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Creating, Naming, and Justifying Fractions

Fractions are one of the most difficult topics for students to learn in elementary school. In fact, children often find the topic of fractions to be nonsensical and mysterious. Consider, for example, the following exposition, which highlights how senseless fraction operations can appear: When we add or subtract fractions, we have to find a common denominator, but not when we multiply or divide. And once we get a common denominator, we add or subtract the numerators, but not the denominators, despite the fact that when we multiply, we multiply both the numerators and the denominators, and when we divide, we divide neither the numerators nor the denominators. Although no teach