVE TO BE
WHITE, JUST TWO PAGES WHERE
THEY ARE REGULAR SIZE,
8-BY-11, OKAY?
AND ONE THING I'M GOING TO
WANT FROM YOU, ONE WHERE IT
CAN JUST BE A RECYCLABLE PAGE
BECAUSE WE ARE GOING TO BE
DOING A LITTLE ACTIVITY WHERE
YOU ARE GOING TO BE FOLDING
IT, AND THE OTHER PIECE OF
PAPER, I WOULD LIKE YOU TO
WRITE THE FOLLOWING;

A paper appears on screen. It shows three columns. The first column reads “number of folds, 1,2,3,4,10, n.”
The second column reads “number of sections.”
The third column reads Sections as power of 2.”

She explains AND HERE WE GO.
THERE'S THREE COLUMNS.
I WOULD LIKE YOU TO
PUT THE FIRST COLUMN NUMBER OF FOLDS, SECOND NUMBER OF SECTIONS, THIRD SECTIONS AS POWER OF 2.
SO IF YOU COULD DO THAT
RIGHT NOW, WRITE THE THREE
DIFFERENT COLUMNS.
OKAY, ASSUMING YOU ARE DONE,
OR MAKE SURE YOU HAVE YOUR
OTHER PIECE OF PAPER HERE.
YOU'RE GOING TO NOTICE I HAVE
HERE, NUMBER OF FOLDS BEING ONE.
SO PUT THAT IN YOUR COLUMN.
ONE.
THEN YOU'RE GOING TO TAKE YOUR
OTHER PIECE OF PAPER, AND IF
YOU ARE A LITTLE BIT BEHIND,
YOU'LL CATCH UP AS WE GO ALONG.
AND YOU ARE GOING TO TAKE
IT, AND THE SECTION THAT IS
LONGER, YOU ARE GOING
TO FOLD IT IN TWO.
JUST LIKE I'M DOING.
OKAY?

She folds it in 2.

She continues THEREFORE, THERE IS ONE FOLD.
AS YOU CAN TELL, I WANT
YOU TO DO THE SAME.
AND YOU ARE GOING TO TELL ME,
WHAT IS THE NUMBER OF SECTIONS?
WELL, YOU LOOK AT IT, AND YOU
CAN SEE HERE, THERE ARE TWO.

She points to the 2 sections and writes down 2 in the second column.

She says SO PUT THAT AS AN ANSWER.
HOW CAN I WRITE THIS,
THESE NUMBER OF SECTIONS
AS A POWER OF TWO?
CALL ME BY LETTING
ME KNOW THAT.
CALL BY PRESSING POUND NINE.
AND LET ME KNOW HOW CAN I
WRITE THIS NUMBER AS A POWER
OF TWO?
AND I'M CALLING JACK
MINER ONCE AGAIN.
HI, VANESSA?

Vanessa says YEAH.

Lorraine says HELLO.
CAN YOU LET ME KNOW HOW WOULD
I WRITE THIS NUMBER IN THE
POWER OF TWO?

She answers TWO TO THE EXPONENT ONE.

She says OKAY, WE'RE
GOING TO SAY,

She says TO THE POWER ONE.

Lorraine folds the paper once more and says VERY GOOD.
AND IF I WERE TO TAKE A PIECE
OF PAPER, AND YOU CAN DO THE
SAME, IF I FOLD IT AGAIN,
AND YOU DO THAT AS WELL,
HOW MANY SECTIONS
DO YOU NOTICE?

Vanessa says FOUR.

Lorraine says VERY GOOD.
SO WE NOTICE ONE,
TWO, THREE, FOUR.

She writes down 4.

She asks AND HOW WOULD YOU WRITE
THAT AS A POWER OF TWO?

Vanessa says TWO TO THE EXPONENT TWO?
OR POWER OF TWO, SORRY.

Lorraine writes it down in the third column and says OKAY, THANKS.
AND WHAT I WOULD LIKE,
THANKS VERY MUCH, VANESSA.
WHAT I'D LIKE FROM YOU IS
FOR YOU TO FOLD IT AGAIN IN
THREE, AS WELL THEN IN FOUR,
AND TELL ME WHAT ARE THE
ANSWERS TO THE NUMBER OF
SECTIONS, AS WELL AS
SECTIONS AS A POWER NINE.

She folds it once more.

She says ONCE YOU'VE DONE THREE AND
FOUR, CALL BY PRESSING
POUND NINE.
AND I'M CALLING STEPHANIE.
HELLO?

Stephanie says HELLO?

Lorraine says HI.
HAVE YOU FOLDED
IT THREE TIMES?

She answers YEAH.

Lorraine says AND HOW MANY DO YOU NOTICE?

Stephanie says THERE'S EIGHT SECTIONS.

Lorraine answers YEAH, ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN, EIGHT.
AND HOW WOULD WE
WRITE THAT HERE?

She says THAT WOULD BE TWO TO
THE POWER OF THREE.

Lorraine says GREAT.
AND DID YOU DO
IT ANOTHER TIME?

She answers YEAH.

Lorraine writes the results down and says ALL RIGHT.
YOU'RE A LITTLE AHEAD
OF ME, THAT'S GOOD.
AND HOW MANY DID YOU NOTICE?

She says 16.

Lorraine says THAT'S RIGHT, 16.
AND HOW DID YOU WRITE
THAT TO THE POWER OF TWO?

She says TWO TO THE POWER OF FOUR.

Lorraine says OKAY, THANKS VERY
MUCH, STEPHANIE.

Stephanie says YOU'RE WELCOME.

Lorraine says NOW YOU ARE GOING TO BE
ANSWERING A QUESTION HERE.
AND YOU WILL REQUIRE YOUR
PHONES TO ANSWER THIS QUESTION.
AND YOU MIGHT WANT TO HAVE YOUR
THREE COLUMNS IN FRONT OF YOU.

A light blue slate reads “Question number 1, each time you fold the paper, the number sections, 1 quadruples. 2 triples. 3 doubles.”

Lorraine points to the bar on the right of the slate and says AND YOU CAN TELL 83 PERCENT
OF YOU HAVE ANSWERED.
LET'S TRY A FEW MORE.

A graph appears. It shows three columns representing the 3 options. The first one is labelled 6; the second is labelled 5 and the third is labelled 32.

She continues AND IF WE LOOK AT OUR BAR
GRAPH, THE MAJORITY OF YOU
FEEL THE ANSWER DOUBLES.
AND I'M GOING TO CALL IN ONE
OF YOU HERE, WHO HAS ANSWERED
NUMBER ONE.
AND LET'S SEE WHY.
I'M CALLING COLLEGE AVENUE.
WE'RE CALLING COLLEGE AVENUE.
HELLO?

A voice answers HI.

Lorraine says HI.
WHY DID YOU ANSWER NUMBER
ONE AS IN QUADRUPLES?

He says I DID NOT.

She says OH, I HAVE YOU DOWN
HERE AS NUMBER ONE.

He says I ANSWERED NUMBER THREE.

Lorraine says OH, MAYBE BY ACCIDENT
YOU PRESSED NUMBER ONE.
THANKS.

He answers OKAY.

