(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
EXPRESSIONS AND EQUATIONS.
SO, REALLY, WHAT I WANT
TO DO IS MAKE SURE
THAT YOU UNDERSTAND WHAT MAKES
AN EXPRESSION AN EXPRESSION
AND WHAT MAKES AN
EQUATION AN EQUATION.
SO WE ARE USED TO SEEING
NUMERICAL EXPRESSIONS THAT
LOOK LIKE THESE, WHERE
THEY JUST HAVE NUMBERS.

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

Numerical expressions:
9 plus 8
30 divided by 3
12 times 1 minus 5

Algebraic expressions
5 plus x
M minus N
B times h divided by 2

Algebraic equations
8 plus 4 equals n plus 5
2 times n plus 3 equals 11
A equals b times h divided by 2

Miss Liu continues BUT AS WE GET OLDER WE GET INTO
SYMBOLS AND THINGS LIKE THAT.
THEN WE GET INTO ALGEBRA, AND
THAT'S WHERE WE COME ACROSS
ALGEBRAIC EXPRESSIONS
AND ALGEBRAIC EQUATIONS.
SO WHEN WE TAKE A LOOK AT THEM,
WHAT MAKES THEM DIFFERENT?
LET'S TAKE A LOOK.
SO OVER HERE WHEN WE TAKE A LOOK
AT JUST ALGEBRAIC EXPRESSIONS
WE NOTICE THAT THE DIFFERENCE
BETWEEN THIS AND NUMERICAL
EXPRESSIONS IS THAT ALL OF
A SUDDEN WE NOW HAVE THESE
LETTERS THAT ARE IN
OUR NUMBER STATEMENTS.
AND WE JUST DON'T KNOW WHY.

As she points at the algebraic expressions on the board, she says SO THESE LETTERS HERE THAT WE
HAVE, LIKE X, FOR 5 PLUS X,
OR THE M AND THE N, THESE ARE
WHAT WE CALL THE UNKNOWNS.
SO THEY'RE ACTUALLY
WHAT WE CALL VARIABLES,
AND THEY JUST REPRESENT
UNKNOWN QUANTITY.
SO THINGS THAT WE DON'T KNOW
THAT WE NEED TO FIND OUT,
OR IT COULD JUST BE
LIKE A PLACE HOLDER.
SO IN THIS CASE WE HAVE
MORE VARIABLES HERE.
BUT IF WE TAKE A LOOK AT
EQUATIONS, SIMILAR TO
EXPRESSIONS, EXCEPT THAT NOW
ALL OF A SUDDEN THEY'VE GOT
THOSE EQUAL SIGNS.

As she points at the equal signs she says SO THOSE EQUAL SIGNS TELL US
THAT THE ONE SIDE HAS TO BE
BALANCED WITH THE OTHER.
AND THAT'S WHAT MAKES
THIS AN EQUATION.
THAT'S WHERE THAT
WORD COMES FROM.
THERE'S ALSO ONE MORE THING
I WANT TO TAKE A LOOK AT
THAT MIGHT BE A BIT
DIFFERENT FOR YOU.
FOR INSTANCE, THIS
2N OR THIS BH.
WHERE THERE'S NO OPERATION,
IT'S JUST THERE.
WHY IS THAT?
WELL, IF WE TAKE
A LOOK OVER HERE,
AND WE SEE THE B TIMES
H IS DIVIDED BY 2,
I'M JUST GOING TO
ERASE THAT THERE,
SO YOU CAN SEE
IT A BIT BETTER.
SOME STUDENTS WHEN THEY'RE
WRITING AND ME TOO WITH
MY WRITING SOMETIMES, WE
HAVE THIS X THAT'S SUPPOSED
TO MEAN MULTIPLY, BUT SOME
PEOPLE MIGHT GET CONFUSED
AND THINK IT'S
ACTUALLY A VARIABLE.
SO IN ORDER TO MAKE THINGS A BIT
CLEARER WHEN WE'RE WRITING
ALGEBRAIC EXPRESSIONS
OR EQUATIONS IT'S BEST
WHEN IT'S MULTIPLY WE CAN
JUST PUT THE TWO TOGETHER
SIDE BY SIDE.
SO, FOR INSTANCE, IF WE
HAD M MULTIPLIED BY N,
WE COULD ACTUALLY
REWRITE THAT AS MN
AND THAT WOULD MEAN
MULTIPLY WITH THE TWO
BESIDE EACH OTHER.
SO THAT'S SOMETHING TO THINK
ABOUT WHEN WE'RE DEALING WITH
EXPRESSIONS AND EQUATIONS.
SO JUST TO RECAP THINGS
THAT WE TALKED ABOUT,
THE DIFFERENCE BETWEEN
NUMERICAL AND ALGEBRAIC
EXPRESSIONS IS THAT IN
ALGEBRAIC YOU HAVE THESE
LETTERS THAT WE CALL
VARIABLES THAT REPRESENT
OUR UNKNOWN VALUES.
AND THEN THE DIFFERENCE
BETWEEN ALGEBRAIC
EXPRESSIONS AND EQUATIONS
IS THAT EQUAL SIGN.
THAT TELLS US THAT, IN
THIS CASE, THE TWO SIDES
ARE BALANCED AND WE
HAVE VARIABLES IN BOTH
THAT WE NEED
TO FIGURE OUT.
SO HOPEFULLY YOU LEARNED
SOMETHING NEW TODAY,
AND I WILL SEE
YOU NEXT TIME.