Usefulness of the number line

A number line is a useful model for learning about decimal numbers and is probably the only model that is used after students leave school. In practical settings, it is used in the form of a measuring tape or a scale such as on a thermometer. In graphing, number lines are used for axes. In higher mathematics, the "real line" is an important object of study. Hence it needs to be thoroughly understood.

Number lines are good to:

	show the size and order of numbers
	show all types of numbers together (positive, negative, fractions, decimals, whole numbers)
	illustrate the density of the real numbers
	model addition and subtraction of numbers and multiplication as repeated addition.

A number on a number line is first represented by the length of a line segment, that is, by the distance from the origin ZERO to the point. Then the endpoint of the line segment is used to represent the number, instead of the length. Using number lines to illustrate operations (+, -, x by whole number) requires students to be able to represent numbers by both points and distances.

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A case for vertical number lines

Number lines are more naturally drawn vertically so that "more" is "up" instead of "to the right". Students can then use their intuition and avoid the extra cognitive load associated with remembering whether right or left is "more". Whilst printing considerations may dictate horizontal number lines in books, teachers can draw vertical number lines in class. This will also assist students learning about negative numbers. Many common scales are read vertically, such as thermometers. Furthermore, Cartesian coordinate geometry requires the use of both vertical and horizontal number lines and hence familiarity with both is an advantage.

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Subdividing the number line using DecimalLine

Number lines drawn by students can be difficult to segment even into tenths, while hundredths and thousandths are usually out of the question! One useful solution to the problem of resolution is to use DecimalLine, a software tool that automatically re-scales the number line to the resolution desired.

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