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

Lesson overview

Expand to review the lesson summary and core properties.

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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