Singapore Math: Grade 3a Unit 2 (part 5) Video Lecture | Mathematics Lesson for Grade 3 (Singapore) - Personal Learning

let's now try to understand how we can
add it add four-digit numbers to each
other so let's say I have the problem
2803 2803 and i want to add that to I've
got a little small plus sign here you
almost can't see it because I'm doing it
so far to the left I'm adding that to
1443 and this is the same problem that
they have on page 24 of the book let's
think about how we can do this so I'm
going to do it simultaneously here on in
this top left corner of the video but at
the same time I'm going to draw it out
with the place notation so we know the
different the different number of places
let's say this is the ones place ones
tens hundreds I'll just write hund
and thousands thousands here so that we
don't so that things can stay relatively
neat there you go
okay so how do we represent two thousand
eight hundred and three if we were to
put it into these place buckets see we
have two thousands so let me draw that
as sawsan on mom we do everything in the
same color but the same color as this
two thousand eight hundred three so we
have two thousands right so that's one
thousand two thousand and each of these
are thousands all right if two thousands
we have eight hundreds so let's see let
me see if I can try eight hundred one
two three four five six seven eight each
of these are 100 100 100 100 you can't
see it so I don't know why I'm writing
it but let's each of that just says 100
on each of them probably can't read it
how many tens together well we have no
tens right and how many ones we have
three one two
you three each of those are ones so I
have just represented two thousand two
thousand eight hundred eight hundred and
three using our our place value buckets
right now let's represent 1443 the same
way and I'll do all of those in yellow
so it has one thousand so it is 1400 so
one two three four each of these are a
hundred you know once again I'm taking
the time to draw it in there although
I'm sure you can't read it and then we
have four tens right this is a forty so
one two three four each of these are ten
ten ten ten and then we have three ones
one two three now that we've represented
both numbers this is just how we
represented in our in our base ten
number system I know the word base ten
might be confusing to you but this is
our decimal number system which is based
on the number ten or nine numerals and
this is doing the same thing but using
our place value buckets thousands
hundreds tens in ones place so let's add
it up so first we go to the ones place
and we say well what is three ones plus
three ones
well three ones plus three ones that's
just equal to six ones right and if we
go to the ones place here we see that we
have six ones one two three four five
six good enough now let's move on to the
tens place we have zero tens plus four
tens well that's going to be equal to
four tens and four tens is the same
thing as 40 and when we go to the tens
place here we see the same thing one two
three four tens and this was the zero up
here so we have 40 here or four tens and
that's this 4 right 4 tens one two three
four six ones and now let's go to the
hundreds place and this is where it gets
interesting how many hundreds do we have
well we have one two three four five six
seven eight nine ten eleven twelve
hundreds here and also if we said eight
plus four there's 12 well we can't write
a 12
in one of in one of our places in our
number right we can only write it
something zero one two three four five
six seven eight or nine those are the
only numerals that I can put in any
given place so how do we solve that
problem well what we can do is we could
take ten of these hundreds and we can
cash them in for a thousand so let's do
that so let's take this one two three
four five six seven eight nine ten so
let's take these let's take these ten
hundreds and move them over and put them
into the thousands place well ten
hundreds are equal to one thousand right
that's all I did I took ten of these and
I took them out of the hundreds place
and I put them into the thousands place
and so these aren't here anymore
I'll just draw it kind of like that so
if we do that how many how many hundreds
do we have left well we have one two
left so if two hundreds left so we could
put two there and then how many
thousands do we have well we have the
two plus the 1 and then we have the 1000
here that we had cashed in with from all
from ten hundreds so the ones that we
cashed in we could put there right that
one is this one and so we add up a
thousands one two three four thousand or
one plus two is three plus one is four
and if you had you know if you've ever
learned to carry that's essentially what
we did but I really want you to
understand what happened three plus
three is six 0 plus 4 is 4 8 plus 4 the
kind of the way I learned in the 80s
when I was in third grade was
essentially you say 8 plus 4 is 12
write the 2 and carry the 1 and that
works but the problem with that is you
really don't know what you're doing
you're just kind of doing something you
know like a robot you don't understand
why that works but the reason why it
works is you're actually saying 8 plus 4
is 12 or you could say 800 plus 400 is
1200 and what you do is you say well I'm
out of that 1200 I'm gonna put 200 here
and then the other thousand I'm going to
convert into a 1000 and then you say
1,000 plus the tooth
1,000 is 4,000 and that's essentially
what we did here let's do let's do
another problem actually let's do well
if I look at problem number one on the
next page it seems like they just wanted
to do some exercise and so let's just do
