164 Multiplication and Division ConceptsPartial Products
CONCEPT:
What is the Partial Products Concept?
The partial products concept is a multiplication strategy
that involves breaking down a larger problem into smaller,
more manageable problems. The traditional algorithm for
multiplication involves procedures, such as aligning digits in
columns and always starting with the ones. For many students
the rules of the traditional algorithm are meaningless. They
cannot remember what to do because they do not understand
the math. Alternatives to algorithms such as partial products
help build students’ conceptual understanding. With partial
products, it does not matter if the columns are aligned or if the
student starts with the ones. There is no need to “bring down
a zero” or “put the big number on top.” Let’s look at 6 x 14.
Using the distributive property, we break it down into smaller
problems, 6 (10 + 4) = (6 x 10) + (6 x 4). Here, 60 is part of the
product and 24 is part of the product. These partial products
are easily combined into the total product of 84.CCSS
Operations and Algebraic Thinking
Number and Operations in Base TenFormative Assessment
To fi nd out if a student understands the partial products
concept ask the student to solve the following equations:
13 x 4 = 26 x 5 = 52 x 7 =
16 x 12 = 18 x 27 = 46 x 27 =
Have the student explain how he solves each problem. Invite
the student to try the problems without aligning the digits in
columns and without starting with the ones.