Time Near the End of a Time Range: Complete Guide for 3rd Grade

Master understanding time near the end of a time range with these 5 detailed exercises including comprehensive explanations, rules, and visual learning aids.

Exercises: Time Near the End of a Time Range (1-3)
1 Identifying End Times
Exercise 1
A school day runs from 8:00 AM to 3:00 PM. Which time is closer to the end of the day: 11:00 AM or 2:30 PM? How do you know?
Key Definitions:

Time Range: The period between a start time and an end time. For example, 8:00 AM to 3:00 PM.

End of Range: The final time in a time range (3:00 PM in this example).

Close to End: A time that is near the final time in the range, with less time remaining.

Method:
  1. Identify the start and end times of the range
  2. Calculate how much time remains from each option to the end
  3. Compare the remaining times
  4. Determine which has less time remaining
Time Range
8:00 AM to 3:00 PM
Option 1
11:00 AM (2 hours to end)
Option 2
2:30 PM (30 minutes to end)
Step 1: Identify the time range

Start time: 8:00 AM

End time: 3:00 PM

Step 2: Calculate remaining time for 11:00 AM

From 11:00 AM to 3:00 PM = 4 hours

Step 3: Calculate remaining time for 2:30 PM

From 2:30 PM to 3:00 PM = 30 minutes

Step 4: Compare the remaining times

30 minutes < 4 hours

So 2:30 PM is closer to the end of the day

2:30 PM is closer to the end
Final answer:

2:30 PM is closer to the end of the day. At 2:30 PM, only 30 minutes remain until the end of the school day, while at 11:00 AM, 4 hours remain.

Applied rules:

• Time Remaining: End time - Current time = Time remaining

• Comparison: Less time remaining means closer to end

• Units: Convert to same units for comparison

2 Comparing Times in a Schedule
Exercise 2
A movie theater shows movies from 10:00 AM to 9:00 PM. Which is closer to the end of the showing time: 3:00 PM or 7:45 PM? How much time remains in each case?
Definition:

Time Comparison: Determining which of two times is closer to the end of a specified time range by calculating remaining time for each.

Time Range
10:00 AM to 9:00 PM
Option 1
3:00 PM (6 hours to end)
Option 2
7:45 PM (1 hour 15 min to end)
Step 1: Identify the time range

Start: 10:00 AM, End: 9:00 PM

Step 2: Calculate remaining time for 3:00 PM

From 3:00 PM to 9:00 PM = 6 hours

Step 3: Calculate remaining time for 7:45 PM

From 7:45 PM to 9:00 PM = 1 hour 15 minutes

Step 4: Compare the times

1 hour 15 minutes < 6 hours

So 7:45 PM is closer to the end

Step 5: Verify the calculations

Check: 7:45 PM + 1 hour 15 minutes = 9:00 PM ✓

7:45 PM is closer (1 hr 15 min vs 6 hr)
Final answer:

7:45 PM is closer to the end of the showing time. At 3:00 PM, 6 hours remain until 9:00 PM, but at 7:45 PM, only 1 hour and 15 minutes remain until the end.

Applied rules:

• Time Calculation: End - Current = Remaining time

• Comparison: Shorter remaining time = closer to end

• Verification: Add remaining time to current time to check

3 Activity Duration Near End
Exercise 3
A library opens at 9:00 AM and closes at 8:00 PM. If a student arrives at 6:30 PM, how much time does the student have before closing? Is this time near the end of the day?
Definition:

Near the End: A time that is relatively close to the end of a time range, typically within the last 25-30% of the total duration.

Open-Close
9:00 AM to 8:00 PM
Arrival
6:30 PM
Time Until Close
1 hour 30 minutes
Step 1: Calculate total operating time

From 9:00 AM to 8:00 PM = 11 hours

Step 2: Calculate remaining time after arrival

From 6:30 PM to 8:00 PM = 1 hour 30 minutes

Step 3: Determine if it's near the end

25% of 11 hours = 2.75 hours

Since 1.5 hours < 2.75 hours, this is near the end

Step 4: Verify the calculation

Check: 6:30 PM + 1 hour 30 minutes = 8:00 PM ✓

1 hour 30 minutes until close, near end
Final answer:

The student has 1 hour and 30 minutes before the library closes. Since the total operating time is 11 hours, and only 1.5 hours remain, this is considered near the end of the day.

