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

Book overview

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Chapter 15: Division of Thousands, Hundreds, Tens, and Ones

  1. Lesson 1

    Lesson 1: Divide multiples of 10, 100, and 1,000 by single-digit numbers.

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  2. Lesson 2

    Lesson 2: Represent and solve division problems with up to a three-digit dividend numerically and with place value disks requiring decomposing a remainder in the hundreds place.

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  3. Lesson 3

    Lesson 3: Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically.

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  4. Lesson 4

    Lesson 4: Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times.

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  5. Lesson 5

    Lesson 5: Solve division problems with a zero in the dividend or with a zero in the quotient.

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  6. Lesson 6Current

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

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  7. Lesson 7

    Lesson 7: Interpret and find whole number quotients and remainders to solve one-step division word problems with larger divisors of 6, 7, 8, and 9.

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  8. Lesson 8

    Lesson 8: Explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends.

    LearnPractice

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

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 15: Division of Thousands, Hundreds, Tens, and Ones

  1. Lesson 1

    Lesson 1: Divide multiples of 10, 100, and 1,000 by single-digit numbers.

    LearnPractice
  2. Lesson 2

    Lesson 2: Represent and solve division problems with up to a three-digit dividend numerically and with place value disks requiring decomposing a remainder in the hundreds place.

    LearnPractice
  3. Lesson 3

    Lesson 3: Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically.

    LearnPractice
  4. Lesson 4

    Lesson 4: Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times.

    LearnPractice
  5. Lesson 5

    Lesson 5: Solve division problems with a zero in the dividend or with a zero in the quotient.

    LearnPractice
  6. Lesson 6Current

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

    LearnPractice
  7. Lesson 7

    Lesson 7: Interpret and find whole number quotients and remainders to solve one-step division word problems with larger divisors of 6, 7, 8, and 9.

    LearnPractice
  8. Lesson 8

    Lesson 8: Explain the connection of the area model of division to the long division algorithm for three- and four-digit dividends.

    LearnPractice