Leap year activity: KS3 and GCSE science
You can use this question and answer activity to explore leap years from both a physics
and maths standpoint, suitable for KS3 through to GCSE. Consider using it on Wednesday
29th February, 2012 as a part of your Physics lesson.
Curriculum Points:
KS3: students should be able to explain that the Earth orbits the Sun, and while it orbits,
the Earth also rotates on its own axis. The Earth’s rotation is responsible for days, and the
orbit around the Sun is responsible for years. See the Boardworks KS3 Space Part 1.ppt.
GCSE Separate Science: students should be able to explain the difference between a
solar day and a sidereal day, and why the position of the stars changes over the course of
a year.
Activity
For your knowledge: Since the reign of Julius Caesar, over 2000 years ago, leap years
have been used to keep the calendars in line with the motion of our planet, which orbits the
Sun every 365.25 (approx) days. While a leap year every fourth year came fairly close to
keeping the calendar correct, after several centuries, it was discovered that the calendar
was 10 days behind the planet’s position in orbit. So in 1582, Thursday 4th October of
the Julian calendar was followed by Friday 15th October of the Gregorian calendar. The
Gregorian calendar is the calendar we use today and defines more complex and more
accurate rules for assigning leap years.
1. Ask students: What determines a year? What determines a day?
Explain to students: A solar day is the length of time it takes for the Sun to appear in the
same position in the sky. A year is the length of time it takes for the Earth to complete one
orbit around the Sun.
2. Ask students: What is a leap year? Why do we need leap years?
Explain to students: There are about 365.25 solar days in one orbit, so the time it takes to
complete one orbit is slightly longer than a common calendar year, which is 365 days. To
compensate for this, an extra day is sometimes added in the calendar on 29th February.
3. Ask students: After one year, approximately how far ahead is our calendar compared to
the Earth’s position in its orbit?
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Explain to students: A common calendar year is 365 solar days. It takes approximately
365.25 days to complete an orbit around the Sun, so the calendar is about 0.25 days
ahead.
4. Ask students: How often should a leap year occur to fix this?
Explain to students: Each common calendar year, the position of the Earth in its orbit is
behind by one quarter of a day. Therefore in four years, one full day will have accumulated,
and this can be corrected by having a leap year.
For your knowledge: The Earth actually takes 365.2422 days to complete an orbit of the
Sun, rather than 365.25 days. Adding in a leap year every four years overcompensates
for the difference, leading to the problems seen using the Julian calendar. The Gregorian
calendar skips leap years occasionally, according to the following rules:
There is a leap year if:
1. The year is evenly divisible by 4;
2. If the year is evenly divisible by 100, it is NOT a leap year, unless;
3. The year is also evenly divisible by 400. Then it is a leap year.
5. Ask students: If leap years are skipped every century, how many leap years occur in a
100 years?
Explain to students: A typical leap year occurs every four years so there are 100 ÷ 4 = 25
leap years, but one is skipped, so there are 24 leap years every hundred years.
6. Ask students: With this adjustment, how long is the average calendar year?
Explain to students: Each leap year adds one extra day to the calendar, so in 100 years,
there will be 24 extra days, which is 24 ÷ 100 = 0.24 extra days per year on average, so
there are 365.24 days per year on average.
7. Ask students: When was the last leap year that fell in the first year of a new century?
2000
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8. Ask students: How many leap years occur in 400 years?
Explain to students: A leap year occurs every four years, so there are 400 ÷ 4 = 100 normal
leap years in 400 years, but every 100 years, a leap year is skipped so 400 ÷ 100 = 4 of
these are dropped except for the one that occurs on a century divisible by 400, so there
are 100 – 4 +1 = 97 leap years in 400 years.
9. Ask students: With this finer adjustment, what is the average length of a calendar year?
Explain to students: A leap year adds an extra day to the calendar year, so in 400 years,
there are 97 extra days. This means each year has 97 ÷ 400 = 0.2425 extra days, and an
average year has 365.2425 days.
For your knowledge: This estimate is closer to the actual length of an orbit, which is
365.2422 days long. Further adjustments can be made, but these won’t be required until
the year 4000!
10. Extension activity:
Ask students to devise alternatives to leap years to keep the calendar in line with the
motion of the planet. They may come up with alternatives such as adding 6 hours to one
day each year or waiting for the calendar to be a week ahead before adding an extra week
to the year. Ask them to brainstorm ideas then discuss the advantages and disadvantages
of the students’ suggestions as a whole-class activity.
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