Ticking Clocks and Turning Calendar

Given: The calendars for February 2024 and February 2025 are shown.

Concept: A leap year has 29 days in February; a non-leap year has 28 days.

Working:
- February 2024 calendar shows dates from 1 to 29, so it has 29 days.
- February 2025 calendar shows dates from 1 to 28, so it has 28 days.

Answer:
- Number of days in Feb 2024 = 29
- Number of days in Feb 2025 = 28

Given: 2024 is a leap year. Leap years occur every 4 years.

Concept: To find the previous leap years, subtract 4 each time. To find the next leap years, add 4 each time.

Working:
- 2 years before 2024: $2024 - 4 = 2020$; $2020 - 4 = 2016$
- 3 years after 2024: $2024 + 4 = 2028$; $2028 + 4 = 2032$; $2032 + 4 = 2036$

Answer: 2016, 2020, 2024, 2028, 2032, 2036

Given: A normal year has 365 days. A leap year has one additional day.

Concept: Leap year = Normal year + 1 extra day (29th February).

Working:
$$365 + 1 = 366 \text{ days}$$

Answer: A leap year has 366 days.

Note: This is a personal/activity-based question. Students should fill in their own favourite festivals and the months in which they are celebrated.

Sample Answer (students may write their own):

| Name of the Festival | Name of the Month |
|---|---|
| Diwali | October/November |
| Holi | March |
| Eid | Varies (Islamic calendar) |
| Christmas | December |
| Independence Day | August |

Students should fill in festivals they personally celebrate.

Note: This is a calendar-based activity question. The answer depends on the actual day when the student is solving it.

Concept: The days of the week in order are: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Sample Answer (assuming today is Wednesday):

a) Today: Wednesday
b) Yesterday: Tuesday
c) Tomorrow: Thursday
d) Day after tomorrow: Friday
e) Day before yesterday: Monday

Students should fill in the actual days based on the current date.

Given: July 1 is a Monday.

Concept: Days repeat every 7 days, so the next Monday is 7 days later, and the one after is 14 days later.

Working:
- Next Monday: $1 + 7 =$ July 8
- Monday after that: $1 + 14 =$ July 15

Answer: The next two Mondays fall on July 8 and July 15.

Given:
- Laali's date of birth: 04/07/2014 (4th July 2014)
- Chotu's date of birth: 04/12/2019 (4th December 2019)

Concept: The person born earlier (in an earlier year) is older.

Working:
- Laali was born in 2014 and Chotu was born in 2019.
- 2014 comes before 2019, so Laali is older.
- Difference in years: $2019 - 2014 = 5$ years and from July to December = 5 months.
- So Laali is 5 years and 5 months older than Chotu.

Laali will turn 5 years old on: $2014 + 5 =$ 4th July 2019 (04/07/2019)

Chotu's 10th birthday: $2019 + 10 =$ 4th December 2029 (04/12/2029)

Answer:
- Laali is older by 5 years and 5 months.
- Laali will turn 5 years old on 4th July 2019.
- Chotu's 10th birthday will be celebrated on 4th December 2029.

Note: This is a hands-on activity question. Students need to check an actual biscuit packet.

Concept:
- Age of packet = Today's date − Manufacturing date
- Days safe to eat = Expiry date − Today's date

Sample Working (assuming Manufacturing date: 1st March 2025, Expiry date: 1st September 2025, Today's date: 15th May 2025):

a) Age of packet:
- From 1st March to 15th May = 2 months and 14 days
- Answer: 2 months 14 days

b) Days safe to eat:
- From 15th May to 1st September = 3 months and 16 days
- Answer: 3 months 16 days

Students should fill in the actual dates from the packet they check.

Note: This is an observation and pattern-finding activity. The answer depends on the year's calendar being used.

Concept: Each month has a different number of days (28/29/30/31). The day on which a date falls shifts forward by the number of days in that month modulo 7.