Lorraine continues IF WE LOOK AT OUR GRAPHICS
OVER HERE,

She points to the three columns on the previous sheet of paper and says THE QUESTION WAS
SAYING, EACH TIME YOU FOLD
THE PAPER, THE NUMBER OF
SECTIONS, WHAT
ARE YOU NOTICING?
IT IS DOUBLING.
TWO BECOMES FOUR, FOUR,
EIGHT, AND THE REASON BEING,
WE'RE ALWAYS MULTIPLYING
IT AGAIN BY TWO.
AND IF YOU KEEP THIS IN
MIND, TRY AND ANSWER THEN
THE FOLLOWING QUESTION,

A light blue slate appears. It reads “Question number 2, Suppose you could fold a piece of paper 10 times. How many sections would you create? 1 200; 2 2 thousand 24, 3 1 thousand 24.”

She continues THEN CALL ME BY PRESSING POUND
NINE TO LET ME KNOW WHY YOU
CHOSE YOUR ANSWER.
HI, I HAVE SAMUEL
FROM COLLEGE AVENUE?

She says MY NAME IS NOT SAMUEL.

Lorraine says OH, IT'S COMING UP AS SAMUEL.
WHAT IS YOUR NAME?

She responds BULGARA.

Lorraine says HELLO.
AND CAN YOU TELL US
WHICH ANSWER YOU CHOSE?

She answers I CHOSE NUMBER THREE.

She asks WHY IS THAT?

She says BECAUSE SOMEONE TOLD ME TO.

She suggests OH, HOW DO YOU THINK
YOU SHOULD DO THIS ONE?
IF WE LOOK AT OUR GRAPHICS
OVER HERE FOR TEN,
YOU SHOULD KNOW
THE POWER HERE.
IF YOU NOTICE THERE'S
SOMETHING OCCURRING HERE.
WHAT ARE YOU NOTICING WITH THE
NUMBER HERE AND THE NUMBER AT
THE POWER OF TWO?

Bulgara says IT DOUBLES.

Lorraine says BE CAREFUL WHAT
YOU ARE SAYING.
I'M SAYING THE NUMBER OF
FOLDS, AND THEN WHEN YOU SEE
SECTIONS OF POWER
OF TWO, WHAT ARE YOU NOTICING
WITH THE EXPONENTS?

Bulgara says THEY ARE INCREASING BY ONE.

Lorraine says THAT'S RIGHT.
JUST LIKE THE NUMBERS THAT
ARE HERE OF THE FOLDS.
DO YOU SEE THE CONNECTION?

She says YES.

Lorraine asks SO IF WE HAD TEN, WHAT WOULD
BE THE POWER OF TWO HERE?

She answers TEN.

Lorraine says THAT'S RIGHT.
AND THEREFORE, TO FIND THE
ANSWER, WHAT DO YOU HAVE TO DO?

She answers TWO TO THE POWER OF TEN.

Lorraine says THAT'S RIGHT.
AND WHAT DOES THAT LOOK LIKE?

She explains TWO TIMES TWO
TIMES TWO TIMES TWO.

Lorraine says EXACTLY.
AND IF WE WERE TO GO TWO TIMES
TWO TIMES TWO TIMES TWO TEN
TIMES, WHAT WOULD
BE YOUR ANSWER THEN?

She says 1 thousand 24.

Lorraine says THAT'S CORRECT.
EXACTLY.
THANKS VERY MUCH.
AND IF WE LOOK AT OUR BAR
GRAPH HERE, THE MAJORITY OF
YOU HAVE ANSWERED
NUMBER THREE.
SO YOU WOULD HAVE TO GO
THROUGH THE WHOLE SECTION AND
DO TWO TIMES TWO TIMES
TWO TIMES TWO, SO BRAVO.
AND YOU CAN SEE YOU CAN
FIGURE THAT OUT YOURSELVES.
NOW, TO GO ONE STEP FURTHER,
IF WE LOOK HERE, WHAT IF

She circles the n in the first column and says WE PUT DOWN JUST THE
NUMBER OF FOLDS BEING N.
WHAT CAN YOU GIVE ME
FOR ANSWERS OVER HERE?
CALL ME BY PRESSING
POUND NINE TO SHARE.
WHAT CAN WE PUT DOWN AS
AN ANSWER FOR SECTIONS
AS POWER OF TWO, AS WELL
AS NUMBER OF SECTIONS?
AND WE WILL CALL NADEPA.

She says HELLO.

Lorraine says HI.
AND WHAT CAN YOU
TELL ME ABOUT?

Nadepa answers I THINK I KNOW THE ANSWER
FOR SECTIONS OF POWER OF TWO.
IT'S N TO THE POWER OF TWO.
I MEAN, TWO TO THE POWER N.

Lorraine says VERY GOOD.
SO TWO TO THE POWER OF N.

She points to the number of sections column and asks AND HOW ABOUT THIS?

She answers I'M TRYING TO
FIGURE THAT OUT.
ANYBODY GOT ANY ANSWERS?
I DON'T KNOW THAT ONE.

She asks AND YOU KNOW WHY
YOU DON'T KNOW?
BECAUSE WE DEFINITELY NEED TO
KNOW THE EXPONENT IN ORDER TO
FIGURE THIS ONE
OUT RIGHT NOW.
OKAY, GOOD FOR YOU.

She answers N TO THE POWER OF N.
OR TWO TO THE POWER N.

Lorraine says TWO TO THE POWER OF N IS FOR
YOUR SECTIONS HERE, BUT YOU
CAN'T FIGURE OUT NOW THE
NUMBER OF SECTIONS UNTIL
YOU FIGURE OUT YOUR N.
OKAY, THANKS VERY MUCH.

She says OKAY.

Lorraine says OKAY, NOW WE'RE GOING TO
BE GOING ONE STEP FURTHER
WITH THAT.
AND IF YOU LOOK AT THIS,
AND YOU ARE GOING TO NEED A
PENCIL, AS WELL AS A
PIECE OF PAPER HERE.

She shows another exercise that reads “Express the number of small squares in each large square as a power. “A” “B” and “C.”

She says WELL, HERE WE HAVE TWO
DIFFERENT SQUARES.

She shows a square marked “a” that is formed by 4 small squares by 4 and a larger one marked “b” that is 6 by 6.

She says AND THEN THERE IS A BUNCH
OF LITTLE SQUARES IN THERE.
WHAT CAN YOU TELL ME, AS FAR
AS EITHER ONE, A OR B, IF YOU
WERE TO EXPRESS THE SMALL
SQUARES IN EACH LARGE SQUARE,
AS A POWER.
HOW COULD YOU DO THAT?
WRITE IT DOWN, FIGURE IT OUT,
THEN CALL ME BY PRESSING
POUND NINE.
AND I'M NOW CALLING SOMEONE
FROM USBORNE CENTRE.
HELLO?

A voice answers HI.
WHAT CAN YOU TELL ME?
HOW CAN I EXPRESS
THAT AS A POWER?

She says FOR A, IT COULD BE FOUR
TO THE POWER OF TWO.

Lorraine asks WHY ARE YOU SAYING THAT?
BECAUSE YOU ARE CORRECT.

She answers BECAUSE THERE ARE FOUR ON THE
TOP, AND FOUR ON THE BOTTOM.
AND IT IS FOUR TO
THE POWER OF TWO.

Lorraine says RIGHT.
WHAT'S FOUR TO
THE POWER OF TWO?

She answers 16.

Lorraine says THAT'S RIGHT.
BECAUSE YOU SAY FOUR
TIMES FOUR WHICH IS 16.
AND IF WE WERE TO COUNT
THEM ALL, YOU ARE CORRECT.
HOW ABOUT FOR B?

She suggests SIX TO THE POWER OF TWO.

Lorraine writes down 6 to the power of 2 as she says THAT'S RIGHT.
AND AGAIN, WHAT IS THAT?

She answers 36.

