Math Intervention 3–5 Grade

Addition and Subtraction Concepts 83

What is the Partial Sums Concept?

The partial sums concept is an addition strategy that involves

combining addends into workable clusters. The traditional

algorithm for addition involves following procedures, such as

aligning digits in columns and always starting with the ones. The

rules of the traditional algorithm are meaningless for many

students. They cannot remember what to do because they do

not understand the math. Alternative algorithms such as partial

sums build conceptual understanding. With partial sums, it does

not matter if columns are aligned or if the student starts with the

ones or not. There is no need to “carry.” For example, 37 + 48 =

70 + 15. In this situation, the tens are clustered (70 is a partial

sum) and the ones are clustered (15 is a partial sum). The partial

sums are easily combined into 85. The idea with partial sums is

to cluster the addends in a way that invites mental math.

CCSS

Operations and Algebraic Thinking

Number and Operations in Base Ten

Formative Assessment

To fi nd out if a student understands the partial sums concept,

ask the student to solve the following equations:

23 + 42 = 26 + 23 = 31 + 39 =

68 + 12 = 57 + 38 = 76 + 17 =

Ask the student to explain how she solves each problem. Invite

the student to try the problems without aligning the digits in

columns and without starting with the ones.

Partial Sums

CONCEPT: