Learn on PengiYoshiwara Core MathChapter 3: Measurement

Lesson 3.3: Units of Measure

In this Grade 8 lesson from Yoshiwara Core Math Chapter 3, students learn how to convert between units of length in both the U.S. customary system (inches, feet, yards, and miles) and the metric system (meters). The lesson introduces conversion factors and unit fractions as tools for setting up and solving unit conversion problems. Students apply these skills through real-world examples involving distances and measurements.

Section 1

📘 Units of Measure

New Concept

This lesson explores how we measure quantities like length and volume. You'll learn to convert between different systems—like from feet to meters—using conversion factors, ensuring your calculations are always accurate no matter the unit.

What’s next

Next, you'll apply this with interactive examples for converting length, area, and volume. Get ready for some hands-on practice cards and challenge problems!

Section 2

English Units of Length

Property

Units of length:

1 foot=12 inches1 \text{ foot} = 12 \text{ inches}
1 yard=3 feet1 \text{ yard} = 3 \text{ feet}
1 mile=5280 feet1 \text{ mile} = 5280 \text{ feet}

A conversion factor is a fraction equal to 1, such as 3 feet1 yard\frac{3 \text{ feet}}{1 \text{ yard}}. We choose the factor that cancels the old units and leaves the new ones. Such conversion factors are also called unit fractions.

Examples

  • A person is 5 feet 4 inches tall. To express this in inches, calculate 5×12+4=645 \times 12 + 4 = 64 inches.
  • A piece of fabric is 90 inches long. To find its length in feet, you divide: 9012=7.5\frac{90}{12} = 7.5 feet.

Section 3

Metric Units of Length

Property

Metric Units of Length:

1 centimeter=10 millimeters1 \text{ centimeter} = 10 \text{ millimeters}
1 meter=100 centimeters1 \text{ meter} = 100 \text{ centimeters}
1 kilometer=1000 meters1 \text{ kilometer} = 1000 \text{ meters}

The conversion factors in the metric system are all powers of 10. This property makes the metric system easy to use, because we can convert between units simply by moving the decimal point.

Examples

  • A table is 2.5 meters long. To convert this to centimeters, you move the decimal two places to the right: 2.5 m=250 cm2.5 \text{ m} = 250 \text{ cm}.
  • A small insect measures 6 millimeters long. In centimeters, this is 6÷10=0.66 \div 10 = 0.6 centimeters.

Section 4

Converting Between Systems

Property

Converting Between Metric and English Units:

1 meter≈1.0963 yards1 \text{ meter} \approx 1.0963 \text{ yards}
1 centimeter≈0.3937 inch1 \text{ centimeter} \approx 0.3937 \text{ inch}
1 inch=2.54 centimeters1 \text{ inch} = 2.54 \text{ centimeters}
1 kilometer≈0.6214 mile1 \text{ kilometer} \approx 0.6214 \text{ mile}

Examples

  • A 10K (10 kilometer) race is being measured in miles. The distance is 10 km×0.6214mikm=6.21410 \text{ km} \times 0.6214 \frac{\text{mi}}{\text{km}} = 6.214 miles.
  • A laptop screen is 15 inches diagonally. In centimeters, this is 15 in×2.54cmin=38.115 \text{ in} \times 2.54 \frac{\text{cm}}{\text{in}} = 38.1 centimeters.

Section 5

Area and Volume Units

Property

To convert units of area, we square the corresponding length conversion factor. To convert units of volume, we cube the length conversion factor.
Area Units:

1 square yard=(3 feet)2=9 square feet1 \text{ square yard} = (3 \text{ feet})^2 = 9 \text{ square feet}
1 square foot=(12 inches)2=144 square inches1 \text{ square foot} = (12 \text{ inches})^2 = 144 \text{ square inches}

Volume Units:

1 cubic yard=(3 feet)3=27 cubic feet1 \text{ cubic yard} = (3 \text{ feet})^3 = 27 \text{ cubic feet}
1 cubic foot=(12 inches)3=1728 cubic inches1 \text{ cubic foot} = (12 \text{ inches})^3 = 1728 \text{ cubic inches}

