# Transcript: Variables

(music plays)

A slate reads "Variables."

Miss Liu stands next to an interactive board.

A caption appears on screen. It reads "Miss Liu. Math Teacher."

Miss Liu says TODAY WE ARE LEARNING

ABOUT VARIABLES.

SO I WANT US TO TAKE A

LOOK AT SOME EXPRESSIONS

AND EQUATIONS THAT

I HAVE UP HERE.

AND THESE ONES ARE A BIT

DIFFERENT THAN THE ONES

YOU'VE SEEN BEFORE.

THESE ONES ACTUALLY HAVE

NUMBERS AND OPERATIONS

WITH THESE LETTERS THAT WE

DON'T KNOW WHAT THEY REPRESENT,

WHAT THEY STAND FOR.

A close-up to the board shows expressions written on it:

5 plus n

g minus g plus g

8 lus 4 equals e plus 5

2 times d plus 3 equals 11

A equals b times h divided by 2.

Miss Liu continues SO THOSE ARE OUR UNKNOWN

VALUES WHICH WE CALL VARIABLES.

AND YOU CAN SEE THEM REPRESENTED

IN EACH OF THOSE EXPRESSIONS

HERE AND EQUATIONS.

I WANT TO TAKE A LOOK AT SOME

OF THE THINGS I'VE NOTICED

THAT'S UP HERE.

SO, FOR INSTANCE, THIS ONE

HERE...

She points at the expression "g minus g plus g" and says

IT LOOKS LIKE WE HAVE

VARIABLES THAT HAVE

BEEN REPEATED.

IS THAT OKAY?

WELL, IF THAT'S THE CASE AND

WE HAVE G SUBTRACTED BY G

AND THEN ADD G, IN THAT

CASE THAT G HAS TO EQUAL

THE SAME THING.

SO IF I SAY THAT G IS EQUAL

TO ONE, THEN THAT MEANS ONE

MINUS ONE PLUS ONE IS WHAT

I'M GOING TO BE SUBSTITUTING

INTO THERE, WHICH SUBSTITUTE

BASICALLY MEANS THAT NUMBER

ONE IS GOING TO SUBSTITUTE,

OR TAKE THE PLACE OF,

THAT VARIABLE G.

SO YOU'LL NOTICE THAT IN

SOME ALGEBRAIC EXPRESSIONS

OR EQUATIONS YOU MIGHT SEE

VARIABLES THAT COME UP

MORE THAN ONE TIME.

THAT'S OKAY.

AS WELL, YOU MIGHT SEE

OTHER TYPES OF EQUATIONS

OR EXPRESSIONS WHERE YOU

HAVE MORE THAN ONE VARIABLE.

LET'S TAKE A LOOK AT

THIS ONE OVER HERE.

She points and says

WE HAVE A IS EQUAL TO B

TIMES H, DIVIDED BY 2.

WE HAVE NOW THREE LETTERS

THAT ARE BEING REPRESENTED

HERE THAT ARE VARIABLES

AND WE DON'T KNOW WHAT

THEY REPRESENT.

SO IS THAT OKAY?

YES, IT IS.

BECAUSE, IN THIS CASE,

THIS ONE'S A FORMULA.

AND IN THIS FORMULA

THAT REPRESENTS BASS

AND THAT REPRESENTS HEIGHT.

AND THIS IS USED TO FIND

THE AREA OF A TRIANGLE.

SO IF I KNOW THE BASE AND

THE HEIGHT OF A TRIANGLE,

THEN I CAN THEN DO

ALL THE OPERATIONS,

SUBSTITUTE IT IN,

FIGURE IT OUT,

AND FIGURE OUT THE

AREA OF THAT TRIANGLE.

SO THERE'S A NUMBER OF THINGS

THAT I WANT TO MAKE SURE

THAT WE TAKE AWAY

WITH US TODAY.

FIRST, THAT VARIABLES ARE

SYMBOLS THAT TAKE THE PLACE

OF UNKNOWN NUMBERS, SO

THINGS THAT WE DON'T KNOW.

THOSE NUMBERS, WE DON'T KNOW

WHAT THEY REPRESENT YET

UNTIL WE HAVE A PROBLEM TO

SOLVE OR THERE'S A CONTEXT

THAT WE'RE GIVEN.

AND THEN WE'LL KNOW.

AND THEN THEY ARE USED TO

REPRESENT QUANTITIES THAT CHANGE

AND AS PLACEHOLDERS

IN FORMULAS.

SO YOU CAN SEE, IT WAS

USED HERE AS A PLACEHOLDER

IN A FORMULA.

AND IT CAN CHANGE BECAUSE

MY G HERE WAS ONE,

BUT THEN LATER ON MAYBE

I HAVE ANOTHER SITUATION AND

IT BECOMES THREE; IT COULD

CHANGE TO ANOTHER NUMBER.

SO THOSE QUANTITIES

WILL CHANGE.

AND THEN THEY ARE FOUND

IN ALGEBRAIC EXPRESSIONS

AND EQUATIONS.

ALL THESE ARE EXAMPLES

OF ALGEBRAIC EXPRESSIONS

AND EQUATIONS.

SO HOPEFULLY YOU'VE LEARNED

SOMETHING NEW ABOUT

VARIABLES TODAY, AND I

WILL SEE YOU NEXT TIME.

