Time and Elapsed Time

For Elementary Students

Units of Time

Time is measured in different units!

1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 week = 7 days
1 year = 365 days (366 in a leap year!)

Think about it like this: Time units are like stacking blocks — smaller units build into bigger ones!

Converting Time

Minutes to Seconds:

Multiply by 60!

Example: 3 minutes = ? seconds

• 3 × 60 = 180 seconds

Hours to Minutes:

Multiply by 60!

Example: 2 hours = ? minutes

• 2 × 60 = 120 minutes

Memory trick: There are 60 seconds in a minute and 60 minutes in an hour!

What Is Elapsed Time?

Elapsed time is how much time passes from start to finish!

Think about it like this: If a movie starts at 2:00 PM and ends at 4:00 PM, the elapsed time is 2 hours!

Finding Elapsed Time: Count Forward!

Example: A class starts at 9:15 AM and ends at 10:45 AM. How long is the class?

Step 1: Count from 9:15 to 10:15 → 1 hour

Step 2: Count from 10:15 to 10:45 → 30 minutes

Total: 1 hour 30 minutes

9:15 ──────→ 10:15 ──→ 10:45
     1 hour      30 min

Another Example

Example: A movie starts at 2:30 PM and ends at 5:00 PM. How long?

Step 1: 2:30 to 3:30 → 1 hour

Step 2: 3:30 to 4:30 → 1 hour

Step 3: 4:30 to 5:00 → 30 minutes

Total: 2 hours 30 minutes

Finding the End Time

If you know the start time and how long, you can find the end time!

Example: A train leaves at 9:50 AM. The trip takes 1 hour 35 minutes. When does it arrive?

Step 1: Start at 9:50 AM

Step 2: Add 1 hour → 10:50 AM

Step 3: Add 35 minutes → 11:25 AM

Answer: 11:25 AM

Crossing 12 O'Clock

Be careful when time crosses 12:00!

Example: Start at 10:30 AM, end at 1:15 PM. How long?

Step 1: 10:30 AM to 12:00 PM → 1 hour 30 minutes

Step 2: 12:00 PM to 1:15 PM → 1 hour 15 minutes

Total: 2 hours 45 minutes

For Junior High Students

Units of Time

Note: Unlike the metric system, time uses base-60 (sexagesimal system) for seconds and minutes, and base-24 for hours.

Converting Time Units

Hours to minutes: Multiply by 60

• 3 hours = 3 × 60 = 180 minutes

Minutes to hours: Divide by 60

• 150 minutes = 150 ÷ 60 = 2 hours 30 minutes

Why 2 hours 30 minutes?

• 150 ÷ 60 = 2 remainder 30
• 2 whole hours plus 30 minutes

Mixed units: Convert the leftover separately

• 200 minutes = ?
• 200 ÷ 60 = 3 remainder 20
• Answer: 3 hours 20 minutes

Days to hours: Multiply by 24

• 2 days = 2 × 24 = 48 hours

Minutes to seconds: Multiply by 60

• 5 minutes = 5 × 60 = 300 seconds

What Is Elapsed Time?

Elapsed time is the amount of time that passes between a start time and an end time.

Formula: elapsed time = end time − start time

Key concept: Elapsed time measures duration — how long something lasts.

Calculating Elapsed Time: Counting Forward Method

The easiest way is to count forward in steps from start to end.

Example: A movie starts at 2:15 PM and ends at 4:45 PM. How long is it?

Method: Count forward in convenient chunks

1. From 2:15 to 3:15 → 1 hour
2. From 3:15 to 4:15 → 1 hour
3. From 4:15 to 4:45 → 30 minutes

Total: 2 hours 30 minutes

Timeline:
2:15 ──────→ 3:15 ──────→ 4:15 ──→ 4:45
     1 hour       1 hour      30 min

Alternative: Subtraction Method

You can also subtract times directly.

Example: 4:45 PM − 2:15 PM

Step 1: Subtract minutes: 45 − 15 = 30 minutes

Step 2: Subtract hours: 4 − 2 = 2 hours

Answer: 2 hours 30 minutes

Note: If minutes don't subtract evenly, borrow 1 hour (60 minutes) from the hours.

