Learn on PengiSaxon Math, Intermediate 4Chapter 4: Lessons 31–40, Investigation 4

Lesson 40: Capacity

In this Grade 4 Saxon Math Intermediate 4 lesson, students learn to identify and use U.S. customary units of liquid capacity, including fluid ounces, cups, pints, quarts, and gallons, and practice converting between these units. The lesson also introduces metric liquid measurement with liters and milliliters, and connects both systems by comparing equivalent measures such as 1 quart versus 1 liter. Hands-on activities guide students through estimating and measuring capacity using real containers, building a foundational understanding of measurement in both systems.

Section 1

📘 Capacity

New Concept

The quantity of liquid a container can hold is the capacity of the container.

What’s next

Next, you’ll explore the U.S. Customary and metric systems, learning how to convert between units like quarts and liters.

Section 2

Capacity

Property

U.S. Liquid Measure conversions:

8 fl oz=1 c 8 \text{ fl oz} = 1 \text{ c}
2 c=1 pt 2 \text{ c} = 1 \text{ pt}
2 pt=1 qt 2 \text{ pt} = 1 \text{ qt}
4 qt=1 gal 4 \text{ qt} = 1 \text{ gal}

Example

  • To find the number of cups in a quart: 1 qt=2 pt=2×(2 c)=4 cups1 \text{ qt} = 2 \text{ pt} = 2 \times (2 \text{ c}) = 4 \text{ cups}.
  • To find the number of fluid ounces in a pint: 1 pt=2 c=2×(8 fl oz)=16 fluid ounces1 \text{ pt} = 2 \text{ c} = 2 \times (8 \text{ fl oz}) = 16 \text{ fluid ounces}.
  • A 5-gallon tank holds 5×4 qt=20 quarts5 \times 4 \text{ qt} = 20 \text{ quarts}.

Explantion

Think of U.S. liquid units as a family tree! Two cups are children of a pint, two pints are children of a quart, and four quarts are children of a gallon. Understanding this family relationship helps you easily convert any amount, making you a master of liquid measurement.

Section 3

Metric liquid measure

Property

The relationship between milliliters and liters:

1000 mL=1 L 1000 \text{ mL} = 1 \text{ L}

Example

  • A 2-liter bottle of soda contains 2×1000=2000 milliliters2 \times 1000 = 2000 \text{ milliliters}.
  • A medicine dropper holding 5 mL5 \text{ mL} has 5÷1000=0.005 liters5 \div 1000 = 0.005 \text{ liters}.
  • To fill a 3.53.5-liter container, you would need 3.5×1000=3500 milliliters3.5 \times 1000 = 3500 \text{ milliliters}.

Explanation

The metric system loves the number 1000! A milliliter is a tiny drop, and you need exactly one thousand of them to fill a one-liter bottle. This makes converting super simple—just multiply or divide by 1000 by moving the decimal point three places. It's that easy!

Section 4

Comparing U.S. and metric measures

Property

The label on a gallon of milk often shows both measures:

1 gal (3.78 L) 1 \text{ gal } (3.78 \text{ L})
This means 1 gallon is approximately equal to 3.78 liters.

Example

  • A liter is slightly larger than a quart, so we can show the comparison like this: 1 liter>1 quart1 \text{ liter} > 1 \text{ quart}.
  • A half gallon is less than two liters: 12 gal1.89 L\frac{1}{2} \text{ gal} \approx 1.89 \text{ L}, so 12 gallon<2 liters\frac{1}{2} \text{ gallon} < 2 \text{ liters}.
  • A 12-gallon tank holds approximately 12×3.78=45.36 liters12 \times 3.78 = 45.36 \text{ liters}.

Explanation

When U.S. customary units and metric units meet, they are not exactly equal! A liter is a little bigger than a quart, which helps you choose the right amount at the store. Just remember that one full gallon is a little less than four liters. Now you know!

Book overview

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Chapter 4: Lessons 31–40, Investigation 4

  1. Lesson 1

    Lesson 31: Word Problems About Comparing

  2. Lesson 2

    Lesson 32: Multiplication Facts: 9s, 10s, 11s, 12s

  3. Lesson 3

    Lesson 33: Writing Numbers Through Hundred Thousands

  4. Lesson 4

    Lesson 34: Writing Numbers Through Hundred Millions

  5. Lesson 5

    Lesson 35: Naming Mixed Numbers and Money

  6. Lesson 6

    Lesson 36: Fractions of a Dollar

  7. Lesson 7

    Lesson 37: Reading Fractions and Mixed Numbers from a Number Line

  8. Lesson 8

    Lesson 38: Multiplication Facts (Memory Group)

  9. Lesson 9

    Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

  10. Lesson 10Current

    Lesson 40: Capacity

  11. Lesson 11

    Investigation 4A: Tenths and Hundredths

  12. Lesson 12

    Investigation 4B: Relating Fractions and Decimals

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Capacity

New Concept

The quantity of liquid a container can hold is the capacity of the container.

