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2015e.00492 Kinzer, Cathy J. Stanford, Ted The distributive property: the core of multiplication. Teach. Child. Math. 20, No. 5, 302-309 (2013). 2013 National Council of Teachers of Mathematics (NCTM), Reston, VA EN F32 D82 multiplication distributive property mathematical concepts mental calculations addition activities
• http://www.nctm.org/publications/article.aspx?id=40208
• Summary: This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core State Standards for Mathematics: (1) Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-size groups, arrays, and area models; and (2) Students recognize area as an attribute of two-dimensional regions. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication. This article explains the DP for teacher reference, then describes the five steps of pre-K to grade 3 learning progression necessary in understanding multiplication. The five steps are: (1) Decomposing small numbers; (2) Fluent mental addition of a one- and a two-digit number; (3) Connecting area and addition; (4) Connecting area and multiplication; and (5) Use the area model and the DP to make connections between multiplication problems. The article then presents five corresponding learning activities that illustrate the steps of the learning progression through games and drawing activities to build and deepen understanding. (ERIC)