Applied rules:

• Total Duration: End time - Start time = Total time

• Remaining Time: End time - Arrival time = Time left

• Near End: Generally within last 25-30% of total time

Time Range Fundamentals
End Time - Start Time = Total Duration
Basic Formula
Time Range
Start to End
Entire period
Near End
Last 25-30%
Close to finish
Remaining
End - Current
Time left
Key Concepts:

Time Range: The span of time from a start time to an end time.

Near End: When a current time is close to the end of the range.

Remaining Time: How much time is left until the end of the range.

Calculation Techniques:
  1. Identify Range: Find the start and end times
  2. Calculate Total: End - Start = Total duration
  3. Find Current: Identify the time in question
  4. Calculate Remaining: End - Current = Time left
  5. Determine Position: Assess if near the end
Tip 1: Convert all times to the same format (AM or PM) before calculating.
Tip 2: Draw a timeline to visualize the time range.
Tip 3: "Near the end" typically means within the last 25-30% of the total time.
Tip 4: Always verify by adding remaining time to current time to get end time.
Common Mistake: Forgetting to convert between AM and PM when calculating time spans.
Memory Aid: "End minus current equals time remaining."
Essential Rules:

• Total duration = End time - Start time

• Remaining time = End time - Current time

• Near end = Within last 25-30% of total duration

• Always verify calculations by checking the sum

Exercises: Advanced Time Range Problems (4-5)
4 Percentage-Based End Time
Exercise 4
A store operates from 7:00 AM to 10:00 PM. What time is at the beginning of the "near end" portion of the day? In other words, from what time is it considered near the end of the day?
Definition:

Percentage-Based Calculation: Finding a specific point in time based on a percentage of the total duration.

Operating Hours
7:00 AM to 10:00 PM
Total Duration
15 hours
Near End Start
7:30 PM
Step 1: Calculate total operating time

From 7:00 AM to 10:00 PM = 15 hours

Step 2: Calculate 25% of total time

25% of 15 hours = 0.25 × 15 = 3.75 hours = 3 hours 45 minutes

Step 3: Find when the "near end" period begins

End time - Near end duration = Start of near end period

10:00 PM - 3 hours 45 minutes = 6:15 PM

Step 4: Verify the calculation

From 6:15 PM to 10:00 PM = 3 hours 45 minutes

3 hours 45 minutes is 25% of 15 hours ✓

Near end starts at 6:15 PM
Final answer:

It is considered near the end of the day starting from 6:15 PM. From this time until 10:00 PM, there are 3 hours and 45 minutes remaining, which is 25% of the total operating time.

Applied rules:

• Percentage Calculation: % of total = (percentage/100) × total time

• Time Subtraction: End time - duration = start time

• Verification: Check that calculated time equals expected percentage

5 Multi-Period Time Range
Exercise 5
A school bus route operates from 6:30 AM to 5:00 PM with a break from 12:00 PM to 1:00 PM. If it's 4:15 PM, how much time remains in the active service period? Is this near the end?
Definition:

Active Service Period: The time when operations are ongoing, excluding breaks or downtime.

