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Teaching equal parts
The misconception is that only the number of parts determines a fraction, without regard for the equality of those parts. This can be avoided or remedied through explicit teaching and the design of learning activities.
Here are some teaching tips to help students avoid the 'number of parts only' misconception.
Avoid simplistic tasks using pre-divided shapes. Instead, engage students in practical tasks using a variety of models, where they must focus on trying to make parts that are the same size.
The challenge of practical tasks is increased when drawing or folding fractions with odd denominators, such as thirds or fifths.
When using the area model for fractions, ensure that students are aware of the attribute of area so they understand what is actually being divided into parts.
Using unusual, irregular or asymmetric shapes encourages students to think creatively and to evaluate the suitability of various shapes for representing particular fractions.
Explicitly teach the importance of equal parts. Provide 'non-examples' of fraction representations so students can see the difference.
Use tasks with contexts that make sense of the need to have equal parts. Social contexts, such as making equal or fair shares for people, focusses attention on forming equal parts.
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