Multiplication is a mystery to many students. Their first experience with this basic arithmetic operation is as a table of facts to memorize. The purpose of this exploration is for students to understand the meaning behind multiplication, eliminating the mystery.
This activity begins with a brief formative assessment of student understanding of multiplication of two-digit numbers. It supports students' understanding of multiplication and its application. Constructivist pedagogy is used to move learning from the concrete (using manipulatives) to the representational (using pictures and diagrams) to the abstract (using algorithms). Students build models of the operation 27 x 15 and its result in a variety of ways. The activity promotes student reasoning and sense making by analyzing various multiplication algorithms (area models, partial products, lattice multiplication, and the traditional method).