Sample Working (for year 2025):
- July 15, 2025 = Tuesday
- July has 31 days → $31 \div 7 = 4$ weeks and 3 extra days → August 15 shifts 3 days forward
- August 15, 2025 = Tuesday + 3 = Friday
- August has 31 days → shifts 3 days forward again
- September 15, 2025 = Friday + 3 = Monday
- September has 30 days → $30 \div 7 = 4$ weeks and 2 extra days → shifts 2 days forward
- October 15, 2025 = Monday + 2 = Wednesday

Pattern noticed: The day on which the 15th falls shifts forward by 3 days for months with 31 days and by 2 days for months with 30 days.

Students should verify this with their own calendar and share observations in class.

Note: This is a research/exploration activity to be done with the help of parents and teachers.

Sample Answer:
- Hindu Calendar (Vikram Samvat): The year begins with the month of Chaitra (usually in March–April). The new year is celebrated as Gudi Padwa or Ugadi.
- Islamic Calendar (Hijri): The year begins with the month of Muharram. Since it is a lunar calendar, the date shifts each year in the Gregorian calendar.
- Sikh Calendar (Nanakshahi): The year begins on 14th March (1st Chet).

Students should explore and note the specific calendar used in their community.

Note: This is a research/exploration activity.

Sample Answer (Hindu Calendar months and approximate English months):

| Hindu Month | Approximate English Month |
|---|---|
| Chaitra | March–April |
| Vaishakha | April–May |
| Jyeshtha | May–June |
| Ashadha | June–July |
| Shravana | July–August |
| Bhadrapada | August–September |
| Ashwina | September–October |
| Kartika | October–November |
| Margashirsha | November–December |
| Pausha | December–January |
| Magha | January–February |
| Phalguna | February–March |

Students should explore the calendar of their own community and make a similar comparison.

Note: This is a research/exploration activity.

Sample Answer:
- Diwali falls in the Hindu month of Kartika (Amavasya — new moon night).
- Holi falls in the Hindu month of Phalguna (Purnima — full moon night).
- Eid-ul-Fitr falls at the end of the Islamic month of Ramadan.
- Guru Nanak Jayanti falls in the Sikh/Hindu month of Kartika (Purnima).

Students should identify festivals from their own community's calendar.

Note: This is an observation-based exploration activity.

Concept: In the Hindu and Islamic calendars, months are based on the lunar cycle.

Pattern observed:
- The full moon (Purnima) falls on the 15th day of every lunar month.
- The new moon (Amavasya) falls on the last day (30th or 29th) of every lunar month.
- The lunar cycle repeats approximately every 29–30 days.
- So the new moon and full moon occur roughly once every month, about 15 days apart from each other.

Students should check their community's calendar and verify this pattern.

Note: This is a research/exploration activity.

Sample Answer:
- In the Hindu calendar, the full moon day is called Purnima and the new moon day is called Amavasya.
- In the Islamic calendar, the new moon marks the beginning of each new month (e.g., the sighting of the crescent moon marks the start of Ramadan or Eid).
- In the Sikh tradition, the full moon day is called Puranmashi and the new moon day is called Masya.

Students should find out the specific names used in their own community's calendar.

Given: A table showing times in AM/PM format and 24-hour digital clock format.

Concept:
- AM times (12:00 AM to 11:59 AM): 12:00 AM = 00:00 hours; 1:00 AM = 01:00 hours, and so on up to 11:59 AM = 11:59 hours.
- PM times (12:00 PM to 11:59 PM): 12:00 PM = 12:00 hours; 1:00 PM = 13:00 hours; add 12 to the hour for 1 PM onwards.

Working:

1. 9:45 AM → 9:45 hours (AM times before noon stay the same)
$$\text{Answer: } 9:45 \text{ hours}$$

2. 11:20 hours → This is before 12:00 noon, so it is AM.
$$\text{Answer: } 11:20 \text{ AM}$$

3. 3:00 PM → $3 + 12 = 15$
$$\text{Answer: } 15:00 \text{ hours}$$

4. 5:20 PM → $5 + 12 = 17$
$$\text{Answer: } 17:20 \text{ hours}$$

5. 20:00 hours → $20 - 12 = 8$, and since it is after 12 noon, it is PM.
$$\text{Answer: } 8:00 \text{ PM}$$

Complete Table:

| Time in AM/PM | Time in digital clock |
|---|---|
| 9:45 AM | 9:45 hours |
| 11:20 AM | 11:20 hours |
| 3:00 PM | 15:00 hours |
| 5:20 PM | 17:20 hours |
| 8:00 PM | 20:00 hours |

Given: Raghav leaves at 8:20 AM and returns at 8:35 AM.

