Solved Exercises on Measurement Word Problems in Grade 3

Master measurement word problems: length, weight, capacity, and time through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Length word problem
Exercise 1
Sarah's ribbon is 3 feet long. She cuts off 8 inches. How long is her ribbon now?
Definition:

Length word problem: A problem involving distances or measurements that requires converting between units

Problem-solving method:
  1. Read the problem carefully and identify what's being asked
  2. Identify the units of measurement involved
  3. Convert all measurements to the same unit
  4. Solve the problem using arithmetic operations
  5. Express the answer in the required unit
Original Length
3 feet
Cut Off
8 inches
Conversion
1 foot = 12 inches
Step 1: Convert feet to inches

3 feet = 3 × 12 = 36 inches

Step 2: Subtract the cut-off amount

36 inches - 8 inches = 28 inches

Step 3: Express the final answer

Sarah's ribbon is 28 inches long

Sarah's ribbon is 28 inches long
Final answer:

Sarah's ribbon is 28 inches long

Applied rules:

• Conversion: 1 foot = 12 inches

• Subtraction: Same units required for subtraction

• Problem-solving: Convert to same unit first

2 Weight word problem
Exercise 2
A bag of apples weighs 4 pounds. If 12 ounces of apples are eaten, how much does the bag weigh now?
Definition:

Weight word problem: A problem involving mass or weight measurements that may require unit conversions

Original Weight
4 pounds
Eaten Amount
12 ounces
Conversion
1 pound = 16 ounces
Final Weight
4 lbs - 12 oz
Step 1: Convert pounds to ounces

4 pounds = 4 × 16 = 64 ounces

Step 2: Subtract the eaten amount

64 ounces - 12 ounces = 52 ounces

Step 3: Convert back to pounds and ounces

52 ÷ 16 = 3 remainder 4, so 3 pounds 4 ounces

The bag weighs 3 pounds 4 ounces
Final answer:

The bag now weighs 3 pounds 4 ounces

Applied rules:

• Conversion: 1 pound = 16 ounces

• Subtraction: Same units required

• Division: To convert to mixed units

3 Capacity word problem
Exercise 3
A large water bottle holds 2 quarts. If 3 cups are poured out, how much water remains?
Definition:

Capacity word problem: A problem involving liquid volume measurements requiring unit conversions

Original Capacity
2 quarts
Poured Out
3 cups
Conversion
1 quart = 4 cups
Remaining
8 - 3 = 5 cups
Step 1: Convert quarts to cups

2 quarts = 2 × 4 = 8 cups

Step 2: Subtract the poured amount

8 cups - 3 cups = 5 cups

Step 3: Express as mixed number if needed

5 cups = 1 quart 1 cup (since 4 cups = 1 quart)

Step 4: Verify the calculation

1 quart 1 cup = 4 + 1 = 5 cups ✓

5 cups (or 1 quart 1 cup) remain
Final answer:

5 cups (or 1 quart 1 cup) of water remain

Applied rules:

• Conversion: 1 quart = 4 cups

• Subtraction: Same units required

• Verification: Check calculations

Measurement Word Problems Summary
1 foot = 12 inches
Length Conversion
Weight
1 pound = 16 ounces
Ounces in a pound
Capacity
1 quart = 4 cups
Cups in a quart
Time
1 hour = 60 minutes
Minutes in an hour
Key definitions:

Measurement word problem: A mathematical problem presented in sentence form that involves measuring length, weight, capacity, or time.

Unit conversion: Changing one unit of measurement to another using known relationships.

Problem-solving strategy: A systematic approach to solve mathematical problems.

Five-step problem-solving method:
  1. Read: Understand what the problem is asking
  2. Plan: Decide what operations to use and identify units
  3. Solve: Perform calculations, including unit conversions
  4. Check: Verify if the answer makes sense
  5. Answer: State the answer in a complete sentence
Tip 1: Always identify the units before starting. Convert to the same unit if needed.
Tip 2: Draw a picture or diagram to visualize the problem.
Tip 3: Look for key words: "more than," "less than," "total," "combined."
Tip 4: Estimate your answer first to check reasonableness.
Common errors: Forgetting to convert units, misreading the question, calculation mistakes.
Success strategy: Read twice, plan once, solve once, check once.
Key conversion facts:

• Length: 1 foot = 12 inches, 1 yard = 3 feet

• Weight: 1 pound = 16 ounces

• Capacity: 1 cup = 8 fluid ounces, 1 pint = 2 cups, 1 quart = 2 pints, 1 gallon = 4 quarts

• Time: 1 minute = 60 seconds, 1 hour = 60 minutes

Solution: Exercises 4 to 5
4 Time word problem
Exercise 4
Emma starts homework at 3:15 PM. She works for 45 minutes. What time does she finish?
Definition:

Time word problem: A problem involving the passage of time or calculating start/end times

Start Time
3:15 PM
Duration
45 minutes
Calculation
3:15 + 45 min
End Time
4:00 PM
Step 1: Start with the beginning time

