Wow I bet you didn't know mr. Boyd had
those moves in you did you okay so third
graders today we are going to be working
with open number lines you're gonna be
doing adding subtracting multiplying and
dividing all using an open number line
now the point of using an open number
line is to build number sense help you
be able to think about numbers and make
sense of numbers so if you're wondering
why are we adding this weird way or
subtracting and multiplying dividing
this different way that's why it helps
you think about numbers and be able to
think about numbers and use the numbers
will help you eventually be able to do
these things mentally in your head all
right but for today I don't want you to
do in your head I want you to work with
me yeah grab a pencil and paper or
whiteboard if you have one that'd be
awesome if you have one work along with
me as we make open number lines to add
subtract multiply and divide all right
let's have fun
so today we are gonna be practicing
adding subtracting multiplying and
dividing all using an open number line
now the purpose of the open number line
is to help us build that number sense
how they manipulate and use numbers to
make things simpler and to help you
eventually be able to do this mentally
in your head so if you're wondering why
are we practicing doing it this weird
way this different way well that's why
it's going to help you be able to think
better okay so we're going to start off
practicing our open number line by
adding 255 plus 78 so working along with
me go ahead and make your open number
line and I like to start off my open
number line using the larger number
because that means I have less to add on
this time I'm going to start off with
255 which means I'm going to add on some
of the eight on the number line so the
number line open number line is all
about adding friendly numbers so instead
of adding 78 all at once I'm gonna break
it up into chunks and do friendly
numbers okay and when I see I have five
ones here nothing goes friendlier with a
five then another five so I am going to
pull five out of eight which will leave
only three left because 5 plus 3
equals eight so pulling that five out
that's what I'm going to start with
adding five so 255 plus 5 that equals
260 so I have a 10 there because 260 is
a new 10 which makes it much friendlier
to work with so 260 what is it going to
take to get that to 300 the next hundred
so 60 that's what I have in the tens if
I add 40 to that that should make a new
hundred so 200
60 plus 40 that equals 300 okay so so
far we have added five once which only
left three ones left and then I just
took out four tens so 70 minus 40 or
seven tens minus four tens
that leaves three tenths 70 minus 40 is
30 so that means instead of 78 now all I
have left is 33 to add so 300 plus 33
that should give you 333 that means my
final total for 255 plus 78 equals 333
all right now let's take a look at
subtracting on an open number line so
instead of adding now we're going to
subtract 255 minus 78 so working with me
make your number line and subtracting is
a little bit different on the number
line we can go ahead and put both 78 and
255 on the number line when you're
subtracting you're trying to find the
difference that means the space in
between the two numbers so we can do
this on the open number line by adding
on 278 until we get to our total of 255
so let's try it
78 let's take this up to the next ten to
the next 10 so I have 78 I'm two away
from the next 10 so 78 plus 2 that
equals 80 so now that now that I'm at 80
have a 10 it's much easier now
take that 10 to the next hundred so ad
and then I have 90 and then 100 so
that's two more tens some means 80 plus
20 now so 80 plus 20 that puts you at
100 so now I want I'm trying to get up
to 255 so to get from 100 to 200 I need
to add 100 100 plus 100 equals 200 so
I'm not 200 now I'm trying to get to 255
well that's easy to get from zeros there
255 there I need to add 55 so 200 plus
55 that equals 255 now to find our
answers we've got to put our jumps
together so putting all of these jumps
together now to get our different okay
so let's start by putting 100 together
with 55 100 plus 55 that equals 155 so
the zeros and the 1 to the tenths place
on it's 55 comes now there's on 800 so I
have 155 and then 20 plus 2 equals 22
so now
putting 155 together with 22 so 5 1 s
plus 2 ones equals 7 5 tens plus 2 tens
equals 7 and then I'm down I don't have
anything in the hundreds place so that
one comes straight down I have a hundred
and seventy seven so that means 255
minus 78 equals my difference is 177 ok
so we looked at adding we looked at
subtracting now let's take a look at
multiplying on the open number line okay
so we're gonna multiply 9 times 4 using
an open number line this is just about
representing more than anything else so
if you're with me
go ahead working along with me make your
number line so when you think
multiplying on a number line 9 times 4
it's like 9 groups of 4 or 9 jumps of 4
so this time we're always going we're
going to start at 0 so which take 9
jumps of 4 or 4 jumps of 9 I think it's
going to be easier to count by horse
than 9 even though it's going to take
more jumps so cutting by fours take 9
jumps of 4 so 1 2 3 4 5 6 7 8 9 jumps
and each of these jumps we're going to
be adding 4
adding four in each of those jumps so
it's real simple I start at zero 0 plus
4 is 4 then I have 4 plus 4 is 8 okay
keep that pattern going until you finish
all 9 jumps to see what your final
product is going to be all right so
after we do all 9 jumps count skip
counting by 4 we finally land on 36 so
that means 9 times 4 equals my product
is 36 excellent work
okay so that's multiplying on the number
line pretty simple right let's take a
look at dividing now on the open number
line okay
so dividing on the number line let's
divide 48 divided by 4 so I'm going to
again working with me make your number
line here already so this works a lot
like multiplication only this time we
already know our total so I know I'm
trying to get to 48 that's my total and
I'm dividing by 4 that means I'm going
to be counting by 4 so starting at 0
count by 4 and see how many jumps it's
going to take to get to 48 so continue
skip County by 4 until you get to 48 and
see how many jumps it should take
right so I finished skip counting by
fours and I got all the way to 48 and I
stopped there because that's my total
it's what I'm trying to get to so now
let's see how many jumps that took we
have 1 2 3 4 5 6 7 8 9 10 11 12 jumps
that means my quotient my answer to 48
divided by 4 equals 12
a little bit that's all folks