Concept: Time taken = Return time − Departure time.

Working:
$$8:35 - 8:20 = 15 \text{ minutes}$$

Answer: Raghav has taken 15 minutes.

Given: Start time = 10:20 AM; Time taken = 25 minutes.

Concept: Finish time = Start time + Time taken.

Working:
$$10:20 + 25 \text{ minutes} = 10:45 \text{ AM}$$
(Since $20 + 25 = 45$ minutes, and 45 < 60, the hour does not change.)

Answer: Raghav finished his homework at 10:45 AM.

The clock should show the minute hand pointing to 9 (45 minutes) and the hour hand between 10 and 11.

Given: Start time = 4:15 PM; Time taken = 45 minutes.

Concept: Finish time = Start time + Time taken.

Working:
$$4:15 + 45 \text{ minutes}$$
$$= 4 \text{ hours } (15 + 45) \text{ minutes}$$
$$= 4 \text{ hours } 60 \text{ minutes}$$
$$= 4 \text{ hours} + 1 \text{ hour} = 5:00 \text{ PM}$$
(Since $15 + 45 = 60$ minutes $= 1$ hour exactly.)

Answer: Muneera finished reading at 5:00 PM.

The clock should show the minute hand pointing to 12 (0 minutes) and the hour hand pointing to 5.

Given: Akira leaves at 8:00 AM; she takes 15 minutes to reach school.

Concept: Finish time = Start time + Time taken; 1 hour = 60 minutes.

Working:
$$8:00 + 15 \text{ minutes} = 8:15 \text{ AM}$$

Relation between 1 hour and 60 minutes:
$$1 \text{ hour} = 60 \text{ minutes}$$
So half an hour $= 30$ minutes, and a quarter hour $= 15$ minutes.

Answer: Akira reaches school at 8:15 AM.

The clock should show the minute hand pointing to 3 (15 minutes) and the hour hand slightly past 8.

Concept: On an analogue clock:
- The short (hour) hand points to the hour.
- The long (minute) hand points to the minutes. Each number on the clock represents 5 minutes (e.g., the hand pointing to 1 = 5 minutes, pointing to 2 = 10 minutes, pointing to 4 = 20 minutes, pointing to 7 = 35 minutes).

Analysis of each clock:

Clock 1:
- Raghu reads 12:04 — He is reading the minute hand position as the number 4 itself (confusing the number with the minutes). This is wrong.
- Raghav reads 12:20 — The minute hand is on 4, so $4 \times 5 = 20$ minutes. Hour hand is on 12. This is correct.
- Rani reads 04:00 — She is reading the minute hand as the hour. This is wrong.

Clock 2:
- Raghu reads 07:07 — He is reading the minute hand number (7) directly as minutes. This is wrong.
- Raghav reads 07:25 — The minute hand is on 5, so $5 \times 5 = 25$ minutes. Hour hand is on 7. This is correct.
- Rani reads 05:35 — She is reading the minute hand as the hour and multiplying the hour hand. This is wrong.

Clock 3:
- Raghu reads 03:07 — He is reading the minute hand number (7) directly as minutes. This is wrong.
- Raghav reads 03:35 — The minute hand is on 7, so $7 \times 5 = 35$ minutes. Hour hand is on 3. This is correct.
- Rani reads 07:15 — She is reading the minute hand as the hour. This is wrong.

Answer: Raghav is correct in all three cases.

How to read a clock correctly:
1. Look at the short (hour) hand — it tells the hour.
2. Look at the long (minute) hand — multiply the number it points to by 5 to get the minutes.
3. Write the time as Hour : Minutes.

For example, if the hour hand is on 3 and the minute hand is on 7: Time $= 3$ hours and $7 \times 5 = 35$ minutes $=$ 3:35.