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Skills Covered

  • Divide by sharing base-ten blocks and with area models
  • Divide 4-digit numbers by 1-digit numbers with partial quotients
  • Use the standard algorithm and write the remainder after R and as a fraction
  • Divide by 2-digit numbers, estimating each digit of the quotient
  • Decide what a remainder means: round up, drop it, or it is the answer
  • Estimate a quotient before dividing

How to Use This Pack

Five pages that build long division step by step. Page 1 shares base-ten blocks equally (369 ÷ 3 is 1 hundred, 2 tens, and 3 ones in each group, trading a hundred for 10 tens when needed) and finds the missing sides of area models, where 738 ÷ 3 is 200 + 40 + 6. Page 2 divides 4-digit numbers by 1-digit numbers with partial quotients: subtract a group of thousands, hundreds, tens, then ones, and add the partial quotients. Page 3 is the standard algorithm in the long-division bracket: divide, multiply, subtract, bring down, with the remainder written after R and as a fraction of the divisor, such as 214 R 1 = 214 1/4. Page 4 moves to 2-digit divisors, with partial quotients and then the standard algorithm, rounding the divisor to estimate each digit. Page 5 shows one division with three questions, where the answer is 7, 6, or 2, then four story problems with 2-digit divisors that start with an estimate and end with what the remainder means.

In the Classroom

Start page 1 with real base-ten blocks and paper plates for the groups, and let students trade a hundred for 10 tens themselves. On page 2, connect each partial quotient to a part of an area model. Before page 4, practice rounding 2-digit divisors and talk about what to do when a digit is too big or too small. Read the example on page 5 aloud and ask students to explain each answer in their own words.

At Home

Share snacks, coins, or cards equally among family members and talk about what is left over. Ask your child whether the leftovers should be shared, saved, or need one more bag, just like the ferry example on page 5.

Tips for Success

  • Divide, multiply, subtract, bring down, then repeat
  • Write each quotient digit above the last digit you divided into
  • The remainder must be less than the divisor
  • Write the remainder as a fraction by putting it over the divisor: 214 R 1 is 214 1/4 when dividing by 4
  • Check: quotient × divisor + remainder = dividend
  • Round the divisor to estimate each digit; if the product is too big, try one less

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

  • 4.OA.A.3 Solve multi-step story problems with whole numbers and all four operations, deciding what remainders mean, writing equations with a letter, and checking by estimating.
  • 4.NBT.B.6 Divide numbers up to 9,999 by one-digit numbers, finding quotients and remainders with place-value strategies shown in equations, arrays or area models.
  • 5.NBT.B.6 Divide numbers up to 9,999 by two-digit numbers to find whole-number quotients, with place-value strategies shown in equations, arrays or area models.

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Long Division with Remainders

4th – 5th Grade

A 5-page division pack for 4th and 5th grade. Share base-ten blocks equally and find the missing sides of area models, divide 4-digit numbers with partial quotients, and use the standard algorithm in the long-division bracket, writing the remainder after R and as a fraction. Then divide by 2-digit numbers with partial quotients and the standard algorithm, estimating each digit, and solve story problems where the remainder decides the answer. Every page comes in color and in black and white. Answer keys included.

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What’s Included

  • 5 worksheets in color and in black and white, with answer keys (15 pages)
  • Base-ten sharing, area models, and partial quotients for 1-digit divisors
  • The standard algorithm in the bracket, with remainders after R and as fractions
  • 2-digit divisors with an estimate for each digit, and story problems about remainders
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This worksheet is free to download, print, copy, and hand out in your classroom or at home. You do not need to create an account, and there are no watermarks on the PDF.