Singapore Math: Grade 3a Unit 2 (part 10) Video Lecture | Mathematics Lesson for Grade 3 (Singapore) - Personal Learning

welcome back in this video we're gonna
do a few more subtraction problems
involving borrowing and I really want to
make sure we do a lot of these because I
think this is where when people first
learn it there's the most confusion but
once you really understand what you're
doing hopefully you find that that it's
it's pretty straightforward and then
we'll do a couple of work problems let's
do the last couple problems on page 33
and the what is it the the primary
mathematics 3a book this is the US
Edition so we let's say we have and
actually I'm going to do this one
several ways because I want to show you
that all of these ways are equivalent
maybe what you learn in your school is a
little bit different but they're all
essentially doing the same thing and I
want you to learn that so we have eight
thousand and seven minus three thousand
four hundred and twenty nine so how do
we think about this well 3 is less than
eight but all of these numbers are
greater than the numbers above them
right so we're going to have to do some
borrowing so there's a couple of ways
you could do this I'm actually gonna
write the problem over again right here
because I want to do it two different
ways one way I'm going to explain what's
actually happening and one way is
actually just really really fast so
let's go over the fast way first because
it never hurts to know how to do these
problems really really fast so let's say
if I started at the ones place here and
I have the seven but the seven is less
than this nine so I have to I have to
take something from the rest of the
number right and the only thing I ever
take is you know if I have if I'm in the
ones place the only thing I ever take is
ten right so think of it this way and
they ignore it if it confuses you but I
have seven here and then this 8,000 or I
could just if I just look at those three
places those that 800 what is that
that's eight hundred tens right why do I
say that well because the last zero and
the 800 is actually in the tens place so
you can and this is kind of Sal math I
don't think this is really taught
anywhere but it's a really fast way of
doing some of these borrowing problems
you could view this as 800 tens you need
110 here so that you can make the seven
into a 17 so what do you do well you
borrow
of those 810 sowhat's 810 s - 110 what's
800 - one
well it's 799 799 and then you take that
extra 10 and you add it to the ones
place and you get 17 and then you're
ready to subtract
17 minus 8 I'm sorry 17 minus 9 is 8 9
minus 2 is 7 9 minus 4 is 5 7 minus 3 is
4 now you should only do what I just did
if you're really comfortable with how
things are working and you understand
the intuition don't try to skip steps if
you're not sure what the step is and on
the left side now I'll do it kind of in
the foolproof way so that you you really
make sure you understand what you're
doing so we have the same problem
because it's the numbers on top are
smaller than the numbers on the bottom
and of course it's the same problem
because it's well it's the same problem
so here we can actually start borrowing
on we can start going from left to right
and there it's going to have the exact
same result as you'll see in a second
the same color so this 0 is less than
this 4 right the 0 hundreds is less than
400s
so and we have 8,000 here so why don't
we take one of these 8 thousands so we
only have 7,000 left and convert it to
10 hundreds so we convert 10 hundreds
but now we have this zero tens is less
than two tens so let's take some of this
10 hundreds or let's take one of these
10 hundreds so we only have 900 left and
give one of those hundreds to the tens
place and now we have 10 tens all right
well we're almost done but we see that
the 7 ones is less than the 9 ones so
why don't we borrow 10 from the tens
place so if we borrow 10 we only have
nine 10s left and then we add that 10 to
the ones place when we have 17 notice
the end product was the exact same thing
we now have a 7,000 a 900 a 90 and a 17
in the ones place and we could subtract
17 from 9
it's sorry 9 from 17 is 8 2 from 9 or 9
minus 2 is 7 9 minus 4 is 5 and 7 minus
3 is 4 so the same result and they got
it the same place and I want you to
think about why both of these worked and
hopefully I gave you a little intuition
as far as why they worked let's do a
couple more I might not do all of them
just depending on how much time we have
so let's say we have nine thousand four
hundred and three minus four thousand
two hundred and seventy-five four is
less than nine two is less than four but
seven is not less than zero and 3 is not
less than five but actually let me do it
this the two ways that we just learned
because I think this will be instructive
and it's good to to see all the
different ways and maybe you'll come up
with a new way of doing it actually my
cousin when he was eight figured out a
new way but and and it actually was was
pretty fast but anyway let's go back to
this problem so what's the the
conventional way or I guess nothing's
are conventionally there they're
teaching how they they've changed how
they teach these things every year it
seems like but we could say well the
four is less than a nine so we're cool
they're the two is less where this is
