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Chapter Notes: Time

Time is something we use every day! We look at clocks to know when to wake up, when school starts, and when our favorite shows come on. Learning to read and work with time helps us plan our day and stay on schedule. In this chapter, we will explore how to read clocks, understand different units of time, solve problems with time, and even work with calendars.

Understanding Units of Time

Time is measured in different units, just like we measure length in inches or feet. The most common units of time are seconds, minutes, hours, days, weeks, months, and years. Each unit helps us measure different lengths of time.

Basic Time Units

Here are the basic units of time and how they relate to each other:

  • Second (sec): The smallest unit we usually work with. A second is a very short amount of time-about as long as it takes to say "one-Mississippi."
  • Minute (min): A minute is made up of 60 seconds. It takes about one minute to tie your shoes.
  • Hour (hr): An hour is made up of 60 minutes. A typical TV show without commercials lasts about 30 minutes, so two shows would be one hour.
  • Day: A day has 24 hours. This includes daytime when the sun is up and nighttime when we sleep.
  • Week: A week has 7 days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.
  • Month: A month is about 4 weeks long. Most months have 30 or 31 days, except February which has 28 or 29 days.
  • Year: A year has 12 months or 365 days (366 days in a leap year).

Converting Between Time Units

Sometimes we need to change from one unit of time to another. This is called converting. Here are the key conversions to remember:

ConversionRelationship
Seconds to Minutes60 seconds = 1 minute
Minutes to Hours60 minutes = 1 hour
Hours to Days24 hours = 1 day
Days to Weeks7 days = 1 week
Weeks to Years52 weeks = 1 year (approximately)
Months to Years12 months = 1 year

Example:  Sarah's piano lesson is 120 minutes long.

How many hours is her lesson?

Solution:

We know that 60 minutes = 1 hour.

To find how many hours are in 120 minutes, we divide: 120 ÷ 60 = 2

Sarah's piano lesson is 2 hours long.

Example:  A movie lasts 3 hours.

How many minutes is that?

Solution:

We know that 1 hour = 60 minutes.

To find how many minutes are in 3 hours, we multiply: 3 × 60 = 180

The movie is 180 minutes long.

Reading Analog Clocks

An analog clock is the kind of clock with a round face and hands that point to numbers. It has three hands: the hour hand, the minute hand, and sometimes a second hand.

Parts of an Analog Clock

  • Hour hand: This is the shorter hand. It shows what hour it is.
  • Minute hand: This is the longer hand. It shows how many minutes past the hour it is.
  • Second hand: This is usually the thinnest hand. It moves quickly and shows the seconds.
  • Numbers: The clock face has numbers 1 through 12 around the edge.

How the Clock Hands Work

The clock face is divided into 12 sections for the 12 hours. Each number represents 5 minutes when we are counting minutes. Here's how to count by fives around the clock:

  • 12 = 0 minutes (or 60 minutes)
  • 1 = 5 minutes
  • 2 = 10 minutes
  • 3 = 15 minutes
  • 4 = 20 minutes
  • 5 = 25 minutes
  • 6 = 30 minutes
  • 7 = 35 minutes
  • 8 = 40 minutes
  • 9 = 45 minutes
  • 10 = 50 minutes
  • 11 = 55 minutes

Reading the Hour

To read the hour, look at where the short hour hand is pointing. If it is pointing exactly at a number, that is the hour. If it is between two numbers, the hour is the smaller number.

Think of the hour hand like someone walking around a track. Even if they are halfway to the next marker, they haven't reached it yet, so we count where they came from.

Reading the Minutes

To read the minutes, look at where the long minute hand is pointing. Count by fives for each number the minute hand has passed from the 12. If the minute hand is between two numbers, count the extra tick marks (each tick mark is 1 minute).

Example:  The hour hand is between 3 and 4.
The minute hand is pointing at 6.

What time is it?

Solution:

The hour hand is between 3 and 4, so the hour is 3.

The minute hand is pointing at 6, which represents 30 minutes (because 6 × 5 = 30).

The time is 3:30 or three-thirty.

Example:  The hour hand is just past 7.
The minute hand is pointing at 9.

What time is it?

Solution:

The hour hand is just past 7, so the hour is 7.

The minute hand is pointing at 9, which represents 45 minutes (because 9 × 5 = 45).

The time is 7:45 or seven forty-five.

