Telling Time to Quarter Past and Quarter To - Second Grade Mathematics
Just as a dollar can be divided into four 25-cent quarters, a 60-minute clock face can be partitioned into four equal 15-minute quarters. When 15 minutes have passed, the minute hand has traveled one-quarter of the way around the circle, pointing directly at the 3; we call this landmark quarter past. When 45 minutes have passed, only 15 minutes remain before the next hour arrives, pointing directly at the 9; we call this landmark quarter to. In this chapter, you will master reading and writing time to the quarter-hour, understand the mathematical fraction behind 15-minute intervals, and navigate the subtle movements of the hour hand.
The Four Quarters of an Hour
Dividing a clock face into four equal quadrants reveals the 15-minute rhythm of time.
The Four Clock Quarters (60 Minutes Divided by 4):
12 (00 min - On the Hour)
|
| Quadrant 1 (15 min)
9 -----------+----------- 3 (15 min - Quarter Past)
(45 min - |
Quarter To) | Quadrant 2 (15 min)
6 (30 min - Half Past)
60 minutes / 4 = 15 minutes per quarter!
The Quarter Landmarks:
Quarter 1 (15 minutes): Minute hand points at 3. Called "Quarter past" (or 15 minutes after). Quarter 2 (30 minutes): Minute hand points at 6. Called "Half past" (or 30 minutes after). Quarter 3 (45 minutes): Minute hand points at 9. Called "Quarter to" (or 15 minutes before the next hour). Quarter 4 (60 minutes): Minute hand points at 12. Completes the hour!
Understanding "Quarter Past" (:15)
When 15 minutes have elapsed, the minute hand points horizontally to the right at the 3.
Analog Clock at 4:15 (Quarter Past Four):
12
11 1
10 2
9 +=========> 3 <--- Minute Hand points directly at 3!
8 \ 4
7 \ 5 <--- Hour Hand is slightly past 4!
6
Digital Display: 04:15
Read Aloud: "Four fifteen" or "Quarter past four"
Hand Position at :15
At 4:15, the minute hand points straight at the 3 (15 minutes). Look at the short hour hand: it is not pointing directly at the 4 anymore! Because 15 minutes (one-quarter of the hour) has passed, the hour hand has moved one-quarter of the distance between 4 and 5. It sits just slightly past the 4.
Understanding "Quarter To" (:45)
"Quarter to" is one of the most sophisticated phrases in time-telling because it looks forward to the upcoming hour!
Analog Clock at 4:45 (Quarter to Five):
12
11 1
10 2
Minute <=== + 3
Hand at 9 8 / 4
7 / 5 <--- Hour Hand is VERY CLOSE to 5!
6
Digital Display: 04:45
Read Aloud: "Four forty-five" or "Quarter to five"
The Dual Wording of :45
When the digital clock reads 04:45, you can express it in two different ways: Way 1 (Looking back): "Four forty-five" (45 minutes have passed since 4 o'clock). Way 2 (Looking forward): "Quarter to five" (There is only one quarter of an hour—15 minutes—remaining until 5 o'clock arrives!).
The Hour Hand Trap at :45
At 4:45, three-quarters of the hour has passed, so the hour hand has traveled three-quarters of the way toward 5. It looks almost as if it is pointing directly at 5! Do not be fooled! The minute hand is at 9, which means 5 o'clock has NOT arrived yet. It will not be 5 o'clock for another 15 minutes. The hour is still 4, so the digital time is 4:45.
Practice Exercises
Exercise 1: An analog clock has its minute hand pointing at 3 and its hour hand resting slightly past 8. Write the time in digital notation and state two different ways to read it aloud.
Exercise 2: An analog clock shows the minute hand pointing at 9 and the hour hand resting very close to 2. Write the time in digital notation, and explain why the hour digit is 1 and not 2.
Exercise 3: How many minutes are in one quarter of an hour? How many minutes are in three quarters of an hour?
Exercise 4: Explain why the phrase "quarter to six" describes the digital time 5:45 rather than 6:45.
Solutions and Explanations
Solution to Exercise 1: In digital notation, the time is written as 08:15. Two ways to read it aloud are: "Eight fifteen" and "Quarter past eight" (or "fifteen minutes after eight").
Solution to Exercise 2: The digital time is 01:45. Although the hour hand is very close to 2, the minute hand is at 9 (45 minutes), meaning 15 minutes still remain before 2 o'clock officially arrives. Because the hour hand has not yet reached the 2, it is still the 1 o'clock hour.
Solution to Exercise 3: There are 15 minutes in one quarter of an hour (60 / 4 = 15). There are 45 minutes in three quarters of an hour (15 + 15 + 15 = 45).
Solution to Exercise 4: The word "to" in "quarter to six" means "until" or "before." It indicates that exactly one quarter of an hour (15 minutes) remains before 6:00 arrives. Subtracting 15 minutes backward from 6:00 lands at 5:45. The time 6:45 would be a quarter to seven.