Integers on the Number Line 2
Task
Below is a number line with 0 and 1 labeled:
 Find and label the numbers $2$ and $4$ on the number line. Explain.
 Find and label the numbers $(2)$ and $(4)$ on the number line. Explain
 Find and label the number $0$ on the number line. Explain.
IM Commentary
The goal of this task is to study, with a number line, why it makes sense for a whole number $a$ that Â $(a) = a$. The negative sign preserves the distance from 0 but switches the direction from 0. There are only two directions to go on the number line: left and right. Â Therefore, if we switch directions twice this will bring us back to our original direction from 0. Â Since the distance from 0 does not change, this means that taking the opposite of a negative number will produce a positive number with equal distance from 0. Â This reasoning will be foundational for future 7th grade work where students must reason about the opposite of quantities such as (2 + 8) and (2 + 8). Â
This task complements https://www.illustrativemathematics.org/illustrations/283 which investigates plotting negative integers on the number line.Â
Solution

The numbers 2 and 4 are both negative and so they are both located to the left of 0. To place 2 on the number line, we need to move two units to the left of 0 and for 4 we move four units to the left of 0. The unit has been marked on the number line (in the positive direction) so we can count 2 and 4 equal tick marks to place 2 and 4 as shown below:
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For (2) we are looking for the negative or opposite of 2. Since 2 is two units to the left of 0 this means that (2) will be two units to the right of 0. Similarly (4) is 4 units to the right of 0. These are plotted on the number line below:
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Notice that (2) = 2 and (4) = 4. The first negative sign switches us from the right of 0 to the left of 0 and the second negative sign puts us back where we started.

Since 0 is neither to the right nor to the left of 0, taking the opposite of 0 will give 0, that is 0=0. For a positive number, such as 2, the opposite or 2 is a negative number. For a negative number such as 4, the opposite or (4) is positive. The number 0 is neither positive nor negative so we must have 0=0.
Integers on the Number Line 2
Below is a number line with 0 and 1 labeled:
 Find and label the numbers $2$ and $4$ on the number line. Explain.
 Find and label the numbers $(2)$ and $(4)$ on the number line. Explain
 Find and label the number $0$ on the number line. Explain.