Solved Exercises on Elapsed Time to the Nearest Hour in Grade 3

Master elapsed time calculations: finding duration between times rounded to the nearest hour through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Elapsed Time
Exercise 1
Sarah started reading at 2:00 PM and finished at 5:00 PM. How much time passed?
Definition:

Elapsed Time: The amount of time that passes between a start time and an end time.

Elapsed Time Method:
  1. Identify the start time and end time
  2. Count the hours from start to end
  3. If minutes are involved, round to the nearest hour
Step 1: Identify start and end times

Start time: 2:00 PM, End time: 5:00 PM

Step 2: Count the hours

From 2:00 PM to 3:00 PM = 1 hour
From 3:00 PM to 4:00 PM = 1 hour
From 4:00 PM to 5:00 PM = 1 hour

Step 3: Add the hours together

1 + 1 + 1 = 3 hours

3 hours passed
Final answer:

3 hours passed between 2:00 PM and 5:00 PM.

Applied rules:

• Time Subtraction: End time - Start time = Elapsed time

• Counting Hours: Each full hour represents 1 unit of time

• Rounding: Times already on the hour don't require rounding

2 Elapsed Time with Rounding
Exercise 2
The movie started at 6:45 PM and ended at 9:15 PM. How much time passed? Round to the nearest hour.
Definition:

Rounding to the Nearest Hour: Round times ending in 30 minutes or more up to the next hour, otherwise round down.

Step 1: Round start time

6:45 PM is closer to 7:00 PM than to 6:00 PM, so round UP to 7:00 PM

Step 2: Round end time

9:15 PM is closer to 9:00 PM than to 10:00 PM, so round DOWN to 9:00 PM

Step 3: Calculate elapsed time

From 7:00 PM to 8:00 PM = 1 hour
From 8:00 PM to 9:00 PM = 1 hour
Total: 2 hours

Step 4: Verify the rounding

Original: 6:45 PM to 9:15 PM = 2 hours 30 minutes
Rounded: 7:00 PM to 9:00 PM = 2 hours

2 hours passed
Final answer:

About 2 hours passed between 6:45 PM and 9:15 PM when rounded to the nearest hour.

Applied rules:

• Rounding Rule: Minutes ≥ 30 round UP, Minutes < 30 round DOWN

• Estimation: Rounding simplifies time calculations

• Accuracy: Rounded time gives a good approximation of actual time

3 Crossing Midnight
Exercise 3
Alex went to bed at 10:00 PM and woke up at 7:00 AM. How many hours did he sleep?
Definition:

Crossing Midnight: When calculating elapsed time that goes past 12:00 AM, split the calculation into two parts: before midnight and after midnight.

Step 1: Identify the time periods

Before midnight: 10:00 PM to 12:00 AM
After midnight: 12:00 AM to 7:00 AM

Step 2: Calculate time before midnight

From 10:00 PM to 11:00 PM = 1 hour
From 11:00 PM to 12:00 AM = 1 hour
Total: 2 hours

Step 3: Calculate time after midnight

From 12:00 AM to 1:00 AM = 1 hour
From 1:00 AM to 2:00 AM = 1 hour
From 2:00 AM to 3:00 AM = 1 hour
From 3:00 AM to 4:00 AM = 1 hour
From 4:00 AM to 5:00 AM = 1 hour
From 5:00 AM to 6:00 AM = 1 hour
From 6:00 AM to 7:00 AM = 1 hour
Total: 7 hours

Step 4: Add the two periods together

2 hours (before midnight) + 7 hours (after midnight) = 9 hours

Alex slept for 9 hours
Final answer:

Alex slept for 9 hours from 10:00 PM to 7:00 AM.

Applied rules:

• Splitting Periods: Break time calculations at midnight (12:00 AM)

• AM/PM Understanding: AM comes after PM in chronological order

• Sequential Addition: Add separate time periods to get total elapsed time

Elapsed Time Rules and Methods
Elapsed Time = End Time - Start Time
Time Calculation Formula
Rounding Rule
≥ 30 min → Round Up
Round to nearest hour
Time Subtraction
End - Start = Elapsed
Calculate duration
Crossing Midnight
Split at 12:00 AM
Calculate in two parts
Key Definitions:

Start Time: The beginning time of an event

End Time: The finishing time of an event

Elapsed Time: The total amount of time that passes between start and end

Basic Rule: Subtract the start time from the end time to find elapsed time.
Rounding: Round to the nearest hour when instructed.
Crossing Midnight: Split calculations at 12:00 AM for overnight events.
Tip 1: Use a number line to visualize time passing from start to end.
Tip 2: When crossing midnight, think of it as two separate time periods.
Tip 3: For rounding, if minutes are 30 or more, round up; less than 30, round down.
Solution: Exercises 4 to 5
4 Real-Life Application
Exercise 4
A soccer game started at 3:25 PM and lasted for 1 hour and 50 minutes. What time did it end? Round to the nearest hour.
Definition:

Time Addition: Adding a duration to a start time to find the end time.