Examples

  • A room has an area of 270 square feet. To buy carpet sold by the square yard, you calculate 270 sq ft÷9sq ftsq yd=30270 \text{ sq ft} \div 9 \frac{\text{sq ft}}{\text{sq yd}} = 30 square yards.
  • A container has a volume of 3 cubic feet. To find its volume in cubic inches, you multiply: 3 cu ft×1728cu incu ft=51843 \text{ cu ft} \times 1728 \frac{\text{cu in}}{\text{cu ft}} = 5184 cubic inches.

Section 6

Liquid Measure

Property

English Units:

1 cup=8 fluid ounces1 \text{ cup} = 8 \text{ fluid ounces}
1 pint=2 cups1 \text{ pint} = 2 \text{ cups}
1 quart=2 pints1 \text{ quart} = 2 \text{ pints}
1 gallon=4 quarts1 \text{ gallon} = 4 \text{ quarts}

Metric Units & Conversions:

1 liter≈1.06 quarts1 \text{ liter} \approx 1.06 \text{ quarts}
1 milliliter (ml)=1 cubic centimeter (cc)1 \text{ milliliter (ml)} = 1 \text{ cubic centimeter (cc)}

Examples

  • A recipe calls for 5 cups of broth. To see how many pints that is, you calculate 5 cups÷2cupspint=2.55 \text{ cups} \div 2 \frac{\text{cups}}{\text{pint}} = 2.5 pints.
  • A large container holds 3 gallons of water. This is equivalent to 3 gal×4qtgal=123 \text{ gal} \times 4 \frac{\text{qt}}{\text{gal}} = 12 quarts.

Book overview

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Chapter 3: Measurement

  1. Lesson 1

    Lesson 3.1: Volume and Surface Area

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  2. Lesson 2

    Lesson 3.2: Exponents

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  3. Lesson 3Current

    Lesson 3.3: Units of Measure

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  4. Lesson 4

    Lesson 3.4: Circles and Spheres

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  5. Lesson 5

    Lesson 3.5: Large Numbers

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Lesson overview

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Expand

Section 1

📘 Units of Measure

New Concept

This lesson explores how we measure quantities like length and volume. You'll learn to convert between different systems—like from feet to meters—using conversion factors, ensuring your calculations are always accurate no matter the unit.

What’s next

Next, you'll apply this with interactive examples for converting length, area, and volume. Get ready for some hands-on practice cards and challenge problems!

Section 2

English Units of Length

Property

Units of length:

1 foot=12 inches1 \text{ foot} = 12 \text{ inches}
1 yard=3 feet1 \text{ yard} = 3 \text{ feet}
1 mile=5280 feet1 \text{ mile} = 5280 \text{ feet}

A conversion factor is a fraction equal to 1, such as 3 feet1 yard\frac{3 \text{ feet}}{1 \text{ yard}}. We choose the factor that cancels the old units and leaves the new ones. Such conversion factors are also called unit fractions.

Examples

  • A person is 5 feet 4 inches tall. To express this in inches, calculate 5×12+4=645 \times 12 + 4 = 64 inches.
  • A piece of fabric is 90 inches long. To find its length in feet, you divide: 9012=7.5\frac{90}{12} = 7.5 feet.

Section 3

Metric Units of Length

Property

Metric Units of Length:

1 centimeter=10 millimeters1 \text{ centimeter} = 10 \text{ millimeters}
1 meter=100 centimeters1 \text{ meter} = 100 \text{ centimeters}
1 kilometer=1000 meters1 \text{ kilometer} = 1000 \text{ meters}

The conversion factors in the metric system are all powers of 10. This property makes the metric system easy to use, because we can convert between units simply by moving the decimal point.

Examples

  • A table is 2.5 meters long. To convert this to centimeters, you move the decimal two places to the right: 2.5 m=250 cm2.5 \text{ m} = 250 \text{ cm}.
  • A small insect measures 6 millimeters long. In centimeters, this is 6÷10=0.66 \div 10 = 0.6 centimeters.

