Singapore Math Grade 3a Unit 2 (part 1) Video Lecture - Lesson for Grade

we will now continue on with our with
our instruction or our lectures on on
third grade Singapore Math and what I
really like about this this whole
Singapore Math way of teaching is that
they start with fairly simple concepts
but they really make sure that you have
a deep deep deep understanding of what
the concepts what the concept is and all
the different ways to think about it so
for example today I'm going to start
talking about addition and subtraction
you might say well I already know how to
add and subtract and you probably do and
maybe you'll find this easy but I think
you'll find that if as we go through all
of the lectures you might discover some
new insights or some new ways of looking
at something that you thought was really
really really easy so let's say that I
wanted to know well well first of all
you know about addition of subtraction
right if I say I want to add 1 & 2 you
would say well that's just 1 plus 2 that
equals 3 and I'm going to reduce you to
what could be a new word or actually two
new words and that's sum and difference
so the sum is essentially when you say
to find the sum of two numbers you're
essentially adding them and when you
save the difference you're essentially
saying how different are the two numbers
and I'll give you a bunch of examples
let me so let's say I have in the
Singapore math book I'm actually on page
18 and I'm just using their problems I'm
doing a few adaptations this is the this
is the this is the 3 a primary
mathematics book but I'll do some
adaptations but for the most part I'm
just doing their problems and with a
little bit of my commentary so let's say
I had 4 they draw flowers but let's say
I just have 4 circles and I have 7
circles right below it 1 2 3 4 5 6 7 and
our question is what is the sum what is
the sum of 4 and 7 well I just said
taking the sum of two numbers is just
like adding the two numbers so taking
the sum of
four and seven is the same thing as
taking the sum of seven and four and of
course if we're just going to add the
two numbers we just have to know what
four plus seven is and you should
hopefully know that offhand if you don't
you can count these circles up here one
two three four five six seven eight nine
ten eleven all right the sum is
essentially how much do we have when we
combine the two numbers or the sum now
what if I were to ask you what is the
difference between between and that's
kind of an important and important word
between four and seven so as I said a
difference tells you what when someone's
asking what's the difference they want
to know how different are the two
numbers so how different are four this
is four up here this is four up here and
this is seven how different are four and
seven well there's a there's four would
be seven if it had three more right if
we if we drew three if four was three
larger it would be the same thing as
seven so when someone is is saying what
is the difference between four and seven
they're literally asking you how much do
you have to increase the the smaller
number to get the bigger number or how
much you could also say well to get from
seven to four I have to take three out
of seven so but either way you look at
it the difference between the two is
three and how do you calculate it well
you subtract the smaller number from the
larger number so you say seven minus
four is equal to three and that three is
the difference between the two you could
view it as how much do you have to
increase the smaller number to get the
bigger number or how much do you have to
decrease the bigger number to get the
smaller number or just you know how big
is the I don't wanna use the same word
but you know how how different are they
anyway
I don't want to beat a dead horse as
they say so let me draw some some cubes
Singapore mat style
so they draw eight cubes let's see I'm
gonna try to approximate I'll do it in a
slightly different color that you only
use two colors throughout the whole book
let me see well that's not what I wanted
to do but good enough let's see they
want to do eight so let me drive it
divide it in two first let me see that's
about the middle and then if I divide it
in two again here and here that'll be
four they have to divide each of these
and do to get eight that's because I
wanted them to be relatively so that's
eight and then they have five and so
five I'll use a different color for five
let's see but I wanted to eat match up
so that's one two three four five and
well let me split it up there you get
one two three and so they want to they
they tell us well you know eight plus
five that's I'm using them eight plus
five is equal to and they say blank well
we're just adding the two numbers you
might not know it already but you should
visualize it well what's eight plus five
it's like if you took these and you put
them at this end right here how many how
would be the total length of the longer
bar or what is the combined length of
the two bars right one two three four
five six seven eight nine ten eleven
twelve thirteen right and you probably
find that really really really easy but
the reason why they're doing that is so
that you realize how the sum is
different from the difference so for
example you know we could have rewritten
this statement as the sum of eight and
five is thirteen what my phone's ringing
I'm not gonna answer it I think I think
that's someone getting me to either
donate money or buy dish networks or or
whatever so now let's do but we you know
this is the sum that's the easy part now
what what would you say if I asked you
what is the difference what is
the difference what is the difference
between eight and thirteen and I could
have sent it either way and that's where
writing it as the difference as opposed