A slate reads "Variables."

Miss Liu stands next to an interactive board.

A caption appears on screen. It reads "Miss Liu. Math Teacher."

Miss Liu says TODAY WE ARE LEARNING

ABOUT VARIABLES.

SO I WANT US TO TAKE A

LOOK AT SOME EXPRESSIONS

AND EQUATIONS THAT

I HAVE UP HERE.

AND THESE ONES ARE A BIT

DIFFERENT THAN THE ONES

YOU'VE SEEN BEFORE.

THESE ONES ACTUALLY HAVE

NUMBERS AND OPERATIONS

WITH THESE LETTERS THAT WE

DON'T KNOW WHAT THEY REPRESENT,

WHAT THEY STAND FOR.

A close-up to the board shows expressions written on it:

5 plus n

g minus g plus g

8 lus 4 equals e plus 5

2 times d plus 3 equals 11

A equals b times h divided by 2.

Miss Liu continues SO THOSE ARE OUR UNKNOWN

VALUES WHICH WE CALL VARIABLES.

AND YOU CAN SEE THEM REPRESENTED

IN EACH OF THOSE EXPRESSIONS

HERE AND EQUATIONS.

I WANT TO TAKE A LOOK AT SOME

OF THE THINGS I'VE NOTICED

THAT'S UP HERE.

SO, FOR INSTANCE, THIS ONE

HERE...

She points at the expression "g minus g plus g" and says

IT LOOKS LIKE WE HAVE

VARIABLES THAT HAVE

BEEN REPEATED.

IS THAT OKAY?

WELL, IF THAT'S THE CASE AND

WE HAVE G SUBTRACTED BY G

AND THEN ADD G, IN THAT

CASE THAT G HAS TO EQUAL

THE SAME THING.

SO IF I SAY THAT G IS EQUAL

TO ONE, THEN THAT MEANS ONE

MINUS ONE PLUS ONE IS WHAT

I'M GOING TO BE SUBSTITUTING

INTO THERE, WHICH SUBSTITUTE

BASICALLY MEANS THAT NUMBER

ONE IS GOING TO SUBSTITUTE,

OR TAKE THE PLACE OF,

THAT VARIABLE G.

SO YOU'LL NOTICE THAT IN

SOME ALGEBRAIC EXPRESSIONS

OR EQUATIONS YOU MIGHT SEE

VARIABLES THAT COME UP

MORE THAN ONE TIME.

THAT'S OKAY.

AS WELL, YOU MIGHT SEE

OTHER TYPES OF EQUATIONS

OR EXPRESSIONS WHERE YOU

HAVE MORE THAN ONE VARIABLE.

LET'S TAKE A LOOK AT

THIS ONE OVER HERE.

She points and says

WE HAVE A IS EQUAL TO B

TIMES H, DIVIDED BY 2.

WE HAVE NOW THREE LETTERS

THAT ARE BEING REPRESENTED

HERE THAT ARE VARIABLES

AND WE DON'T KNOW WHAT

THEY REPRESENT.

SO IS THAT OKAY?

YES, IT IS.

BECAUSE, IN THIS CASE,

THIS ONE'S A FORMULA.

AND IN THIS FORMULA

THAT REPRESENTS BASS

AND THAT REPRESENTS HEIGHT.

AND THIS IS USED TO FIND

THE AREA OF A TRIANGLE.

SO IF I KNOW THE BASE AND

THE HEIGHT OF A TRIANGLE,

THEN I CAN THEN DO

ALL THE OPERATIONS,

SUBSTITUTE IT IN,

FIGURE IT OUT,

AND FIGURE OUT THE

AREA OF THAT TRIANGLE.

SO THERE'S A NUMBER OF THINGS

THAT I WANT TO MAKE SURE

THAT WE TAKE AWAY

WITH US TODAY.

FIRST, THAT VARIABLES ARE

SYMBOLS THAT TAKE THE PLACE

OF UNKNOWN NUMBERS, SO

THINGS THAT WE DON'T KNOW.

THOSE NUMBERS, WE DON'T KNOW

WHAT THEY REPRESENT YET

UNTIL WE HAVE A PROBLEM TO

SOLVE OR THERE'S A CONTEXT

THAT WE'RE GIVEN.

AND THEN WE'LL KNOW.

AND THEN THEY ARE USED TO

REPRESENT QUANTITIES THAT CHANGE

AND AS PLACEHOLDERS

IN FORMULAS.

SO YOU CAN SEE, IT WAS

USED HERE AS A PLACEHOLDER

IN A FORMULA.

AND IT CAN CHANGE BECAUSE

MY G HERE WAS ONE,

BUT THEN LATER ON MAYBE

I HAVE ANOTHER SITUATION AND

IT BECOMES THREE; IT COULD

CHANGE TO ANOTHER NUMBER.

SO THOSE QUANTITIES

WILL CHANGE.

AND THEN THEY ARE FOUND

IN ALGEBRAIC EXPRESSIONS

AND EQUATIONS.

ALL THESE ARE EXAMPLES

OF ALGEBRAIC EXPRESSIONS

AND EQUATIONS.

SO HOPEFULLY YOU'VE LEARNED

SOMETHING NEW ABOUT

VARIABLES TODAY, AND I

WILL SEE YOU NEXT TIME.

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