Emma starts at 3:15 PM

Step 2: Add the duration

From 3:15 PM, add 45 minutes

Step 3: Count by intervals

3:15 + 45 minutes = 3:15 + 45 = 3:60 = 4:00

Step 4: Express the final time

Emma finishes at 4:00 PM

Emma finishes at 4:00 PM
Final answer:

Emma finishes her homework at 4:00 PM

Applied rules:

• Time addition: Add minutes to minutes

• Carry over: 60 minutes = 1 hour

• Verification: Check if the time makes sense

5 Multi-step word problem
Exercise 5
A rope is 5 feet long. It is cut into 3 equal pieces. How long is each piece in inches?
Definition:

Multi-step problem: A problem requiring multiple operations to reach the solution

Original Length
5 feet
Number of Pieces
3 pieces
Conversion
1 foot = 12 inches
Final Answer
20 inches each
Step 1: Convert feet to inches

5 feet = 5 × 12 = 60 inches

Step 2: Divide the total length by number of pieces

60 inches ÷ 3 = 20 inches

Step 3: Express the answer in required unit

Each piece is 20 inches long

Step 4: Verify the result

20 inches × 3 pieces = 60 inches = 5 feet ✓

Each piece is 20 inches long
Final answer:

Each piece of rope is 20 inches long

Applied rules:

• Conversion: 1 foot = 12 inches

• Division: Equal sharing requires division

• Verification: Multiply back to check

Comprehensive Measurement Word Problems Guide
\text{New Amount} = \text{Original Amount} \pm \text{Change Amount}
General Problem Formula
Key definitions:

Word problem: A mathematical problem expressed in ordinary language rather than mathematical notation

Conversion: Changing from one unit of measurement to another

Estimation: Finding an approximate answer to check reasonableness

Complete problem-solving process:
  1. Understand: Read the problem carefully and identify what is being asked
  2. Identify: Find the important information and units
  3. Plan: Decide on the operations needed and unit conversions
  4. Solve: Carry out the calculations step by step
  5. Check: Verify the answer makes sense
  6. Communicate: Write the answer in a complete sentence
Tip 1: Circle or underline key numbers and units in the problem.
Tip 2: Draw pictures or models to represent the situation.
Tip 3: Always convert to the same unit before adding or subtracting.
Tip 4: Check if your answer is reasonable by estimating.
Common errors: Mixing units, misreading problems, calculation mistakes, forgetting to answer the question asked.
Success strategies: Practice regularly, use visual aids, show all work, check answers.
Essential measurement facts:

• Length: 12 inches = 1 foot, 3 feet = 1 yard

• Weight: 16 ounces = 1 pound

• Capacity: 8 ounces = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon

• Time: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day

Measurement Problem-Solving Strategy
Problem-Solving Steps
The 5-step approach to solving measurement word problems:
Read → Plan → Solve → Check → Answer

Strategy Explanation:

  • Read: Understand the problem completely
  • Plan: Identify operations and unit conversions needed
  • Solve: Perform calculations systematically
  • Check: Verify the answer makes sense
  • Answer: Express the solution appropriately

Questions & Answers

Question: I get confused when problems have different units like feet and inches. How do I know when to convert them?

Answer: You need to convert units when you're performing operations (addition, subtraction) with different units. Here's the rule:

  • Before adding or subtracting measurements, convert them to the same unit.
  • If the problem asks for the answer in a specific unit, convert your final answer to that unit.
  • When multiplying or dividing, keep track of the units in your calculations.

Example: If you have 3 feet and 8 inches, convert the 3 feet to inches (3 × 12 = 36 inches), then add: 36 + 8 = 44 inches.

Always read the question carefully to see what unit the answer should be in!

Question: How do I know whether to add or subtract in measurement word problems?

Answer: Look for key words and phrases in the problem:

  • Add when: "total," "altogether," "combined," "more than," "increased by," "sum"
  • Subtract when: "left," "remaining," "less than," "decreased by," "take away," "difference"
  • Multiply when: "each," "times," "product," "groups of," "equal parts"
  • Divide when: "per," "each," "shared equally," "split into," "how many groups"

Also consider the context: If something is being added to a quantity, you add. If something is being taken away, you subtract.

Always reread the problem to make sure your operation makes sense!

Question: My answer seems too big or too small. How can I check if it's reasonable?

Answer: Estimation is your best tool for checking reasonableness! Here's how:

  • Round numbers: Make the numbers easier to work with mentally
  • Do a quick calculation: Get an approximate answer
  • Compare: See if your exact answer is close to your estimate

Example: If the problem is 3 feet minus 8 inches, estimate: 36 inches - 8 inches ≈ 30 inches. If your answer is 28 inches, that's reasonable.

Also think about real-world benchmarks: A person isn't 100 feet tall, and a pencil isn't 2 miles long!

Always ask yourself: "Does this answer make sense in the context of the problem?"