Numbers can represent a wide range of values and,
for this video, we’re going to use a value
that can be both counted and measured;
steps up the screen.
For the sake of simplicity in this video, we’ll only consider whole numbers of steps
but the same principles apply with distances
that are not a whole number of steps.
Let’s start by taking some steps up the screen,
even more than one step at a time.
We’ll mark the steps next to each other
so we can look back at our path.
To track our progress, let’s draw a line next to our path
and mark it with the number of steps we
  are *up* from our starting point.
As a line with numbers next to it,
 let’s call it a number line.
This arrow here shows that there is no
upper limit to our number line.
We could just keep walking forwards
forever and adding more steps.
We would just have to zoom out a little on
our number line to see these steps.
Our total distance up the screen is
now the sum of our steps
and we can show this with an equation.
By convention, number lines are
shown horizontally with negative to the left
and positive to the right but it is rotated
here to allow the equation to be shown with
steps in line with the arrows.
We can also take steps towards the bottom
of the screen and these subtract from our
total distance up so we’ll call them “minus
steps”. They are the same size as the forward
steps but in the opposite direction. Using
+ and - like this is called “directed numbers”
So what happens when we want to walk further
down the screen than our start position?
Well, we can do this by extending our path in the
opposite direction, still using the same starting
point with a zero mark to show that it is
zero steps from our starting point.
Now, as we step below our starting point,
we need to start using negative numbers
because we are “negative steps”
above our starting point.
As with the positive direction, we
can continue our negative direction
forever as well, always getting
further below our starting point.
Once you have your number line set up, you
can add and subtract as much as you like.
Addition steps move you up the
screen in the positive direction
and subtraction steps move you down
the screen in the negative direction.
Your final position is the answer to the equation
with all the addition and subtraction steps.
