Transcript: Algebraic Expressions
(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 ALGEBRAIC EXPRESSIONS.
FIRST THING, LET'S TAKE A
LOOK AT THIS EXPRESSION HERE.
A close-up to the board reads "5 plus j. I have 5 jellybeans and my friend Mike has given me some more. How many jellybeans do I now have?"
Miss Liu continues HOW DO WE KNOW THAT
IT'S AN EXPRESSION?
WELL, IT'S BECAUSE IT INCLUDES
A NUMBER, IT INCLUDES OPERATION,
AND IT ALSO INCLUDES A LETTER
WHICH REPRESENTS SOMETHING
WE DON'T KNOW, AN UNKNOWN VALUE,
WHICH WE CALL A VARIABLE.
SO WHAT I WANT TO DO IS TAKE
A LOOK AT A PROBLEM THAT
THIS EXPRESSION COULD REPRESENT,
AND THEN JUST THINK ABOUT
HOW WE COULD ACTUALLY USE
THIS EXPRESSION TO HELP US
FIGURE OUT AN ANSWER OR
FIGURE OUT A SOLUTION
TO THIS PROBLEM OVER HERE.
SO I HAVE FIVE JELLYBEANS.
I LOVE JELLYBEANS.
AND MY FRIEND MIKE HAS
GIVEN ME SOME MORE.
SO THE QUESTION NOW IS HOW MANY
JELLYBEANS DO I NOW HAVE?
WELL, IN ORDER TO SOLVE THIS
I DON'T EVEN KNOW HOW MANY
JELLYBEANS MIKE
HAS GIVEN ME.
SO, IN THIS CASE, BECAUSE I
DON'T KNOW WHAT J IS,
OR THOSE JELLYBEANS WHICH
I AM GOING TO REPRESENT
BY THE LETTER J IN THE
EXPRESSION, THEN I CAN JUST
DO SOME TRIALS.
Using a black marker she creates a table with two columns and writes "Input" in the first column.
She says SO I CAN CREATE A TABLE OF
VALUES WHERE WE HAVE WHAT
WE CALL AN INPUT
AND THESE ARE NUMBERS
THAT COULD REPRESENT THE J.
AND WHATEVER NUMBER OF
JELLYBEANS THAT MIKE HAS
GIVEN ME, I CAN
PUT THEM IN THERE.
AND THEN THE OUTPUT,
WHICH WILL BE THE TOTAL
NUMBER OF JELLYBEANS
THAT I HAVE AT THE END
ONCE HE'S GIVEN
ME SOME MORE.
In the second column, she writes "Output."
She says SO I KNOW THAT SAY MIKE HAS
GIVEN ME THREE JELLYBEANS.
SO IF I HAVE THREE JELLYBEANS
I'M GOING TO TAKE A LOOK
AT MY EXPRESSION, THAT J
NOW WE KNOW THE VALUE.
WE KNOW THAT IT'S THREE.
SO FIVE PLUS THREE TO REPLACE
THAT J IS MY NEW EXPRESSION.
TAKING A LOOK AT THAT,
FIVE PLUS THREE,
LET'S FIGURE OUT WHAT
FIVE PLUS THREE IS.
SO LET'S TAKE OUT
THAT NUMBER LINE.
LET'S DRAW IT OVER HERE.
She draws a number line and writes down the number "5", then adds a second mark to the right of 5 and writes "plus 3" on top of it.
She says STARTING AT FIVE WITH HOW MANY
I HAD, AND THEN MIKE GAVE ME
THREE MORE.
I CAN EITHER JUST JUMP ONE
AT A TIME, BUT I THINK
I'M PRETTY GOOD THAT I CAN
ACTUALLY DO ONE BIG JUMP.
AND SOME OF YOU MAY BE
ABLE TO DO THAT, TOO.
SOME OF YOU MAY BE ABLE TO
JUST DO ONE AT A TIME,
AND THAT'S OKAY.
