There is an inverse relationship between multiplication and division.
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A certain amount of practice is necessary to develop fluency with computational strategies; however, the practice must be motivating and systematic if students are to develop fluency in computation, whether mental, with manipulative materials, or with paper and pencil.
In grade three, students developed an understanding of the meanings of multiplication and division of whole numbers through activities and practical problems involving equal-sized groups, arrays, and length models. In addition, grade three students have worked on fluency of facts for 0, 1, 2, 5, and 10.
Composing and decomposing numbers flexibly forms a basis for understanding properties of the operations and later formal algebraic concepts and procedures.
The development of computational fluency relies on quick access to number facts. There are patterns and relationships that exist in the facts. These relationships can be used to learn and retain the facts.
Multiplication can also refer to a multiplicative comparison, such as: “Gwen has six times as many stickers as Phillip”. Both situations should be modeled with manipulatives.