We are going to talk about
the four basic operations today but we're going to start with addition and subtraction.
This should be a quick lesson. I know that
we already know how to add and
subtract
but I want to review the rules for adding and subtracting with negatives
because that's an area where
my students often get
hung up throughout the year so
this should be just a quick review to get us going. When we have and basic addition or
subtraction problem
it's usually set up something like this.
I think a lot of us have just basically
memorized the rules
here but I want to remind you that this
always comes back to the
number line so I've put a number line here for us to use. The first number in an equation like this one
tells us where to begin on the number line. So
the 1 is telling us that we're going to start at 1 on the number line.
Then we have the operator. Either the plus sign or the minus sign.
That is telling us which direction to move. A plus sign will move to the right
on the number line. If it's a minus sign we'll move to the left.
So in this case we're going to move to the right. And the next number tells us how far to move.
So we're going to move to the right
three spaces:
one... two... three spaces
and we land on the 4. So that's why the answer to this problem
is 4. Hopefully this basic setup can help
you do more complex problems
with negatives. So here we have -3 plus 5. Most of my students know right away this is
either going to be a 2, a -2, an 8 or a -8
but they get mixed up on which one it
should be.
So the number line can help us here. We start on negative
3; we move five spaces to the right.
So were eliminating
negative 8 as a possibility. It can't be -8 because we would have to move left to get to -8.
So now we're going to move five spaces. We've already passed
-2 and after we move five spaces
it should be clear that we'll land on the 2. We're not going to get as far as the positive 8 so our answer to
this problem
is two.
Try one on your own... Since this has
a minus sign, we're gonna start on the two
and move to the left this time. Move to the left three spaces,
so people get mixed up on whether this
answer would be one or negative
one but if you think about moving on the number line it has to be
-1. And here's one
more for you.
Start on the negative 2. Move two spaces to the left.
So we land on -4. Now here's a problem that seems to have a plus
and a minus. Students ask me all the time
"What is the difference between a minus and a negative sign?"
and that's kind of a tricky question to
answer.
Every time you have a problem
there's always an operator so if there's
only
one sign, then it's a minus. But if you already have an operator,
like this problem has an operator in the middle,
and then the minus sign, that sign
is really going with the number over here so that's a negative sign.
So here we would read this as "Four plus negative three".
When you have an operator
and a negative sign, the rule is change the
operation
- so change in this case from a
plus to a minus -
and take away the negative sign so
instead of "four plus negative three",
the plus changes to a minus and the negative goes away.
Four minus three. We know that's 1.
If we had this,
this would be read as "four minus negative three".
The first sign is the operator: that's the minus.
And the next is the sign of this number so that's the negative. We would change the
minus sign to a plus sign and take away the negative.
So imagine what it's going to look like.
Four plus three. And we know that's seven. Here's one for you to try.
The sign with the one, that's a negative sign.
So we would say "Negative one". That's not affected by this operator.
It comes before 1
Here we have two... we have a minus sign and a negative sign.
So those combine. This gets changed
to a plus and the negative sign goes away.
So we end up with "Negative one plus two"
and if we imagine the number line that's
starting on -1, we're going to use spaces
to the right
that gives us positive 1. We'll practice this some more tomorrow.
Good job!
