Parents often ask why we introduce multiplication differently from the traditional algorithm. Gaining an understanding of the meaning of multiplication, including using a variety of strategies for solving equations with multiplication, helps the students think algebraically. Each multiplication fact is not a single bit of information to be memorized, but is related to other multiplication facts.
When multiplying 2-digit numbers, students are first asked to remember the array model taught in Third Grade. This video demonstrates how the array can be built with Base-10 blocks:
Area models for Multiplication (Partial Products)
We can represent the product of a multiplication array by breaking it down into smaller arrays with easy-to-calculate parts. Because we are finding the parts, we call this method Partial Products. It is sometimes called the grid method or "windowpane".
Long Multiplication Using the Grid (or Windowpane)
Using the traditional algorithm is the goal, but taking steps along the way to ensure understanding and allow for organization of the steps lets students keep track of their thinking.