[cheerful upbeat music] ♪ WHAT UP, COOL CATS?

DID YOU KNOW THAT THERE ARE 293 WAYS TO MAKE CHANGE FOR A DOLLAR?

YEAH, MATH HELPS YOU MAKE CHANGE FOR A DOLLAR AND COUNT THE COINS YOU MIGHT HAVE FOUND BETWEEN THE COUCH CUSHIONS.

SO, LET'S START YOUR MATH LESSON NOW AND SEE WHAT WE CAN LEARN.

♪ HI, MATHEMATICIANS.

IT'S ME, MS. ALTMAN, AND IT'S AMAZING TO SEE YOU.

BEFORE WE GET STARTED, LET'S TAKE A MOMENT TO GRAB SOME SUPPLIES THAT WE WILL NEED FOR OUR TIME TOGETHER TODAY.

YOU WILL NEED PAPER AND A PENCIL.

I'M GOING TO GO AND GET MINE.

WHY DON'T YOU DO THE SAME?

SEE YOU IN A LITTLE BIT.

♪ ALRIGHT, I'VE GOT MY SUPPLIES, AND I SEE YOU HAVE YOURS TOO.

TODAY, WE ARE GOING TO LEARN A NEW STRATEGY FOR FINDING THE AREA OF A RECTANGLE.

YOU HAVE PROBABLY LEARNED ABOUT AREA IN SCHOOL, AND IF NOT, I'M PRETTY SURE THE "AREA" UNIT WILL BE TAUGHT SOON.

UNTIL THEN, LET'S GO OVER SOME IMPORTANT CONCEPTS REGARDING AREA.

WE CAN MEASURE AREA BY PARTITIONING A SHAPE INTO EQUAL SQUARES AND COUNTING THE SQUARE UNITS.

LET'S LOOK IN MY BACKYARD...

THE ENTIRE AREA OF MY BACKYARD.

I AM PLANNING TO BUILD A FENCE FOR MY DOG IN THIS SMALL AREA.

LET'S USE A RECTANGLE TO REPRESENT THE AREA I WANT TO BUILD A FENCE FOR MY DOG.

WE CAN MEASURE THIS AREA BY PARTITIONING IT INTO EQUAL SQUARES AND THEN COUNTING THE SQUARE UNITS.

NOW THAT OUR RECTANGLE HAS BEEN PARTITIONED INTO EQUAL SQUARES, PLEASE HELP ME COUNT THE SQUARE UNITS OF THIS AREA IN MY BACKYARD.

YOU READY?

AWESOME!

LET'S COUNT.

SO, HOW MANY SQUARE UNITS IS THIS AREA IN MY BACKYARD?

RIGHT, IT'S 20 SQUARE UNITS.

NOW, I WANT YOU TO LOOK MORE CLOSELY AT THE AREA WHERE WE WILL BUILD MY DOG'S FENCE AGAIN.

DID YOU NOTICE THAT WHEN WE PARTITIONED OUR RECTANGLE INTO SQUARE UNITS, IT NOW LOOKS LIKE AN ARRAY?

DO YOU SEE THAT?

IF NOT, LET'S TAKE A LOOK AGAIN.

WHEN YOU LOOK ACROSS, YOU WILL SEE THE 4 ROWS.

NOW, LOOK UP AND DOWN, AND YOU WILL SEE THE 5 COLUMNS.

GREAT, YOU SEE IT NOW?

[ding] OH!

THAT'S MY "A-HA!

MOMENT" SOUND.

NOW THAT WE SEE AN ARRAY, WE NOTICE THAT WE CAN COUNT THE SQUARES A DIFFERENT WAY, INSTEAD OF COUNTING EACH INDIVIDUAL SQUARE.

OH, MY!

THAT'S EXCITING.

DO YOU MIND IF I SHARE OUR THINKING WITH OUR OTHER MATHEMATICIAN FRIENDS?

GREAT.

INSTEAD OF COUNTING EACH SQUARE UNIT, ONE OF OUR FRIENDS DISCOVERED THAT THEY COULD COUNT THE UNIT SQUARES IN GROUPS.

