Learn on PengiIllustrative Mathematics, Grade 5Chapter 6: Place Value Patterns and Decimal Operations

Lesson 4: Multi-step Conversion Problems: Customary Length

In this Grade 5 Illustrative Mathematics lesson, students solve multi-step problems involving customary length unit conversions between inches, feet, and yards. Unlike metric conversions, these require multiplying and dividing by numbers such as 12 and 3, so students apply prior skills with whole numbers and fractions to convert strategically in both directions. The lesson is part of Chapter 6 on Place Value Patterns and Decimal Operations and addresses standard 5.MD.A.1.

Section 1

Customary Unit Conversion Factors

Property

A conversion factor is a ratio of two equivalent measurements.
Below are common conversion factors for the customary system.

Length

  • 11 foot (ft) =12= 12 inches (in)
  • 11 yard (yd) =3= 3 feet (ft)
  • 11 mile (mi) =5,280= 5,280 feet (ft)

Section 2

Converting Larger Customary Units to Smaller Units

Property

To convert a measurement from a larger customary unit to a smaller one, multiply the number of larger units by the conversion factor.

  • Pounds to Ounces: 1 pound=16 ounces1 \text{ pound} = 16 \text{ ounces}
  • Yards to Feet: 1 yard=3 feet1 \text{ yard} = 3 \text{ feet}
  • Feet to Inches: 1 foot=12 inches1 \text{ foot} = 12 \text{ inches}

Examples

Book overview

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Chapter 6: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Place Value Patterns and Powers of 10

  2. Lesson 2

    Lesson 2: Metric Conversion with Powers of Ten

  3. Lesson 3

    Lesson 3: Multi-step Conversion Problems: Metric Units

  4. Lesson 4Current

    Lesson 4: Multi-step Conversion Problems: Customary Length

  5. Lesson 5

    Lesson 5: Add and Subtract Fractions with Equivalent Expressions

  6. Lesson 6

    Lesson 6: Subtract Fractions: Multiple Strategies

  7. Lesson 7

    Lesson 7: Solve Problems

  8. Lesson 8

    Lesson 8: Put It All Together: Add and Subtract Fractions

  9. Lesson 9

    Lesson 9: Representing Fractions on a Line Plot

  10. Lesson 10

    Lesson 10: Problem Solving with Line Plots

  11. Lesson 11

    Lesson 11: Compare Products Using Diagrams

  12. Lesson 12

    Lesson 12: Compare Without Multiplying

  13. Lesson 13

    Lesson 13: Compare to 1

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Customary Unit Conversion Factors

Property

A conversion factor is a ratio of two equivalent measurements.
Below are common conversion factors for the customary system.

Length

  • 11 foot (ft) =12= 12 inches (in)
  • 11 yard (yd) =3= 3 feet (ft)
  • 11 mile (mi) =5,280= 5,280 feet (ft)

Section 2

Converting Larger Customary Units to Smaller Units

Property

To convert a measurement from a larger customary unit to a smaller one, multiply the number of larger units by the conversion factor.

  • Pounds to Ounces: 1 pound=16 ounces1 \text{ pound} = 16 \text{ ounces}
  • Yards to Feet: 1 yard=3 feet1 \text{ yard} = 3 \text{ feet}
  • Feet to Inches: 1 foot=12 inches1 \text{ foot} = 12 \text{ inches}

Examples

Book overview

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

Continue this chapter

Chapter 6: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Place Value Patterns and Powers of 10

  2. Lesson 2

    Lesson 2: Metric Conversion with Powers of Ten

  3. Lesson 3

    Lesson 3: Multi-step Conversion Problems: Metric Units

  4. Lesson 4Current

    Lesson 4: Multi-step Conversion Problems: Customary Length

  5. Lesson 5

    Lesson 5: Add and Subtract Fractions with Equivalent Expressions

  6. Lesson 6

    Lesson 6: Subtract Fractions: Multiple Strategies

  7. Lesson 7

    Lesson 7: Solve Problems

  8. Lesson 8

    Lesson 8: Put It All Together: Add and Subtract Fractions

  9. Lesson 9

    Lesson 9: Representing Fractions on a Line Plot

  10. Lesson 10

    Lesson 10: Problem Solving with Line Plots

  11. Lesson 11

    Lesson 11: Compare Products Using Diagrams

  12. Lesson 12

    Lesson 12: Compare Without Multiplying

  13. Lesson 13

    Lesson 13: Compare to 1