Step 1: Add the full hour to start time

3:25 PM + 1 hour = 4:25 PM

Step 2: Add the remaining minutes

4:25 PM + 50 minutes = 4:75 PM = 5:15 PM (since 75 minutes = 1 hour 15 minutes)

Step 3: Round to the nearest hour

5:15 PM is closer to 5:00 PM than to 6:00 PM, so round DOWN to 5:00 PM

Step 4: Verify the calculation

Start: 3:25 PM, Duration: 1 hour 50 minutes, End: 5:15 PM ≈ 5:00 PM

The game ended at 5:00 PM (rounded)
Final answer:

The soccer game ended at approximately 5:00 PM when rounded to the nearest hour.

Applied rules:

• Time Addition: Add hours and minutes separately

• Conversion: 60 minutes equals 1 hour

• Rounding: Apply rounding rules after calculating exact time

5 Multi-Day Elapsed Time
Exercise 5
A camping trip started on Saturday at 4:00 PM and ended on Sunday at 11:00 AM. How many hours did the trip last?
Definition:

Multi-Day Elapsed Time: Calculating time that spans across multiple days, including overnight periods.

Step 1: Break down the time periods

Saturday: 4:00 PM to 12:00 AM (midnight)
Overnight: 12:00 AM Saturday night to 12:00 AM Sunday morning
Sunday: 12:00 AM to 11:00 AM

Step 2: Calculate Saturday evening time

From 4:00 PM to 5:00 PM = 1 hour
From 5:00 PM to 6:00 PM = 1 hour
From 6:00 PM to 7:00 PM = 1 hour
From 7:00 PM to 8:00 PM = 1 hour
From 8:00 PM to 9:00 PM = 1 hour
From 9:00 PM to 10:00 PM = 1 hour
From 10:00 PM to 11:00 PM = 1 hour
From 11:00 PM to 12:00 AM = 1 hour
Total: 8 hours

Step 3: Calculate overnight time

From 12:00 AM Saturday night to 12:00 AM Sunday morning = 12 hours

Step 4: Calculate Sunday morning time

From 12:00 AM to 1:00 AM = 1 hour
From 1:00 AM to 2:00 AM = 1 hour
From 2:00 AM to 3:00 AM = 1 hour
From 3:00 AM to 4:00 AM = 1 hour
From 4:00 AM to 5:00 AM = 1 hour
From 5:00 AM to 6:00 AM = 1 hour
From 6:00 AM to 7:00 AM = 1 hour
From 7:00 AM to 8:00 AM = 1 hour
From 8:00 AM to 9:00 AM = 1 hour
From 9:00 AM to 10:00 AM = 1 hour
From 10:00 AM to 11:00 AM = 1 hour
Total: 11 hours

Step 5: Add all time periods together

8 hours (Saturday evening) + 12 hours (overnight) + 11 hours (Sunday morning) = 31 hours

The camping trip lasted 31 hours
Final answer:

The camping trip lasted 31 hours from Saturday 4:00 PM to Sunday 11:00 AM.

Applied rules:

• Day Separation: Calculate time for each day separately

• Overnight Calculation: Account for the full 12-hour period from midnight to midnight

• Sequential Addition: Add all time periods to get the total elapsed time

Key Concepts: Elapsed Time, Definitions, Methods, and Formulas
Elapsed Time = End Time - Start Time
Time Calculation Formula
Key definitions:

Elapsed Time: The amount of time that passes between a start time and an end time

Start Time: The time when an event begins

End Time: The time when an event finishes

Complete methodology:
  1. Identify times: Find the start and end times of the event
  2. Check for crossing midnight: If the time period goes past 12:00 AM, split the calculation
  3. Calculate each period: Count the hours between times
  4. Add periods together: Combine all time periods for the total
Tip 1: Draw a timeline to visualize the passage of time.
Tip 2: For rounding, think: "Is it closer to the next hour or the previous hour?"
Tip 3: Remember that 12:00 AM is midnight, and 12:00 PM is noon.
Tip 4: Check your answer by adding the elapsed time back to the start time.
Common errors: Forgetting to cross midnight, incorrect rounding, miscounting hours.
Exam preparation: Practice with various time combinations, work on rounding skills, understand AM/PM differences.
Formulas to know by heart:

• Basic Formula: Elapsed Time = End Time - Start Time

• Rounding Rule: Minutes ≥ 30 round UP, Minutes < 30 round DOWN

• Crossing Midnight: Split calculation at 12:00 AM

• Time Addition: Start Time + Duration = End Time

Exercise with Visualization: Daily Schedule
Exercise 6: Time Management
Daily schedule for a 3rd grader:
Wake up: 7:00 AM
Breakfast: 7:30 AM - 8:00 AM
School: 8:00 AM - 3:00 PM
Homework: 3:30 PM - 4:30 PM
Dinner: 6:00 PM - 6:30 PM
Bedtime: 8:30 PM
How many hours are spent awake during the day?

