teaching time-telling

Teaching Time-TellingAuthor(s): Glenn NelsonSource: The Arithmetic Teacher, Vol. 29, No. 9 (May 1982), pp. 31-34Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41190165 .

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Teaching Time-Telling By Glenn Nelson

Rarely does anyone go through a day without making reference to time. Adults and children make time allot- ments for the day's tasks and use a clock or watch to measure such allot- ments. However, although nearly all children do eventually learn some- thing about telling time and reading a clock, there is usually dissatisfaction about the effectiveness with which this topic can be taught. Reisman (1972) has noted this concern and has done much investigation of it.

The topic of time is separated into two areas for instructional purposes, time-telling skill and the concept of time. Skill in telling time would be indicated by the student's ability to read a clock or set a clock, while a concept of time would be evident in a student's understanding of various units of time, their duration, and their relationships to events. These two areas are treated separately because the time-telling skill has such importance in the real world and can be taught earlier than time concepts.

Before looking at a series of activities to teach time-telling, several fea- tures of this sequence should be noted. One is that an attempt has been made to simplify the confusing lan- guage often encountered initially. Take, for instance, some of the different expressions that can be used to state the time shown here:

Glenn Nelson is an associate professor of mathematics education at the University of Northern Iowa in Cedar Falls, Iowa. He teach- es content and methods courses at the under- graduate and graduate levels.

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Forty-five (minutes) after six Forty-five (minutes) past six Fifteen (minutes) till seven Fifteen (minutes) of seven Quarter till seven Quarter of seven Quarter before seven Six forty-five

If we insert the optional word, minutes, in each of the first four state- ments we obtain at least a dozen different acceptable expressions of the time indicated. Needless to say, determining the position of the hands on the clockface and their meaning can be only a part of the difficulty in telling time when one considers the profusion of terms used to state the time in oral and written form. In the beginning, much of the problem can be solved by limiting the terminology to "minutes after" the hour.

Another characteristic of the sequence is that, after working with time to the hour, time is read to the minute prior to being read to the half- hour or to the quarter-hour.

A third feature is the incorporation of the tactile sense along with the visual and auditory senses.

Lastly, the connection between the movement of the minute hand and the

hour hand is reinforced by a teaching- aid clock that accurately demon- strates this relationship.

A Sequence of Activities

The face of a clock

Write the numerals 1 through 12 on a clockface. Give the learner a drawing of a clockface like the following, marked off at twelve equal intervals but on which there are no numerals or minute markings.

Where does the numeral 1 go on this clockface? Write it in. Where do the numerals 2, 3, 4, up to 12 go? Write them in. What numeral goes at the top of the clockface? On the bottom?

The hands of a clock

In the following activities, teacher and learner should use a teaching clock with hands that are geared as a regular clock's hands are and that can be touched. Using an ungeared clock, whose hands move independently, produces problems not encountered with real clocks, such as attempting to determine whether the following

May 1982 31



clock is supposed to represent half- past three or half-past four.

Such unneeded difficulties, which don't arise in the real world, are avoided by using a geared clock.

Hour hand, minute hand

The learner needs to learn to distin- guish between the hour hand and the minute hand. Give the learner a clock.

How are the hands of the clock different? Which hand tells us the number of minutes? The number of hours? Move the minute hand straight to the top. What numeral does the hour hand point to now? Close your eyes. Tve moved the clock's hands. Can you feel which is the hour hand?

Time to the hour

Have the learner move the minute hand so that it is straight up.

Does the hour hand point directly at an hour marking or between two hour markings? Whenever the minute hand points directly to the top of the clock, the hour hand points directly to an hour marking and we say, "It is o'clock."

To avoid confusion in the future, do not refer to the hour numeral when indicating the position of the minute hand. For the time being, the question of why the minute hand means 0, or 60, when it points to 12 is best avoided.

Have the learner practice setting the clock and reading the clock. For example:

Set this clock to show 9 o'clock. Ten o'clock.

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What time does this clock show?

This clock?

Close your eyes. I've set the hands to show a certain hour. Where do you think the minute hand is pointing? Check by touching the clock-

face. Now, can you feel where the hour hand is? Guess what time it shows. Look and see if you were right. Now you set the hands to show some hour and I'll guess. Am I right?

Give the learner experience with clocks in different orientations. For example:

Close your eyes. I've set the clock to show a certain o'clock, but I'm not going to give the clock to you as I did the last time. This time I'll turn it around.

Can you tell what time it shows? Look. Were you right? Now you do it for me.

The direction the hands move

In order to read the number of minutes after the hour, it is important that the learner know the position of the zero-minute mark and the direction in which the clock hands move.

In which direction do the hands of a real clock move? Move the minute hand of this clock in a clockwise direction.

Explain to the learner that often the minute hand is not pointing straight up and that we also have to be able to tell time whenever this occurs.

Whenever the minute hand is pointing straight up to the top of the clock, is the hour hand pointing

32 Arithmetic Teacher



right at an hour marking or between two hour markings? What if the minute hand is not pointing straight up? This hour hand is between what two hours?