Reading Digital Clocks

A digital clock shows time using numbers instead of hands. The time is shown in this format: hour:minutes. For example, 8:15 means 8 hours and 15 minutes.

Digital clocks can show time in two ways:

  • 12-hour format: Uses numbers 1 through 12, with AM for morning times and PM for afternoon and evening times.
  • 24-hour format: Uses numbers 0 through 23 to show all hours of the day without needing AM or PM.

Understanding AM and PM

AM stands for the Latin words "ante meridiem," which means "before noon." AM times are from midnight (12:00 AM) until just before noon (11:59 AM).

PM stands for "post meridiem," which means "after noon." PM times are from noon (12:00 PM) until just before midnight (11:59 PM).

Think of AM as morning times when you wake up and go to school. PM is afternoon and evening times when you come home and get ready for bed.

Elapsed Time

Elapsed time is the amount of time that passes from one moment to another. When we calculate elapsed time, we find out how long something took or how much time passed between two events.

Finding Elapsed Time

To find elapsed time, we can count forward from the start time to the end time. There are different strategies we can use:

  • Count by hours first, then minutes: Jump ahead by whole hours, then add the remaining minutes.
  • Use a number line: Draw a timeline and mark the start time and end time, then count the jumps.
  • Break it into parts: Find how many minutes until the next hour, then count the hours, then add any extra minutes.

Example:  Emma starts reading at 2:15 PM.
She finishes at 3:45 PM.

How long did Emma read?

Solution:

Start time: 2:15 PM
End time: 3:45 PM

From 2:15 to 3:15 is 1 hour (60 minutes).

From 3:15 to 3:45 is 30 more minutes.

Total elapsed time: 1 hour + 30 minutes = 1 hour 30 minutes

Emma read for 1 hour and 30 minutes.

Example:  A soccer game starts at 10:20 AM.
It ends at 12:05 PM.

How long did the soccer game last?

Solution:

Start time: 10:20 AM
End time: 12:05 PM

From 10:20 to 11:20 is 1 hour.

From 11:20 to 12:20 would be another hour, but we only go to 12:05.

From 11:20 to 12:05 is 45 minutes (because from 11:20 to 12:00 is 40 minutes, and from 12:00 to 12:05 is 5 more minutes: 40 + 5 = 45).

Total elapsed time: 1 hour + 45 minutes = 1 hour 45 minutes

The soccer game lasted 1 hour and 45 minutes.

Finding Start or End Time

Sometimes we know the elapsed time and either the start time or the end time, but we need to find the missing time. We can count forward to find an end time or count backward to find a start time.

Example:  Marcus starts his homework at 4:10 PM.
He works for 1 hour and 25 minutes.

What time does he finish?

Solution:

Start time: 4:10 PM
Elapsed time: 1 hour 25 minutes

First, add 1 hour: 4:10 + 1 hour = 5:10 PM

Then add 25 minutes: 5:10 + 25 minutes = 5:35 PM

Marcus finishes his homework at 5:35 PM.

Example:  A movie ends at 8:50 PM.
The movie is 2 hours and 15 minutes long.

What time did the movie start?

Solution:

End time: 8:50 PM
Elapsed time: 2 hours 15 minutes

We need to count backward. First, subtract 2 hours: 8:50 - 2 hours = 6:50 PM

Then subtract 15 minutes: 6:50 - 15 minutes = 6:35 PM

The movie started at 6:35 PM.

Working with Calendars

A calendar is a chart that shows the days, weeks, and months of the year. Calendars help us keep track of dates, plan events, and know what day of the week it is.

Days of the Week

There are 7 days in a week. Here they are in order:

  1. Sunday
  2. Monday
  3. Tuesday
  4. Wednesday
  5. Thursday
  6. Friday
  7. Saturday

Months of the Year

There are 12 months in a year. Here they are in order with the number of days in each month:

MonthNumber of Days
January31
February28 (or 29 in a leap year)
March31
April30
May31
June30
July31
August31
September30
October31
November30
December31

A helpful rhyme to remember: "Thirty days has September, April, June, and November. All the rest have thirty-one, except February, which has twenty-eight, and twenty-nine in a leap year."

Reading a Calendar

A monthly calendar shows all the days of one month arranged in rows by weeks. Sunday is usually the first day shown in each row, and Saturday is the last day. Each box on the calendar shows one day of the month.

