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Fraction parts can be counted in groups, similar to the way we skip count whole numbers.
A non-unit fraction can be described as an accumulation of two or more of the unit fraction.
This task requires students to interpret the meaning of multiplication beyond whole numbers. Specifically, students see that when multiplying whole numbers by fractions, they can call on their understanding of what multiplication means with whole numbers. For example, they will use the number line to think of 5 times one-fourth not only as 5 groups of one-fourth, but as the result of an amount that is 5 times as much as one-fourth. The notation of the whole number as the first factor and the fraction as the second factor is deliberate. Although we want students to realize that multiplication is commutative and that the order of the factors does not matter, the meaning of 5 × 1/4 is different from 1/4 × 5 (the later representation is dealt with in fifth grade standards). In this lesson, we also address the common misconception that we can multiply both the numerator and the denominator by the whole number to find the product. This is a procedural misconception and precisely why we use a conceptual approach that employs the number line as a tool.
Vocabulary: multiple, factor, product, numerator, denominator, fraction
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