negative numbers negative numbers are
less than zero and they are smaller than
positive numbers
...than positive numbers: we can
easily put them on a number line so here
is our positive number line 0 1 2 3 4 5
6 smaller than zero because all of these
are bigger than 0 these are all our
positive numbers they get bigger and
bigger and bigger as we go this way
smaller than 0 are our negative numbers
so 1 less than 0 is negative 1 negative
2 and these get smaller and smaller and
smaller as we go that way
 the number line is a pretty useful way of looking
at negative numbers we go this way when
we add so if I had 2 plus 1 I'd go this
way
so when it's a positive number or a
positive increase we are going this way
when it's a decrease we move towards the
negative side so remembering the
direction of positive to the right on
the number line and negative to the left
is really useful and that's why we often
call positive and negative numbers
directed numbers... so this goes for
positive and negative numbers and the
positive or the negative is the
direction of the number positive
 and negative numbers are also
quite useful so this is still following
this sentence negative numbers are
useful for describing things like debt I
can talk about having negative $100
because I owe somebody $100 temperature
of course
the temperature easily drops down to
negative 8 degrees Celsius over night in
winter in Canberra that means 8 degrees
below zero and was losing something as
opposed to gaining something often
now when we do our simple sums with
negative numbers we're actually going to
keep it pretty focused on the number
line there are other ways of thinking
about negative numbers and I'll talk
about those as well but when we have to
do a sum like this negative 5 plus 2
what's happening on the number line is
that we're starting at negative 5 and
we're going up so plus gaining towards
the positive side the right we're going
up 1 2 and we get to negative 3 so this
is saying we start at negative 5 and we
gain 2 and we get to negative 3 which is
very clear on a number line if we have
negative 1 plus 4 we are starting at
negative 1 and going up 4 1 2 3 4 we get
to O we get to 3 so using the number
line with this is our starting point and
this is our direction and how many we go
in that direction is really a pretty
easy way of dealing with negative
numbers now to support you in your test
because you don't have calculators we'll
make sure you've got a number line
zero in the middle up to positive 20
down to negative 20 so we can do these
problems just by using the number line
start up 3 negative 7 so 3 minus 7 means
I'm going to go 7 in the negative
direction and that's 1 2 3 4 5 6 7 this
is negative 4 if you find that you're
often going kind of a bit off and
accidentally end up at negative 5 you'll
need to be a little more careful you can
also use a texta or not a permanent
marker not a ballpoint pen not pencil or
anything or market but a texta is fine
to do actually drawing on it 3 - 7 mins
7 this way 1 2 3 4 5 6 7 get your answer
and the reason we say texta is that with a tissue you can wipe that off
and be ready for your next question so
this number line is here to really help
you you can always try thinking through
the other ways of talking about adding
and subtracting with negative numbers
and here's your number line to double
check now here's one negative 2 minus 3
that means we start at negative 2 and we
go - so towards the negative another 3
negative 2 1 2 3 and we get to negative
5 so being very careful about using your
number line is a pretty good strategy
now other ways of thinking about adding
and subtracting some people are just
going to think of it as their opposites
3 take away 8 taking away 8 means we're
going in the opposite direction to the 3
take away 3 get down to 0 and then I've
got another 5 I can take that away and I
get down to negative 5
that's an okay way of thinking about it
negative two plus five move up by two to
get to zero and then there's another
three we're on three one way of thinking
about it is a tug-of-war team negative
and team positive so folks that's my
pink pen team negative and team positive
everyone on each team is exactly equal
so if we had two people on team negative
and two people on team positive nothing
zero
nobody would win the tug-of-war the
questions you ask yourself is how many
on each team and then which team wins by
how many
so...
this question here : remember
that the minus... the negative... goes with
the number after it plus five so you can
see that's a positive how many on each
team? two on team negative five on team
positive - so which team would win?
obviously team positive wins: by how many?
They had three people over: they win by
an extra three people ... now.. plus because
positive doesn't need a plus and an
answer let's tackle it for this one will
we know the answer how many on team
positive? three... remember invisible plus
how many on team negative? eight.  which team wins? team negative has far more
people... they win - and they had five extra
people compared to team positive so they
win so it's negative five 
Negative three plus two which team wins ? it's team...
negative by one player.  Negative three
minus four a negative or a -? still
counts as team negative team positive
didn't even show up
team negative wins by seven players so
it's another way of thinking about it up
to you which way you do it the number
line is there for the test if you feel
safest with that
