Division – Remainder and Regrouping

After we learn about Multiplication of 1-digit numbers with 3-digit numbers, we’ll next go deeper into division. The concept of remainder is specific to division and may be challenging for some students. Hence, before jumping straight into division with remainder, it is better to first understand the concepts of quotient and remainder, and treat cases with and without regrouping separately. For this lesson, we’ll cover three objectives – mental division, introducing quotient and remainder with regrouping, and finally division with regrouping.

Mental Division

For mental division, we’ll first start with a simple division and use it to illustrate bigger numbers. For example, for 360 ÷ 9, we have:

division with remiander - mental division

Quotients and Remainder

Here, we discover that, when we divide a number of concrete objects into equal groups, we’d sometimes find that there are objects “left over” as remainder. In such cases, we’ll simply write the answer as a quotient and a remainder. For example, 24 ÷ 2 vs 25 ÷ 2:

division with remiander - quotient and remainder

Division Without Regrouping – Without Remainder

We first work on division problems that do not involve regrouping and remainder to get students familiarized with the operation, e.g.

division without regrouping and remainder

Division Without Regrouping – With Remainder

Next, add problems that involve remainder, e.g.

Division with remainder no regrouping

Division With Regrouping

Then, we’d introduced division problem that involves regrouping. For example,

Division with remainder

Here, 4 tens cannot be divided evenly by 3 (since we’re only dealing with whole numbers). Hence, we regroup one of the tens with the ones to get 15 ones.

We can also see that the number 45 can be decomposed into 30 + 15 and show the decomposition using number bonds.

Related Resources

Video explanation and lesson plan (member’s resource)

Common Core Standards

  • B6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

Suggested Workbook Series

  • Math in Focus workbook (3A) Chapter 8 – Division (pages 147 to 158)
  • Primary Mathematics workbook (Common Core Edition) (3A) Chapter 3 – Multiplication and Division (pages 97 to 124)

Supplementary Worksheets


Related Resources

For more related resources, please refer to our Multiplication and Division page.

1 thought on “Division – Remainder and Regrouping”

  1. I think using base ten blocks is easier or money if they can “unitize” .. or Montessori stamp game (of course!!!)

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