Math Intervention 3–5 Grade

Multiplication and Division Concepts 169

Partial Quotients

CONCEPT:

What is the Partial Quotients Concept?

The partial quotients concept is a division strategy that

involves consecutive approximations. Like partial products,

this concept is as an alternative to the traditional algorithm.

For some students the rules of long division are diffi cult

to remember and they miss steps resulting in incorrect

answers. The beauty of the partial quotients concept is the

focus on building conceptual

knowledge of division through

estimation. Students estimate

how many multiples of the

divisor they should work with

each time they divide. These

partial quotients are combined

to name the complete quotient.

Remainders are easily

identifi ed.

CCSS

Operations and Algebraic Thinking

Formative Assessment

To fi nd out if a student understands partial quotients ask the

student to solve the following equations:

5 √125 7√3360 16√304 42 √7336

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

she uses the traditional algorithm, ask if she knows another

way. Encourage the student to use estimation to fi nd parts of

the quotient.

14 √ 1092

– 700 50

392

– 280 20

112

– 70 5

42

– 42 3

0

R 0 78 Quotient