Measurement of Time

Lesson: Anatomy of an Analog Clock

An analog clock is a clock with moving hands. It helps us tell time by looking at the clock face, the numbers, and the hands.

Learning the parts of an analog clock is the first step to reading time. When you know what each part does, clocks become much easier to understand.

Main Parts of an Analog Clock

• Clock face: the round part of the clock.
• Numbers: the numbers \(1\) through \(12\) around the clock.
• Hour hand: the short hand that tells the hour.
• Minute hand: the long hand that tells the minutes.
• Center: the middle point where the hands are attached.

The numbers on the clock go in order from \(1\) to \(12\). They are placed in a circle. The \(12\) is at the top, the \(6\) is at the bottom, the \(3\) is on the right, and the \(9\) is on the left.

The Hour Hand

The hour hand is the shorter hand. It points to the hour. If the short hand points to \(4\), the hour is \(4\) o'clock or a little after \(4\).

The hour hand moves slowly. As time passes, it travels from one number to the next. It takes 1 hour to move from one number to the next.

The Minute Hand

The minute hand is the longer hand. It tells how many minutes have passed.

The minute hand moves faster than the hour hand. It goes all the way around the clock in 60 minutes, which is also 1 hour.

When the minute hand points to:

• \(12\), it means \(0\) minutes
• \(1\), it means \(5\) minutes
• \(2\), it means \(10\) minutes
• \(3\), it means \(15\) minutes
• \(4\), it means \(20\) minutes
• \(5\), it means \(25\) minutes
• \(6\), it means \(30\) minutes
• \(7\), it means \(35\) minutes
• \(8\), it means \(40\) minutes
• \(9\), it means \(45\) minutes
• \(10\), it means \(50\) minutes
• \(11\), it means \(55\) minutes

You can see a pattern. The minutes go up by \(5\) each time you move to the next number.

$$5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45,\ 50,\ 55,\ 60$$

Spacing of the Numbers

The numbers on a clock are evenly spaced. That means the space from one number to the next is the same all the way around.

Moving from one number to the next is:

• 1 hour for the hour hand
• 5 minutes for the minute hand

There are \(12\) numbers on the clock. Each step is \(5\) minutes, so all the way around is:

$$12 \times 5 = 60$$

So, one full turn of the minute hand is 60 minutes.

Tick Marks

Many analog clocks also have little lines called tick marks between the numbers. These help show single minutes.

From one number to the next, there are 5 minutes. So there are usually \(5\) little minute spaces from one number to the next.

For example, from \(1\) to \(2\):

• \(1\) stands for \(5\) minutes
• the next little mark is \(6\) minutes
• then \(7\) minutes
• then \(8\) minutes
• then \(9\) minutes
• \(2\) stands for \(10\) minutes

Helpful Clock Facts

• The short hand tells the hour.
• The long hand tells the minutes.
• Each number step on the clock is 5 minutes.
• There are 60 minutes in a full turn around the clock.
• The numbers are arranged in a circle and are evenly spaced.

Worked Example 1: Finding the Hour Hand

A clock has a short hand pointing at \(7\) and a long hand pointing at \(12\). Which hand tells the hour?

Step 1: Look for the shorter hand.

Step 2: The shorter hand is the hour hand.

Answer: The hand pointing to \(7\) tells the hour.

Worked Example 2: Counting Minutes by 5s

The minute hand points to \(4\). How many minutes is that?

Step 1: Count by \(5\)s until you reach \(4\).

\(1 = 5\), \(2 = 10\), \(3 = 15\), \(4 = 20\)

Answer: The minute hand at \(4\) means 20 minutes.

Worked Example 3: Using Both Hands

The short hand points to \(3\). The long hand points to \(6\). What hour and how many minutes do you see?

Step 1: The short hand tells the hour. It points to \(3\), so the hour is \(3\).

Step 2: The long hand tells the minutes. The \(6\) means \(30\) minutes.