Lorraine says THAT IS CORRECT.
SIX TIMES SIX, IS 36.
IF WE WERE TO LOOK AT ALL
OF THESE AND COUNT THEM.
EXCELLENT, THANKS VERY MUCH.
BYE.

She answers BYE.

Lorraine says AND FOR THE REST OF YOU,
I'D LIKE YOU TO LOOK AT THIS
PARTICULAR SQUARE,

She changes the square to a larger one marked “c” that is 7 by 7 squares.

She continues AND I WANT
YOU TO EXPRESS THIS NUMBER
ONCE AGAIN AS A POWER.
AND YOU ARE GOING TO ANSWER
WITH YOUR PHONES FOR THIS
PARTICULAR ONE.

She shows the possible options.

She says OPTION 1, 8 SQUARED, 2, 7 SQUARED, OPTION 3 9 SQUARED.

THEN ONCE WE HAVE YOUR ANSWER,
WE CAN SEE 67 PERCENT, OR
I CAN SEE THAT, HAVE ANSWERED,
STILL A FEW MORE, CALL ME BY
PRESSING POUND NINE TO SHARE
WHY YOU HAVE CHOSEN THAT ANSWER.

A voice says HELLO.

Lorraine says HI.
CAN YOU TELL ME WHAT
YOU HAVE AS AN ANSWER?

He says SEVEN TO THE POWER OF TWO.

Lorraine asks THAT'S RIGHT.
AND WHY IS THAT?

He says THERE ARE SEVEN SQUARES.

She continues THAT'S RIGHT.
SEVEN SQUARES,
AND SEVEN ACROSS.
AND WHAT IS SEVEN
TO THE POWER OF TWO?

He says SEVEN TIMES SEVEN.

She asks WHICH IS EQUAL TO?

He answers 49.

Lorraine comments THAT'S RIGHT.
IF YOU WERE TO COUNT
THEM OUT, IT WOULD BE 49.
WHAT IS ANOTHER NAME WHEN YOU
FIGURE OUT THE LENGTH AND THE
WIDTH, WHEN WE MULTIPLY THEM.
WHAT TO WE CALL THAT?
WHAT DO WE CALL IT WHEN WE
ARE FIGURING OUT ALL OF THIS?

He says COORDINATES.

She explains YEAH, WHEN YOU ARE TRYING TO
FIND, I DON'T WANT TO SAY THE
WORD, IT STARTS WITH AN A.
I WANT TO KNOW THE LENGTH AND
THE WIDTH, AND IT GIVES ME
ALL THIS.

He suggests AREA.

She writes it down and says YES, VERY GOOD.
THE WORD IS AREA.
AND WE ARE GOING TO HAVE TO
KNOW THAT WORD IN ORDER TO
FIGURE OUT OUR NEXT QUESTION.
THANKS VERY MUCH.
AND IF WE LOOK AT WHAT ALL
OF YOU HAVE ANSWERED HERE,
IT'S QUITE INTERESTING.

The graph shows three columns representing the answers. The first column is labelled 2, the second is labelled 43 and the third is labelled 2.

She describes THE MAJORITY OF YOU CHOSE
NUMBER TWO, WHICH IS CORRECT.
SEVEN SQUARED.
SO BRAVO.
NOW, IF SOME OF YOU PLAY
BASEBALL, THIS NEXT QUESTION
SHOULD PROBABLY
BE FAIRLY EASY.

She shows a new question that reads “A baseball diamond is a square with sides approximately 25 centimeters long. Is the area greater or less than 1 thousand square meters? 1, greater. 2, less.”

She continues AND I WANT YOU TO WORK IT
OUT AND THEN TO CALL ME BY
PRESSING POUND NINE AND LET
ME KNOW WHY IT IS YOU CHOSE
THAT ANSWER.
AND AGAIN, YOU'LL BE USING
YOUR PHONES TO SAY WHETHER
IT WAS ONE OR TWO.
I WANT YOU TO CALL ME BY
PRESSING POUND NINE TO SHARE
HOW DID YOU FIGURE THIS OUT?
70 PERCENT OF YOU
HAVE ANSWERED.
SO WE STILL NEED 30 PERCENT.
HELLO, STEPHANIE?

Stephanie says HI.

Lorraine asks HI.
AND WHAT DID YOU COME
UP WITH AS AN ANSWER?

She answers I GOT LESS THAN 1 thousand.

Lorraine circles option 2 and says AND YOU ARE CORRECT.
CAN YOU TELL ME HOW YOU
FIGURED THIS ONE OUT?

She answers 25 TIMES 25.

Lorraine says THAT'S RIGHT.
AND WHY ARE YOU SAYING 25?

She says BECAUSE AREA IS SQUARED.

Lorraine says THAT'S RIGHT.
WELL, LET'S IMAGINE
THAT SQUARED.
AND THIS IS 25 WHAT?

Lorraine draws a square on a new sheet of paper and writes 25 on the left side.

She answers TO THE POWER OF 2.

Lorraine says BE CAREFUL.
WHAT IS IT SAYING?
A SQUARE WITH SIDES
APPROXIMATELY?

Stephanie answers 25 METRES LONG.

Lorraine says THAT'S RIGHT.
SO WHAT IS THIS 25?

Stephanie says METRES.

Lorraine writes 25 below the square and says VERY GOOD.
AND WHAT'S THIS?

Stephanie says 25 METRES.

She continues THAT'S RIGHT BECAUSE
IT'S A PERFECT SQUARE.
WHAT DO YOU HAVE TO DO
TO FIGURE OUT THE AREA?

Stephanie answers YOU HAVE TO
MULTIPLY 25 BY 25.

Lorraine says OKAY, 25 METRES, TIMES 25
METRES, AND WHAT DOES THAT
GIVE YOU?

She responds 625 METRES SQUARED.

Lorraine says THANK YOU.
VERY IMPORTANT THAT WE NOTICE
WHEN WE HAVE TWO, AND THEY
ARE BEING MULTIPLIED,
THEY BECOME SQUARED.
SO 625 METRES SQUARED.
AND IF WE GO BACK TO OUR
QUESTION, IT'S SAYING, IS THE
AREA GREATER OR LESS
THAN A THOUSAND?
YOU ARE CORRECT, IT IS LESS.
AND IF WE LOOK AT WHAT THE
REST OF YOU HAVE ANSWERED,
THANKS VERY MUCH, STEPHANIE,
YOU CAN TELL THAT THE MAJORITY
OF YOU SAW THAT IT WAS LESS.

A graph shows two columns representing the student answers. The first column is labelled 8 and the second is labelled 40.

She continues THERE ARE STILL A FEW OF YOU
THAT ARE UNCLEAR, AND YOU HAVE
TO GO THROUGH THE WHOLE
STEPS LIKE STEPHANIE DID.
JUST TO SEE IF YOU ARE
UNDERSTANDING THAT, MAYBE WE
CAN GET THE EIGHT THAT ARE
UNCLEAR TO UNDERSTAND A LITTLE
BIT CLEARER, LET'S TRY
THAT ONE MORE TIME.
AND YOU ARE GOING TO CALL ME
BY PRESSING POUND NINE TO
SHARE HOW YOU
FOUND THE ANSWER.
IT SAYS, ONE HECTARE,
AND
HECTARE IS WHAT'S USED TO
MEASURE AREAS OF LAND. SO, ONE HECTARE, IS THE AREA OF A SQUARE WITH SIDE LENGTH 10 SQUARED METERS. EXPRESS THE NUMBER OF SQUARE METERS IN A HECTARE AS A POWER.
SO CALL ME BY PRESSING POUND
NINE, AND SHARE WITH ME HOW DO
I FIGURE THIS ONE OUT.
HELLO.

