﻿(music plays)

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
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