Hi, I’m Rob. Welcome to Math Antics.
In this lesson, it’s finally time for us to learn about time.
Like distance, time is something you can measure and represent as a number.
But we use different units to measure time
and also different devices to make the measurements.
There are lots of different units of time
from really small ones like nanoseconds to really big ones like centuries.
But in this video, we’re only going to learn about four of the most common units of time:
seconds, minutes, hours and days.
You should be really familiar with a day… ya know… cuz you encounter one every day.
A day is the amount of time it takes the Earth to rotate on its axis one time.
So it’s pretty much the fundamental unit of time for our planet.
But as important as a day is, we need smaller units of time for planning daily activities,
so people decided to divide up each day into 24 equal chunks of time called hours.
Even though an hour is only one twenty-fourth of a day, it’s still a pretty long time,
so we divide hours up into even smaller units called minutes.
Specifically, each hour is divided up into 60 minutes, so a minute is one sixtieth of an hour.
And to get even smaller units of time,
we divide up each minute into 60 equal parts called seconds, so a second is one sixtieth of a minute.
Going from the smallest to the biggest, you should memorize that
60 seconds equals 1 minute.
60 minutes equals 1 hour.
And 24 hours equals one full day.
There are some common abbreviations for these units that you should know too:
‘d’ for days,
‘h’ for hours,
‘min’ for minutes,
and ’s’ for seconds.
One of the earliest devices for measuring time was called a sundial.
It was basically a flat disc with a triangular pointer in the middle.
As the earth rotated, the shadow of the pointer would slowly change position
and point to different markings on the edge of the circle,
which represented different times of the day.
Are you tired of ‘The Man’ telling you what time it is?
Now you can get the time directly from the source with the sun-o-matic 3000!
Just put it in your yard and let the sun do the rest!
For daytime use only. Not for use in cloudy conditions.
Times may not be accurate depending on latitude. Some calibration required.
The sundial was a really cool invention, but it had a lot of limitations.
Fortunately, there are much better modern devices for keeping track of time.
In fact, you probably have one hanging on your wall at home or in your classroom
that looks something like this.
This ‘traditional clock’ is designed to keep track of three different units of time:
seconds, minutes and hours.
That’s why it has three different pointers or “hands”.
This thin red pointer is called the “second hand” because it helps us keep track of seconds.
This thicker black pointer is called the “minute hand” because it helps us keep track of minutes,
and this shorter black pointer is called the “hour hand” because it helps us keep track of hours.
Oh… and the circle itself is often referred to as the “clock face”.
A clock is actually kinda complicated, so to see how it works,
let’s start with a version that has everything removed
except for the second hand and the 60 marks around the edge of the clock face.
Why are there 60 marks around the edge? You’ll see in just a minute…
Starting with the second hand pointing straight up at the top of the clock face,
if the hand rotates to the right so that it’s pointing at the next mark,
that means that one second of time has passed, so we’ll label that mark 1.
The next mark will be 2,
the next 3 and so on until we get all the way around and the hand is pointing straight up again.
That means exactly 60 seconds have passed, so we’ll label that mark with a 60.
But we could have labeled that top mark as a zero since that’s where the sequence of numbers starts.
That’s one of the cool things about a clock being a circle.
The starting point is also the ending point.
So as soon as you hit the end (60 seconds),
you are also back at the beginning (0 seconds).
The reason that there’s exactly 60 marks around the edge of a clock
is that 60 seconds equals 1 minute.
That means when the second hand makes one full rotation around the clock face,
exactly one minute of time has passed.
And if it makes two full rotations, two minutes have passed.
And if it makes three rotations, three minutes have passed, and so on….
So even though the second hand is counting seconds,
it also helps us know how many minutes have passed.
But, how are we gonna keep track of those minutes?
That’s where the minute hand comes in handy, so let’s add it back to our simple clock.
The minute hand works a lot like the second hand.
The main difference is that it travels slower; 60 times slower to be exact.
Since a minute is 60 times longer than a second,
while the second hand travels all the way around the clock,
the minute hand only moves from one mark to the next.
