Learn on PengiEureka Math, Grade 4Chapter 15: Division of Thousands, Hundreds, Tens, and Ones

Lesson 6: Interpret division word problems as either number of groups unknown or group size unknown.

In this Grade 4 Eureka Math lesson from Chapter 15, students learn to interpret division word problems by identifying whether the unknown is the number of groups or the group size. Using tape diagrams and long division, students work through multi-digit division problems — such as dividing 1,868 milliliters equally into 4 containers — to distinguish between these two problem types. By the end of the lesson, students can both solve and write their own word problems that target each type of unknown.

Section 1

Two Meanings of Division: Quotative and Partitive

Property

Division word problems can be categorized into two types based on the unknown information:

  1. Group Size Unknown (Partitive Division): The total is divided into a known number of groups. The goal is to find the size of each group.
Total÷Number of Groups=? (Group Size)Total \div Number\ of\ Groups = ?\ (Group\ Size)
  1. Number of Groups Unknown (Quotative Division): The total is divided by a known group size. The goal is to find the number of groups.
Total÷Group Size=? (Number of Groups)Total \div Group\ Size = ?\ (Number\ of\ Groups)

Section 2

Using Long Division to Find the Unknown

Property

Once a word problem is represented by a division equation, use the long division algorithm to find the unknown value. The equation will be in the form Total÷Known Value=Unknown ValueTotal \div \text{Known Value} = \text{Unknown Value}, where the 'Known Value' is either the number of groups or the size of each group.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Two Meanings of Division: Quotative and Partitive

Property

Division word problems can be categorized into two types based on the unknown information:

  1. Group Size Unknown (Partitive Division): The total is divided into a known number of groups. The goal is to find the size of each group.
Total÷Number of Groups=? (Group Size)Total \div Number\ of\ Groups = ?\ (Group\ Size)
  1. Number of Groups Unknown (Quotative Division): The total is divided by a known group size. The goal is to find the number of groups.
Total÷Group Size=? (Number of Groups)Total \div Group\ Size = ?\ (Number\ of\ Groups)

Section 2

Using Long Division to Find the Unknown

Property

Once a word problem is represented by a division equation, use the long division algorithm to find the unknown value. The equation will be in the form Total÷Known Value=Unknown ValueTotal \div \text{Known Value} = \text{Unknown Value}, where the 'Known Value' is either the number of groups or the size of each group.

Examples