Schedule
6:30 AM to 5:00 PM
Break
12:00 PM to 1:00 PM
Active Time Left
45 minutes
Step 1: Calculate total scheduled time

From 6:30 AM to 5:00 PM = 10 hours 30 minutes

Step 2: Calculate active service time

Active time = Total time - Break time

Active time = 10 hours 30 minutes - 1 hour = 9 hours 30 minutes

Step 3: Determine active time after break

Before break: 6:30 AM to 12:00 PM = 5 hours 30 minutes

After break: 1:00 PM to 5:00 PM = 4 hours

Total active: 5 hours 30 minutes + 4 hours = 9 hours 30 minutes

Step 4: Calculate remaining active time at 4:15 PM

From 4:15 PM to 5:00 PM = 45 minutes

Step 5: Determine if it's near the end

25% of 9 hours 30 minutes = 2.375 hours = 2 hours 22.5 minutes

Since 45 minutes < 2 hours 22.5 minutes, this is near the end

45 minutes active time left, near end
Final answer:

There are 45 minutes of active service time remaining. Since the total active service time is 9 hours and 30 minutes, and only 45 minutes remain, this is considered near the end of the service period.

Applied rules:

• Active Time: Total time - Break time = Active operational time

• Remaining Calculation: End of active period - Current time

• Near End Assessment: Compare to 25-30% of active time

Complete Time Range Summary
Remaining Time = End Time - Current Time
Core Formula
Key definitions:

Time Range: The period between a start time and an end time.

Near End: When a current time is close to the end of the range (typically within 25-30%).

Remaining Time: How much time is left until the end of the range.

Complete methodology:
  1. Identify Range: Locate the start and end times
  2. Calculate Total: Determine the total duration of the range
  3. Assess Current: Identify the time in question
  4. Calculate Remaining: Subtract current from end time
  5. Determine Proximity: Assess if near the end using percentages
Tip 1: Always convert times to the same format before calculating.
Tip 2: Draw timelines to visualize complex time ranges.
Tip 3: Remember that "near the end" is subjective but typically means 25-30%.
Tip 4: Always verify your calculations by adding back the remaining time.
Common errors: Mixing AM/PM formats, forgetting breaks in schedules, miscalculating percentages.
Key memorization: End - Current = Remaining, Near end ≈ 25-30% of total.
Essential rules to remember:

• Total duration = End time - Start time

• Remaining time = End time - Current time

• Near end = Within last 25-30% of total duration

• Always verify calculations by checking the sum

• Consider breaks when calculating active time periods

Questions & Answers

Question: How do I know if a time is "near the end"? Is there a specific rule for how close it has to be?

Answer: There isn't a strict rule, but generally, "near the end" means within the last 25-30% of the total time range:

  • If an activity runs for 4 hours, "near the end" would be the last 1 hour (25%)
  • If a day runs from 8 AM to 8 PM (12 hours), "near the end" would be after 5 PM (last 3 hours)
  • This is about 1/4 to 1/3 of the total time

The exact percentage can vary depending on context, but 25-30% is a good guideline to use!

Think of it like a race: if you're in the last quarter of the race, you're near the end!

Question: What if the time range crosses from AM to PM? How do I calculate the total time then?

Answer: When calculating across AM and PM, you can think of it in parts:

  • From 9:00 AM to 3:00 PM: Calculate as 9:00 AM to 12:00 PM (3 hours) + 12:00 PM to 3:00 PM (3 hours) = 6 hours total
  • Or convert to 24-hour format: 9:00 to 15:00 = 6 hours
  • From 10:00 AM to 2:00 PM: This is 4 hours (you can count: 10-11-12-1-2)

The key is to remember that 12:00 PM is noon, and times continue from there. So 1:00 PM is 13:00 in 24-hour time, 2:00 PM is 14:00, and so on.

Practice with simple examples first, then move to more complex ones!

Question: How can I practice identifying time near the end of a range at home? What are some real-life examples?

Answer: There are many opportunities at home:

  • TV shows: What time is near the end of a 30-minute program?
  • Bedtime: If bedtime is 8:00 PM, is 7:30 PM near the end of playtime?
  • Meal times: If dinner is at 6:00 PM, is 5:15 PM near the end of the afternoon?
  • Sports practice: When is practice near ending?
  • Store hours: When is a store near closing time?

Make it fun by setting up your own time ranges and asking yourself: "Is this time near the end?" You can also look at TV guides, store hours, or school schedules to practice!

The more you practice with real situations, the better you'll get at estimating time relationships!