Answer: The clock shows 3 hours and 30 minutes, or 3:30.

Worked Example 4: Understanding the Clock Circle

A student says, “From \(12\) to \(3\) is \(3\) minutes.” Is that correct?

Step 1: Remember that each number step is \(5\) minutes.

Step 2: Count the steps: from \(12\) to \(1\) is \(5\), to \(2\) is \(10\), to \(3\) is \(15\).

Answer: No, that is not correct. From \(12\) to \(3\) is 15 minutes.

How to Remember

1. Find the short hand. It tells the hour.
2. Find the long hand. It tells the minutes.
3. Count minutes by 5s around the clock.
4. Remember that one full circle is 60 minutes.

Brief Summary

An analog clock has a clock face, numbers, an hour hand, and a minute hand. The short hour hand tells the hour, and the long minute hand tells the minutes. The numbers are evenly spaced around the clock, and each step from one number to the next is \(5\) minutes. When the minute hand goes all the way around once, it has moved \(60\) minutes, or \(1\) hour.

Lesson: Telling Time to the Nearest Five Minutes

We use clocks every day to know when to wake up, eat lunch, go to school, and go to bed. Learning to tell time helps us understand our day.

Today we will learn how to tell time to the nearest five minutes. That means we will read times like 1:05, 2:10, 3:25, and 4:55.

A clock has 2 hands:

• The short hand tells the hour.
• The long hand tells the minutes.

To tell time to the nearest five minutes, we look carefully at both hands. First, find the hour with the short hand. Then, count the minutes by fives using the long hand.

Step 1: Read the hour hand

The short hand points to the hour. Sometimes it points right at a number. Sometimes it is between two numbers. If it is between two numbers, the hour is the smaller number it has already passed.

For example, if the short hand is between 4 and 5, the hour is still 4.

Step 2: Read the minute hand

The long hand tells the minutes. We count by 5s around the clock.

Here is how the numbers on the clock match the minutes:

• At 12 = 00 minutes
• At 1 = 05 minutes
• At 2 = 10 minutes
• At 3 = 15 minutes
• At 4 = 20 minutes
• At 5 = 25 minutes
• At 6 = 30 minutes
• At 7 = 35 minutes
• At 8 = 40 minutes
• At 9 = 45 minutes
• At 10 = 50 minutes
• At 11 = 55 minutes

We can think of it like skip-counting:

$$0,\ 5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45,\ 50,\ 55$$

Every time the minute hand moves from one number to the next number, 5 minutes pass.

Important tip: When we write time, the minutes need 2 digits. So we write 5 minutes as 05, not just 5.

For example:

• 1 hour and 5 minutes = 1:05
• 7 hours and 10 minutes = 7:10

Worked Example 1

The short hand is on 3. The long hand points to 12.

Step 1: The hour is 3.

Step 2: The minute hand at 12 means 00 minutes.

So the time is 3:00.

Worked Example 2

The short hand is just past 6. The long hand points to 4.

Step 1: The hour is 6 because the short hand has passed 6.

Step 2: Count by fives to 4:

$$5,\ 10,\ 15,\ 20$$

So the minute hand shows 20 minutes.

The time is 6:20.

Worked Example 3

The short hand is between 8 and 9. The long hand points to 7.

Step 1: The hour is 8 because the short hand has not reached 9 yet.

Step 2: Count by fives to 7:

$$5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35$$

So the minute hand shows 35 minutes.

The time is 8:35.

Worked Example 4

The short hand is between 11 and 12. The long hand points to 11.

Step 1: The hour is 11.

Step 2: Count by fives to 11:

$$5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45,\ 50,\ 55$$

So the minute hand shows 55 minutes.

The time is 11:55.

How to check your answer

1. Look at the short hand and say the hour.
2. Look at the long hand and count by 5s.
3. Write the time with a colon, like 4:25.
4. If the minutes are less than 10, use a 0 first, like 2:05.