For example, if both hands start straight up at the top of the clock,
while the second hand travels all the way around the clock (counting out 60 seconds as it goes)
the minute hand will only travel from 0 to 1 because only 1 minute has passed.
Then, while the second hand travels around the clock a second time,
the minute hand will travel from 1 to 2 because 2 minutes will have passed.
Notice that we use the exact same set of 60 marks to measure both seconds and minutes,
but the different hands tell you how to interpret those marks.
If the second hand is pointing at the 5th mark, it means 5 seconds,
but if the minute hand is pointing at the 5th mark, it means 5 minutes.
Of course, being able to quickly tell which mark a hand is pointing at is tricky
since clocks don’t usually number every mark.
So to make it easier, the inventors of the clock decided to make every 5th mark bigger (or bolder)
so you could skip count by 5’s which helps you quickly tell where the hands are pointing.
For example, if the second hand is pointing right here,
you can tell right away that it’s just two marks past the 15th mark,
so it’s pointing at 17 seconds (since 15 + 2 = 17).
And if the minute hand is pointing here,
you’ll quickly see that it’s just two marks before the 40th mark,
so it’s pointing to 38 minutes (since 40 - 2 = 38).
These bigger marks are so helpful for reading a clock
that you should memorize the values they represent when the minute or second hands are pointing at them;
especially the ones that break the clock face up into quarters.
Okay, so now you know how the second and minute hands work…
when the second hand goes all the way around, the minute hand increases by 1.
But what happens when the minute hand eventually goes all the way around and has counted out 60 minutes?
If you paid close attention at the beginning of the video, you probably know the answer.
60 minutes equals one hour.
So when the minute hand goes all the way around, it means 1 hour of time has passed.
That means we’re gonna need to add the hour hand back to our clock to keep track of hours.
But the hour hand doesn’t use the 60 marks on the edge of the clock in the same way that the other hands do.
Why not?
Because there aren’t 60 hours in a day. There’s only 24.
If hour hand just moved one mark for each hour,
it wouldn’t make it all the way around the clock face in a single day.
Ideally, it would be nice if we could have the hour hand go around the clock once per day,
but unfortunately the 60 marks on the clock don’t divide evenly by 24.
That means you can’t find a nice whole number to skip count to 24 by.
For example, if you had the hour hand move two marks for each hour…
it still wouldn’t go far enough to make it all the way around the clock in a day.
And if you had it move three marks for each hour, it would go too far!
Fortunately, the inventors of the clock came up with a clever compromise.
They realized that even though 24 hours doesn’t divide evenly into 60,
half of a day (which is 12 hours) does.
60 divided by 12 equals 5, and 5 is a nice whole number to skip count by.
If fact, we already have bigger marks on our clock face every 5 marks
which makes this idea really convenient.
If the hour and minute hands start pointing straight up,
as the minute hand goes all the way around the clock counting out 60 minutes,
the hour hand will slowly move past the first 5 marks which means 1 hour has passed.
Then, as the minute hand goes all the way around again,
the hour hand will move past the next 5 marks which means that 2 hours will have passed.
This continues on until the hour hand makes it all the way around the clock
and gets to the 12 hour mark back at the top.
Just like with minutes and seconds,
the top position on the clock represents both the beginning and the end of the counting sequence.
For minutes and seconds, that means the top position represents both 60 and 0,
but for the hour hand, that top spot represents both 12 and 0.
Of course, 12 hours is only half a day.
That means in order for this clock to keep track of one whole day,
the hour hand needs to make two full trips around the clock face.
It counts out 12 hours the first half,
and then 12 more for the second half.
That means each hour mark is passed twice during the day,
so we need a way to distinguish them.
And that’s where “a.m.” and “p.m.” can help us out.
A.m. stands for ante meridiem which just means “before noon”
and p.m. stands for post meridiem which means “after noon”.
To see how the a.m. and p.m. labels work with the 12 hours on our clock-face to keep track of a full day,
let’s compare them to a simpler modern time-keeping system called the 24 hour clock.
In that system, the 24 hours of the day are just labeled zero through 23.
In other words, at the beginning of the day (which happens to be midnight)
the time is zero hours and zero minutes.
As the hours pass by, you eventually get to the time 23 hours and zero minutes
which means you’re starting the 24th hour of the day.
