Fractions as a measure
Fractions as units of measure strongly connect with the concepts and processes of linear measurement.
Scales are used to make linear measurements. When we measure an interval using a ruler, the unit of measure might be centimetres. Each centimetre represents a length that is one-hundredth of a whole metre. The measurement from the start of the interval to its endpoint tells us how many units the endpoint is from zero. If we want a more accurate measurement we could subdivide the units (centimetres) into smaller equal parts (millimetres).
Instead of a ruler, think of a number line. The distance between 0 and 1 can be divided into equal lengths. For example, the distance can be divided into 5 parts to create a unit of measure called one-fifth. Marking a point on the number line and labelling it as \(\frac 1 5\) means the point is a distance of one unit from 0. The unit \(\frac{1}{5}\) can be divided into smaller parts. For example: dividing \(\frac{1}{5}\) into two equal parts creates the new unit of \(\frac{1}{10}\).
For more information, read the article Measurement Matters: Fraction Number Lines and Length Concepts are Related on the AAMT website.
Using the measure model
The 'fraction as a measure' idea is best demonstrated using a linear model. The measure model supports the understanding that a fraction is a number, with a position on a number line.