Common mistakes to avoid

• Do not use the long hand for the hour. The long hand is for minutes.
• Do not use the bigger number when the short hand is between two numbers. Use the number it already passed.
• Do not forget the 0 in times like 5:05.

Practice thinking

If the minute hand points to:

• 2, the minutes are 10
• 6, the minutes are 30
• 9, the minutes are 45
• 10, the minutes are 50

If the short hand is between 2 and 3, the hour is still 2.

Quick strategy

Say this in your head:

Short hand first, long hand second.

That will help you remember what to read first.

Summary

To tell time to the nearest five minutes, read the short hand for the hour and the long hand for the minutes. Count the minutes by 5s around the clock: 00, 05, 10, 15, and so on. If the short hand is between two numbers, use the smaller number it has already passed.

Learning About A.M. and P.M.

We use clocks to tell what time it is. But sometimes the same number can happen two times in one day. For example, there is a 7 o'clock in the morning and a 7 o'clock later in the day.

That is why we use a.m. and p.m.. These letters help us know which part of the day we mean.

What Do A.M. and P.M. Mean?

a.m. means the time from midnight until before noon. These are the morning hours.

p.m. means the time from noon until before midnight. These are the afternoon, evening, and night hours.

You do not need to memorize big words. Just remember:

• a.m. = morning
• p.m. = afternoon, evening, and night

Parts of the Day

A day has different parts. A.M. and P.M. help us place times into the correct part of the day.

• Morning → a.m.
• Afternoon → p.m.
• Evening → p.m.
• Night → p.m. for the times before midnight

Here are some common examples:

• 7:00 a.m. → eating breakfast
• 8:00 a.m. → going to school
• 12:00 noon → p.m.
• 3:00 p.m. → after school
• 6:00 p.m. → eating dinner
• 9:00 p.m. → going to bed

A Helpful Way to Remember

If the sun is coming up and it is the morning, it is usually a.m.

If it is later in the day, like after lunch, at dinner time, or when it is getting dark, it is usually p.m.

Special Times: Midnight and Noon

There are two special times to know:

• 12:00 midnight starts a new day. It is a.m.
• 12:00 noon is in the middle of the day. It is p.m.

You can think of it like this:

$$12{:}00\ \text{midnight} = a.m.$$

$$12{:}00\ \text{noon} = p.m.$$

How to Decide A.M. or P.M.

Ask yourself these questions:

1. Is it in the morning? Then choose a.m.
2. Is it in the afternoon or evening? Then choose p.m.
3. Is it 12:00 noon? That is p.m.
4. Is it 12:00 midnight? That is a.m.

Worked Example 1

Question: Maria eats breakfast at 7:00. Is that 7:00 a.m. or 7:00 p.m.?

Think: Breakfast is in the morning.

Answer: Maria eats breakfast at 7:00 a.m.

Worked Example 2

Question: Jay plays outside after school at 4:00. Is that 4:00 a.m. or 4:00 p.m.?

Think: After school is in the afternoon.

Answer: Jay plays outside at 4:00 p.m.

Worked Example 3

Question: A child goes to bed at 8:00. Is that 8:00 a.m. or 8:00 p.m.?

Think: Bedtime is usually in the evening or night.

Answer: Bedtime is usually 8:00 p.m.

Worked Example 4

Question: The time is 12:00 noon. Is it a.m. or p.m.?

Think: Noon is the middle of the day.

Answer: 12:00 noon is p.m.

Let’s Compare

Look at these two times:

• 6:00 a.m. → early morning
• 6:00 p.m. → evening

They both say 6:00, but they happen at different times of day. A.M. and P.M. help us know which one we mean.

More Everyday Time Clues

• Wake up → usually a.m.
• Eat lunch → usually p.m. at 12:00 noon or after
• School starts → usually a.m.
• School ends → usually p.m.
• Dinner → usually p.m.
• Sleeping at night → usually p.m.

