Singapore Math: Grade 3a; Unit 1 (part 1) Video Lecture | Mathematics Lesson for Grade 3 (Singapore) - Personal Learning

let's say that I love to collect marbles
and I'd love to do it so much that
sooner or later my my entire room filled
with marbles and it's just this huge
mess and when I look at them I have no
idea how many marbles I've collected so
I have all of these marbles so I decide
to do a little bit organization so I
could draw out my room looks like
initially but it would fill the screen
with marbles so what I say well you know
maybe I could get organized by I could
take ten marbles at a time so let's say
you know let me draw ten marbles one two
three four five six seven eight nine ten
and I put them in in cans in marble cans
that exactly fit ten marbles right so
let's say that the exactly fit ten
marbles so let me draw let me see how
well I can draw a marble can actually
let me draw my marble cannon in purple
so that's my marble can and let's say
that it fits exactly ten marbles of
course I could draw my my ten one two
three four five six seven eight nine ten
so it had exactly ten marbles in it and
I call this a ten can so this is not a
tin can a 10 can so this is 1/10 1/10 so
good enough at least this you know I put
all my marbles and in 10 cans so I might
have a few left over less than 10
because obviously had 10 I would put it
into a 10 can but I put them all in 10
cans but then I I I'm such an ambitious
marble collector that I've collected so
many 10 cans that I can't even see how
many I've collected I my room is now
full of these so I say well why don't I
put these 10 cans or the marbles in them
into an even bigger can so I take
essentially 10 of these 10 cans and I
just decided to do 10 just because that
happens to be the base system that we
live in and I don't want to confuse you
with base systems but take my word for
it so I take 10 of these let me see if I
can draw them that's one
2/3 apologize if I'm boring you
4/5 halfway there six seven eight nine
ten as you can see my drawing gets worse
as I as I get tired so these are ten
cats each one has one two three four
five six seven eight nine ten marbles
and I'm not going to do it for all of
them but you can imagine they're all
they all have exactly ten marbles so I
take a bunch of let me let me just
finish this so you know that there are
ten marbles in each of the ten cans not
ten cans
ten cans dum de dum dum to them these
are ten cans
that's say well I don't want you to
think that they're only six I want to
give the impression that there are ten
and each one and I'll take these ten and
I'll put them into what I call a hundred
can and that makes sense right because
if I have ten cans with each of them
holding ten marbles then I have 100
marbles right ten cans times ten marbles
per can so I take ten cans at a time and
I put them into these bigger cans which
I've recently purchased and I called
these hundred cans so a hundred can
looks like that and it's nice because
it's doesn't get confused with the word
ten so my hundred can looks something
like that
this hasn't been drawn to scale a
hundred can would be roughly ten times
the size of a ten can I could actually
draw the ten cans in here but I said I
just pour all the marbles in so I have
just I could say a ton of marbles we
know exactly how many marbles are 100
can there are 100 marbles in them right
it makes sense ten ten cans take all the
marbles in them and you get 100 can so
this is 100 100
fair enough I'm I now look at my room
and there seems to be some reasonable
organization going on but once again I
am such a good marble collector that
even the hundred cans of dude I have I
have hot I have tons of hundred cans
looking around the room and and once
again I can just look at my room and I
don't know how many marbles I have so I
start putting those together and I
create something called a thousand can
so I take ten hundred cans let me see if
I could drop so it's not going to be
scale so this is one hundred can this
big thing that I drew in brown I'm gonna
do the same thing that's one that's two
three four five six seven eight nine ten
and these are 100 can so that you know
this looks small but I just drew it that
way so I could fit it but you know if I
had to draw out that scale the marbles
are all you know it's really full of
marbles you almost can't see each
individual marble because I drew it so
small now this is just full of marbles
each of these cans has a hundred marbles
this this big thing is the same thing as
this thing right here each of these have
a hundred marbles 100 marbles so if I
were to pour all of these marbles into a
humongous can a humongous can this is
massive and I'm not my drawing won't do
it justice because I have to fit it on
the screen but it's going to be it's
going to be ten times the volume of this
can or ten times the size of that
hundred can I mean you could imagine if
that's the size of a hundred cans is
going to be a ten can right so and it's
going to be full of marbles I mean the
marbles are so small to be like little
dots right they're just going to fill up
the whole thing
you can't even at this scale it would be
hard to even see how many marbles you
have in there and that is a thousand can
let me do it in green
so this is a 1,000 can 1,000 can and
just you have a sense of scale if this
is the size of a thousand let me show
you how I so all of these these ten
hundreds right and and hopefully you
know that if I have a hundred times ten
I get a thousand and if you didn't I you
know it now
so if I get ten of these hundred cans
and I pour all the marbles into this
thousand I can pour all of them into
this big can and I have a thousand
marbles in this can and this is a sense
of scale if this is the size of a ten of
a thousand can so I did a thousand can
in green if this is then this would be
the size of a hundred can and then a ten
can would look something like this a ten
can would be like tiny it would be like
it would be like that size just so you
have a sense of scale that thing would
look like that if this big thousand can
is this size and then an individual
marble would be like a little dot it
would be like that no no like that I
don't know if you can even see it that's
how small it would be so fair enough now
not only am i a marble collector but
I've I have filed for patents on these
various scans and I won't go into what a
patent is but me you can ask someone but
I have invented these cans for helping
me organize my situation so let's let's
take a couple of situations that I
encounter as a marble collector and