A male voice answers HELLO.

Lorraine says HI.
HOW WOULD YOU
FIGURE THIS ONE OUT?

He answers TEN TIMES TEN.

She asks AND WHY ARE YOU
SAYING TEN TIMES TEN?

He explains BECAUSE YOU HAVE TO
GO BY THE SIDES OF IT.

She asks AND WHAT ARE THE SIDES?

He says TEN METRES.

She asks ARE THEY TEN METRES?

He responds TEN METRES SQUARED.

She asks ARE THEY TEN METRES SQUARED?

He says TEN SQUARED METRES.

Lorraine says YES.
AND VERY IMPORTANT
YOU SAY IT LIKE THAT.
BECAUSE THE WAY ORIGINALLY
YOU'RE PUTTING THE METRES
THERE SQUARED.
SO TEN SQUARE METRES.
THAT'S JUST ONE SIDE.
SO WHAT DOES THAT MEAN,
TEN SQUARE METRES?

He says TEN TIMES TEN.

She draws a square and writes down 10 squared meters next to it as she says THAT'S RIGHT.
SO IT'S TEN SQUARED METRES,
WHICH YOU ARE SAYING IS THE
SAME AS TEN TIMES TEN BECAUSE
WE'RE ALL GREAT AT THAT AT
THAT POINT.

She points to the word meters and asks ARE THE METRES SQUARED HERE?

He says HUH?

She repeats ARE THE METRES SQUARED HERE?

He says NO.

She points to the horizontal side and says NO, THEY'RE NOT.
AND HOW ABOUT THIS LENGTH?

He says THAT'S TEN.

She suggests LOOK AT IT AGAIN.

She holds the question for him to read.

She asks SO WHAT IS THIS?

He says TEN SQUARED METRES.

She says TEN SQUARED METRES.
SO HOW DO I FIGURE IT OUT?
WHAT DO I HAVE TO DO?

He says 100 TIMES 100.

She says OKAY, YOU COULD WRITE IT
LIKE THAT, BUT IT'S 100 WHAT,
DOGS, CATS, WHAT?

He responds METRES.

She says VERY GOOD.
OR WHAT'S ANOTHER WAY OF
WRITING IT IF WE JUST WANT TO
KEEP IT THE WAY IT LOOKS.

He says TEN TIMES TEN
TIMES TEN TIMES TEN.

She points to the words 10 square meters and says OR HOW ABOUT JUST
THE WAY IT LOOKS?
LET'S KEEP IT SIMPLE.

He says TEN SQUARED TIMES TEN SQUARED.

She says OKAY, BUT YOU'RE
FORGETTING SOMETHING.
TEN SQUARED WHAT?

He answers METRES.

She says THANK YOU.
VERY IMPORTANT WE PUT
ALL THE INFORMATION IN.
TEN SQUARED METRES.
AND DO YOU REMEMBER LAST WEEK
WE TALKED ABOUT SOMETHING?

She points to both tens to the power of 2 and asks WHAT ARE THESE?

He answers THE BASE.

She says THAT'S RIGHT.
IF BOTH BASES ARE THE SAME,
AND THEY ARE BEING MULTIPLIED,
WHAT CAN WE DO
WITH THE EXPONENTS?

He says PLUS THEM.

She answers THAT'S RIGHT.
SO WHAT'S THE ANSWER?

Voices are heard in the background.

He says WHAT ARE YOU TALKING ABOUT?

Lorraine chuckles and says LET HIM ANSWER.

He says A HUNDRED.

She says BE CAREFUL.
THE SAME BASE, AND WHAT
DID YOU JUST TELL ME,
THE SAME BASE, YOU CAN?

He suggests FOUR.

She write ten to the power of 4.

Lorraine says THAT'S RIGHT.
AND WHAT HAPPENS
TO THE METRES?

He adds THEY STAY METRES.

She says YES.
BUT WHEN YOU MULTIPLY
A METRE WITH A METRE?

He says THEY SQUARE.

Lorraine writes down square meters and says THAT'S RIGHT.
BECAUSE NOW IT'S THE AREA.
SO THE ANSWER IS ACTUALLY TEN TO THE POWER OD 4 METERS SQUARED OR IF YOU WANT TO WRITE IT ALL OUT WHAT IS IT?

He says THEN THOUSAND METERS SQUARED.

She explains THEY MEAN THE SAME THING,
BUT IT'S JUST ONE METHOD.
I PURPOSELY PUT A TRICKY ONE
THERE WHERE I WANTED IT
TO BE SQUARED.
IT'S THE SAME AS SAYING 100
METRES, WHERE WE COULD HAVE
WRITTEN A HUNDRED TIMES A
HUNDRED, BUT IT WAS JUST A
DIFFERENT METHOD TO REINFORCE
THE BASES AND ADDING.
OKAY, THANKS VERY MUCH.
AT THIS POINT, WE'RE GOING TO
BE TALKING ABOUT PROBABILITY.
AND PROBABILITY BEING A BIG
PART OF YOUR QUESTIONS IN YOUR
EXERCISES FOR THIS WEEK.
THE EXPONENTS, AS WELL, ARE
A PART OF YOUR EXERCISES.
SO YOU WANT TO MAKE SURE YOU
UNDERSTAND WHAT IT IS WE'VE
JUST DONE.
AT THE END OF THE LESSON, IF
YOU HAVE ANY MORE QUESTIONS,
YOU CAN CALL IN BY PRESSING
POUND NINE, OR YOU CAN
ASK YOUR TEACHER.
I'M SURE THEY'D BE VERY PLEASED
TO HELP YOU OUT, AS WELL.
AND FOR THE NEXT SECTION HERE.

A blue slate appears. It reads “Probability, if the outcomes of an experiment are equally likely, then the probability of an event is the number of outcomes favourable to the event divided by the total number of outcomes.”

She says WELL, THIS SOUNDS
ABSOLUTELY WONDERFUL,
BUT WHAT DOES IT MEAN?
IF YOU HAVE IN FRONT OF YOU,
I'LL BRING THAT RIGHT IN,

She shows a die and says A DIE.
OKAY?
I WANT YOU TO TELL ME THE
PROBABILITY OF EACH EVENT THAT
I'M GOING TO MENTION ON
A ROLL OF A FAIR DIE.
AND THIS DIE, AS YOU
CAN TELL, HAS SIX SIDES.
IT'S NOT A TRICKY ONE.
IT'S FAIR.
AND I WANT YOU TO WRITE
DOWN ON A PIECE OF PAPER
THE FOLLOWING.

She shows a question on a piece of paper. It reads “Write the probability of each event on a roll of a fair die.
A, number 6. B, a number less than 3. C, an odd number. D, either 3 or 6. E, a number greater than 2.

She says ONCE YOU FIGURED THESE OUT,
PRESS POUND NINE AND SHARE
THEM WITH THE REST OF US.
I HAVE ONE CALL, SO SOME
OF YOU ARE STILL UNCLEAR.
A FEW MORE, GOOD.
HELLO.

A boy says HI.

Lorraine says HI.
CAN YOU TELL US ONE OF
THE ANSWERS AND WHY?

He says I THINK FOR A, THE
PROBABILITY OF GETTING
SIX WOULD BE ONE.
BECAUSE THERE'S ONLY
ONE SIX ON THE DICE.

She says OKAY, SO YOU'RE SAYING EVERY
ONE TIME I'M GOING TO GET SIX
EVERY TIME?