a couple quick exercise and then I'll do
another problem where we learned to
carry or I guess you could call it
regroup I don't exactly know what the
exact terminology is so they say they
gave us a bunch of problems they say
find the value of some problem a they
say is 4 to 6 3 plus 5
well we could do this one almost in our
head right this is 4260 3 plus 5
this is just 5 right so we can just add
the 5 to the ones place and we get 4268
right 5 plus 3 is 8 b 4260 3 plus 20 so
this is interesting so this 2 here where
is that that's in the tens place so we
could add that to and I'm naturally not
gonna write them on top of each other
because I want you to understand how to
do this in your head this is a tenths
place we have a six of the tenths place
here so let's add the tens places right
the ones place is a 0 so 0 plus 3 is 3
and then the 2 plus the 6 is 8 and then
you have 4200 and that makes sense 4200
63 plus 20 what's 63 plus 20 it's 83 all
right and then of course you have the
4200 in front of it problem C 4260 3
plus 400 well we could think about it
the same way on this number there's
nothing in the ones place nothing in the
tenths place in the hundreds place I
have a 4 right so all I have to do is
add in the hundreds place here
so I add the 4 to the hundreds place
here to the to write this 4200 63 if I
had 400 to it I get 4663
4663 right all I said is 4,000 that
doesn't change 2 plus 4 is 6 and then 63
problem D 4260 3 plus 3000 once again we
only have there's a zero in every place
except a thousand so we will have to pay
attention to the thousands
so what's three thousand plus four
thousand it's seven thousand and then we
just have the two hundred sixty-three
plus nothing else seven thousand two
hundred sixty-three
now what were the reason why they're
giving you us these exercises they want
you to realize it you know you might
think this is hard you know I'm adding
two four-digit numbers but you really
just have to keep track of one of the
places at a time in this case four
thousand plus three thousand is seven
thousand and then the rest of you have
the two hundred sixty three problem e
four thousand two hundred sixty three
plus four hundred and twenty five now
see if you could do this one in your
head so we could add the ones three plus
five is eight add the tens six plus two
is eight and then add the hundreds 2
plus 4 is 6 and then you have a four
thousand there's no thousands here so
it's four thousand six hundred and
eighty-eight and they have one last one
so the problem we have is all of them
are four thousand two hundred sixty
three and we have plus three thousand
four hundred and twenty five and if you
notice it's from the different problems
we had a three thousand year we had it
four hundred here we had a twenty here
we had at five here right so essentially
where this is kind of the combination of
all of the problems we've done so far so
how do we do it well we can add first
just the ones place three plus five is
eight sixty plus 20 is eight right six
plus two 200 plus 400 is six and four
thousand plus three thousand is seven
six the 7688 hopefully you didn't find
that too scary let's do one more problem
and this one will what we'll do the
place value buckets just to really hit
the point home so let's say we were
doing 2048 plus 2 so let's say this is
the thousands place hundreds place tens
place I'll call this thousands and this
is the ones place so how many ones do we
have in this number we have eight ones
2048 one two three four five six seven
eight right that's the eight ones we
have four tens draw a line here one two
three four
each of these are do them as a $10 bill
maybe we have no hundreds and how many
thousands we have 1000 we have mm all
right mm and what are we adding to it
we're just adding two or two ones so
this two I'll do it in magenta we're
just adding two one two so what do we
get when we add it up well let's think
about it how many ones do we have we
have one two three four five six seven
eight nine ten ones we have ten ones
here
so we can't write a 10 and the ones did
in the ones digit place 4 in the ones
place we can only write something zero
through nine right 10 is you can't write
a 10 digit number where you only need
one digit so what we can do is let's
cash in or let's convert these 10 ones
what can we change them into we can
change all of these into a 10 we can
change all of these into a 10 and then
if we take all of these convert meant to
10 move it here then we have nothing
left here so what do we have now we have
zero ones how many tens do we have one
two three four five tens no hundreds and
mm so it's 20 I'm sorry it's 2050 and so
2048 plus two is two
2,050 and that should make sense to you
intuitively right what's 48 plus 248
plus 1 is 49 so 48 plus 2 is 50 or
another way to think about it you know
this 2,000 is just kind of there right
because we're not doing anything with
the hundreds or thousands place the
other way to think about if we write it
like this 48 plus 2 you say 8 plus 2 is
10 this is kind of a traditional way
that a lot of people have learned it
maybe your parents learned this to do
this way or they say 8 plus 2 is 10 you
write 10 where you're at the zero you
carry the 1 and they say 1 plus 4 is 5
now that always works but it's important
to realize what you really did when you
say this you're actually saying 8 plus 2
is 10
instead of writing that 10 in the ones
place I'm going to convert all of them
into one more 10 in the tens place and
so I have zero ones and one 10 right
eight plus two is zero ones and 1 10 and
then have one 10 plus 4 tenths is equal
to five tenths or 50 so that's what we
did there and I will see you in the next
video