Section 4

Converting Between Systems

Property

Converting Between Metric and English Units:

1 meter≈1.0963 yards1 \text{ meter} \approx 1.0963 \text{ yards}
1 centimeter≈0.3937 inch1 \text{ centimeter} \approx 0.3937 \text{ inch}
1 inch=2.54 centimeters1 \text{ inch} = 2.54 \text{ centimeters}
1 kilometer≈0.6214 mile1 \text{ kilometer} \approx 0.6214 \text{ mile}

Examples

  • A 10K (10 kilometer) race is being measured in miles. The distance is 10 km×0.6214mikm=6.21410 \text{ km} \times 0.6214 \frac{\text{mi}}{\text{km}} = 6.214 miles.
  • A laptop screen is 15 inches diagonally. In centimeters, this is 15 in×2.54cmin=38.115 \text{ in} \times 2.54 \frac{\text{cm}}{\text{in}} = 38.1 centimeters.

Section 5

Area and Volume Units

Property

To convert units of area, we square the corresponding length conversion factor. To convert units of volume, we cube the length conversion factor.
Area Units:

1 square yard=(3 feet)2=9 square feet1 \text{ square yard} = (3 \text{ feet})^2 = 9 \text{ square feet}
1 square foot=(12 inches)2=144 square inches1 \text{ square foot} = (12 \text{ inches})^2 = 144 \text{ square inches}

Volume Units:

1 cubic yard=(3 feet)3=27 cubic feet1 \text{ cubic yard} = (3 \text{ feet})^3 = 27 \text{ cubic feet}
1 cubic foot=(12 inches)3=1728 cubic inches1 \text{ cubic foot} = (12 \text{ inches})^3 = 1728 \text{ cubic inches}

Examples

  • A room has an area of 270 square feet. To buy carpet sold by the square yard, you calculate 270 sq ft÷9sq ftsq yd=30270 \text{ sq ft} \div 9 \frac{\text{sq ft}}{\text{sq yd}} = 30 square yards.
  • A container has a volume of 3 cubic feet. To find its volume in cubic inches, you multiply: 3 cu ft×1728cu incu ft=51843 \text{ cu ft} \times 1728 \frac{\text{cu in}}{\text{cu ft}} = 5184 cubic inches.

Section 6

Liquid Measure

Property

English Units:

1 cup=8 fluid ounces1 \text{ cup} = 8 \text{ fluid ounces}
1 pint=2 cups1 \text{ pint} = 2 \text{ cups}
1 quart=2 pints1 \text{ quart} = 2 \text{ pints}
1 gallon=4 quarts1 \text{ gallon} = 4 \text{ quarts}

Metric Units & Conversions:

1 liter≈1.06 quarts1 \text{ liter} \approx 1.06 \text{ quarts}
1 milliliter (ml)=1 cubic centimeter (cc)1 \text{ milliliter (ml)} = 1 \text{ cubic centimeter (cc)}

Examples

  • A recipe calls for 5 cups of broth. To see how many pints that is, you calculate 5 cups÷2cupspint=2.55 \text{ cups} \div 2 \frac{\text{cups}}{\text{pint}} = 2.5 pints.
  • A large container holds 3 gallons of water. This is equivalent to 3 gal×4qtgal=123 \text{ gal} \times 4 \frac{\text{qt}}{\text{gal}} = 12 quarts.

Book overview

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

Continue this chapter

Chapter 3: Measurement

  1. Lesson 1

    Lesson 3.1: Volume and Surface Area

    LearnPractice
  2. Lesson 2

    Lesson 3.2: Exponents

    LearnPractice
  3. Lesson 3Current

    Lesson 3.3: Units of Measure

    LearnPractice
  4. Lesson 4

    Lesson 3.4: Circles and Spheres

    LearnPractice
  5. Lesson 5

    Lesson 3.5: Large Numbers

    LearnPractice