to subtracting is different if I could
have said what is the difference between
thirteen and eight either way it doesn't
matter we just want to know how far oh
no sorry that's not between eight and
thirteen now one another difference
really although that's an interesting
question to answer as well but what is
the difference between eight and five
eight and five right what is the
difference between eight and five how so
how far apart are they essentially well
if we look here if we have these this
blue five if we added three more cubes
we would get eight or if we took these
three cubes off of the eight we would
have gotten five so either way you would
have to change one of the numbers by
three to get the other one all right so
the difference between eight and five is
the same thing as 8 minus 5 which is
equal to 3 hopefully you're getting the
hang of it and actually even more
important than just being able to the
problem because I think you find this
type of problem to be extremely easier
this type of problem to be extremely
easy I want you to understand kind of on
a deeper level what it's really saying
it's saying how far apart of these
numbers that it doesn't want you to say
oh boy I've already memorized what eight
and five are it with the what you know
eight minus five is it wants you to
really we really want you to think about
what it's just saying how how different
are the two numbers you literally can
just read the sentence literally that's
all it means
so let's say that I had two bars I'm not
gonna break them up any more let's say
that the length of this bar is I don't
know it's 90 maybe it's 90 millimeters
maybe it's 90 miles who knows the length
of that bar is 90 and let's say that I
have another bar right here
we turned my phone ring her back on my I
had it off the other day when I was
recording these videos and my wife
called and she couldn't get me and and
she questioned whether I cared about her
anymore so it's very important when
loved ones call that you pick up the
phone anyway back to back to them that
problem what was that doing okay so I
had another bar right here and let's say
the length of that bar let's say the
length of this bar is 54 so I will ask
you the same questions that we've been
asking this entire video what is the sum
of 90 and 54 and I'm also going to ask
you what is what is the difference the
hardest part of these problems is
probably reading my handwriting what is
the difference between 90 and 54 well
once again the sum they're saying well
what happens when you combine these two
blocks if I put this block here and I
couldn't do that let me see if I put
that block here you would get a it would
add on over here roughly about that long
and so you want the sum you want the
length of the entire thing and hopefully
you know how to add two numbers but if
you don't we can work it out it's 54
plus 90 so let's do 90 plus 54 0 plus 4
is 4 5 plus 9 is 14 144 which also is 12
times 12 but in anyway I'm grading
off-topic anyway the sum of 90 and 54 is
90 plus 54 which is 144 and then what is
the difference between 90 and 54 now
this is I think where it gets a little
bit more conceptually easy interesting
when you think about difference you want
to know how far a part of the two
numbers or what would I have to add to
54 to get 90 or what would I have to
take to subtract from 90 to get to 54
either of those is the difference and so
we could just say 90 minus 54 right the
way to calculate the difference is to
subtract the smaller from the larger
number we could say 90 minus 54 and
we're going to do this might be a little
bit of a review from second grade but we
could you should hope actually it's not
a bad idea to memorize it and I'll give
you a way to think about it what's the
difference between 60 and 50 for the
difference 54 is 6 away from 60 right
and what's the different I and 60 all
right the difference let me let me say
it this way I'm running out of space but
90 minus 60 is equal to 30 right and 60
minus 54 is equal to 6 so 90 minus 54 is
actually 36 that's how I do it in my
head act it's a little bit off the
Singapore math curriculum but maybe
maybe you'll find something like that
interesting but the other way to do it
and we'll go into more detail in and in
terms of how does borrowing or
regrouping work but you could say 90
minus 54 and this is just classic
borrowing we could say well let me
borrow a 10 let me borrow one from the
tens place and that becomes 10 in the
ones place right just going back to our
place value so we took it you know we
essentially cashed in a $10 chip and got
10 $1.00 chips and then we take that 10
minus the 4 is 6 and then 8 minus 5 is
36 so either way the difference between
90 and 54 is 36 and now this is
interesting what is the difference what
is different what is the difference
between
90 and 36 so what would you have to add
to 36 to get 90 or what would you have
to subtract from 90 to get 36 well let
me give you a hint we know the
difference between 90 and 54 is 36 if I
drew a block here of exactly length 36
it would look something like this right
that is of not in my drawing but in the
idea that is of length 36 so there's a
couple of ways we could think about it
the difference between 54 and 90 is 36
that's how that's how much one would
have to grow or one would have to shrink
or the difference between 1954 is 36 the
sum of 54 and 36 is 90 right and also
the difference between 90 and 36 is 54
and why is that because imagine if this
wasn't here and we just had that
question was what is the difference
between 90 and 36 well we could say well
we could increase 36 by 54 to the left
to get 90 or we could decrease 90 by 54
to the right to get 36
well anyway hopefully you found this
vaguely insightful and I did not either
bore or confuse you and I will see you
in the next video see you soon