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Number Lines



Number lines are two-dimensional representations of the relationships between numbers. Number lines are like a map of numbers. To understand more about number lines, and what number lines are good for keep reading.

Timelines: a Starting Point

Timelines are the most familiar form of lines with numbers, so let’s begin from there. Here is an example of a timeline.

Timelines show divisions of time that can be large or small. They often have equal divisions for a certain span of time. Depending on the timeline, the spacing might be by days, months, years, decades, centuries, or any other period of time. But whatever the division, it’s usually the same throughout the entire line. However, if this doesn’t suit the purpose, the divisions can be as large or as small as serves the need.

No matter what period of time is covered on timelines, the lowest numbers (the earliest years) are always toward the left and the higher numbers (the later years) are always towards the right. Also, timelines can be as long or as short as fits the need. They start and stop wherever you like.

Number  Lines and Time Lines

Number lines are like timelines that have equal divisions. They also have lower numbers towards the left and higher numbers towards the right. But they have some differences as well.

• Timelines can be horizontal or vertical; number lines are virtually always shown as horizontal.

• Number lines go on forever. Unlike timelines, number lines are infinite. This is symbolized by their being drawn with an arrow on each end like this:

• Number lines have a central mark that must always be there: 0 (zero).

To the right of the zero are the positive integers. They do not have to be marked as positive: they’re understood to be positive. To the left of the zero are the negative integers. They are each marked with a minus sign, like this:

To some people this may look strange and unfamiliar. If you are one of them, just imagine a weather thermometer: it is does not go on forever, it’s true, and it’s oriented vertically. But still, it has the positive and negative numbers and zero.

What Number Lines Are Good For

Because many people have difficulty with the concept of adding and subtracting a negative numbers or a mix of positive and negative numbers, number lines can be highly useful in helping them visualize the process. You can think about it like this:

  • If both numbers are positive  or zero and are being added, you can begin with either one and count to the right. For example: 1 + 2 =   Start at 1 and count 2 to the right, and you get 3.
  • If both numbers are negative and are being added, you can begin with either one and count to the left. For example: -1 + (-2) = Start at -1 and count 2 to the left, and you get -3.
  • If both numbers are positive and one is being subtracted from the other, start with the first one and count to the left. For example 1 -  2 =  Start at 1 and count 2 to the left, and you get -1.
  • If both numbers are negative and one is being subtracted from the other, start with the first one and count to the right. For example -2 - (-3) Start at -2 and count 3 to the right, and you get 1.