E. Spatial Sense · Angles, Rectangles, Grids and Measurement

Units of Time: Seconds to Centuries

E2.3About 35 minutes

Learning goals

I can tell how units of time are related, from seconds to centuries.
I can change a time from one unit to another, like hours to minutes.
I can write a time using two units, like 1 h 30 min.
I can choose a sensible unit of time.

Words to know

second (s)
A very short unit of time. 60 seconds = 1 minute.

minute (min)
60 minutes = 1 hour.

hour (h)
24 hours = 1 day.

decade
10 years.

century
100 years. More than one are called centuries.

leap year
A year with 366 days. It has an extra day, February 29. Leap years come every 4 years (with a few exceptions).

Remember from Grade 3

You told time to the minute and learned that 60 seconds = 1 minute and 60 minutes = 1 hour. You also used timers and stopwatches.

This year you will connect all the units of time, from tiny seconds to giant centuries, and switch between them.

Let's start with a hockey game

In NHL hockey, a game has 3 periods of 20 minutes each. How long is that? 20 + 20 + 20 = 60 minutes, which is 1 hour of playing time. (The breaks make the real game longer!)

To solve problems like this, we need to know how the units of time fit together.

Unit	Is the same as
1 minute	60 seconds
1 hour	60 minutes
1 day	24 hours
1 week	7 days
1 year	12 months, or 52 weeks and 1 day, or 365 days (366 in a leap year)
1 decade	10 years
1 century	100 years (10 decades)

How units of time are related. Months have 28, 29, 30 or 31 days.

Top: 60 seconds make a minute, 60 minutes make an hour, 24 hours make a day, and 7 days make a week. Bottom: 10 years make a decade, and 10 decades make a century.

Changing to a smaller unit

When you change to a smaller unit, you get more of them, so you multiply.

3 hours to minutes: each hour is 60 minutes. 3 × 60 = 180 minutes.
2 weeks to days: 2 × 7 = 14 days.

Worked example

Example 1: Hours to minutes

A movie is 2 hours long. How many minutes is that?

1 hour = 60 minutes.
2 hours = 2 × 60 = 120 minutes.

2 h = 120 min

Changing to a bigger unit

When you change to a bigger unit, you get fewer of them. Make groups. Sometimes there are some left over, so you use two units.

Worked example

Example 2: Minutes to hours and minutes

Amir's swimming lesson is 90 minutes long. Write it in hours and minutes.

Make a group of 60 minutes: that is 1 hour.
90 − 60 = 30 minutes left over.
30 minutes is not enough for another hour.

90 min = 1 h 30 min (an hour and a half).

Worked example

Example 3: Days to weeks and days

Winter break is 17 days long. How many weeks and days is that?

Make groups of 7: 7 + 7 = 14. That is 2 weeks.
17 − 14 = 3 days left over.

17 days = 2 weeks 3 days

Worked example

Example 4: Decades and centuries

Canada became a country (Confederation) in 1867. In 1967, how long had it been? What about in 2017?

1967 − 1867 = 100 years. That is 1 century.
2017 − 1867 = 150 years. That is 1 century and 5 decades (100 + 50).
That is why Canada celebrated its 150th birthday in 2017!

In 1967: 1 century. In 2017: 150 years, or 1 century and 5 decades.

A timeline from Confederation in 1867 to 2017 (each small tick is one decade). From 1867 to 1967 is 1 century; 50 more years make 150 years in 2017.

Remembering the days in each month

A rhyme many Canadians learn: "Thirty days has September, April, June and November. All the rest have thirty-one, except February alone, which has 28 days clear, and 29 in each leap year."

Or use your knuckles: make a fist. Touch your first knuckle and say "January", the dip after it "February", the next knuckle "March", and so on. When you reach July on your last knuckle, go back to the first knuckle for August. Months on a knuckle have 31 days. Months in a dip have 30 days, except February.

Choosing a sensible unit

Blinking, a sneeze: seconds
Brushing your teeth, a recess: minutes
A school day, a long car trip: hours
Summer holidays: weeks or months
How old you are: years
How long a tall maple tree takes to grow: decades

Just for fun

If you are 10 years old, you have already lived for more than 3650 days. Happy (more than) 3650th day!

Hands-on activity

My time facts poster

You need: paper, pencils or markers, a calendar and a clock or timer.

Use a stopwatch or timer: how many times can you clap in 60 seconds? That's 1 minute of clapping!
Look at a calendar. Count the days in each month and write them on your poster. Which months have 31 days?
Figure out how many days old you are, roughly: your age × 365. (A grown-up can help with the multiplying, or use a calculator to check.)
Ask a grown-up how many decades old they are. Ask an older relative or neighbour what changed in their life in the last few decades.
Draw your poster with the time chain: second → minute → hour → day → week → year → decade → century.

Math talk: "Which unit of time do you use most? Which do you use least?"

Your turn

How many minutes are in 4 hours?

How many days are in 3 weeks?

Write 75 minutes in hours and minutes.

How many seconds are in 2 minutes?

How many years are in 3 decades?

How many hours are in 2 days?

Which unit would you use for how long it takes to tie your shoes?

More practice: warm-up

How many seconds are in 1 minute?

How many hours are in 1 day?

How many months are in 1 year?

How many years are in 1 century?

How many days are in a leap year?

More practice: on your own

Write 100 seconds in minutes and seconds.

Write 30 days in weeks and days.

A baby is 18 months old. Write the age in years and months.

Which is longer: 150 minutes or 2 hours? By how much?

How many days are in April, May and June together?

Challenge

A school day has 5 hours of class time. How many minutes is that? How many minutes in a 5-day school week?

Grandpa says he is 7 decades and 4 years old. How old is he? How many centuries old is that, about?

Without a calendar, explain why a year is 52 weeks and 1 day, not exactly 52 weeks.

Check your understanding

Quiz

How many minutes are in 3 hours?

1 week is the same as...

How many years are in a decade?

Write 130 minutes in hours and minutes.

Which unit is best for measuring how long a sneeze takes?

Which month has 30 days?

For parents and teachers

Big idea: The Ontario curriculum (E2.3) asks Grade 4 students to solve problems involving elapsed time by applying the relationships between different units of time. This lesson builds those relationships (seconds, minutes, hours, days, weeks, months, years, decades and centuries). The next lesson uses them to find elapsed time.

Common difficulties:

Treating time like base ten. 1 h 30 min is not 1.30 hours, and 90 minutes is not "0 h 90 min". There are 60 minutes in an hour, not 100.
Forgetting leftovers when changing to a bigger unit (17 days = 2 weeks 3 days).
Months. Different months have different numbers of days. Keep a calendar handy.

How to help: Use real times: "Practice is 90 minutes. How many hours is that?" "Your cousin is 18 months old. How many years?" Count down the days to a holiday together and change them into weeks and days.