BEFORE I SHARE THIS STRATEGY, DO YOU HAVE AN IDEA OF HOW YOU CAN COUNT THE UNIT SQUARES IN GROUPS?

YOU DO?

WELL, TURN AND SHARE YOUR THINKING WITH A TRUSTED ADULT OR FRIEND.

YOU CAN ALSO SHARE IT WITH ME.

I'LL GIVE YOU A FEW SECONDS.

I SEE THAT SOME OF MY FRIENDS ARE STILL THINKING, SO LET ME GIVE YOU A CLUE.

ARE YOU READY FOR THAT CLUE?

GREAT.

TRY COUNTING EACH SQUARE UNIT BASED ON THEIR COLUMNS.

HOW MANY SQUARE UNITS ARE IN EACH COLUMN?

YES, THERE ARE 4 SQUARE UNITS IN EACH COLUMN.

SO, INSTEAD OF COUNTING EACH INDIVIDUAL SQUARE, WE CAN COUNT THEM IN GROUPS OF 4.

LET'S COUNT THEM TOGETHER.

20 SQUARE UNITS.

NOW COUNT THE SQUARES IN EACH ROW.

HOW MANY SQUARES ARE IN EACH ROW?

THAT'S RIGHT, 5.

WE CAN COUNT THE SQUARE UNITS IN GROUPS OF 5.

LET'S COUNT THEM TOGETHER.

20 SQUARE UNITS.

HOW CAN WE USE THIS INFORMATION TO COME UP WITH A DIFFERENT WAY TO FIND THE AREA OF A RECTANGLE?

THAT'S RIGHT.

INSTEAD OF COUNTING THE SQUARE UNITS INDIVIDUALLY OR BY GROUPS, WE CAN MULTIPLY THE SIDE LENGTHS.

LET'S LOOK AT THE ROWS AND COLUMNS OF THE RECTANGLE AGAIN.

WE HAVE A 4 BY 5 RECTANGLE.

4 X 5.

THAT GIVES US THE SAME 20 SQUARE UNITS OF MEASURED AREA.

LET'S LOOK AT IT ANOTHER WAY.

NOW WE HAVE A 5 BY 4 ARRAY.

5 X 4.

THAT GIVES US THE SAME 20 SQUARE UNITS OF MEASURED AREA.

WE CALL THE 5 X 4 OR THE 4 X 5 SIDE LENGTHS THE "DIMENSIONS" OF THIS RECTANGLE.

LET'S TRY ANOTHER PROBLEM.

WE HAVE A RECTANGLE WITH THE DIMENSIONS 3 X 4.

BESIDES COUNTING EACH INDIVIDUAL SQUARE OR BY GROUPS, HOW CAN WE FIGURE OUT THE AREA?

THAT'S RIGHT.

YES, IT'S 12.

WE CAN CHECK OUR WORK BY PARTITIONING THE RECTANGLE AND COUNTING THE SQUARES.

LET'S COUNT THE SQUARE UNITS TOGETHER.

12 SQUARE UNITS.

YOU'RE DOING AN AMAZING JOB WITH THIS.

DO YOU WANT TO TRY A CHALLENGE?

ME TOO.

LET'S DO IT.

CAN WE USE MULTIPLICATION TO HELP US?

AWESOME.

PLEASE FIND THE DIMENSIONS OF A RECTANGLE THAT HAS AN AREA OF 24 SQUARE UNITS.

I'LL WAIT SO YOU CAN FIGURE OUT THE ANSWER.

OH!

IT LOOKS LIKE A FEW OF OUR MATHEMATICIANS WOULD LIKE A HINT TO HELP THEM GET STARTED.

WOULD YOU LIKE A HINT BEFORE WE GO OVER YOUR ANSWERS?

OKAY.

I WILL GIVE YOU A FEW MOMENTS TO COME UP WITH YOUR ANSWER.

OH, WOW!

THAT HINT MUST HAVE BEEN REALLY HELPFUL, BECAUSE YOU'RE GIVING ME A LOT OF POSSIBLE ANSWERS.

I'LL SHARE A FEW OF YOUR THOUGHTS.

LET'S LOOK AT 4 X 6.

