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Number of parts only
During the first few years of school, students begin applying the concept of parts and wholes; they work with halves, then quarters and eighths. Some students will only notice the number of parts, without realising the parts must be equal.
Even though these students might develop appropriate understandings like 'the larger the number of parts, the smaller the parts will be', the misconception that it is only the number of parts that define a fraction may persist.
When looking at a written fraction, students with this misconception interpret the denominator as indicating the number of parts, without realising the fraction label only applies if the parts are equal.
Unequal areas
An example of this misconception — number of parts only — is when students do not attend to the equality of parts in area diagrams.
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.
Paper folding
Paper folding is an example of a practical activity that focusses students' attention on the need to create equal parts to represent fractions.
Cassowary fractions
The digital learning objects provide contexts to help focus student thinking on the equality of parts, not just the number of parts.
