The Partial Products Algorithm

Partial Products
Text Box: Many teachers report that students have a variety of difficulties learning and implementing the standard multiplication algorithm. Take a second to reflect on mistakes that you have seen students make. Some of the common errors teachers have reported include: confusion about which number to “carry” and which number to “write down”, confusion about zeros used as place holders (or why we teach children to “move over”). The reason for these confusions is that there is no understanding of why we do these conventions, and where they come from. They are seen as just a series of rules to remember. When teaching this algorithm to students, we suggest that teachers help students clearly define terms and explain the underlying place value concepts. These are partial products because they are part of the whole product. In this case, the product is 168, but within the product, we have four partial products. Product is the answer when we multiply How can students determine the number of partial products there will be? Why is this the case? Answer: The number of partial products is the product of the number of digits in each factor.