Fraction models offer students the opportunity to see the concept of fractions at work, a concrete or tangible tool that visually represents a fraction and illustrates fraction concepts such as combining or separating fractional units and fraction comparisons (larger or smaller).
Area fraction models, also called region models, are photographic guides to fractions as ratios or comparisons of parts to a whole. Students begin by creating a geometrical shape on the area model. This shape represents the whole unit and is the denominator. Then, using the appropriate dividers, students create equal slices, or parts of the shape. These parts become the numerators. Circular fraction templates are the most common, and teachers play games such as Take My Order and Serve Up Fractions, where students divide paper plate templates into equal sections designated for pizza toppings or food portions. Other types of area models are paper strips folded equally to represent fractional portions of the strip, pattern blocks and geoboards.
Linear models, also called measurement models, demonstrate the fractions between numbers. Most commonly, teachers use rulers, fraction bars and number lines to explain fractions as sections of a whole number. Linear models such as fraction bars use one colored strip of segmented paper and a transparent sheet with a specific amount of squares colored in to represent fractional amounts. Students can also use fraction bars to create number lines to understand the use and location of fractional use in math.
Set models describe fractional form and function using sets of colored blocks, cubes, chips and foam shapes. With these models, teachers give students two sets of colored blocks or shapes. They then set up a practical situation in which fractions determine amounts and comparisons. For example, teachers may tell students, "You have a bag of 10 marbles. Three-tenths of those marbles are black." Students create a set of one-colored marbles, using the chips or shapes, and then swap out three of those to the chips of the other color to demonstrate their knowledge of the fractional concept.