Try Thinking About Your Day

You can learn a.m. and p.m. by thinking about your own schedule.

• What time do you wake up?
• What time do you eat lunch?
• What time do you go to bed?

If it happens in the morning, use a.m.. If it happens later in the day, use p.m..

Common Mistakes to Watch Out For

• Do not pick a.m. for dinner time. Dinner is usually p.m.
• Do not pick p.m. for getting ready for school in the morning. That is usually a.m.
• Remember: 12:00 noon = p.m.
• Remember: 12:00 midnight = a.m.

Quick Summary

A.M. and P.M. tell us which part of the day a time belongs to.

a.m. is for morning, from midnight to before noon.

p.m. is for afternoon, evening, and night, from noon to before midnight.

When you are not sure, think about the activity. Breakfast and school in the morning are usually a.m.. After school, dinner, and bedtime are usually p.m.

Analog and Digital Conversions means showing the same time in two different ways.

• Analog clock: a clock with hands.
• Digital clock: a clock with numbers, like 3:00.

In this lesson, we will learn how to match a time on an analog clock to the same time on a digital clock.

On an analog clock, there are 2 important hands:

• The short hand shows the hour.
• The long hand shows the minutes.

A digital clock shows time with numbers in this order:

hour : minutes

For example, in 4:30, the 4 is the hour and the 30 is the minutes.

Let’s remember what the long hand means on an analog clock.

• If the long hand points to 12, the minutes are 00.
• If the long hand points to 6, the minutes are 30.

These are the most common times to match in 2nd Grade:

• o’clock times, like 7:00
• half past times, like 7:30

How to read an analog clock and write the digital time:

1. Look at the short hand to find the hour.
2. Look at the long hand to find the minutes.
3. Write the time as hour:minutes.

How to read a digital clock and make the analog time:

1. Look at the first number to find the hour.
2. Look at the last two numbers to find the minutes.
3. Put the short hand on the hour.
4. Put the long hand on 12 for 00 minutes or on 6 for 30 minutes.

Helpful clue: When the minutes are less than 10 on a digital clock, we still write 2 numbers for the minutes.

For example:

• 5:00, not 5:0

Here is a quick matching guide:

• Long hand at 12  digital minutes are 00
• Long hand at 6  digital minutes are 30

Now let’s look at some worked examples.

Example 1: Analog to Digital

The short hand points to 3.

The long hand points to 12.

The hour is 3 and the minutes are 00.

So the digital time is 3:00.

Example 2: Analog to Digital

The short hand points to 8.

The long hand points to 6.

The hour is 8 and the minutes are 30.

So the digital time is 8:30.

Example 3: Digital to Analog

The digital clock says 6:00.

The hour is 6, so the short hand points to 6.

The minutes are 00, so the long hand points to 12.

That makes the analog clock show 6 o’clock.

Example 4: Digital to Analog

The digital clock says 10:30.

The hour is 10, so the short hand points to 10.

The minutes are 30, so the long hand points to 6.

That makes the analog clock show half past 10.

Let’s compare two times:

• 4:00 means the short hand is at 4 and the long hand is at 12.
• 4:30 means the short hand is at 4 and the long hand is at 6.

Even though both times have the same hour, the minutes are different.

Tips for success

• Always find the short hand first for the hour.
• Then find the long hand for the minutes.
• Remember: 12 means 00 minutes.
• Remember: 6 means 30 minutes.
• Digital clocks always show time with numbers, like 2:00 or 2:30.

Try thinking about these:

• If the short hand is at 9 and the long hand is at 12, the digital time is 9:00.
• If the short hand is at 1 and the long hand is at 6, the digital time is 1:30.
• If the digital time is 7:00, the analog clock has the short hand at 7 and the long hand at 12.
• If the digital time is 12:30, the analog clock has the short hand at 12 and the long hand at 6.

Summary

Analog clocks and digital clocks can show the same time in different ways.

To change from analog to digital, read the short hand for the hour and the long hand for the minutes.

