We will start by drawing a number line that shows all integers between -5 and 5. There are eleven integers between (and including) -5 and 5.
b
Distance is positive. For any number, - n and n are the same distance away from 0.
This is true for all the integers. Let's summarize this in a table.
Integer
Distance from Zero
-5
5
-4
4
-3
3
-2
2
-1
1
0
0
1
1
2
2
3
3
4
4
5
5
c
Let's put the points from the table in Part B on a coordinate plane. Let's also draw a line indicating the pattern.
d
Let's now make a conjecture about what we have shown about an integer and its distance from zero. The pattern is different for positive and negative integers.
For positive numbers, the distance of the number from zero is the same as the number itself.
For negative numbers, the negative sign disappears when we find the distance. The reason for this is that distance is never negative.
