How to Tell Time

Date: 11/23/98 at 18:53:39
From: Lucas Anderson
Subject: I need help with learning to tell time please.

I know how to read time by the hour and half hour, but it's the minutes 
after, before and all those in between that I get stuck on. For 
example, how does 1:35 look, and what does it mean?

Thank you,
Lucas

Date: 11/24/98 at 12:06:10
From: Doctor Peterson
Subject: Re: I need help with learning to tell time please.

Hi, Lucas. It sounds like you are just about where my seven-year-old 
daughter was recently in learning about clocks. I'll tell you some of 
what I've told her.

The most important thing in learning to read minutes on a clock is to 
be able to count by fives! The big numbers on a clock tell what hour it 
is when the hour hand points there, but each one also stands for five 
minutes. It may be very helpful if you can get (or make out of a paper 
plate) a clock face with minute markings like this:

                          0
                      *********
             55 ******    12   ****** 5
             ***11        ^         1***
           **             |             **
         **               |               **
     50 *                 |                 * 10
       *10                |                 2*
      *                   |                   *
     *                    |                    *
     *                    |                    *
    *                     |                     *
 45 *9                    o                    3* 15
    *                         \                 *
     *                            \            *
     *                                \        *
      *                                       *
       *8                                   4*
     40 *                                   * 20
         **                               **
           **                           **
             ***7                   5***
             35 ******    6    ****** 25
                      *********
                          30

Once you get used to it, you should be able to imagine the minute 
numbers around the outside, by just counting by fives, but for now, 
use a picture like this to make it easier.

The first step in learning to tell time is to ignore the minute hand 
and just watch the short hand. You might even like to play with a real 
clock that you can set. We used a broken one. Turn the knob, and you'll 
see the hour hand move smoothly around the clock, from 12 at noon back 
to 12 at midnight, while the minute hand races wildly around and 
around. When it points exactly at the 4, it's 4 o'clock. When it's 
halfway from the 4 to the 5, its "half-past 4." You already know about 
that.

Clocks once were made just like that with no minute hand! But people 
decided it would be helpful to know more accurately just how long it is 
after 4, or how long before 5, so they added the minute hand, which 
goes around once for every hour. (Turn the knob on your clock and watch 
how the minute hand goes around.) When the minute hand is at 12, the 
hour hand is pointing exactly at an hour. When it has gone exactly 
half-way around, and points at the 6, the hour hand is exactly half-way 
between the hours, so it's "half-past" the hour. (Set your clock to 
that time and see what I mean!) When the minute hand points to the 3, 
it has gone a quarter of the way around, so it's "a quarter past" the 
hour. So when the clock looks like this, it's a quarter past 4, because 
the hour hand is PAST the 4 (on its way to 5) and the minute hand is a 
QUARTER of the way around:

                          0
                      *********
             55 ******    12   ****** 5
             ***11                  1***
           **                           **
         **                               **
     50 *                                   * 10
       *10                                  2*
      *                                       *
     *                                         *
     *                                         *
    *                                           *
 45 *9                    o------------------->3* 15
    *                       \                   *
     *                         \               *
     *                            \            *
      *                              \        *
       *8                                   4*
     40 *                                   * 20
         **                               **
           **                           **
             ***7                   5***
             35 ******    6    ****** 25
                      *********
                          30

Now it's time to look at the minutes. An hour is 60 minutes; a quarter 
of that is 15 minutes. So our "quarter past 4" is the same as 15 
minutes past 4. That's what it means when the minute hand points at 
the 15 on the outside of my clock. We write this as 4:15. The 4 is the 
last number the hour hand pointed at, and the 15 is the number the 
minute hand points at.

So here's the time you asked about, 1:35:

                          0
                      *********
             55 ******    12   ****** 5
             ***11                  1***
           **                           **
         **                               **
     50 *                                   * 10
       *10                                  2*
      *                            /          *
     *                           /             *
     *                        /                *
    *                       /                   *
 45 *9                    o                    3* 15
    *                    /                      *
     *                  /                      *
     *                 /                       *
      *               /                       *
       *8           /                       4*
     40 *          /                        * 20
         **       /                       **
           **    /                      **
             ***7                   5***
             35 ******    6    ****** 25
                      *********
                          30

The hour hand is past the 1, in fact more than halfway to the 2; the 
minute hand points to the "35" (where a normal clock only says "7"), 
meaning it's 35 minutes past the hour. That's a little more than 
half-past one.

Now, you can also call this 25 minutes before 2. How do you know that? 
Because you can count by fives while you imagine the minute hand 
continues around to the 12. It will take 5 minutes to get to the 8, 
10 to get to 9, then 15, 20, 25 minutes to get to the 12. So it's 25 
minutes until the next hour, which is 2.

The hardest times to read are when it's just before an hour. That's 
when it's important to understand how the hour hand moves. Suppose 
it's just five minutes before 2 o'clock. Then the hour hand is almost 
at the 2, and the minute hand is at the "55" (11). But we read this 
as 1:55, not 2:55, because it's 55 minutes AFTER 1 (and 5 minutes 
BEFORE 2):

                          0
                      *********
             55 ******    12   ****** 5
             ***11                  1***
           **    \                      **
         **       \                       **
     50 *          \                        * 10
       *10          \                       2*
      *               \               /       *
     *                 \           /           *
     *                  \       /              *
    *                    \   /                  *
 45 *9                    o                    3* 15
    *                                           *
     *                                         *
     *                                         *
      *                                       *
       *8                                   4*
     40 *                                   * 20
         **                               **
           **                           **
             ***7                   5***
             35 ******    6    ****** 25
                      *********
                          30

The last step will be to learn to read minutes between the fives. That 
can wait until you're ready. It's best if you have a clock that has a 
little mark at every minute. But usually we don't need to be that 
exact. If the minute hand points near the 7, but not exactly, you can 
just say "It's about 1:35." (I'd just say it's half-past, but my 
daughter won't let me, now that she knows what time it REALLY is!)

Have fun playing with clocks.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/