Learn on PengiIllustrative Mathematics, Grade 5Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

Lesson 9: Practice Division with Partial Quotients

In this Grade 5 lesson from Illustrative Mathematics Chapter 4, students practice multi-digit division using the partial quotients strategy to build fluency and accuracy. Learners apply their understanding of place value to break division problems into manageable parts, recording each partial quotient step by step. This lesson reinforces the division concepts developed throughout the chapter's focus on wrapping up multiplication and division with multi-digit numbers.

Section 1

Applying the Partial Quotients Algorithm

Property

To find the final quotient using the partial quotients method, add all the individual partial quotients together.
The process is complete when the remaining dividend is less than the divisor.

Final Quotient=Partial Quotient1+Partial Quotient2+ \text{Final Quotient} = \text{Partial Quotient}_1 + \text{Partial Quotient}_2 + \dots

Examples

Section 2

Dividing When a Partial Dividend is Smaller than the Divisor

Property

If a partial dividend is less than the divisor, place a 00 in the corresponding place value of the quotient. Then, bring down the next digit to form a new partial dividend.

Examples

Section 3

Finding a Missing Dimension of a Rectangular Prism

Property

If you know the volume of a rectangular prism and two of its three dimensions (length, width, height), you can find the missing dimension by using division.

Given the volume formula V=l×w×hV = l \times w \times h:

h=Vl×worl=Vw×horw=Vl×hh = \frac{V}{l \times w} \quad \text{or} \quad l = \frac{V}{w \times h} \quad \text{or} \quad w = \frac{V}{l \times h}

Book overview

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

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Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

  1. Lesson 1

    Lesson 1: Estimate and Find Products

  2. Lesson 2

    Lesson 2: Partial Products: Diagrams and Algorithms

  3. Lesson 3

    Lesson 3: Standard Algorithm: Introduction and Practice

  4. Lesson 4

    Lesson 4: Standard Algorithm: Multi-digit Numbers with Composing

  5. Lesson 5

    Lesson 5: Build Multiplication Fluency

  6. Lesson 6

    Lesson 6: The Birds

  7. Lesson 7

    Lesson 7: World's Record Folk Dance

  8. Lesson 8

    Lesson 8: Partial Quotients: Strategy and Algorithm

  9. Lesson 9Current

    Lesson 9: Practice Division with Partial Quotients

  10. Lesson 10

    Lesson 10: Find Missing Side Lengths

  11. Lesson 11

    Lesson 11: World's Record Noodle Soup

  12. Lesson 12

    Lesson 12: Fractions as Partial Quotients (Optional)

  13. Lesson 13

    Lesson 13: Lots of Milk

  14. Lesson 14

    Lesson 14: Real-World Applications: Trash Problems

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Applying the Partial Quotients Algorithm

Property

To find the final quotient using the partial quotients method, add all the individual partial quotients together.
The process is complete when the remaining dividend is less than the divisor.

Final Quotient=Partial Quotient1+Partial Quotient2+ \text{Final Quotient} = \text{Partial Quotient}_1 + \text{Partial Quotient}_2 + \dots

Examples

Section 2

Dividing When a Partial Dividend is Smaller than the Divisor

Property

If a partial dividend is less than the divisor, place a 00 in the corresponding place value of the quotient. Then, bring down the next digit to form a new partial dividend.

Examples

Section 3

Finding a Missing Dimension of a Rectangular Prism

Property

If you know the volume of a rectangular prism and two of its three dimensions (length, width, height), you can find the missing dimension by using division.

Given the volume formula V=l×w×hV = l \times w \times h:

h=Vl×worl=Vw×horw=Vl×hh = \frac{V}{l \times w} \quad \text{or} \quad l = \frac{V}{w \times h} \quad \text{or} \quad w = \frac{V}{l \times h}

Book overview

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

Continue this chapter

Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

  1. Lesson 1

    Lesson 1: Estimate and Find Products

  2. Lesson 2

    Lesson 2: Partial Products: Diagrams and Algorithms

  3. Lesson 3

    Lesson 3: Standard Algorithm: Introduction and Practice

  4. Lesson 4

    Lesson 4: Standard Algorithm: Multi-digit Numbers with Composing

  5. Lesson 5

    Lesson 5: Build Multiplication Fluency

  6. Lesson 6

    Lesson 6: The Birds

  7. Lesson 7

    Lesson 7: World's Record Folk Dance

  8. Lesson 8

    Lesson 8: Partial Quotients: Strategy and Algorithm

  9. Lesson 9Current

    Lesson 9: Practice Division with Partial Quotients

  10. Lesson 10

    Lesson 10: Find Missing Side Lengths

  11. Lesson 11

    Lesson 11: World's Record Noodle Soup

  12. Lesson 12

    Lesson 12: Fractions as Partial Quotients (Optional)

  13. Lesson 13

    Lesson 13: Lots of Milk

  14. Lesson 14

    Lesson 14: Real-World Applications: Trash Problems