Indicate the minute markings and explain that the minute marking to which the minute hand points tells us how many minutes it is after a certain o'clock.

Set the clock to show exactly 7 o'clock. Now set it to show 1 minute after 7 o'clock ... 2 minutes ... 5 minutes ... 10 minutes after 7 o'clock.


This clock?

Close your eyes. I've set the clock to show 5 minutes after some hour. Touch the clockface. Can you tell what hour marking the hour hand has just passed? What time do you think the clock says? Look and see if you are right.

You set the clock for me and I'll try to guess by touching the clock.

Five-minute intervals

The ability to count by fives is a prerequisite to this more efficient method of determining the number of minutes after the hour. Also, as far as the terminology is concerned, it may be appropriate to occasionally omit the terms minutes and o'clock.

Set the clock to show 5 (10, 15, ... 60) minutes after 4 o'clock. What hour mark shares the same mark as the 5-minute mark? the 10-minute mark? the 15-minute mark? ... the 60-minute mark? What is another name for 60 minutes after 4 o'clock? Sixty minutes after 4 o'clock is the same as 0 minutes after what hour? How many minutes are there in one hour? Set the clock to show 5 minutes after 5 o'clock. Without counting by ones, can you set the clock to show 20 minutes after 5 o'clock? to show 35 minutes after 5 o'clock? 45 minutes after 5 o'clock? 15 minutes after 6 o'clock? 55 minutes after 12 o'clock? Without setting the clock, tell me another name for 60 minutes after 2 o'clock. Close your eyes. This time I've set the clock for 11 o'clock. Can you set it for 60 minutes after 11? Can you set it for 15 after 12? for 30 after 12? for 45 after 12?

Set the clock for 40 after 3; for 42 after 3. Counting by fives and then by ones, set the clock for 17 after 4 o'clock; for 54 minutes after 4.

Much practice will probably be re- quired for the previous step as there is often some difficulty in "shifting" from counting by fives to counting by ones.

Use counting by fives, then by ones, to tell what time this clock says.

What time is this?

Other common terminology As shown earlier, there are many different ways of expressing the same time. Although the expressions "15 after 6" or "15 minutes after 6 o'clock" are acceptable for telling someone the time, it is important that learners also understand terms such as "quarter past," "quarter of," and "half past" when they hear them. This goal is probably best accom- plished by the somewhat casual intro- duction of these expressions by the teacher (such as was done in the last set of activities, where the words minutes and o'clock were sometimes omitted), but some specific introduc- tory activities are suggested here.

You can now tell time, but sometimes people use different words to say the same time. Set the clock for 30 after 1.

May 1982 33



We can also call this "half past 1." Can you guess why we might call this "half past 1"? Yes, the hour hand has traveled half way from 1 o'clock to 2 o'clock. The position of the minute hand tells us that it has traveled half way around the clockface. Set the clock for 30 minutes after 2 o'clock. Set the clock for half past 2. What about these times? Tell me two different ways of saying this time.

Close your eyes. I've set the clock for half past some hour. By touching the hands, can you tell what time it says? Are you right? You set the clock for half after some hour for me.

You may run through similar se- quences for "quarter past (after)" and "quarter of (till, to)."

Set the clock for quarter of (till , to) 8. This is how many minutes after 7? How many minutes till 8? We sometimes call this "15 minutes of (till, to) 8 o'clock.'.' Set the clock to show 10 minutes of 8; to show 3 minutes to 8; to show 22 minutes till 9."

Note that we use the terms minutes of minutes to, or minutes till the next hour only if it is after half past the previous hour.

Tell me three different ways of saying this time.

This time.

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Digital expressions of time

Digital clocks and watches are becom- ing more and more common. It would not be surprising if a survey of out- door clocks on banks or other build- ings in the neighborhood revealed that most are digital. Also, if you have a telephone time service, the time is probably announced digitally.

For this activity, the geared clock and a digital clock or representation of a digital clock, with moveable numerals, should be used. The same time should be displayed simultaneously on a standard clockface and on a digital clockface. These displays should then be compared.


This picture of a digital clock says the same time. Can you tell which numeral tells the hour? the minutes after the hour?

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If appropriate, an alternative form of expressing time can be introduced.

Set this clock to show the same time as is shown on the picture of the digital clock. What time does each clock show? We sometimes say the time with just the numbers. For example, this time could be read as "seventeen after two" or as "two, seventeen."

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2:17 Tell me two different ways of saying this time.

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Each of the previous activities has been illustrated with very few examples. Certainly many other examples may need to be provided for your learners. It is hoped, however, that these activities will be helpful to you in teaching time-telling skills.

Reference

Reisman, Fredricka K. A Guide to the Diagnos- tic Teaching of Arithmetic. Columbus, Ohio: Charles E. Merrill, 1972. щ

34 Arithmetic Teacher



teaching time-telling

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