Learn on PengiPengi Math (Grade 4)Chapter 9: Measurement, Data & Real-World Math

Lesson 3: The Customary System: Conversions & Operations

In this Grade 4 Pengi Math lesson from Chapter 9, students learn to recognize and compare customary units of length, capacity, and weight, then build two-column conversion tables to identify patterns and conversion factors. They practice converting mixed number measurements like 1 1/2 ft to smaller units using multiplication and double number lines. The lesson also covers adding and subtracting mixed customary units through strategies such as regrouping, making the next whole unit, and compensation.

Section 1

Customary Units of Length

Property

The primary customary units of length are the inch, foot, yard, and mile.

1 foot (ft)=12 inches (in)1 \text{ foot (ft)} = 12 \text{ inches (in)}
1 yard (yd)=3 feet (ft)1 \text{ yard (yd)} = 3 \text{ feet (ft)}
1 mile (mi)=1,760 yards (yd)=5,280 feet (ft)1 \text{ mile (mi)} = 1,760 \text{ yards (yd)} = 5,280 \text{ feet (ft)}

Examples

  • To convert 5 feet to inches: 5 ft×12inft=60 in5 \text{ ft} \times 12 \frac{\text{in}}{\text{ft}} = 60 \text{ in}
  • To convert 21 feet to yards: 21 ft÷3ftyd=7 yd21 \text{ ft} \div 3 \frac{\text{ft}}{\text{yd}} = 7 \text{ yd}
  • To convert 2 miles to feet: 2 mi×5,280ftmi=10,560 ft2 \text{ mi} \times 5,280 \frac{\text{ft}}{\text{mi}} = 10,560 \text{ ft}

Explanation

Length in the customary system is measured using inches, feet, yards, and miles. To convert from a larger unit to a smaller unit, you multiply by the appropriate conversion factor. For example, to change feet to inches, you multiply by 12. To convert from a smaller unit to a larger unit, you divide.

Section 2

Customary Units of Capacity

Property

The customary system uses specific units to measure capacity, which is the amount a container can hold.

1 cup (c)=8 fluid ounces (fl oz)1 \text{ cup (c)} = 8 \text{ fluid ounces (fl oz)}
1 pint (pt)=2 cups (c)1 \text{ pint (pt)} = 2 \text{ cups (c)}
1 quart (qt)=2 pints (pt)1 \text{ quart (qt)} = 2 \text{ pints (pt)}
1 gallon (gal)=4 quarts (qt)1 \text{ gallon (gal)} = 4 \text{ quarts (qt)}

Section 3

Customary Units of Weight

Property

The customary system uses ounces, pounds, and tons to measure weight.

1 pound (lb)=16 ounces (oz)1 \text{ pound (lb)} = 16 \text{ ounces (oz)}
1 ton (T)=2,000 pounds (lb)1 \text{ ton (T)} = 2,000 \text{ pounds (lb)}

Book overview

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Chapter 9: Measurement, Data & Real-World Math

  1. Lesson 1

    Lesson 1: Data Representation: Line Plots & Fractions

  2. Lesson 2

    Lesson 2: The Metric System: Conversions & Operations

  3. Lesson 3Current

    Lesson 3: The Customary System: Conversions & Operations

  4. Lesson 4

    Lesson 4: Time: Conversions & Operations

  5. Lesson 5

    Lesson 5: Geometric Measurement: Area & Perimeter

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Customary Units of Length

Property

The primary customary units of length are the inch, foot, yard, and mile.

1 foot (ft)=12 inches (in)1 \text{ foot (ft)} = 12 \text{ inches (in)}
1 yard (yd)=3 feet (ft)1 \text{ yard (yd)} = 3 \text{ feet (ft)}
1 mile (mi)=1,760 yards (yd)=5,280 feet (ft)1 \text{ mile (mi)} = 1,760 \text{ yards (yd)} = 5,280 \text{ feet (ft)}

Examples

  • To convert 5 feet to inches: 5 ft×12inft=60 in5 \text{ ft} \times 12 \frac{\text{in}}{\text{ft}} = 60 \text{ in}
  • To convert 21 feet to yards: 21 ft÷3ftyd=7 yd21 \text{ ft} \div 3 \frac{\text{ft}}{\text{yd}} = 7 \text{ yd}
  • To convert 2 miles to feet: 2 mi×5,280ftmi=10,560 ft2 \text{ mi} \times 5,280 \frac{\text{ft}}{\text{mi}} = 10,560 \text{ ft}

Explanation

Length in the customary system is measured using inches, feet, yards, and miles. To convert from a larger unit to a smaller unit, you multiply by the appropriate conversion factor. For example, to change feet to inches, you multiply by 12. To convert from a smaller unit to a larger unit, you divide.

Section 2

Customary Units of Capacity

Property

The customary system uses specific units to measure capacity, which is the amount a container can hold.

1 cup (c)=8 fluid ounces (fl oz)1 \text{ cup (c)} = 8 \text{ fluid ounces (fl oz)}
1 pint (pt)=2 cups (c)1 \text{ pint (pt)} = 2 \text{ cups (c)}
1 quart (qt)=2 pints (pt)1 \text{ quart (qt)} = 2 \text{ pints (pt)}
1 gallon (gal)=4 quarts (qt)1 \text{ gallon (gal)} = 4 \text{ quarts (qt)}

Section 3

Customary Units of Weight

Property

The customary system uses ounces, pounds, and tons to measure weight.

1 pound (lb)=16 ounces (oz)1 \text{ pound (lb)} = 16 \text{ ounces (oz)}
1 ton (T)=2,000 pounds (lb)1 \text{ ton (T)} = 2,000 \text{ pounds (lb)}

Book overview

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

Continue this chapter

Chapter 9: Measurement, Data & Real-World Math

  1. Lesson 1

    Lesson 1: Data Representation: Line Plots & Fractions

  2. Lesson 2

    Lesson 2: The Metric System: Conversions & Operations

  3. Lesson 3Current

    Lesson 3: The Customary System: Conversions & Operations

  4. Lesson 4

    Lesson 4: Time: Conversions & Operations

  5. Lesson 5

    Lesson 5: Geometric Measurement: Area & Perimeter