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The calendar

Measurement · level 2, lesson 5 of 6

A question to start

Leah was born on February 29, 2016. In February 2024 she turned 8 years old. But how many times has she had a birthday party on her real birthday, February 29?

Only 2 times: in 2020 and in 2024. Most years, February has only 28 days, so there is no February 29 at all! In the other years Leah celebrates on February 28 or March 1.

Why does February sometimes get an extra day? The answer is up in the sky: it is about how long the Earth takes to go round the Sun. In this lesson you will learn how the calendar measures long stretches of time, how to remember how many days each month has, and why every fourth year is a little longer.

The idea

Days, weeks, months, years

A calendar measures time in bigger and bigger pieces.

  • A day: the Earth spins round once. 24 hours.
  • A week: 7 days. Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
  • A month: about 4 weeks, but not exactly: 28, 29, 30 or 31 days.
  • A year: 12 months, which is 365 days (or 366 in a leap year). In one year, the Earth goes all the way round the Sun once.

The 12 months, in order, are: January, February, March, April, May, June, July, August, September, October, November, December. Then January again, and a new year starts. Like the days of the week, the months go round in a circle.

In Canada, winter is mostly in December, January and February; spring in March, April and May; summer in June, July and August; and fall in September, October and November.

How many days in each month: the knuckle trick

The months do not all have the same number of days. Here is a famous trick to remember them. Make a fist with one hand and look at your knuckles: the bumps, and the dips between them.

JanAug MarOct MayDec Jul FebSep AprNov Jun knuckle: 31 days dip: 30 days (February: 28 or 29)

Start on the first knuckle and say the months in order, touching a knuckle, then a dip, then a knuckle, and so on:

  • January on a knuckle, February in a dip, March on a knuckle, April in a dip, May on a knuckle, June in a dip, July on the last knuckle.
  • Then jump back to the first knuckle for August, and keep going: September in a dip, October on a knuckle, November in a dip, December on a knuckle.

Knuckle months have 31 days. Dip months have 30 days, except February, which has 28 days (29 in a leap year).

So the 31-day months are January, March, May, July, August, October and December. The 30-day months are April, June, September and November.

Notice something odd: July and August are next to each other and both have 31 days. That is why you jump back to the first knuckle for August: July and August both land on knuckles.

There is also an old rhyme that starts "Thirty days hath September, April, June and November." Use whichever helps you remember.

Checking that it makes 365

Let us check that the months add up to a whole year.

  • 7 months have 31 days. 7 lots of 31 is 217 days.
  • 4 months have 30 days. 4 lots of 30 is 120 days.
  • February has 28 days.

217 and 120 make 337, and 28 more makes 365. It works!

Reading a calendar page

A calendar page shows one month. Each row is one week, and each column is one day of the week.

Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

This month has 30 days and starts on a Monday. The Mondays are coloured: the 1st, 8th, 15th, 22nd and 29th. Do you see the pattern? Each Monday is 7 more than the one before, because a week is 7 days. Going down one row on a calendar always means 7 days later. Going right one square means 1 day later.

This is a quick way to find days. "What day is the 22nd?" Start at the 1st, which is a Monday. Add 7s: 8, 15, 22. So the 22nd is a Monday too.

Why your birthday moves along the week

A year is 365 days. How many weeks is that? 52 weeks is 52 lots of 7, which is 364 days. So a year is 52 weeks and 1 day.

That one extra day is why your birthday moves! If your birthday is on a Sunday this year, then next year it will be 365 days later: 52 whole weeks (bringing you back to Sunday) and 1 more day. So next year it is on a Monday. Each year, your birthday moves one day along the week. In a year where February 29 comes before your birthday, it moves two days, because that year has 366 days.

For example, May 10 was a Saturday in 2025, a Sunday in 2026, a Monday in 2027, and then a Wednesday in 2028 (skipping Tuesday, because February 29, 2028 comes before May 10).

Leap years: why February gets an extra day

The Earth takes about 365 days and a quarter of a day to go round the Sun once. But a calendar can only have whole days. So we use 365, and every year we are a quarter of a day short.

  • After 1 year: a quarter of a day short.
  • After 2 years: half a day short.
  • After 3 years: three quarters short.
  • After 4 years: a whole day short!