What’s next

Next, you’ll explore the U.S. Customary and metric systems, learning how to convert between units like quarts and liters.

Section 2

Capacity

Property

U.S. Liquid Measure conversions:

8 fl oz=1 c 8 \text{ fl oz} = 1 \text{ c}
2 c=1 pt 2 \text{ c} = 1 \text{ pt}
2 pt=1 qt 2 \text{ pt} = 1 \text{ qt}
4 qt=1 gal 4 \text{ qt} = 1 \text{ gal}

Example

  • To find the number of cups in a quart: 1 qt=2 pt=2×(2 c)=4 cups1 \text{ qt} = 2 \text{ pt} = 2 \times (2 \text{ c}) = 4 \text{ cups}.
  • To find the number of fluid ounces in a pint: 1 pt=2 c=2×(8 fl oz)=16 fluid ounces1 \text{ pt} = 2 \text{ c} = 2 \times (8 \text{ fl oz}) = 16 \text{ fluid ounces}.
  • A 5-gallon tank holds 5×4 qt=20 quarts5 \times 4 \text{ qt} = 20 \text{ quarts}.

Explantion

Think of U.S. liquid units as a family tree! Two cups are children of a pint, two pints are children of a quart, and four quarts are children of a gallon. Understanding this family relationship helps you easily convert any amount, making you a master of liquid measurement.

Section 3

Metric liquid measure

Property

The relationship between milliliters and liters:

1000 mL=1 L 1000 \text{ mL} = 1 \text{ L}

Example

  • A 2-liter bottle of soda contains 2×1000=2000 milliliters2 \times 1000 = 2000 \text{ milliliters}.
  • A medicine dropper holding 5 mL5 \text{ mL} has 5÷1000=0.005 liters5 \div 1000 = 0.005 \text{ liters}.
  • To fill a 3.53.5-liter container, you would need 3.5×1000=3500 milliliters3.5 \times 1000 = 3500 \text{ milliliters}.

Explanation

The metric system loves the number 1000! A milliliter is a tiny drop, and you need exactly one thousand of them to fill a one-liter bottle. This makes converting super simple—just multiply or divide by 1000 by moving the decimal point three places. It's that easy!

Section 4

Comparing U.S. and metric measures

Property

The label on a gallon of milk often shows both measures:

1 gal (3.78 L) 1 \text{ gal } (3.78 \text{ L})
This means 1 gallon is approximately equal to 3.78 liters.

Example

  • A liter is slightly larger than a quart, so we can show the comparison like this: 1 liter>1 quart1 \text{ liter} > 1 \text{ quart}.
  • A half gallon is less than two liters: 12 gal1.89 L\frac{1}{2} \text{ gal} \approx 1.89 \text{ L}, so 12 gallon<2 liters\frac{1}{2} \text{ gallon} < 2 \text{ liters}.
  • A 12-gallon tank holds approximately 12×3.78=45.36 liters12 \times 3.78 = 45.36 \text{ liters}.

Explanation

When U.S. customary units and metric units meet, they are not exactly equal! A liter is a little bigger than a quart, which helps you choose the right amount at the store. Just remember that one full gallon is a little less than four liters. Now you know!

Book overview

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

Continue this chapter

Chapter 4: Lessons 31–40, Investigation 4

  1. Lesson 1

    Lesson 31: Word Problems About Comparing

  2. Lesson 2

    Lesson 32: Multiplication Facts: 9s, 10s, 11s, 12s

  3. Lesson 3

    Lesson 33: Writing Numbers Through Hundred Thousands

  4. Lesson 4

    Lesson 34: Writing Numbers Through Hundred Millions

  5. Lesson 5

    Lesson 35: Naming Mixed Numbers and Money

  6. Lesson 6

    Lesson 36: Fractions of a Dollar

  7. Lesson 7

    Lesson 37: Reading Fractions and Mixed Numbers from a Number Line

  8. Lesson 8

    Lesson 38: Multiplication Facts (Memory Group)

  9. Lesson 9

    Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

  10. Lesson 10Current

    Lesson 40: Capacity

  11. Lesson 11

    Investigation 4A: Tenths and Hundredths

  12. Lesson 12

    Investigation 4B: Relating Fractions and Decimals