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Time and Calendar - Calendar and Leap Year

Grade 3ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A calendar is a structured chart that helps us keep track of days, weeks, and months in a year. Imagine it as a large rectangular grid where each box represents a date, and the columns represent the seven days of the week starting from Sunday or Monday.

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There are 1212 months in a year. Some months have 3131 days, some have 3030 days, and February is special. You can visualize this using the 'Knuckle Rule': Make a fist; the 'bumps' or knuckles represent months with 3131 days (Jan, Mar, May, July, Aug, Oct, Dec) and the 'dips' between knuckles represent months with 3030 days (Apr, June, Sept, Nov).

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An ordinary year has exactly 365365 days. In an ordinary year, the month of February has 2828 days.

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A leap year occurs once every 44 years and contains 366366 days. The extra day is added to February, making it 2929 days long instead of 2828. Visually, a leap year calendar for February will show an extra row or box for the date 2929.

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To identify a leap year, we look at the last two digits of the year. If the number formed by these digits is exactly divisible by 44 (leaving no remainder), it is a leap year. For example, in the year 20242024, the last two digits are 2424, and 24÷4=624 \div 4 = 6, so it is a leap year.

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Dates are commonly written in the format DD/MM/YYYYDD/MM/YYYY or DD−MM−YYYYDD-MM-YYYY. For example, the 5th5^{th} of September 20232023 can be written as 05/09/202305/09/2023. The first two digits represent the day, the middle two represent the month number, and the last four represent the year.

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A week always consists of 77 consecutive days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday. No matter the month or year, this sequence never changes.

📐Formulae

1 week=7 days1 \text{ week} = 7 \text{ days}

1 year=12 months1 \text{ year} = 12 \text{ months}

1 ordinary year=365 days1 \text{ ordinary year} = 365 \text{ days}

1 leap year=366 days1 \text{ leap year} = 366 \text{ days}

1 year≈52 weeks1 \text{ year} \approx 52 \text{ weeks}

Leap Year=Year where (last 2 digits)÷4 has remainder 0\text{Leap Year} = \text{Year where (last 2 digits)} \div 4 \text{ has remainder } 0

💡Examples

Problem 1:

Calculate the total number of days in the months of April, May, and June combined.

Solution:

  1. Identify the days in each month: April = 3030 days, May = 3131 days, June = 3030 days.
  2. Add them together: 30+31+3030 + 31 + 30
  3. Calculation: 30+31=6130 + 31 = 61; 61+30=9161 + 30 = 91. Total = 9191 days.

Explanation:

We use the knowledge of how many days are in each specific month and perform a simple addition to find the total period.

Problem 2:

Is the year 20192019 a leap year? Show your working.

Solution:

  1. Look at the last two digits of the year 20192019, which are 1919.
  2. Divide 1919 by 44: 19÷4=4 with a remainder of 319 \div 4 = 4 \text{ with a remainder of } 3
  3. Since there is a remainder of 33, the year is not exactly divisible by 44. Therefore, 20192019 is an ordinary year, not a leap year.

Explanation:

To check for a leap year, we divide the last two digits by 4. If the division is not perfect (has a remainder), it is a normal 365-day year.