ARE THE DIMENSIONS OF A 4 X 6 RECTANGLE 24 SQUARE UNITS?

LET'S PARTITION THE RECTANGLE INTO SQUARES TO SEE IF WE ARE CORRECT.

LET'S CHECK OUR WORK BY COUNTING THE SQUARE UNITS.

24 SQUARE UNITS!

GOODNESS GRACIOUS!

I'M ALMOST OUT OF BREATH.

I THINK I'LL CHECK OUR WORK NEXT TIME BY SKIP COUNTING.

A RECTANGLE WITH SIDE LENGTHS OF 4 AND 6 IS CORRECT.

YOU COULD HAVE WRITTEN 4 X 6 OR 6 X 4 AS YOUR ANSWER.

LET'S WORK THROUGH ONE MORE EXAMPLE.

ONE OF OUR MATHEMATICIANS USED THE DIMENSIONS 3 X 8.

DO YOU THINK OUR FRIEND IS CORRECT?

I'LL GIVE YOU A CHANCE TO WORK THAT OUT ON YOUR PAPER.

DRAW A RECTANGLE WITH THE DIMENSIONS 3 AND 8, TO SEE IF IT WILL GIVE YOU THE AREA OF 24 SQUARE UNITS.

♪ WELL, LET'S USE SKIP COUNTING TO CHECK OUR WORK THIS TIME BY COUNTING THE GROUPS OF 3 IN EACH COLUMN.

READY?

24 SQUARE UNITS.

SO, A 3 X 8 RECTANGLE, OR AN 8 X 3 RECTANGLE, HAS 24 SQUARE UNITS.

DID YOU ENJOY THAT CHALLENGE?

I DID TOO.

WELL, AFTER THIS LESSON, I CHALLENGE YOU TO FIND THE DIMENSIONS OF A RECTANGLE THAT HAS AN AREA OF 48 SQUARE UNITS.

I KNOW YOU CAN DO IT, MATHEMATICIANS.

SO, LET'S REVIEW WHAT WE HAVE LEARNED TODAY.

WE LEARNED THAT... WE ALSO LEARNED THAT... NOW YOU HAVE 3 STRATEGIES TO HELP YOU FIND THE AREA OF A RECTANGLE.

WE ALSO WERE CHALLENGED TO FIND THE DIMENSIONS OR THE SIDE LENGTHS, OF A RECTANGLE IF WE WERE PROVIDED THE AREA.

THANK YOU FOR LEARNING WITH ME TODAY.

BYE, MATHEMATICIANS!

WAIT A SECOND, WAIT... A SECOND.

DROP EVERYTHING YOU'RE DOING, AND CHECK OUT THIS SUPER COOL VIDEO.

♪ ♪ OOH, OOH, OOH ♪ [female voices] ♪ HELLO ♪ ♪ HELLO ♪ ♪ HELLO ♪ ♪ HELLO ♪ ♪ HELLO ♪ HI, EVERYONE.

I'M MS. RAVEN, AND TODAY, WE ARE GOING TO GET ACTIVE.

I WANT YOU GUYS TO JOIN ME BY MOVING YOUR ARMS FROM SIDE TO SIDE.

WE'RE JUST GOING TO SWING THEM HERE.

AND EVERY TIME I SWING, MY TOE IS TAPPING.

GOOD JOB, AND WE'LL LIFT THEM UP.

AND BACK TO OUR CENTER.

AND THIS TIME, WE'RE JUST GOING TO CURL OUR BICEPS IN.

AND BACK TO CENTER.

YOU'RE DOING GREAT.

WE'RE GOING TO COME UP THIS TIME.

HERE WE GO.

AND UP!

AND BACK TO CENTER.

GOOD.

AND BICEPS.

GREAT JOB, AND THANK YOU FOR JOINING ME TODAY.

I WILL SEE YOU NEXT TIME.

OKAY, OKAY, OKAY, OKAY, OKAY, OKAY.

GUESS WHAT?

A "JIFFY" IS AN ACTUAL UNIT OF TIME.

IT MEANS 1/100 OF A SECOND.

THAT'S LIKE...

FASTER THAN I CAN SNAP.

