Singapore Math Grade 3a; Unit 1 (part 7) Video Lecture - Lesson for Grade

let's do a couple more problems
involving place value and number order
so let's say I were to give you the
digits the digits I'm giving you are 0 4
& 5 and what I want you to do is first
of all figure out all of the three-digit
numbers that can be produced with 0 4 &
5 and then I want you to tell me which
of those are the are the smallest and
which of those are the largest and one
thing to keep in mind is you can't have
0 as the first digit right because if
it's zeros of the first digit you really
don't have a three-digit number for
example the number 0 4 5 this really
isn't a three-digit number this is just
45 which is a two-digit number so that
one is not allowed so with that said
maybe you want to pause it and try to
figure out all of the ways you can
construct a three-digit number that
doesn't start with 0 with the digits 0 4
& 5 and you should do that right now
well I'm assuming that you have unpause
so let's let's see all of the numbers
that you can do and actually we could do
both parts of both parts of this problem
simultaneously how can we get a really
large number well the way we get the
largest number is by putting our largest
digit in the largest place value so
notice this is a three-digit number
we'll put it in the hundreds place so
the the large the way we construct the
largest possible number we put the
largest number in the hundreds place so
we say 500 let's put the second largest
number in the tens place 40 and then
there's put and then we have to use the
zero so we'll put that there so this is
going to be the largest and you'll see
when we list the other ones but it I
hope it makes sense why because this you
bring the largest number of the hundreds
and the second largest number in the
tens let's figure out all of the other
combinations that we can get of these
three numbers so it could be five
hundred and four right just switching
the four and the zero zero and the four
we could get or we could have switched
the four and the five here so we could
get 450 right or we could switch the
five and the zero here and you get 400
and five and that's all of them I mean
there were these these I guess we could
call them permutations and you haven't
learned that he had someone good too
into it but the other two would have
been this but these don't count because
they start with a zero so you can't
count this so we already figured out
that this is the largest and once again
we know 540 is largest larger than 504
because 40 is larger than 4 and as you
know the logic we used when we
originally saw this prompt so that's the
largest and what's the smallest well I
just happened to put them in in order
from largest to smallest this is the
smallest and why is that we put the
smallest possible digit in the hundreds
place and we couldn't put a zero by it
by the rule and then after we put that
there we put the smallest possible digit
that we could put in the tens place and
that was zero because that was allowed
and so we've got four hundred and five
let's do another similar problem let's
say I have the digit zero seven to eight
and I'm asking you what is the largest
four digit number that I can construct
out of these four digits and once again
the rule is that zero can't be the first
digit although that wouldn't help you
much anyway so what's the largest number
I can build here so it's gonna be a four
digit number so this is going to be you
know you're gonna have thousands place
hundreds place tens place and ones place
right so just like we talked about in
that that that probably did a few
seconds ago how do we construct the
largest number well what place value
matters the most the thousands place
matters the most right if we're going
back to counting marbles you care about
how many of the buckets of thousands you
have that those that's where most of the
marbles take place so the thousands
place matters a lot the thousands place
because whatever digit here you're
essentially saying that times a thousand
so you wanna put the largest number
there so the largest number out of these
that's eight
to cross that out we use that and then
the hundreds place we ready use the
eight you want to put the highest number
that you could fit there and the
hundreds because whatever numbers here's
going to be multiplied by a hundred so
out of these was the next large number
it's seven and then we use the same
logic for the tens place what's the next
largest number there was gonna be the
two and then we're left with the zero
and if that wasn't completely obvious to
you I I encourage you to try out all of
the different ways to rearrange these
numbers and you'll see that when you put
the largest number in the thousands
place because you're saying that's eight
thousand right let's say if we'd switch
these then you would only had seven
thousand eight hundred and out what that
would have been much smaller than eight
thousand seven hundred let's do a
similar exercise but now let's try to
figure out the smallest digit we can
form so let's say the numbers are three
seven four and nine so what's the
smallest four digit number that I can
form out of these three numbers close do
the places again this thousands hundreds
tens ones so if we want to create create
the smallest there's two ways of
thinking about it we could put the
largest number in the ones place and
then the second largest in the tens and