So every 4 years, we add one whole day to catch up: February 29. A year with February 29 is called a leap year. It has 366 days. Leap years are the years that you reach when you count by 4s: 2016, 2020, 2024, 2028, 2032.

Why do we need to catch up at all? If we never added the extra days, the calendar would slowly drift. After about a hundred years it would be almost a month out of step, and one day Canadians would be having snowy weather in the calendar's "summer".

Mostly every 4 years. The extra bit is actually a tiny bit less than a quarter of a day. Adding a day every 4 years adds a little too much, so very rarely we skip a leap year: the years ending in 00 are not leap years, unless you can split them into groups of 400 exactly. So 1900 was not a leap year and 2100 will not be one, but 2000 was a leap year. You will not have to worry about this until the year 2100!

A year on Mars

Mars is farther from the Sun and moves more slowly, so it takes much longer to go round: a Mars year lasts 687 Earth days, almost two of our years. So on Mars, each season lasts much longer, and you would have a birthday only about every 23 months.

Worked examples

Example 1. How many days? How many days are in October? In June? In February 2028?

  1. Count on your knuckles: January (knuckle), February (dip), March (knuckle), ..., July (last knuckle), jump back: August (knuckle), September (dip), October (knuckle). October has 31 days.
  2. June lands in a dip: 30 days.
  3. February has 28 days, or 29 in a leap year. 2028 is in the count by 4s (2024, 2028), so it is a leap year: 29 days.

Example 2. Days of the week on a calendar. In the calendar page above, what day is the 19th? What day is the 30th?

  1. The 1st is a Monday, so the Mondays are 1, 8, 15, 22, 29.
  2. The 19th is 4 days after the 15th (a Monday): Tuesday 16, Wednesday 17, Thursday 18, Friday 19.
  3. The 30th is 1 day after the 29th (a Monday): Tuesday.

Example 3. How many days until? It is June 25. Camp starts on July 3. How many days until camp?

  1. June has 30 days (a dip on the knuckles).
  2. From June 25 to June 30 is 5 days (26, 27, 28, 29, 30).
  3. From June 30 to July 3 is 3 more days (July 1, 2, 3).
  4. 5 and 3 make 8 days.

Example 4. Is it a leap year? Is 2030 a leap year? Is 2032?

  1. Count by 4s from 2024: 2024, 2028, 2032.
  2. 2030 is not in the list: not a leap year (February has 28 days).
  3. 2032 is in the list: a leap year (February has 29 days).

Try it

  1. How many days are in a week? How many months in a year?
  2. Use the knuckle trick: how many days are in March? In November? In August?
  3. Which month comes just after September? Just before March?
  4. On a calendar, the 3rd of a month is a Wednesday. What date is the next Wednesday? And the one after that?
  5. How many days are there in July and August together?
  6. Your birthday is on a Thursday this year, and there is no February 29 between this birthday and the next one. What day will it be on next year?
  7. Is 2036 a leap year? How about 2026?
  8. Tara says, "Every month has 30 days, so a year has 12 lots of 30, which is 360 days." What is wrong?
Answers
  1. 7 days in a week. 12 months in a year.
  2. March is on a knuckle: 31. November is in a dip: 30. August is on the first knuckle again: 31.
  3. October comes after September. February comes before March.
  4. Add 7: the 10th. Add 7 again: the 17th.
  5. Both have 31 days. 31 and 31 make 62 days.
  6. Friday. A year is 52 weeks and 1 day, so the birthday moves one day along: Thursday to Friday.
  7. Count by 4s: 2024, 2028, 2032, 2036. So 2036 is a leap year. 2026 is not in the list, so it is not.
  8. Not every month has 30 days. Seven months have 31 days and February has only 28 (or 29). Altogether a year has 365 days (366 in a leap year), not 360.

Common mistake

Forgetting the jump at July and August. On the knuckles, July is on the last knuckle and August starts again on the first one. Both have 31 days. If you put August in a dip, you will get it wrong.

Thinking every 4th year is always a leap year. That is right for all the years you will see for a long time, but years ending in 00 skip it unless they can be split into groups of 400. 2000 was a leap year; 2100 will not be.

Where it leads