OKAY, WELL, HERE'S TODAY'S MATH LESSON.

IT'S COMING TO YOU IN, LIKE, 3 OR 4 JIFFIES.

DID YOU CATCH THAT?

♪ HELLO, THIRD-GRADE FRIENDS.

DIANE HERE.

I'M SO HAPPY TO SEE YOU.

TODAY, WE'RE GOING TO BE TALKING ABOUT STRATEGIES FOR ADDITION AND SUBTRACTION.

BEFORE WE GET STARTED, LET'S REVIEW WHAT WE KNOW ABOUT THE WORD "STRATEGIES."

LET'S USE THE FRAYER MODEL TO HELP US OUT.

ARE YOU READY?

LET'S GET STARTED.

TO MAKE OUR FRAYER MODEL, YOU WILL NEED A PIECE OF PAPER AND A PEN, A PENCIL, OR A MARKER.

I'M GOING TO GET MY SUPPLIES.

YOU GO AHEAD AND DO THE SAME.

♪ NOW THAT WE HAVE OUR SUPPLIES, LET'S BEGIN TO MAKE OUR FRAYER MODEL.

LET'S TAKE A PIECE OF PAPER AND FOLD IT IN HALF, HAMBURGER-STYLE, AND THEN, FOLD IT IN HALF AGAIN, TO MAKE 4 EQUALLY-SIZED RECTANGLES.

THEN, IN THE CORNER OF OUR PAPER, WHERE ALL SIDES ARE FOLDED, WE'RE GOING TO FOLD DOWN TO MAKE A SMALL TRIANGLE.

ALRIGHT.

WHEN YOU UNFOLD YOUR PAPER, IT SHOULD LOOK LIKE THIS.

DOES YOURS LOOK LIKE MINE?

OKAY, GREAT.

WE'RE GOING TO START WITH WRITING THE WORD "STRATEGIES" IN THE CENTER DIAMOND, BECAUSE THIS IS THE WORD WE NEED TO UNDERSTAND MORE ABOUT.

ALRIGHT.

THEN, IN THE UPPER-LEFT RECTANGLE, WE'RE GOING TO DEFINE THIS TERM.

SO, LET'S WRITE THE WORD "DEFINITION" HERE.

IN THE UPPER-RIGHT RECTANGLE, WE'RE GOING TO PROVIDE AN EXAMPLE OF A STRATEGY.

SO, LET'S WRITE "EXAMPLE" HERE.

AND THEN, IN THE LOWER-LEFT RECTANGLE, WE'LL PROVIDE A NON-EXAMPLE, OR WHAT STRATEGIES ARE NOT.

SO, WRITE "NON-EXAMPLE" HERE.

FINALLY, IN THE LOWER-RIGHT RECTANGLE, WE'LL DRAW A PICTURE TO HELP US VISUALIZE WHAT STRATEGIES ARE.

SO, LET'S WRITE THE WORD "PICTURE" HERE, TO REMIND US OF WHAT WE'RE SUPPOSED TO DO.

NOW, WE'RE GOING TO DEFINE THE WORD "STRATEGY" TOGETHER.

SO, LET'S WRITE THE DEFINITION IN OUR UPPER-LEFT RECTANGLE.

A STRATEGY IS...

SO, IF I WANT TO SOLVE A PROBLEM INVOLVING ADDITION AND SUBTRACTION, I COULD USE ESTIMATION, FRIENDLY NUMBERS, OR OTHER STRATEGIES TO HELP ME THINK THROUGH THE PROBLEM.

I'M GOING TO GIVE YOU SOME TIME TO WRITE THE DEFINITION IN YOUR FRAYER MODEL.

♪ ALRIGHT.

AS WE USE STRATEGIES TO HELP US THINK THROUGH THE MATH IN TODAY'S LESSON, YOU'LL BE ABLE TO ADD EXAMPLES, NON-EXAMPLES, AND DRAW A PICTURE TO SHARE YOUR GROWING TOOLBOX OF MATH STRATEGIES.

LET'S PLACE OUR FRAYER MODEL TO THE SIDE AND TAKE A LOOK AT THIS EMAIL FROM ONE OF MY STUDENTS.

