**ERIC Number:**EJ1014362

**Record Type:**Journal

**Publication Date:**2013-Apr

**Pages:**9

**Abstractor:**ERIC

**Reference Count:**9

**ISBN:**N/A

**ISSN:**ISSN-1073-5836

The Distributive Property in Grade 3?

Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl

Teaching Children Mathematics, v19 n8 p498-506 Apr 2013

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication and addition (arithmetic). The third-grade standards also suggest that students use the commutative, associative, and distributive properties of multiplication
(CCSSI 2010). Traditionally, multiplication has been a major topic for third grade. Linked to repeated addition of equal-size groups, multiplication logically follows the study of addition. Introducing rectangular arrays to represent groups (rows) of equal size illustrates both numeric and geometric interpretations of multiplication and naturally introduces the concept of area (CCSSI 2010). Rotating the rectangular arrays illustrates the commutative property of multiplication (see fig.1), and determining the number of tiles needed to build a multicolor rectangle allows students to demonstrate their understanding of conservation of area and to discover a geometric interpretation of the distributive property. Although multiplication is typically a focus of third-grade mathematics (NCTM 2006), third-grade textbooks usually include few, if any, concepts of area or distribution and no geometric interpretation of the distributive property, which raises at least two questions: (1) Are third graders ready for the reasoning needed to understand these concepts? And, if they are, (2) how can integrated exploration of these topics help students make connections that deepen their conceptual understanding of these topics and others already in the curriculum? Helping students make connections like those illustrated here allows them to deepen their conceptual understanding (Baek 2008; Clements 1999; CCSSI 2010; NRC 2005) that the distributive property is not an algorithm but a property, a characteristic that holds throughout mathematics--arithmetic, geometry, algebra, and other branches as well. (Contains 14 figures.)

Descriptors: Academic Standards, State Standards, Geometric Concepts, Concept Formation, Mathematics Instruction, Elementary School Mathematics, Elementary School Students, Multiplication, Mathematics, Algebra, Mathematics Materials, Grade 3, Arithmetic

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Elementary Education; Grade 3

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A