To find a date on a calendar:

  1. Find the month you need.
  2. Look for the number of the day you want.
  3. Check which column it is in to find the day of the week.

Counting Days on a Calendar

We can use a calendar to count how many days are between two dates or to find what date it will be after a certain number of days.

Example:  Today is March 8.
Lisa's birthday party is on March 22.

How many days until her party?

Solution:

Start date: March 8
End date: March 22

We count from March 8 to March 22 (not counting March 8 itself).

22 - 8 = 14

There are 14 days until Lisa's birthday party.

Example:  A library book is checked out on April 5.
It is due back in 14 days.

What is the due date?

Solution:

Start date: April 5
Days to add: 14

April 5 + 14 days = April 19

We can also count it out: April has 30 days. From April 5, we count forward 14 days.

5 + 14 = 19

The book is due on April 19.

Solving Multi-Step Time Problems

Some time problems require us to use more than one step to find the answer. We might need to add times, subtract times, or convert between different units. The key is to break the problem into smaller parts and solve one step at a time.

Example:  Brandon's family left home at 9:30 AM for a road trip.
They drove for 2 hours and 45 minutes before stopping for lunch.
Lunch took 30 minutes.

What time did they finish lunch?

Solution:

Start time: 9:30 AM
Driving time: 2 hours 45 minutes
Lunch time: 30 minutes

First, find when they arrived for lunch: 9:30 AM + 2 hours = 11:30 AM, then 11:30 AM + 45 minutes = 12:15 PM

Next, add lunch time: 12:15 PM + 30 minutes = 12:45 PM

They finished lunch at 12:45 PM.

Example:  A school day is 6 hours and 30 minutes long.
School starts at 8:15 AM.

What time does school end?

Solution:

Start time: 8:15 AM
Length of school day: 6 hours 30 minutes

First, add 6 hours: 8:15 AM + 6 hours = 2:15 PM

Then add 30 minutes: 2:15 PM + 30 minutes = 2:45 PM

School ends at 2:45 PM.

Adding Times

When we add times together, we add the hours and minutes separately. If the minutes add up to 60 or more, we convert 60 minutes into 1 hour and add it to the hours.

Example:  Olivia practices piano for 45 minutes in the morning and 35 minutes in the afternoon.

How long does she practice in total?

Solution:

Morning practice: 45 minutes
Afternoon practice: 35 minutes

Add the minutes: 45 + 35 = 80 minutes

Since 80 minutes is more than 60, we convert: 80 minutes = 1 hour and 20 minutes

Olivia practices for a total of 1 hour and 20 minutes.

Subtracting Times

When we subtract times, we subtract the hours and minutes separately. If we need to subtract more minutes than we have, we borrow 1 hour (which equals 60 minutes) from the hours.

Example:  A basketball game is 2 hours and 15 minutes long.
So far, 1 hour and 40 minutes have passed.

How much time is left in the game?

Solution:

Total game time: 2 hours 15 minutes
Time passed: 1 hour 40 minutes

We need to subtract: 2 hours 15 minutes - 1 hour 40 minutes

We can't subtract 40 from 15, so we borrow 1 hour from the 2 hours. Now we have: 1 hour 75 minutes - 1 hour 40 minutes

Subtract: 1 - 1 = 0 hours, and 75 - 40 = 35 minutes

There are 35 minutes left in the game.

Time Zones

A time zone is a region of Earth that has the same time. Because Earth is round and the sun shines on different parts at different times, we have different time zones. When it is daytime in one part of the world, it is nighttime in another part.

The United States has several time zones. The main ones are:

  • Eastern Time (ET)
  • Central Time (CT) - 1 hour behind Eastern
  • Mountain Time (MT) - 2 hours behind Eastern
  • Pacific Time (PT) - 3 hours behind Eastern

If it is 3:00 PM in New York (Eastern Time), it is 2:00 PM in Chicago (Central Time), 1:00 PM in Denver (Mountain Time), and 12:00 PM (noon) in Los Angeles (Pacific Time).

Example:  It is 4:30 PM in Boston, which is in the Eastern Time zone.
Your cousin lives in Seattle, which is in the Pacific Time zone.

What time is it in Seattle?

Solution:

Boston time: 4:30 PM Eastern Time

Pacific Time is 3 hours behind Eastern Time.

Subtract 3 hours: 4:30 PM - 3 hours = 1:30 PM

It is 1:30 PM in Seattle.

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