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FRACTION MODELS

We use models to represent and illustrate the mathematical idea of a fraction. When the term fraction model is used it refers to the instructional materials used in teaching fractions. The three most commonly used fraction models are:

1. The linear model

linear-model 

2. The area model

 area-model

3. The discrete model

 discrete-model

Of the three models used to illustrate the idea of a fraction, the area model is by far the most commonly used model. However, each of the three models has a number of preliminary understandings that need to be developed before students can effectively use the models. For example, to use the area model of fractions students must first know what area is, identify the area of the part, identify the area of the whole and be able to compare the two areas by direct or indirect measurement.

Comparing the areas of two pieces that form a whole starts with superposing one piece on the other, typically through folding, to directly compare the parts (see Show me one-half). This can lead to recognising that two congruent pieces forming a whole are each half of the area of the whole shape. However, comparing the areas of parts of a shape requires an understanding of area as covering.

When students are able to measure the areas of shapes using uniform informal units they have the background knowledge necessary to interpret an area fraction model.

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The Numeracy Continuum Introduction Video