Making Algorithms Meaningful

Partial Products

 

 

 

The Partial Products Algorithm is a natural extension of the work Dr. Bezuk illustrated with the base 10 blocks.  When teaching this algorithm to students, we suggest that teachers help students clearly define terms and explain the underlying place value concepts.

 

1. 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.

2. Product is the answer when we multiply.

3. 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.  In this case, there are 2 digits in each factor (tens and ones), so the total number of partial products is 2x2=4.  The conceptual basis for this pattern will be explored later in this lesson.

Partial Products

Figure 2. Partial Products example.