After that last hour passes, it starts back over at zero for the next day.
On the traditional clock face, at midnight,
the hour hand is pointing straight up at 12,
so instead of calling it “zero o’clock”, we call it “12 midnight” or “12 a.m.”
Then the first 12 hours of the day pass one by one using the a.m. label…
1 a.m.,
2 a.m.,
3 a.m.,
on up to 11 a.m.
When the hour hand gets to 11 a.m.,
you’re beginning on the 12th hour of the day
and as soon as the 60 minutes of that hour pass by,
the hour hand will be back up at the top of the clock pointing at 12 again,
but this time we’re going to call that position “12 noon” or “12 p.m.”
Then the clock continues on counting out the last 12 hours of the day
using the p.m. label…
1 p.m.,
2 p.m.,
3 p.m.,
on up to 11 p.m.
When the hour hand gets to 11 p.m.,
it means you’re starting the last (or 24th) hour of the day.
After that last hour passes, the hour hand points straight up at 12 again
which is now “12 midnight” or “12 a.m.”
and the cycle starts all over for the next day.
Let’s briefly summarize what we’ve learned about the clock so far
before moving on to a few examples of “telling time”.
Each time the second hand rotates all the way around the clock,
1 minute has passed and the minute hand advances one mark.
Each time the minute hand goes all the way around the clock,
1 hour has passed and the hour hand advances 5 marks.
Each time the hour hand goes around the clock, 12 hours have passed which is half a day.
The first 12 hours are called the a.m. hours
and the second 12 hours are called the p.m. hours.
If this is your first time learning how a clock works, it might seem kinda confusing,
but don’t worry.
The more you practice looking at a clock and noticing which hands are pointing to which marks,
the faster you’ll be able to tell what time it is.
In fact, let’s practice that a few times now so you get the hang of it
before doing more practice on your own.
Let’s start with this clock face.
What time of day is it displaying?
The hour hand is past the 7 but not to 8 yet, so the hour is 7.
The minute hand is pointing directly at the 3, but remember…
that’s the 3rd group of 5 marks for minutes or seconds.
So it’s pointing gat the 15 minute mark.
And the second hand is pointing straight up, which is the 0 second mark.
So the time is 7 hours, 15 minutes and zero seconds.
Oh… and that’s how you write a time using numbers.
You write the hours first, then minutes and then seconds (if necessary) all separated by colons.
But is this 7:15 a.m. or p.m.?
To tell that you need to know if it’s before noon or after noon (the half way point of the day).
Books or tests sometimes give you a clue about whether
the time is before noon or after noon so you can figure it out.
Or they may just tell you if it’s a.m. or p.m.
In this case, we’re given the clue, “soon the sun will set”,
so we know it’s afternoon or 7:15 p.m.
How about this example? What time is this clock displaying?
The hour hand is past the 10 but not to 11 yet, so the hour is 10.
The minute hand is just past the 4, which is the 20 minute mark,
but it’s not to 21 yet, so the the minute is 20.
And the second hand is pointing at the 9 which is the 45 second mark,
so the time is 10 hours 20 minutes and 45 seconds.
And this time you’re given the clue, “it’s a beautiful morning”,
so you know that it’s 10:20 a.m. since morning comes before noon.
And finally, what time of day is this clock displaying?
The hour hand is past the 12 but not yet to the 1, so it’s “12 something”.
The minute hand is pointing just a hair past the 6, which is the 30 minute mark so the minute is 30.
And there’s no second hand on this clock (not all clocks have them),
so we’re only concerned about the time to the nearest minute in this example.
Lastly, this clock face is actually labeled a.m.
so we know that the time of day is 12:30 a.m. which is 30 minutes past midnight.
Alright, so now you know how seconds, minutes, hours and days all relate to each other.
You also know how a traditional clock works to help you keep track of these units of time as they pass by.
And importantly, you’ve learned how to read the hands of the clock face so that you can tell what time of day it is.
Remember that the way to get good at anything in math is to practice, so be sure to practice telling time on your own.
As always, thanks for watching Math Antics and I’ll see ya next time!
Learn more at www.mathantics.com