Customary Units of Capacity
Semester 4B · Chapter 10 · Lesson 4 · MATH-4B-C10-L04
Before you begin: prerequisite check
Recall: Equal-group multiplication/division. Attempt these questions independently first.
How many ounces of weight are in 4 lb 4 oz?
Show answer and reasoning
Each pound weighs 16 ounces. 4×16+4=68.
How many ounces of weight are in 2 lb 1 oz?
Show answer and reasoning
Each pound weighs 16 ounces. 2×16+1=33.
Rename 56 oz as pounds and ounces.
Show answer and reasoning
56 = 16×3+8.
Key vocabulary
- metric unit
- meter, gram or liter family with decimal relationships
- customary unit
- inch, foot, pound or gallon family with its own conversion factor
- mixed units
- one measurement written using two units
- reference whole
- the full quantity of which a fraction is taken
Understand the concept
Capacity describes how much a container can hold. In U.S. customary measure, two cups make one pint, two pints make one quart, and four quarts make one gallon. That means a gallon contains sixteen cups. Model the relationship as a branching number bond: one gallon splits into four quarts, each quart into two pints, each pint into two cups. When adding volumes from different containers, change to a common unit first. A fluid ounce is a unit of capacity, unlike the ounce of weight used for masses.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Convert 8 gallons to cups.
Each gallon has 16 cups; multiply by 8.
Check 1: try it yourself
Convert 9 gallons to quarts.
Show answer and reasoning
Each gallon has 4 quarts; multiply by 9.
Worked example 2
Convert 6 gallons to cups.
Each gallon has 16 cups; multiply by 6.
Check 2: try it yourself
Convert 2 pints to cups.
Show answer and reasoning
Each pint has 2 cups; multiply by 2.
Worked example 3
Convert 2 quarts to pints.
Each quart has 2 pints; multiply by 2.
Check 3: try it yourself
Convert 3 quarts to cups.
Show answer and reasoning
Each quart has 4 cups; multiply by 3.
Guided practice
Convert 9 quarts to pints.
Show answer and reasoning
Each quart has 2 pints; multiply by 9.
How many whole quarts are in 6 pints?
Show answer and reasoning
Divide by 2 pints per quart: 6÷2=3.
Convert 4 quarts to cups.
Show answer and reasoning
Each quart has 4 cups; multiply by 4.
How many whole pints are in 6 cups?
Show answer and reasoning
Divide by 2 cups per pint: 6÷2=3.
Explain how a gallon can equal 16 cups even though 1 gallon is 4 quarts.
Show answer and reasoning
Use the unit chain gallon→4 quarts→2 pints each→2 cups each.
Independent practice
Convert 5 gallons to quarts.
Show answer and reasoning
Each gallon has 4 quarts; multiply by 5.
Convert 9 gallons to cups.
Show answer and reasoning
Each gallon has 16 cups; multiply by 9.
Convert 7 quarts to pints.
Show answer and reasoning
Each quart has 2 pints; multiply by 7.
How many whole gallons are in 8 quarts?
Show answer and reasoning
Divide by 4 quarts per gallon: 8÷4=2.
Convert 5 quarts to pints.
Show answer and reasoning
Each quart has 2 pints; multiply by 5.
Convert 8 quarts to cups.
Show answer and reasoning
Each quart has 4 cups; multiply by 8.
Convert 7 pints to cups.
Show answer and reasoning
Each pint has 2 cups; multiply by 7.
Convert 5 quarts to cups.
Show answer and reasoning
Each quart has 4 cups; multiply by 5.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Convert 7 quarts to cups. Explain or sketch the mathematical relationship.
Show answer and reasoning
Each quart has 4 cups; multiply by 7. State which quantities or geometric properties justify the method.
A learner claims: “Four quarts make four cups.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 1 quart = 4 cups, so 4 quarts = 16 cups. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Convert 3 gallons to cups.
Show answer and reasoning
Each gallon has 16 cups; multiply by 3.
How many whole gallons are in 128 cups?
Show answer and reasoning
Divide by 16 cups per gallon: 128÷16=8.
Convert 6 quarts to cups.
Show answer and reasoning
Each quart has 4 cups; multiply by 6.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.