He says NO.
WELL, IT WOULD BE LIKE,

She asks HOW WOULD YOU
WRITE THAT DOWN?

He says ONE OUT OF SIX.

She says PERFECT.
BECAUSE IT SAVES THE DIE WILL
SHOW SIX ABOUT ONE SIXTH OF
THE TIME, LIKE YOU ARE SAYING.

She writes 1 over 6 and says SO THAT'S WHAT YOUR
ANSWER WOULD BE.
ONE SIXTH IS THE PROBABILITY.
EXCELLENT.
AND CAN YOU TRY ONE MORE?

He says FOR B, FOR GETTING A
NUMBER LESS THAN THREE,
IT WOULD PROBABLY BE
THREE OUT OF SIX.

He explains AND WHY DO YOU THINK THAT?
HOW MANY NUMBERS ARE LESS
THAN THREE ON THE DIE?

He says THREE.
OR TWO.

She asks AND WHAT ARE THEY?

He says TWO AND ONE.

She repeats TWO AND ONE, RIGHT.
SO TWO OUT OF SIX.
THAT'S RIGHT.
AND CAN WE SIMPLIFY THAT?

He says ONE OUT OF THREE.

She writes 1 over 3 and says SO FOR EVERY THIRD TIME YOU
ROLL IT, YOU SHOULD PROBABLY
GET A NUMBER LESS THAN THREE.
OKAY?
GREAT.
THANKS VERY MUCH.
CAN SOME OF YOU CALL
IN TO SHARE C, D AND E?
HI, ADAM?

Adam says YES.

She asks CAN YOU GIVE US ONE OF
THE ANSWERS HERE, AND WHY?

He says NUMBER C.

She says OKAY.

He says IT'S ONE HALF.

She asks WHY ARE YOU SAYING THAT?
WHAT NUMBERS ARE ACTUALLY
ODD IN ONE TO SIX?

He says ONE, THREE AND FIVE.

She says ONE, THREE AND FIVE.
AND THEREFORE, IT'S?

He responds THREE OVER SIX.

She says AND AS YOU MENTIONED...?

He says ONE-HALF.

She says PERFECT.
COULD YOU DO ONE MORE?

He says FOR D, TWO OVER SIX.

She says PERFECT.
OR ONE-THIRD.
I'M GETTING KIND OF SMALL
HERE, BUT THAT'S GREAT.
LET'S GO TO ONE MORE.
THANKS VERY MUCH.
LET'S TRY,
BRANDY AT JACK MINER.
HI.

Brandy says HELLO.

Lorraine asks AND WHAT CAN YOU TELL US?

Brandy says IT WOULD BE FOUR OUT OF SIX.

Lorraine says WHY ARE YOU SAYING THAT?
A NUMBER GREATER THAN TWO.
HOW MANY NUMBERS ARE
GREATER THAN TWO?

She answers FOUR.

Lorraine asks AND WHAT ARE THEY?

Brandy responds THREE, FOUR, FIVE, AND SIX.

Lorraine says GREAT.
SO YOU'RE SAYING
FOUR OVER WHAT?

She says SIX.

Lorraine says SO FOR EVERY SIXTH ROLL, YOU'RE
GOING TO GET FOUR OF THEM
SHOULD MOST LIKELY THE
PROBABILITY WOULD BE GREATER
THAN TWO.
AND IF YOU SIMPLIFY THAT?

She says TWO-THIRDS.

Lorraine writes down the answer and says YEAH, TWO-THIRDS.
SO ALL THAT'S
TELLING YOU IS WHAT?
WHAT DOES TWO-THIRDS MEAN?

She says EVERY TWO TIMES --

Lorraine says BE CAREFUL.
EVERY?

She corrects herself and says EVERY THREE TIMES YOU ROLL
THE DICE, YOU SHOULD HAVE A
NUMBER GREATER THAN TWO?

Lorraine says OKAY, FOR EVERY THIRD ROLL,
FOR EVERY THREE ROLLS,
HOW MANY OF THEM WILL BE
LESS OR GREATER THAN TWO?

Brandy says TWO.

Lorraine says THAT'S RIGHT.
SO EVERY TIME, AND THERE'S
ONE GREATER THAN TWO,
LET'S TRY THAT AGAIN.
NOT THIS ONE.
AND THERE IT IS.
SO IT IS KIND OF TELLING YOU
EVERY TIME YOU ROLL THREE
TIMES, YOU GET TWO
GREATER THAN TWO.
EXCELLENT, THANK YOU.
LET'S TRY SOMETHING.
HERE ARE FIVE REGIONS, OKAY?

She shows a pie chart with five equal regions.

She shows them and says AND THESE ARE FIVE
EQUAL REGIONS.
I KNOW THESE TWO, MY PURPLE
AND BLUE ARE KIND OF BLENDED
TOGETHER, BUT THEY
ARE ALL EQUAL.
THERE'S A PURPLE REGION, A
BLUE ONE, A GREEN, A YELLOW
AND A RED, OKAY?
AND THE QUESTION I'M ASKING
YOU IS HOW MANY TIMES WOULD
YOU EXPECT THE PAPER CLIP,

She points to a paper clip at the centre of the circle and continues
WHICH WOULD BE THIS PAPER
CLIP, IF I WERE TO FLICK IT
AROUND, HOW MANY TIMES WOULD
YOU EXPECT THE PAPER CLIP TO
LAND IN THE YELLOW REGION
IN A HUNDRED SPINS?
HOW MANY TIMES WOULD YOU
EXPECT THE PAPER CLIP TO LAND
IN THE YELLOW REGION
IN A HUNDRED SPINS?
AND WHY?
HI.

A boy answers HI.

Lorraine asks AND WHAT IS YOUR ANSWER?

He says 20.

She asks OKAY, WHY ARE YOU SAYING 20?
YOU ARE CORRECT.

He explains 100 DIVIDED BY FIVE.

She asks WHY ARE YOU SAYING
100 DIVIDED BY FIVE?

He explains BECAUSE YOU HAVE 100 SPINS,
DIVIDED BY FIVE SECTIONS.

She says OKAY, EXCELLENT.
THAT'S EXACTLY IT.
OR YOU COULD SAY THE
PROBABILITY IS ONE OUT OF FIVE
TIMES 100, AND YOUR ANSWER
BEING 20, WHICH IS EXCELLENT.
SO NOW WE ARE UNDERSTANDING
THIS QUITE NICELY.
THANK YOU VERY MUCH.
I'M GOING TO PUT YOU INTO
ANOTHER SITUATION WHERE
YOU NEED YOUR PENCIL TO
ANSWER THIS AND PAPER.
I'M PURPOSELY GOING TO
COVER THIS SECTION UP.

She shows another question that reads “What is the probability of each event? 1, red. 2, green. 3, yellow. 4, white.
She covers a section of the question with a drawing of a jar full of marbles. 3 are white, 4 green, 1 red and 2 are purple marbles.

She says I WANT YOU TO ANSWER ONE TO
FOUR AND THEN PRESS POUND
NINE, OR I MIGHT JUST CALL YOU
WHEN I'M READY TO, TO SHARE
WHAT IS THE PROBABILITY OF
EACH EVENT OF GETTING A RED
MARBLE, AND AS YOU CAN TELL
WE HAVE GREEN MARBLES,
WHITE MARBLES, AND RED MARBLE.
PUT THAT ON A PIECE
OF PAPER, ANSWERS,
AND THEN, I WILL CALL YOU.
HELLO.

A male voice says HELLO.

