If you teach long division, it is helpful to keep a variety of strategies in your math toolbox. Using partial quotients to divide is one long division strategy that is essential for every upper elementary math toolbox!

Let’s explore how you can use division with partial quotients with your students!

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Why Teach the Partial Quotients Strategy?

Long division is a challenging math skill for most upper elementary students. Even with lots of practice, some students struggle to remember all of the steps and basic facts required for long division.

Teaching more than one long division strategy is a good idea because all students learn and comprehend information differently. A student may not understand using standard algorithm to divide. But, show them a different strategy and it may click quickly.

You may be familiar with using partial products for long multiplication. Like the multiplication strategy, partial quotients uses fewer steps and breaks long division into smaller parts that are easier for students to compute. Of all the long division models and methods that I have taught, using partial quotients to divide is consistently a favorite for my students.

Using Partial Quotients to Divide

The following shows step-by-step instructions for solving 476 ÷ 4.

STEP 1: Write the equation inside a division bracket. Draw a line down the right side of the problem.

STEP 2: Multiply the divisor by any number to find a group that will fit into the dividend. Write the number you multiplied the divisor by on the outside of the line. Subtract the multiple from the dividend.

**Math Tip: It is best to multiply by numbers that are easy to find products for. Easy numbers to multiply by include 200, 100, 50, 20, 10, 5, and 2.

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STEP 3: Repeat the process until you get to 0.

STEP 4: Add the numbers to the right of the line to find the quotient.

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When using partial quotients to divide, the quotient will always be the same but the way you find the quotient may differ. The images below show two different ways to find the quotient with partial quotients for the problem 363 ÷ 3.

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What About Remainders?

If you are unable to subtract to 0, the leftovers make the remainder.

In the problem 455 ÷ 6, the last difference (5) is smaller than the divisor (6). Therefore, 5 is the remainder.

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More Long Division Strategies

Using partial quotients to divide is my favorite long division strategy that is not standard algorithm.

But, there are also many other division strategies you can use. My long division units teach students the following long division methods in addition to standard algorithm:

  • repeated subtraction
  • partial quotients
  • place value with models
  • place value without models
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All of my no-prep division units come with step-by-step instructions for teaching each strategy and lesson. They also come with worksheets, games and centers, digital activities, and assessments to use when teaching long division.

Two versions are available—

  • Long division with up to 3-Digit Dividends: These lessons use up to 3-digit dividends and a 1-digit divisor. They are specifically aligned to the 4th-grade Virginia Math Standards of Learning (SOLs) although they will also work with most math standards that require students to solve division problems with up to 3-digit dividends.
  • Long division with up to 4-Digit Dividends: These lessons use up to 4-digit dividends and 2-digit divisors. They are specifically aligned to the 5th-grade Virginia Math Standards of Learning (SOLs) although they will also work with most math standards that require students to solve division problems with up to 4-digit dividends and 2-digit divisors.
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