Analysis: Calculate the time from wake up to bedtime.

  • Wake up: 7:00 AM
  • Bedtime: 8:30 PM
  • From 7:00 AM to 8:00 AM = 1 hour
  • From 8:00 AM to 9:00 AM = 1 hour
  • ...continuing to 8:00 PM to 8:30 PM = 12.5 hours total
  • Rounded to nearest hour: 13 hours

Questions & Answers

Question: My 3rd grade students are confused about AM and PM. How can I help them understand the difference?

Answer: Here are helpful ways to teach AM and PM:

  • Memory aid: AM = "After Midnight" (from midnight to noon), PM = "Past Midday" (from noon to midnight)
  • Visual reference: "AM is Morning, PM is Past Midday"
  • Daily activities: Connect times to familiar activities

Examples:

  • AM: Wake up at 7:00 AM, eat breakfast at 8:00 AM, lunch at 12:00 PM
  • PM: Eat dinner at 6:00 PM, go to bed at 8:00 PM

Create a daily timeline showing activities in AM and PM to reinforce the concept.

Question: My child struggles with rounding time to the nearest hour. What strategies can help them?

Answer: Effective strategies for rounding time:

  • Visual clock: Show the minutes hand at 12, 15, 30, 45 positions
  • Rule of thumb: If minutes are 30 or more, round UP to next hour; if less than 30, round DOWN
  • Halfway point: Think of 30 minutes as the halfway point to the next hour

Examples:

  • 2:15 rounds down to 2:00 (less than 30 minutes)
  • 2:45 rounds up to 3:00 (more than 30 minutes)
  • 2:30 rounds up to 3:00 (exactly 30 minutes)

Practice with a real clock showing different minute positions to build intuition.

Question: I don't understand how to count hours when something starts in the morning and ends in the evening. It's confusing!

Answer: Here's a simple way to handle AM to PM time calculations:

  1. Count to noon: First, count hours from start time to 12:00 PM
  2. Count afternoon hours: Then count from 12:00 PM to end time
  3. Add them together: Combine both counts for total

Example: From 9:00 AM to 4:00 PM

  • 9:00 AM to 10:00 AM = 1 hour
  • 10:00 AM to 11:00 AM = 1 hour
  • 11:00 AM to 12:00 PM = 1 hour
  • 12:00 PM to 1:00 PM = 1 hour
  • 1:00 PM to 2:00 PM = 1 hour
  • 2:00 PM to 3:00 PM = 1 hour
  • 3:00 PM to 4:00 PM = 1 hour
  • Total: 7 hours

You can also think: "From 9:00 AM to 4:00 PM is 7 hours because 4:00 PM is the same as 16:00 in 24-hour time, and 16 - 9 = 7."

Question: When do I need to split the calculation at midnight? I'm not sure when this is necessary.

Answer: You need to split at midnight when your time period crosses over from one day to the next. Here's how to identify it:

  • Look for PM to AM: Any time that goes from PM to AM crosses midnight
  • Look for later time being smaller: If the end time number is smaller than the start time number and both are PM or both are AM
  • Common examples: Going to bed at 9:00 PM and waking up at 7:00 AM

Example: From 10:00 PM to 7:00 AM

  • Before midnight: 10:00 PM to 12:00 AM = 2 hours
  • After midnight: 12:00 AM to 7:00 AM = 7 hours
  • Total: 2 + 7 = 9 hours

If you start and end on the same day within the same AM or PM period, you don't need to split at midnight!

Question: How do I know if I should round up or down? Sometimes I get confused about 30 minutes.

Answer: Here's an easy rule to remember for rounding to the nearest hour:

  • Minutes 0-29: Round DOWN to the previous hour (e.g., 3:15 → 3:00)
  • Minutes 30-59: Round UP to the next hour (e.g., 3:45 → 4:00)
  • Exactly 30 minutes: Round UP to the next hour (e.g., 3:30 → 4:00)

Think of 30 minutes as the halfway point - it's exactly in the middle, so we round up to the next hour.

More examples:

  • 2:05 rounds down to 2:00 (5 minutes < 30)
  • 2:29 rounds down to 2:00 (29 minutes < 30)
  • 2:30 rounds up to 3:00 (exactly 30 minutes)
  • 2:45 rounds up to 3:00 (45 minutes > 30)

The key is: if the minutes part is 30 or more, round up!