She asks AND WHAT DO YOU HAVE
FOR ONE OF THE ANSWERS.
TELL US WHICH ONE AND WHY.

He says FOR THE RED ONE,
I'VE GOT ONE OVER TEN.

She asks WHY IS THAT?

He explains BECAUSE THERE
IS ONLY ONE RED.

She writes the answers as he answers.

She says HOW ABOUT GREEN?

He says FOUR OVER TEN.

She says CAN YOU SIMPLIFY THAT?

He says OKAY, TWO OVER FIVE.

She asks AND WHAT DOES THAT
MEAN, TWO OVER FIVE?

He says TWO FIFTHS.

She asks again OKAY, BUT WHAT IS
THAT EVEN TELLING ME?
WHY ARE YOU EVEN
SAYING FOUR OUT OF TEN?

He explains EVERY TIME YOU GET
TWO, YOU TAKE FIVE.
EVERY TIME YOU TAKE
FIVE, YOU GET TWO.

She says THAT'S RIGHT.
EVERY TIME YOU GO IN
THERE AND TAKE FIVE OUT,
YOU'LL HAVE TWO GREEN ONES.
HOW ABOUT YELLOW?

He says ZERO.

She asks HOW ABOUT WHITE?

He says THREE.

She asks THREE WHAT?

He answers OVER TEN.

She says THAT'S RIGHT.
AND WHY IS IT IMPORTANT
TO PUT THE TEN THERE?

He responds BECAUSE THERE'S TEN MARBLES.

She explains THAT'S RIGHT.
FOR EVERY TEN THAT YOU TAKE
OUT, YOU ARE OBVIOUSLY GOING
TO GET THREE WHITE
ONES, CORRECT?
BECAUSE YOU ARE GOING
TO TAKE THEM ALL OUT.
EXCELLENT.
THANKS VERY MUCH.
AND CAN WE HAVE YOU,
PLEASE, FIGURE OUT THESE
AND PRESS POUND NINE.

She moves the jar of marbles and uncovers a different set of options. They read “5, green or red. 6, not white. 7, purple. 8, green, white or purple.”

She says AND I'M CALLING FLAMBOROUGH.
HELLO.

A boy says HELLO.

She says HI.
WHAT CAN YOU GIVE
US FOR NUMBER FIVE?
WHAT IS THE PROBABILITY
OF GREEN OR RED?

He answers ONE OUT OF TWO.

She writes the answers as he gives them.

Lorraine asks HOW DID YOU GET
ONE OUT OF TWO?

He explains BECAUSE THERE IS FIVE TOTAL.

She says THAT'S RIGHT.
SO FIVE OUT OF TEN.
AND WHAT DOES THAT
ONE OVER TWO MEAN?

He says FOR EVERY TWO YOU TAKE OUT,
YOU'LL GET ONE GREEN OR RED.

She answers EXCELLENT.
CAN YOU GIVE ME FOR NOT WHITE?
WHAT ARE THE PROBABILITIES
OF NOT GETTING A WHITE ONE?

He says SEVEN OUT OF TEN.

Lorraine says VERY GOOD.
AND HOW DID YOU
FIGURE OUT THAT ONE?

He explains BECAUSE THERE ARE
SEVEN THAT AREN'T WHITE.

She comments EXCELLENT.
HOW ABOUT PURPLE?

He answers I GOT ONE OUT OF FIVE.

She asks AND HOW DID YOU
GET ONE OUT OF FIVE?

He says BECAUSE THERE IS ONE TO
TAKE OUT FOR EVERY FIVE.

She says OKAY, EXCELLENT.
AND HOW ABOUT GREEN,
WHITE OR PURPLE?

He answers NINE OUT OF THE TEN.

She says THAT'S RIGHT.
WHAT DOES THAT MEAN AGAIN?

He explains THERE'S ONE RED, SO FOR NINE,
YOU JUST TAKE THAT AWAY
FROM TEN.

She asks OKAY, BUT WHEN I SAY NINE OUT
OF TEN, WHAT DOES THAT MEAN?

He responds FOR EVERY TEN, YOU CAN TAKE
OUT NINE THAT ARE GREEN,
RED OR PURPLE.

Lorraine says EXCELLENT.
THANKS VERY MUCH.
WE CAN SEE WE ARE
DOING VERY WELL HERE.
YOU'RE UNDERSTANDING
PROBABILITY QUITE NICELY.
I HAVE IN FRONT OF ME

She shows a Styrofoam cup and says A TIM HORTON'S CUP.
OKAY?
AND ON THIS TIM HORTON'S CUP,
IT SAYS I HAVE A CHANCE OF
WINNING A VAN, OR
15 VANS, IF I LIKE.
I HAVE A CHANCE OF
WINNING 5 THOUSAND BICYCLES.
AND THERE'S APPROXIMATELY
12 MILLION PRIZES HERE.
WHAT ARE THE PROBABILITIES
OF ME WINNING A PRIZE
WITH THIS CUP?
WHAT DO I NEED TO DO
TO FIGURE THIS OUT?
I CAN WIN LOTS OF PRIZES,
AND I'M KIND OF CURIOUS
WHETHER I HAVE WON.
AND HELP ME OUT.
HOW CAN I FIGURE OUT THE
PROBABILITY OF WINNING A PRIZE
WITH THIS TIM HORTON'S CUP?
AND I'M CALLING SOMEONE
FROM USBORNE CENTRE.
CENTRAL, SORRY.
USBORNE CENTRAL.
HI.

A voice says HELLO?

Lorraine says HELLO.
WHAT DO I NEED TO KNOW TO
FIGURE OUT WHAT ARE THE ODDS
OF ME WINNING THE PROBABILITY?

He says YOU ROLL UP THE RIM.

She smiles and says WELL, THAT WOULD REALLY
HELP, WOULDN'T IT?
BUT WHAT IF I CAN'T SEE THE
RIMS, AND I'M JUST THINKING,
SHOULD I BOTHER BUYING ONE?
WHAT ARE MY
PROBABILITIES OF WINNING?
WHAT DO I NEED TO FIGURE OUT?
WHAT'S IMPORTANT
INFORMATION I NEED TO KNOW?

He says THE TOTAL NUMBER OF PRIZES.

She answers OKAY, THAT'S TRUE.
THE TOTAL NUMBER OF PRIZES.
SO IF WE GO DOWN HERE.
I'M GOING TO TELL YOU BECAUSE
THE CUP SAYS APPROXIMATELY

She writes down 12 million on a sheet of paper and says 12 MILLION PRIZES.
OKAY?
WHAT ELSE DO I NEED TO KNOW?
OKAY, WE'LL TRY SOMEONE ELSE.
THANKS VERY MUCH.

He says OKAY.

Lorraine says LET'S SEE HERE, LET'S
TRY LEANNE, I BELIEVE,
FROM JACK MINER.
SO LEANNE FROM JACK MINER,
IF YOUR PHONE IS RINGING.
AND THE REST OF YOU CAN
BE THINKING ABOUT THIS.
WHAT IS THE PROBABILITY
OF WINNING A PRIZE.
IF THERE ARE 12 MILLION
PRIZES, WHAT DO I NEED TO KNOW?

A boy says HELLO?

She says HI.
SO WHAT DO I NEED TO KNOW?

He says YOU'D NEED TO KNOW HOW MANY
CUPS THAT ARE BEING SOLD.

She answers YES, VERY GOOD.
AND OBVIOUSLY,
DO YOU KNOW THAT?

He says NO.

