Over the course of her teaching career, this author learned to create environments in which both the teacher and learners embrace understanding. She introduced new concepts with a general question or word problem and encouraged students to find solutions with a strategy of their choice. By using this instructional method, she allowed her students to demonstrate their ability to master multiplicative concepts with the use of arrays. For example, students demonstrated the area model by constructing rectangular arrays with square-inch tiles to illustrate such problems as 4 × 3 with four rows of three tiles. Students could then build on this knowledge to illustrate abstract thinking by drawing open arrays to solve multiplication problems up to three digits by two digits. Prior exposure to the multiplicative area model with whole numbers helped students construct strategies to solve fraction problems with a high level of comfort when using arrays. This article was designed to show how fourth-grade students with a strong multiplicative and fractional foundation respond to the concept of multiplying fractions without traditional algorithms. The author concludes that this study suggests that strategically engineered problems help children construct algorithms and make generalizations of their own. Self-constructed algorithms have a longer lasting effect on students' understanding of fractions. This article could be used as a catalyst for future research, and perhaps provide suggestions to educators on the benefits of arrays for successfully teaching fourth graders the concept of multiplying fractions. A bibliography is included.