To change from digital to analog, use the hour number for the short hand and the minutes number for the long hand.

Remember the big idea:

• 12 on the long hand = 00 minutes
• 6 on the long hand = 30 minutes

When you know that, you can match many analog and digital times correctly.

Elapsed Time in Whole Hours means finding out how many full hours pass from one time to another.

We use clocks every day. We look at the time when school starts, when lunch begins, and when it is time to go home. Sometimes we want to know, “How long was that?” That is called elapsed time.

In this lesson, we will learn how to find elapsed time when the time changes by whole hours only. That means we are counting hours like 1 hour, 2 hours, or 3 hours, not parts of an hour.

Important idea: One full turn from one hour number to the next on a clock is 1 hour.

For example:

• From 2:00 to 3:00 is 1 hour.
• From 5:00 to 7:00 is 2 hours.
• From 9:00 to 12:00 is 3 hours.

When we work with whole hours, the times usually end with :00. That means the minute hand is pointing to the 12.

Here are some clock reminders:

• The short hand tells the hour.
• The long hand tells the minutes.
• When the long hand points to 12, it is exactly an hour, like 4:00 or 8:00.

How to find elapsed time in whole hours:

1. Look at the start time.
2. Look at the end time.
3. Count how many hours pass from the start time to the end time.

You can count by saying each next hour.

For example, from 1:00 to 4:00:

• 1:00 to 2:00 = 1 hour
• 2:00 to 3:00 = 2 hours
• 3:00 to 4:00 = 3 hours

So the elapsed time is 3 hours.

You can also think of it like counting on the clock numbers.

From 6:00 to 9:00, count:

• 6 to 7 = 1 hour
• 7 to 8 = 2 hours
• 8 to 9 = 3 hours

So from 6:00 to 9:00, $$3 \text{ hours}$$ pass.

Worked Example 1

Sam starts reading at 2:00. He stops at 5:00. How much time passed?

Count the hours:

• 2:00 to 3:00 = 1 hour
• 3:00 to 4:00 = 2 hours
• 4:00 to 5:00 = 3 hours

Answer: Sam read for 3 hours.

Worked Example 2

A movie begins at 10:00 and ends at 12:00. How long is the movie?

Count from 10:00 to 12:00:

• 10:00 to 11:00 = 1 hour
• 11:00 to 12:00 = 2 hours

Answer: The movie is 2 hours long.

Worked Example 3

School starts at 8:00 and ends at 3:00. How many hours is that?

Count on by hours:

• 8:00 to 9:00 = 1 hour
• 9:00 to 10:00 = 2 hours
• 10:00 to 11:00 = 3 hours
• 11:00 to 12:00 = 4 hours
• 12:00 to 1:00 = 5 hours
• 1:00 to 2:00 = 6 hours
• 2:00 to 3:00 = 7 hours

Answer: School lasts 7 hours.

Worked Example 4

Mia goes to the park at 11:00. She goes home at 4:00. How much time passed?

Let’s count:

• 11:00 to 12:00 = 1 hour
• 12:00 to 1:00 = 2 hours
• 1:00 to 2:00 = 3 hours
• 2:00 to 3:00 = 4 hours
• 3:00 to 4:00 = 5 hours

Answer: Mia was at the park for 5 hours.

Tips to help you:

• Make sure the minute hand is on 12 for whole hours.
• Start at the beginning time and count up to the ending time.
• Each jump from one hour to the next is 1 hour.
• If you are not sure, use your finger to point and count each hour one at a time.

Let’s think about it another way.

If you start at 3:00 and end at 6:00, you can count:

$$3:00 \rightarrow 4:00 \rightarrow 5:00 \rightarrow 6:00$$

There are 3 jumps, so the elapsed time is 3 hours.

Be careful:

• Do not count the start time as an hour all by itself.
• Count the hours that pass between the times.

