The number line model can be used to solve a multiplication problem such as 3 x 6. This is represented on the number line by three jumps of six or six jumps of three, depending on the context of the problem. [Graphic cannot be reproduced.]
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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.
Dot patterns should be presented in both regular and irregular arrangements. This will help students to understand that numbers are made up of parts, and will later assist them in combining parts as well as counting on. [Graphic cannot be reproduced.]
Concrete models should be used initially to develop an understanding of addition and subtraction facts.
Composing and decomposing numbers flexibly forms a basis for understanding properties of the operations and later formal algebraic concepts and procedures.
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.