Lorraine says YOU DON'T, EXACTLY.
AND I DON'T KNOW THE EXACT
NUMBER BECAUSE TIM HORTON'S
COULDN'T TELL ME WHEN I ASKED
THEM, SO I WILL LET YOU KNOW
THAT, LET'S SAY IT'S
APPROXIMATELY 120 MILLION AND I'M
SURE IT'S MORE THAN THIS
JUST FOR THE SAKE OF MAKING
IT EASY FOR US,
120 MILLION CUPS.

She writes the number on the paper.

She asks WHAT DO I NEED TO DO TO FIGURE
OUT WHAT ARE MY ODDS OF WINNING?

He says YOU'D HAVE TO DIVIDE 120
MILLION BY 12 MILLION.

He says YES.
AND WHAT CAN I
START DOING HERE?

He suggests GETTING RID OF THE ZEROS.

She says YES.
AND HOW MANY ZEROS
CAN I GET RID OF?

He says SIX IN EACH NUMBER.

She crosses them out and says PERFECT.
NOW I'M DOWN TO THIS.
WHAT CAN I DO?

He says YOU CAN DIVIDE 120 BY 12.

She says THAT'S RIGHT.
SO THIS GOES ONCE, 12 GOES
IN THERE, 12 GOES IN HERE.

He says YOU GET TEN.

She says RIGHT.
SO WHAT ARE MY ODDS OF
WINNING A PRIZE WHEN I BUY
A TIM HORTON'S CUP?

He says ONE IN TEN.

She says THAT'S RIGHT.
WHEN I MENTION ONE IN TEN,
THAT MEANS A LOT OF PRIZES.
I CAN WIN A COFFEE, A DONUT,
I CAN WIN A BIKE, I CAN WIN A
VAN AND SO ON.
NOW, WHAT ARE MY ODDS BECAUSE
YOU ARE DOING SO WELL HERE,
WHAT WOULD I NEED TO
DO TO FIGURE OUT THE ODDS
OF WINNING A VAN?
WHAT DO I NEED TO DO?

He says YOU WOULD HAVE TO DIVIDE
120 MILLION BY HOW MANY
VANS THERE ARE.

She says I'M TELLING YOU
THERE ARE 15 VANS.
SO WHAT AM I FIGURING OUT?
WHAT DO I DO?

He says DIVIDE THE NUMBER OF CUPS
SOLD BY THE NUMBER OF VANS.

She writes 12 million divided by 15 and says THAT'S RIGHT.
AND WHAT NUMBER GOES
INTO BOTH OF THEM?

He says THREE.

She says OKAY, LET'S TRY THREE.
THREE GOES INTO 15?

He says FIVE TIMES.

She says AND THREE GOES
INTO LET'S SAY, 12?

He says FOUR TIMES.

She continues YEAH, THEN THE
ZEROS CONTINUE ON.
SO IT'S 40 MILLION.
DOES THE NUMBER FIVE
GO IN THERE FURTHER?
INTO 40 MILLION?

He says IT GOES INTO 40 EIGHT TIMES.
SO IT WOULD BE 8 MILLION.

She says THAT'S RIGHT.
SO EVERY TIME, LET'S SAY IF
THERE WERE THAT MANY CUPS,
I WOULD HAVE, OUT OF 8 MILLION
CUPS I BUY, I HAVE A CHANCE
OF WINNING 1 VAN.
THAT'S RIGHT, EXCELLENT.
YOU DID VERY WELL.
AND MAYBE FOR SOME OF YOU, FOR
A CHANGE, THANKS VERY MUCH
FOR YOUR CALL.
LET'S TRY ONE MORE.
THAT CAN TELL ME, WHAT ARE
THE ODDS OF NOT WINNING?
THE PROBABILITY OF NOT
WINNING ANYTHING WHEN I GO
TO BUY THIS CUP.
HELLO?

A girl says HELLO?

Lorraine asks HI.
CAN YOU TELL ME HOW I FIGURE
OUT THE PROBABILITIES OF NOT
WINNING ANYTHING?
WHAT DO I NEED TO DO?

She chuckles and answers I DON'T KNOW.

Lorraine smiles and says YOU'RE NOT SURE.
HOW MANY CUPS DO WE
KNOW THAT WE HAVE?

She answers 120 MILLION.

Lorraine writes it down and says OKAY, GOOD.
AND HOW CAN I FIGURE OUT THE
CUPS THAT DON'T HAVE A PRIZE?
LIKE HOW MANY DO HAVE A PRIZE?
DO YOU REMEMBER THAT NUMBER?
JUST THE LARGE NUMBER.
DO YOU REMEMBER APPROXIMATELY
HOW MANY PRIZES?
AND IT'S RIGHT THERE.

She says 12 MILLION.

Lorraine continues SO 12 MILLION.
I KNOW 12 MILLION OF
THESE CUPS HAVE A PRIZE,
HOW MANY DO NOT?
WHAT DO I HAVE TO DO?

She suggests YOU HAVE TO SUBTRACT.

Lorraine says THAT'S RIGHT.
SO WHAT IS 120 MILLION
MINUS 12 MILLION?
I'LL JUST WRITE IT
REALLY SMALL DOWN HERE?

She says 180, SORRY, 108.

Lorraine says 108.
AND WHAT IS THAT 108 AGAIN?

She answers PEOPLE NOT WINNING THE CUPS.

Lorraine says CUPS WITH NO PRIZE, RIGHT?

She answers RIGHT.

She asks WHAT IS THE PROBABILITY?
WHAT DO I NEED TO DO
TO FIGURE OUT THE PROBABILITY
OF NOT WINNING?
WE KNOW THERE'S 108 MILLION OF
THESE CUPS THAT DON'T HAVE A
PRIZE IN THEM.
BUT WHAT IS THE PROBABILITY?
WHAT DO I NEED TO DO?

She says YOU HAVE TO DIVIDE.

Lorraine says THAT'S RIGHT, DIVIDE.
SO WHAT DO I DO
WITH THE ZEROS HERE?

The girl says YOU GET RID OF THEM.

Lorraine says THAT'S RIGHT.
HOW MANY CAN I GET RID OF?

She says SIX.

She crosses them out and says OKAY, LET'S GET RID
OF ALL THESE SIX.
HOW CAN I BRING THIS SMALLER?
WHAT NUMBER GOES IN BOTH?

She says TWO.

Lorraine says OKAY, LET'S TRY TWO.

She says TWO INTO TEN IS FIVE.

Lorraine says OKAY.

She says TWO INTO EIGHT IS FOUR.

Lorraine says OKAY.
AND HOW ABOUT INTO THIS?

The girl says SIX INTO 12.

Lorraine says OKAY.

The girl says AND ZERO.

Lorraine asks CAN I PUT THIS
EVEN SMALLER?

She says YUP.

Lorraine asks WHAT OTHER NUMBER
GOES IN HERE?

She answers YOU CAN DIVIDE IT BY NINE.
SORRY.

Lorraine suggests TRY SOMETHING SMALL.

The girl asks PARDON?

Lorraine says TRY SOMETHING SMALL.

She says SOMETHING SMALLER?
FOUR?
SIX?

Lorraine says OR EVEN SMALLER THAN THAT.
WHAT'S THE OBVIOUS THAT
GOES INTO BOTH OF THESE?

She answers TWO.

Lorraine says THAT'S RIGHT, TWO.
AND WHAT'S TWO IN HERE?
INTO 54?

The girl says TWO INTO FIVE IS TWO.
14 IS 7.

Lorraine says PERFECT, 27.
TWO INTO SIX IS?

She says THREE.

Lorraine says AND TWO INTO ZERO THEN?

She says ZERO.