For example, from 7:00 to 9:00 is not 9 hours. We count from 7 to 8 and from 8 to 9. That is 2 hours.

Quick practice ideas:

• From 4:00 to 6:00 = 2 hours
• From 1:00 to 2:00 = 1 hour
• From 9:00 to 11:00 = 2 hours
• From 12:00 to 3:00 = 3 hours

Summary

Elapsed time in whole hours tells how many full hours pass from a start time to an end time. To solve, begin at the start time and count each hour until you reach the end time. Each step to the next hour is 1 hour.

Elapsed Time in Half Hours means finding out how much time passes when the clock moves by 30 minutes, or by groups of 30 minutes.

A half hour is the same as 30 minutes. On a clock, when the minute hand moves from one number to the next big half-turn, 30 minutes have passed.

We can use what we know about clocks to count elapsed time. Elapsed time means how long something lasts, from the start time to the end time.

Important clock facts:

• When the minute hand points to 12, it is :00.
• When the minute hand points to 6, it is :30.
• A half hour means: $$30 \text{ minutes} = \text{half an hour}$$
• Two half hours make one whole hour: $$30 + 30 = 60 \text{ minutes} = 1 \text{ hour}$$

When we find elapsed time in half hours, we often count by 30 minutes.

Here is a simple way to do it:

1. Find the start time.
2. Find the end time.
3. Count forward by half hours until you reach the end time.
4. Add the half hours you counted.

Helpful idea: Each jump of 30 minutes is one half hour.

For example:

• From 2:00 to 2:30 = 30 minutes
• From 2:30 to 3:00 = 30 minutes
• From 2:00 to 3:00 = 1 hour

Let’s look at some worked examples.

Example 1: One half hour

A movie starts at 4:00 and ends at 4:30. How much time passes?

Start at 4:00. Count to 4:30.

That is 1 half hour.

$$30 \text{ minutes}$$

Answer: The movie lasts 30 minutes.

Example 2: Two half hours

Practice starts at 1:30 and ends at 2:30. How much time passes?

Count by half hours:

• 1:30 to 2:00 = 30 minutes
• 2:00 to 2:30 = 30 minutes

Add them together:

$$30 + 30 = 60 \text{ minutes}$$

Answer: Practice lasts 1 hour.

Example 3: Three half hours

A family leaves at 5:00 and gets home at 6:30. How much time passes?

Count forward by half hours:

• 5:00 to 5:30 = 30 minutes
• 5:30 to 6:00 = 30 minutes
• 6:00 to 6:30 = 30 minutes

Now add:

$$30 + 30 + 30 = 90 \text{ minutes}$$

Since 60 minutes is 1 hour, 90 minutes is 1 hour 30 minutes.

Answer: The family was gone for 1 hour 30 minutes.

Example 4: Start at :30 and end at :00

Reading time begins at 9:30 and ends at 11:00. How much time passes?

Count by half hours:

• 9:30 to 10:00 = 30 minutes
• 10:00 to 10:30 = 30 minutes
• 10:30 to 11:00 = 30 minutes

That is 3 half hours.

$$3 \times 30 = 90 \text{ minutes}$$

Answer: Reading time is 1 hour 30 minutes.

Tips for Success

• Look at the minute hand first.
• If the minute hand is on 12, the time ends in :00.
• If the minute hand is on 6, the time ends in :30.
• Count slowly by 30 minutes: :00, :30, next hour :00, next hour :30.
• If you count 2 half hours, that is 1 hour.

Try thinking about it this way:

If you eat lunch from 12:00 to 12:30, that is half an hour.

If you play from 3:30 to 4:30, that is two half hours, or one hour.

What to remember

• Elapsed time means how long something lasts.
• A half hour is 30 minutes.
• Count forward in jumps of 30 minutes.
• Two jumps of 30 minutes make 1 hour.

When you solve elapsed time problems, start at the beginning time and make half-hour jumps until you reach the ending time. This makes the problem easy to see and easy to solve.