Representing fractions

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• Research and Supports
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Representing refers to the process of using symbolic, concrete and pictorial representations as well as words and relevant situations to explore concepts and communicate understanding. There are three general models that Watanabe (2002) illustrates for representations of fractions: linear (number lines), area (partitioned regions), and discrete (set models).

Note: Within the Ontario curriculum (2005), symbolic notation is introduced formally in grade 4. Prior to this, familiarity with fraction terminology such as halves, fourths, fifths supports student understanding.

Research Findings:
Existing literature and the findings of this fractions research project indicates that students should be exposed to number lines and rectangular area models in early grades. These representations support students in understanding the notion that a fraction is a number (for example 13 is a number) as well as enable students to create equal partitions using a variety of strategies. Students frequently make incorrect conclusions when comparing fractions that are close in value using a circle model (such as 410 and 13) as it is difficult to accurately partition a circle into ten equal-sized parts. Flexibility and purposefulness with representations enables students to make selections most appropriate to the context (such as a number line for distance).