**ERIC Number:**EJ868909

**Record Type:**Journal

**Publication Date:**2009-Dec

**Pages:**5

**Abstractor:**ERIC

**Reference Count:**2

**ISBN:**N/A

**ISSN:**ISSN-1072-0839

The Area Model of Multiplication of Fractions

Tsankova, Jenny K.; Pjanic, Karmen

Mathematics Teaching in the Middle School, v15 n5 p281-285 Dec 2009

Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However, it has been found that students often have difficulties applying the algorithm with flexibility. To develop new understanding and skills, students need to recognize how mathematical ideas connect and how they build on previously learned ideas. Teaching the concept of multiplication of fractions must be constructed on students' prior knowledge of algorithms and representations. This article discusses the area model of multiplication of fractions which builds on prior knowledge of multiplication of natural numbers as finding the area of a rectangle. The area model allows students to generalize the algorithm of multiplication of proper fractions, in which the product is less than each of the factors, which is traditionally a challenging and counterintuitive idea for students. It also naturally leads to the distributive property of multiplication in general and even to the multiplication of binomials. (Contains 3 figures.)

Descriptors: Prior Learning, Multiplication, Arithmetic, Mathematical Logic, Mathematics Skills, Mathematical Models, Mathematics Education

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:**Middle Schools

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A