I THOUGHT ABOUT YOU TODAY WHEN I HEARD THIS MATH PROBLEM THAT WAS POSED BY ONE OF MY STUDENTS.

DO YOU WANT TO HEAR IT?

I COULD USE YOUR HELP IN GIVING HER SOME IDEAS ON HOW TO SOLVE IT.

SO, THE EMAIL SHE SENT ME SAYS: WELL, MATHEMATICIANS, DO YOU THINK WE CAN HELP HER?

AWESOME.

WHEN I'M SOLVING A PROBLEM, I LIKE TO START BY SUMMARIZING IT, SO I CAN MAKE SURE THAT I UNDERSTAND WHAT THE PROBLEM IS ASKING ME TO DO.

CAN YOU HELP ME SUMMARIZE THIS PROBLEM, BY TELLING ME WHO IS IN THE PROBLEM?

EXACTLY, ANGELA AND JOSÉ.

AND WHAT DO WE NEED TO FIND OUT?

HOW MANY POINTS ANGELA NEEDS TO GET TO JOSÉ'S SCORE OF 423.

WHAT DO WE ALREADY KNOW?

ANGELA HAS 247 POINTS, AND HER BROTHER HAS 423.

GREAT.

I THINK I UNDERSTAND WHAT THIS PROBLEM IS ASKING ME TO DO.

SO, NOW, LET'S TAKE A MOMENT AND THINK ABOUT HOW WE COULD REPRESENT THIS PROBLEM WITH PICTURES, MODELS, OR NUMBERS.

YOU MAY WANT TO DRAW SOMETHING OUT ON YOUR PAPER AT HOME.

♪ ALRIGHT.

LET'S SEE WHAT YOU GOT.

THOSE ARE ALL GREAT IDEAS.

LET ME SEE IF I CAN SHARE THOSE.

ONE IDEA IS TO USE A BAR MODEL.

ONE BAR HAS 423, AND THE OTHER HAS 247.

THE FIRST BAR SHOWS US JOSÉ'S SCORE OF 423, AND THIS ONE SHOWS ANGELA'S SCORE OF 247.

IF I COMPARE ANGELA'S SCORES TO JOSÉ'S BY PUTTING ANGELA'S BAR ON TOP, WE CAN SEE THAT THERE'S AN UNKNOWN NUMBER OF POINTS NEEDED TO REACH 423.

THAT MODEL REALLY HELPS ME BETTER UNDERSTAND THE PROBLEM.

ANOTHER IDEA THAT I HEARD YOU SHARE INVOLVES A NUMBER LINE.

WE KNOW THAT ANGELA HAS 247 POINTS.

I'LL PUT THIS HERE.

AND THEN, WE NEED TO GET TO JOSÉ'S 423 POINTS, SO, I'LL PUT THAT HERE.

FOR BOTH OF THESE REPRESENTATIONS, IT LOOKS LIKE I NEED TO FIND THE NUMBER OF POINTS NEEDED TO GET FROM 247 TO 423.

WE'LL CALL THAT "THE DISTANCE."

LOOKING AT OUR 2 MODELS, HOW COULD I REPRESENT THIS PROBLEM WITH AN EQUATION?

EXACTLY.

I COULD USE 247 PLUS AN UNKNOWN NUMBER EQUALS 423.

THAT MAKES SENSE TO ME.

BEFORE WE SOLVE, LET'S ESTIMATE THE MISSING ADDEND, SO THAT WE'LL KNOW IF OUR SOLUTION IS REASONABLE.

I'M GOING TO ESTIMATE BY ROUNDING TO THE NEAREST HUNDRED.

SO, 247 IS CLOSEST TO 200, AND 423 IS CLOSEST TO 400.

SO, THAT'S 200 PLUS SOMETHING EQUALS 400.

THAT WOULD BE 200.

ANGELA WOULD NEED ABOUT 200 MORE POINTS TO TIE HER BROTHER.

OKAY.

READY TO SOLVE?

LET'S START BY LOOKING AT OUR EQUATION AGAIN.

WE'LL CALL THIS AN ADDING-UP STRATEGY, AND I'LL USE THE NUMBER LINE TO SHOW THIS.