Example: 5:20 PM − 3:45 PM

Step 1: Can't do 20 − 45, so borrow 1 hour

• 5:20 becomes 4:80 (4 hours and 80 minutes)

Step 2: Subtract minutes: 80 − 45 = 35 minutes

Step 3: Subtract hours: 4 − 3 = 1 hour

Answer: 1 hour 35 minutes

Crossing Noon or Midnight

When the time crosses 12:00, be careful with AM/PM!

Example: Start at 10:30 AM, end at 1:15 PM.

Method 1: Count forward

1. 10:30 AM to 12:00 PM → 1 hour 30 minutes
2. 12:00 PM to 1:15 PM → 1 hour 15 minutes
3. Total → 2 hours 45 minutes

Method 2: Use 24-hour clock

• 10:30 AM = 10:30
• 1:15 PM = 13:15
• Subtract: 13:15 − 10:30 = 2 hours 45 minutes

Finding End Time

If you know the start time and duration, add to find the end time.

Example: A train leaves at 9:50 AM and the trip takes 1 hour 35 minutes. When does it arrive?

Step 1: Start at 9:50 AM

Step 2: Add 1 hour → 10:50 AM

Step 3: Add 35 minutes → 11:25 AM

Answer: 11:25 AM

When adding minutes pushes you past 60, convert the extra into hours. Example: 50 + 35 = 85 minutes = 1 hour 25 minutes.

Another example: 3:40 PM + 2 hours 50 minutes

Step 1: Add hours: 3:40 + 2 hours = 5:40 PM

Step 2: Add minutes: 5:40 + 50 minutes

• 40 + 50 = 90 minutes = 1 hour 30 minutes
• 5:40 + 1 hour 30 minutes = 6:70 PM → convert → 7:10 PM

Easier way:

• 5:40 + 50 = 5:90 = 6:30 PM... wait, let me recalculate
• 5:40 + 20 minutes = 6:00 PM
• 6:00 PM + 30 minutes = 6:30 PM

Finding Start Time

If you know the end time and duration, subtract to find the start time.

Example: A concert ends at 9:30 PM and lasted 2 hours 45 minutes. When did it start?

Method: Subtract duration from end time

9:30 PM − 2 hours 45 minutes

Step 1: Subtract 2 hours: 9:30 − 2:00 = 7:30 PM

Step 2: Subtract 45 minutes: 7:30 − 45 minutes

• Can't do 30 − 45, so borrow 1 hour
• 7:30 becomes 6:90
• 90 − 45 = 45 minutes

Answer: 6:45 PM

12-Hour vs 24-Hour Time

12-hour clock: Uses AM and PM

• Midnight = 12:00 AM
• Noon = 12:00 PM
• 1:00 AM to 11:59 AM (morning)
• 1:00 PM to 11:59 PM (afternoon/evening)

24-hour clock (military time): No AM/PM needed

• Midnight = 00:00
• Noon = 12:00
• 1:00 PM = 13:00
• 11:00 PM = 23:00

Converting:

• AM times: Same in both (but write 00:00 for midnight)
• PM times (after 12): Add 12 to the hour
  • 1:00 PM = 13:00
  • 6:30 PM = 18:30

Real-Life Applications

School: "Class starts at 8:45 AM and ends at 10:20 AM" → Duration: 1 hour 35 minutes

Travel: "Flight departs 6:15 AM, arrives 11:40 AM" → Flight time: 5 hours 25 minutes

Cooking: "Cake bakes for 45 minutes starting at 3:20 PM" → Done at 4:05 PM

Work: "Shift is 7:00 AM to 3:30 PM" → Duration: 8 hours 30 minutes

Common Mistakes

Mistake 1: Forgetting to borrow when subtracting times

❌ 5:20 − 3:45 = 2:−25 (wrong!) ✓ Borrow: 4:80 − 3:45 = 1:35 (correct!)

Mistake 2: Adding more than 60 minutes without converting

❌ 3:40 + 50 minutes = 3:90 (wrong format!) ✓ Convert: 3:90 = 4:30 (correct!)

Mistake 3: Confusing AM and PM when crossing noon

✓ Always check: Does the time cross 12:00?

Tips for Success

Tip 1: Draw a timeline to visualize start and end times

Tip 2: Break elapsed time into chunks (hours first, then minutes)

Tip 3: Remember: 60 minutes = 1 hour

Tip 4: When adding/subtracting, handle hours and minutes separately

Tip 5: Double-check AM/PM when crossing noon or midnight

Practice