so forth or we could say this with the
smallest number in the thousands we want
the smallest number of thousands so we
can either do three thousand seven
thousand four thousand or nine thousand
well we want a small number so let's do
three thousand right that's clearly the
smallest of our choices so then we use
the three and now we have to pick
between seven hundred 400 or 900 so
what's the smallest well seven hundred
four hundred nine hundred well sure 400
is we use it there and then we want we
have to pick between 70 or 90 but we
don't we want to use 70 cuz we're
looking for a small number and then of
course we have the nine there and once
again I encourage you to try try to try
to get a smaller number than what we
just did I hope that makes sense that
when you want the smallest possible
number you want the smallest number in
front of the
thousands and once you use that up and
you want the smallest number on the
hundreds let's see if we can see some
patterns between numbers so let's say I
had the number I'm not sure we're just
gonna write down the number I'm not
gonna read it to you cuz that might give
you a let's have that number six three
four - that's the digit and six four
four - so I have two questions for you
which number is larger and how much
larger is that number
well first we could just read them out
this is six thousand three hundred forty
two this is six thousand four hundred
forty two so we immediately see where
these two numbers different 6,300 6,400
the 42 s are the same so they're
different in the hundreds place right if
we were to do if we were to expand this
out this is 6000 + 300 + 40 + to write
this number on the right is 6000 plus
let me make sure I do the colors right
400 + 40 + 2 and so we see the only
difference between the numbers takes
place in the hundreds place here we have
6000 equal to 6000 40 is equal to 42 is
equal to 2 here we have 300 versus 400
right so this number is clearly the
larger of the two numbers and and how
much larger is it well we just have to
compare the hundreds because everything
else is equal four hundred versus 300
how much larger is 400 and 300 what's
100 larger right you have to add 100 so
you could write 6 3 4 2 + 100 is equal
to 6
4
for two another way you could have
looked at it without expanding it you
could have said well I have 300 s here I
have four hundreds here just looking at
at place value so I need to get one more
hundred to get to this value so you can
kind of do that mental arithmetic you
add one hundred here you would add a one
to this digit so you'd get six four four
two or six thousand four hundred and
forty two let's do one more like that
let's say I had the numbers I could read
them out six thousand four hundred and
forty two just like we had in the
previous one and let's say we have the
number six thousand six thousand five
hundred and forty two and I won't expand
well this year let's expand them out I
don't know I want to slightly do it in
all of the different colors but we could
say this is six thousand plus 400 right
400 plus 40 plus two this is six
thousand plus 500 plus 40 plus two and
what's the difference here well I don't
even have to expand it out to show you
the difference you have a four in the
hundredths place here we have a five in
the hundreds place here so this digit in
the hundreds place is one more than this
digit in the hundreds place so
essentially to go from this entire
number to that entire number we have to
increment the hundreds digit by one or
we need one extra hundred so once again
a number on the right is larger and it's
larger by a hundred you could also see
that here and we expand it to go from
400 to 500 you add a hundred so let's
see if we can use some of these insights
and to see if we can do some quick
mental math so if I were to ask you what
number what number
is 100 more then 6440 to well you could
do this in your head how do you think
about it well if I'm doing 100 more than
that means in the hundreds place I'm
going to add one right because every
incremental digit in the hundreds place
means 100 so essentially to add a
hundred to this I go to the hundreds
place and add one so 6440 - we could do
that in our head plus 100 is equal to
six thousand five hundred and forty -
let's see if we can do that same mental
math to see what what six what what
number is a hundred more than six
thousand five hundred and forty-two so
what number is I'm running out of space
is a hundred more hits well a little
Audrey what number is a hundred more
then six thousand five hundred and
forty-two so once again we have to if we
want to add a hundred to something we
increment to the hundreds digit by 1 so
this is a hunter's digit so it's six
thousand six hundred and forty to write
some really if we wanted to know what
number is a thousand more than six
thousand five hundred forty-two we would
just increment the thousands digit right
if we wanted to add a thousand we would
incur go to the thousands place and add
one we get seven thousand five hundred
forty-two if someone asks you what
number is 10 less than six thousand five
hundred and forty-two well then you go
to the tens place and you would subtract
one from the digit so if you wanted to
subtract ten - ten it would be six
thousand five hundred and we decreased
this digit by 132 anyway I don't want to
confuse you and I think that's about it
for this video I'll see you in the next
one see you soon