I NEED TO START AT 247 AND ADD UNTIL I GET TO 423.

THERE ARE LOTS OF DIFFERENT WAYS THAT WE COULD DO THIS, BUT ONE THING THAT I TRY IS TO USE FRIENDLY NUMBERS, OR THE TENS AND HUNDREDS.

THESE NUMBERS CAN BE EASILY ADDED TOGETHER.

LET'S SEE WHAT THAT MIGHT LOOK LIKE.

RIGHT.

SO, I KNOW THAT IF I ADD 3 TO 247, I LAND ON 250, AND 250 IS A FRIENDLY NUMBER.

250 PLUS 50 MORE WILL PUT ME AT 300, AND 300 IS ANOTHER FRIENDLY NUMBER.

THEN, I CAN ADD 100 MORE, TO GET TO 400.

THEN, ADDING 23 WILL GET ME TO 423.

HOW DO I KNOW HOW MUCH I ADDED ALL TOGETHER?

RIGHT, WE WANT TO LOOK AT THE JUMPS.

SO, WE HAVE ADDED ALL OF OUR JUMPS-- 3, 50, 100, AND 23.

I DON'T HAVE TO ADD IN ANY PARTICULAR ORDER, SO I CAN DO IT IN A WAY THAT MAKES SENSE TO ME, AND YOU CAN DO IT IN A WAY THAT MAKES SENSE TO YOU.

I'M JUST GOING TO ADD IT IN ORDER.

SO, WE HAVE...

SO...

SO, ANGELA NEEDS TO GET 176 POINTS TO TIE WITH HER BROTHER.

IS 176 A REASONABLE ANSWER?

SURE IS.

OUR ESTIMATE WAS 200, AND 176 IS PRETTY CLOSE.

IF I HAD GOTTEN 76 AS MY ANSWER, I WOULD KNOW THAT MY ANSWER WASN'T CLOSE TO MY ESTIMATE, AND THAT I WOULD NEED TO GO BACK AND CHECK MY WORK.

COULD YOU SOLVE THIS IN A DIFFERENT WAY?

I'LL GIVE YOU A MOMENT TO TRY IT ON YOUR OWN.

♪ ALRIGHT, WHAT STRATEGY DID YOU USE?

COULD YOU TELL ME?

OR SHOW ME.

WOW, THOSE ARE ALL GREAT STRATEGIES.

THERE ARE SO MANY DIFFERENT WAYS THAT YOU CAN SOLVE THIS PROBLEM.

DID YOU GET 176 AS YOUR SOLUTION?

GREAT.

FINDING DIFFERENT WAYS TO SOLVE A PROBLEM CAN HELP YOU BECOME A MORE FLEXIBLE THINKER.

AND IT'S FUN.

OH!

BEFORE WE GO, LET'S FINISH UP TODAY BY RETURNING TO OUR FRAYER MODEL.

EARLIER, WE GAVE A DEFINITION FOR STRATEGIES IN MATH.

WE SAID THAT A STRATEGY IS...

IN YOUR FRAYER MODEL, CAN YOU WRITE AN EXAMPLE OF ONE OF THE STRATEGIES THAT WE USED TODAY?

THAT'S RIGHT, WE USED ESTIMATION AND FRIENDLY NUMBERS, LIKE TENS AND HUNDREDS, TO SOLVE THE PROBLEM.

I BET YOU CAME UP WITH OTHER STRATEGIES AS WELL.

AFTER THE LESSON, I WANT TO CHALLENGE YOU TO ADD IN MORE PICTURES AND A NON-EXAMPLE OF MATH STRATEGIES INTO YOUR FRAYER MODEL.

THANKS FOR HELPING ME COMPLETE IT.

SEE Y'ALL.

ALRIGHT, THAT'S ANOTHER DAY OF LEARNING IN THE BOOKS.

GO AHEAD, DAB YOURSELF UP.

UH-HUH, BAM.

PEACE, LOVE, AND LEARNING, HOMIES.

CAPTIONS BY FEATURE SUBTITLING www.featuresubtitling.com [cheerful upbeat music] ♪