SO FIVE INCREASED BY THREE,
GIVES ME A TOTAL OF...
EIGHT JELLYBEANS.
SO NOW I KNOW THAT IF
MIKE GIVES ME THREE
I NOW HAVE EIGHT.
Under "output" she writes 8.
Miss Liu continues BUT LET'S SAY MIKE
DOESN'T GIVE ME THREE.
LET'S CHANGE THAT NUMBER.
SINCE THAT'S A VARIABLE,
IT CAN CHANGE.
SO I'M GOING TO NOW
ERASE THAT THREE.
I'M GOING TO CREATE A NEW INPUT
AND GET RID OF THIS NUMBER LINE.
AND LET'S SAY NOW
HE'S REALLY GENEROUS
AND HE GIVES ME
TEN JELLYBEANS.
Under "Input" she writes 10.
She says SO I HAVE NOW TEN JELLYBEANS
THAT MIKE HAS GIVEN TO ME.
IN MY EXPRESSION HERE I'M GOING
TO CHANGE THAT J TO A TEN.
AND TO FIGURE IT OUT,
FIVE PLUS TEN MORE...
FIVE AND I'M GOING TO
DO A BIG JUMP OF TEN.
FIVE PLUS TEN GIVES ME
A TOTAL OF FIFTEEN.
SO NOW I HAVE FIFTEEN
YUMMY JELLYBEANS
THAT I CAN ALSO SHARE
WITH SOME OF YOU.
Under "output" she writes 15.
She says SO HOPEFULLY YOU'VE
LEARNED A BIT MORE ABOUT
ALGEBRAIC EXPRESSIONS.
UNDERSTANDING THAT IT INCLUDES
NUMBERS, OPERATIONS,
AND THAT UNKNOWN VALUE
WE CALL A VARIABLE.
AND WE CAN USE THOSE
NUMBERS AND CHANGE THEM UP,
WHICH WILL THEN
CHANGE OUR OUTPUT.
SO WE'LL SEE YOU
AGAIN 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 ALGEBRAIC EXPRESSIONS.
FIRST THING, LET'S TAKE A
LOOK AT THIS EXPRESSION HERE.
A close-up to the board reads "5 plus j. I have 5 jellybeans and my friend Mike has given me some more. How many jellybeans do I now have?"
Miss Liu continues HOW DO WE KNOW THAT
IT'S AN EXPRESSION?
WELL, IT'S BECAUSE IT INCLUDES
A NUMBER, IT INCLUDES OPERATION,
AND IT ALSO INCLUDES A LETTER
WHICH REPRESENTS SOMETHING
WE DON'T KNOW, AN UNKNOWN VALUE,
WHICH WE CALL A VARIABLE.
SO WHAT I WANT TO DO IS TAKE
A LOOK AT A PROBLEM THAT
THIS EXPRESSION COULD REPRESENT,
AND THEN JUST THINK ABOUT
HOW WE COULD ACTUALLY USE
THIS EXPRESSION TO HELP US
FIGURE OUT AN ANSWER OR
FIGURE OUT A SOLUTION
TO THIS PROBLEM OVER HERE.
SO I HAVE FIVE JELLYBEANS.
I LOVE JELLYBEANS.
AND MY FRIEND MIKE HAS
GIVEN ME SOME MORE.
SO THE QUESTION NOW IS HOW MANY
JELLYBEANS DO I NOW HAVE?
WELL, IN ORDER TO SOLVE THIS
I DON'T EVEN KNOW HOW MANY
JELLYBEANS MIKE
HAS GIVEN ME.
SO, IN THIS CASE, BECAUSE I
DON'T KNOW WHAT J IS,
OR THOSE JELLYBEANS WHICH
I AM GOING TO REPRESENT
BY THE LETTER J IN THE
EXPRESSION, THEN I CAN JUST
DO SOME TRIALS.
Using a black marker she creates a table with two columns and writes "Input" in the first column.