Lorraine asks SO WHAT IS THAT
TELLING ME 27 OVER 30?
FOR EVERY 30 CUPS I BUY,
WHAT DOES THAT TELL ME?

She answers THERE'S ONLY, YOU ARE
GOING TO LOSE 27 TIMES.

Lorraine unfolds the rim of the cup and says THAT'S RIGHT.
IF I LOOK AT THIS, AND BRING
IT UP MUCH CLOSER, CAN YOU
HELP US AND LET US KNOW
WHAT HAPPENED FOR ME?
AND IT'S NOT THAT CLEAR.
WHAT DOES THAT SAY?

The girl says I CAN'T SEE IT.
PLAY AGAIN.

Lorraine says YES.
SO UNFORTUNATELY BECAUSE
THE PROBABILITY IS SO HIGH,
I DIDN'T END UP WINNING.
BUT THAT GIVES YOU A BIT OF AN
IDEA OF PROBABILITY AS WELL
AS EXPONENTS FOR TODAY.
AND YOUR HOMEWORK, AS YOU ARE
ALL AWARE, GOES AS FOLLOWS,

A blue slate appears. It reads “Homework. Exercises 1 and 2 for Thursday.”

Lorraine says AND AT THIS POINT, WE HAVE A
FEW MINUTES, YOU CAN CALL AND
ASK ANY QUESTIONS YOU MAY
HAVE ABOUT YOUR EXERCISES,
OR IF YOU HAVE ANY QUESTIONS
ABOUT THE LESSON TODAY.
IF NOT, WE'LL SEE YOU ON
THURSDAY, AND WE'LL GO OVER
THE QUESTIONS.
HAVE A NICE FEW DAYS.
THANK YOU.
BYE-BYE.

A voice says HELLO?

Lorraine says HELLO.
HI, YOU HAVE A QUESTION?

He says YES.
IN THE QUESTION YOU JUST
DID, YOU CAN GO SMALLER.

She answers I CAN GO SMALLER.
LET'S LOOK AT THAT.
YOU KNOW WHAT IT IS, TOO?
AND IT'S STILL CORRECT.
OOPS.
THAT'S QUITE BIG.
WHAT NUMBER GOES IN THERE?

She crosses 27 and replaces it for a 9.

He answers THREE.

She says THAT'S RIGHT.
SO FOR EVERY TEN CUPS,
NINE YOU CAN'T WIN.
OR FOR EVERY 30 CUPS,
27 CUPS YOU CAN'T WIN.
FOR EVERY 120 MILLION CUPS YOU
BUY, THERE IS 108 MILLION
YOU WON'T WIN.
THANKS VERY MUCH.
DO YOU HAVE A QUESTION
AS FAR AS THE EXERCISES?

He says EXCUSE ME.

She says YES?

He says ANOTHER PERSON HAS
ANOTHER QUESTION.

Lorraine says SURE.

Another boy says HI.

Lorraine says HI.

He says ON EXERCISE NUMBER TWO.

She says OKAY, ONE SECOND HERE.
EXERCISE NUMBER TWO.
YES?
HELLO?
UNFORTUNATELY, WE
LOST YOUR CALL THERE.
OKAY, IF IT'S QUESTION NUMBER
TWO, UNFORTUNATELY, I DIDN'T
HEAR YOUR QUESTION
THAT YOU HAD.
IF IT IS THIS PARTICULAR ONE,
LET ME BRING IT IN A TAD,
THE SAMURAI SWORD.
IT'S VERY SIMILAR WITH THE
PAPER, YOU KNOW WITH THE
FOLDING AND SO ON.
YOU'VE GOT TO KEEP THAT
IN MIND FOR THIS ONE.
OR IF IT WAS QUESTION THREE,
IT'S VERY SIMILAR AGAIN TO THE
EXERCISE WE DID
WITH THE PAPER.
KEEP THAT IN MIND.

She shows the question with the large fractions on it and continues AND THIS PARTICULAR ONE, IF
THAT'S WHAT YOU'RE ASKING,
I DON'T KNOW, I DON'T HAVE YOU
ON THE LINE JUST YET, THE
EXERCISE HERE, YOU
HAVE TO FIND A SEQUENCE
THAT'S OCCURRING HERE.
AND AS WAS MENTIONED
YESTERDAY, NOTE THAT THIS IS
A SMALLER FRACTION, AND
GRADUALLY GETTING LARGER
OF A FRACTION.
EVEN THOUGH THE DENOMINATORS
ARE GETTING SMALLER,
THE FRACTIONS ARE
GETTING LARGER, OKAY?
AND YOU'VE GOT TO FIGURE
OUT WHAT'S HAPPENING TO THE
DENOMINATORS OVER HERE.
ONCE YOU'VE FIGURED IT OUT

She points to each of the fractions and says BECAUSE WE KNOW THIS IS TERM
ONE, TERM TWO, THREE, FOUR,
TERM FIVE, YOU HAVE TO
GO ALL THE WAY TO TERM 25, AS
WELL AS 24, OBVIOUSLY, TO GET
TO 25, THESE TWO, AND
FIGURE OUT THE COORDINATES,
OR WHATEVER NUMBERS
THEY GIVE YOU.
AND THAT'S THE COORDINATES
FOR OUR NEXT COUNTRY
THAT WE'LL BE GOING TO.
AND, UNFORTUNATELY, WE CAN'T
GET TO YOUR CALLS RIGHT NOW SO
MAYBE YOU CAN ASK YOUR
TEACHERS, AND THEN WE WILL
ANSWER THEM ON THURSDAY.
HAVE A NICE COUPLE OF DAYS.
BYE-BYE.

A boy says HELLO?

She answers HI.

He says HI.
ON EXERCISE TWO.

She asks OKAY, I'M NOT SURE WHICH
EXERCISE, TWO, QUESTION?

He says YEAH, RIGHT THERE,
WHAT YOU HAVE.

The image of the five fractions appears on screen.

She points to the second term “1 over 1162261476” and says THIS ONE RIGHT HERE.
OKAY, YEAH?

He says ON THE SECOND TERM.

She moves it and says I'LL BRING IT IN A TAD HERE.
THIS ONE?

He says YEAH.
THE SEVEN AND THE SIX SHOULD
BE SWITCHED AT THE VERY END.
BECAUSE IF YOU DIVIDE
THEM ALL BY THREE IT WORKS,
EXCEPT FOR THAT ONE.

She underlines the 76 and says OH.
THESE TWO OVER HERE?

He answers YEAH.

She says I'LL HAVE TO CHECK THAT OUT
AND SPEAK WITH STEWART HERE.
OKAY, DEFINITELY.
THANKS VERY MUCH.
I DON'T HAVE A CALCULATOR
WITH ME, SO I'LL VERIFY THAT,
AND I APPRECIATE YOUR CALL.
SO YOU HAVE YOUR
TERMS 24 AND 25?

He answers YEAH.

She says OKAY, DON'T GIVE
THEM TO ME YET.
THAT'S GREAT.
AND YOU ARE?

Adam says ADAM.

She asks ADAM.
AND WHAT SCHOOL?

He answers USBORNE.

She says MAYBE WE'LL CALL YOU ON
THURSDAY FOR THIS ONE,
HOW'S THAT?

He says WE WON'T BE HERE.

She says OH, THAT'S RIGHT.
YOU'RE GOING ON A TRIP.
WELL, ENJOY.
YOU DESERVE IT.
GREAT.
THANKS VERY MUCH
FOR YOUR CALL.

He says BYE.

She says OKAY, BYE.

Watch: Student Session 11