Let’s continue to plot positive and negative numbers on the number line.
We're going to extend the number line by simulating using a compass.
What do we mean by extending the number line?
We are talking about the numbers to the left of 0.
The numbers we've been talking about in previous lessons.
As you move to the left of 0 on a horizontal number line, the value of each number decreases.
The distance between the 0 and the first integer on the right is 1 unit.
This means that the distance between the 0 and the first integer on the right
and on the left of 0 should be the same.
So then, how can we use the compass to create the first value to the left of 0 and confirm our thinking?
We're going to use zero as a center point and construct a circle like this, that passes through the first value to the right of 0.
The circle will cross the left side of the
number line and creates the first value to the left of 0.
Since the distance from the center of the
circle to any point on the circle is equivalent,
1 is now exactly the same distance from zero,
as the first unit to the left.
We can use the compass as a tool to confirm the two values are equidistant from the center of the circle.
If the first number to the right of 0 is 1,
how could you describe the first number to the left of 0? Pause the video now and take some time to think.
Did you get it right?
You could've said the opposite of 1, negative 1, or -1.
If we were to use the compass to place the remaining tick marks on the number line
it would look something like this:
The missing numbers to the left of 0 are the
opposites of the numbers to the right.
The set of whole numbers and their opposites,
including zero, are called integers.
Zero is its own opposite.
Two numbers that are the same distance from zero on the number line are called opposites.
Look at the number line, what are some examples
of opposites that are represented?
You could've said that 1 and -1 are opposites.
2 and -2; 3 and -3 are opposites; and 4 and -4 are opposites.
Determine how far away the number 2 is from 0.
If start at 0 we could say that it is 1, 2 units away.
Then it says, choose a positive number
and a negative number that is each farther away from zero than the number -2.
How far away is negative 2 from zero?
Let's look. One, two units away.
Negative 2 is also 2 units away from zero.
So what is a positive number and a negative number that is each farther away from zero?
You could've said 3 and -3. You could've also said 4 and -4.
Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.
For example, 4 is the opposite of -4, and -4 is the opposite of 4.
They are both the same distance from 0.
1, 2, 3, 4 units.
1, 2, 3, 4 units
But one is negative, and the other is positive.
In this lesson, we wanted to be able to represent negative numbers on a number line.
We wanted to be able to determine or approximate the value of any point on a number line.
And we wanted to understand what it means for numbers to be opposites.