She says SO I CAN CREATE A TABLE OF
VALUES WHERE WE HAVE WHAT
WE CALL AN INPUT
AND THESE ARE NUMBERS
THAT COULD REPRESENT THE J.
AND WHATEVER NUMBER OF
JELLYBEANS THAT MIKE HAS
GIVEN ME, I CAN
PUT THEM IN THERE.
AND THEN THE OUTPUT,
WHICH WILL BE THE TOTAL
NUMBER OF JELLYBEANS
THAT I HAVE AT THE END
ONCE HE'S GIVEN
ME SOME MORE.
In the second column, she writes "Output."
She says SO I KNOW THAT SAY MIKE HAS
GIVEN ME THREE JELLYBEANS.
SO IF I HAVE THREE JELLYBEANS
I'M GOING TO TAKE A LOOK
AT MY EXPRESSION, THAT J
NOW WE KNOW THE VALUE.
WE KNOW THAT IT'S THREE.
SO FIVE PLUS THREE TO REPLACE
THAT J IS MY NEW EXPRESSION.
TAKING A LOOK AT THAT,
FIVE PLUS THREE,
LET'S FIGURE OUT WHAT
FIVE PLUS THREE IS.
SO LET'S TAKE OUT
THAT NUMBER LINE.
LET'S DRAW IT OVER HERE.
She draws a number line and writes down the number "5", then adds a second mark to the right of 5 and writes "plus 3" on top of it.
She says STARTING AT FIVE WITH HOW MANY
I HAD, AND THEN MIKE GAVE ME
THREE MORE.
I CAN EITHER JUST JUMP ONE
AT A TIME, BUT I THINK
I'M PRETTY GOOD THAT I CAN
ACTUALLY DO ONE BIG JUMP.
AND SOME OF YOU MAY BE
ABLE TO DO THAT, TOO.
SOME OF YOU MAY BE ABLE TO
JUST DO ONE AT A TIME,
AND THAT'S OKAY.
SO FIVE INCREASED BY THREE,
GIVES ME A TOTAL OF...
EIGHT JELLYBEANS.
SO NOW I KNOW THAT IF
MIKE GIVES ME THREE
I NOW HAVE EIGHT.
Under "output" she writes 8.
Miss Liu continues BUT LET'S SAY MIKE
DOESN'T GIVE ME THREE.
LET'S CHANGE THAT NUMBER.
SINCE THAT'S A VARIABLE,
IT CAN CHANGE.
SO I'M GOING TO NOW
ERASE THAT THREE.
I'M GOING TO CREATE A NEW INPUT
AND GET RID OF THIS NUMBER LINE.
AND LET'S SAY NOW
HE'S REALLY GENEROUS
AND HE GIVES ME
TEN JELLYBEANS.
Under "Input" she writes 10.
She says SO I HAVE NOW TEN JELLYBEANS
THAT MIKE HAS GIVEN TO ME.
IN MY EXPRESSION HERE I'M GOING
TO CHANGE THAT J TO A TEN.
AND TO FIGURE IT OUT,
FIVE PLUS TEN MORE...
FIVE AND I'M GOING TO
DO A BIG JUMP OF TEN.
FIVE PLUS TEN GIVES ME
A TOTAL OF FIFTEEN.
SO NOW I HAVE FIFTEEN
YUMMY JELLYBEANS
THAT I CAN ALSO SHARE
WITH SOME OF YOU.
Under "output" she writes 15.
She says SO HOPEFULLY YOU'VE
LEARNED A BIT MORE ABOUT
ALGEBRAIC EXPRESSIONS.
UNDERSTANDING THAT IT INCLUDES
NUMBERS, OPERATIONS,
AND THAT UNKNOWN VALUE
WE CALL A VARIABLE.
AND WE CAN USE THOSE
NUMBERS AND CHANGE THEM UP,
WHICH WILL THEN
CHANGE OUR OUTPUT.
SO WE'LL SEE YOU
AGAIN NEXT TIME.
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