4000 is of the nine thousand the 200 is
less in the four hundred cool there but
the seventy is not less than this zero
tens right so why don't we borrow a
hundred so we only have 300 left and
turn that into ten tens but then we have
the 3 is less than 5 so why don't we
borrow one of our ten tens when we have
nine left and put that 10 in the ones
place we have 13 so that was kind of
what I call the conventional way of
doing it the less conventional way of
doing it is to actually start at the
right hand side and say well this 3 is
less than that 5 right the 3 is less
than the 5 so let me borrow from here
wait but I can't borrow from 0 tens but
wait I could go one more space and I
could borrow from 40 tens right for this
is four hundred right but 400 is the
same thing as 40 tens so let me borrow
one of those 40 tens so then I have 39
tens left
and add that extra ten to this base I
get 13 and notice we have the exact same
outcome and we could subtract 13 minus 5
is 8 9 minus 7 is 2 3 minus 2 is 1 9
minus 4 is 5 on this side 13 minus 5 is
8 9 minus 7 is 2 3 minus 2 is 1 9 minus
4 is 5 I encourage you to try to
understand both things I did because
neither of them are magic and they
should make sense to you from a place
value point of view but whichever one
you're more comfortable with stick with
that and just practice tons and tons and
tons of problems and you know if you run
out of problems in your workbook make up
problems that's actually a good way to
learn so let's do one more and I'll and
I think you'll find that this one is
especially quick using the the the
technique that's not necessarily
condoned in your condone means
encouraged or or supported but it's not
necessary condoned by the Singapore Math
but I think it's good for you to learn
every different possible way so if we
have 10,000 right now we're doing a five
digit number but hopefully you know this
is ones tens hundreds place thousands
place ten thousands place every place we
go we're just it's 10 bigger right I
mean hopefully you you if I give you a
seven digit number we could you could
actually deal with it because you just
know every time you go one place to the
left that digit just represents
something 10 times bigger than the digit
to the right right 10 is 10 times bigger
than 100 is 10 times bigger than tens
thousands 10 times bigger than 110,000
is 10 times bigger than 1,000 let's take
10,000 minus 5721 I'll do this one both
ways as well
10,000 minus 5721
so we have a 0 here we need to borrow
something will not honest a borrowed you
have to take it right but you can't take
from 0 you can't take from Jim so let's
start at the left hand side this
thousands is 0 thousands is less than
5,000 so let's borrow from the 10,000
spot
so let's there's only one 10,000 there
so let's take it and let's put it into
the thousand spot so we have ten
thousand down to thousands we don't have
enough hundreds here so let's borrow one
of the thousands and then we have ten
hundreds we don't have enough tens so
let's borrow one of the hundreds not
borrow take one of the hundreds and then
we have ten tens and then well we have
we don't have enough one so let's borrow
one of the tens and then we'll have ten
ones and then we're ready to subtract 10
minus 1 is 9 9 minus 2 is 7 9 minus 7 is
2 9 minus 5 is 4 sorry minus 5 is 4 my
brain is malfunctioning let's do it this
way so how could we think about we could
start at the right hand side we say oh
well this zero is just not acceptable we
need a we need to get a 10 here somehow
so let's look to the left of it we can't
borrow from here we can't borrow from
here and here
we can't borrow from here and here and
here but if we bought if we look at this
entire number 10000 is the same thing as
1,000 tents right this is this thing
that looks like 1,000 since it starts in
the tens place here that's 1,000 tents
right so why we just borrow just one of
them all we need is 110 here right so if
we if we have a thousand of something
and we take one of them how do we how
many do we have left
well what's 1,000 minus 1 it's 999
so this has 1,000 tens if we borrow one
of them
we have 999 10's left and then we take
that 10 that we took our borrowed and we
put it in the ones place 10 minus 1 is 9
9 minus 2 is 7 9 minus 7 is 2 9 minus 5
is 4 do this only if you understand
what's happening or otherwise do this
it's just gonna take you a little bit
longer but either way is fine and they
both should make intuitive sense to you
if you think about the number places and
you know what if they don't I encourage
you to draw out those diagrams like you
have in the Singapore math book where
you have two disks that with a thousand
and hundreds in them or to do the
expanded notation like I have it where
you know I'd write five thousand seven
twenty one is five thousand plus seven
hundred plus twenty plus one do it
either way and you should find that
things work out and in all mathematics I
encourage you even if you can get an a
on a test even if you find the homework
easy play around with the numbers
experiment with them really get a feel
for them because if you really
understand mathematics in the third
grade or the fourth grade when you do
the fifth grade the sixth grade or the
twelfth grade or college or your PhD in
physics it's going to be that much
easier anyway I will see you in the next
video