let's see if these cans are actually
helping me keep track of things so let's
say I just you know I have I have a I
have a big sack of marbles that I I
collected today and I you know I wanna I
don't want to sit and you know it must
be thousands and thousands of marbles so
but I don't want to sit and count them I
have I have better things to do than
count I could be collecting marbles so
what do I do
let's remember thousand is green 100 is
brown ten is this purplish color invert
colors okay so let's say that after
filling up I have this sack of marbles
let me draw the sack and I will do it in
different colors it's a red sack of
marbles so you know it's a sack so the
you know it's time and it's full of
marbles so you know it's just tons of
marbles
in the sack too many to count too many
for me to count so what I do is I pour
them into some of the cans I have right
so let's say I start pouring them to the
cans and I I feel what were the colors
let's say that I feel
three of the hundred marbles so let's
say you know this is this is 100 can
here's another hundred can and here's
another hundred can and I fill them up
as much as I can right I filled them to
the brim with marbles so this is what I
start with and I I pour as many as I can
into this one I was like oh I still have
a ton more and I pour as many I can into
this one I fill it up I pour as many as
I can into this one right and let's say
that I even had another hundred can and
then let's say let's say that I you know
I tried to fill a forth hundred can but
I wasn't able to fill it up all the way
let's say it only filled roughly halfway
so I'm like well I can't use one hundred
can because I still don't know how many
marbles are in this one so first of all
what's our sense of how many marbles we
have so far I filled up three marble
three hundred marble pans let me write
that down so this is one hundred one
hundred can 100 this is 100 this is 100
and then this is one hundred can so you
know these went into those this is one
hundred can so let's just think about it
a couple of different ways I have three
hundred cans here so this has got to be
three hundred marbles and then I had
another hundred can here that I couldn't
fully fill up if I filled it up exactly
to the brim that I would have had four
hundred cans right so this is going to
be so I essentially have three hundred
marbles and I have some extra so how do
I count the extra well I can fill them
into other cans that I might have and so
you can imagine I can use a ten can so
let's start filling that into ten cans
so let's say I take this this kind of
surplus marbles and I start filling ten
cans so right let's say I fill for ten
cans to the brim I fill four of them to
the brim
four of them to the brain movies so you
know each of them have ten in them I
fill four of them in to the brim so I
took those that whatever number I had
here it almost filled up my it may be
halfway filled up my hundred can I
filled four to the brim and then I had
another ten can right here oh that's a
slightly different color but I think you
get the idea and then I had another ten
can that I tried to fill it to the brim
but it was a little bit short it didn't
get completely full right so first of
all let's just get a sense of how many
marbles we have well we had 300 that we
originally filled and then we had these
that we couldn't fill a can with so we
dumped them into some 10 cans so this
was this was 110 this was another 10 and
this was another 10 and this was another
10 and this was something less than 10
so we have 300 here right 3 times 100 we
have 4 ten cans what's 4 times 10 well
that's 40 right let me do that that's 40
what was this this was 300 right 3 times
100 cans and then we have something a
little bit extra this 40 doesn't count
this because we don't want to count cans
that aren't full because we don't know
exactly how many marbles aren't that so
what I do is I say well I don't have
anything small in the 10k and I'm just
going to let those marbles sit out in
the open so I pour those marbles out and
I count those separately because I have
time to count less than 10 marbles and I
have exactly 1 2 3 4 5 6 7 8 9 marbles
there and that's just basic counting I
have 9 marbles so my question to you is
how many total marbles do I have well I
have 300 cans full of marbles which
represents 300 marbles I have 4 10 cans
of marbles that represent 40 marbles
right 4 times 10 and then I couldn't
fill up that last 10 can so I dump them
all out and I counted exactly 9 mob
marbles so I have 300 plus 40 plus 9
let me write that down so 300 well I
already wrote them down but I could
write them down a different way I could
write in - 300 plus what did I what
color did I use I used purple 300 plus
40 plus 9 and I'll do the plus in a
neutral color plus 9 so how many marbles
do I have 1 this is where what you might
you probably already exposed to this on
some level well there's a simple way of
writing 300 plus 40 plus 9 we use what
we call you know number places we could
say well this is equal to let me the
number 349 and the way we know that this
is 349 is because we know that this what
we call place and the place we if you
kind of say that well you know this the
9 is the ones place the 9 tells us
exactly you know after F we filled our
hundreds buckets or our cans our 10s
cans how many did we have left over
that's this place it's the 1 all the way
to the right and before we learn about
decimals but in this situation is 2 1
all the way to the right this is the
ones let me write that this is the ones
place and essentially tells us how many
individual marbles we have the second
one if we go to the left this is called
a tens place and it tells E is
essentially telling us how many 10 cans
we have or how many cans of 10 and then
this the third one to the left
that's the hundreds place hundreds and
all it's telling us is it's essentially
just counting the hundred the hunt the
number of hundred cans we have so a very
easy way you know and the whole reason
why I did this in the beginning I take
my my sack of marbles I fill up three of
the hundred cans then I had some
leftover that I filled up four of the
ten cans and then I had nine left over
before filling up another can so I
immediately know that I have 300 cans
for ten cans and nine single marbles
left over I immediately know I have 349
marbles hopefully I haven't confused you
and I have inspired you to collect
marbles I will see you in the next video
where I'll do more more problems
involving our our marble cans and place
notation see you soon