Making and Reading a Clock Face

Tools:
Compasses, rulers, protractors, calculators, sheet of paper, brad, material to make clock hands.

Prerequisite: Children have already used protractors for measuring angles.

Task:
Drawing a clock face.
The short hand (hour hand) of a clock moves all the way around in 12 hours. So it moves 360/12 = 30 degrees each hour, it moves 3 * 30 = 90 degrees each 3 hours, and it moves 180 degrees (half way around) in 6 hours.

Draw a fairly large circle . Draw the radius straight up to the point which you label with 12. It is when the hour hand is at 12 noon and at 12 midnight. Using a protractor, divide the circle into 12 equal sectors, each having 30 degrees. You may first divide the circle into 4 equal sectors, and later divide each into 3 smaller ones. (We say sectors, because children should draw the RADIUS to each point, and not only mark the point on the circumference, as is done on real clock faces.)

Write numbers for hours (outside the circle) next to POINTS which are at the ends of the radii between the sectors.

Write numbers for minutes (inside the circle) next to POINTS which are at the ends of the radii between the sectors: 5, 10, 15, 20, ..., 50, 55, 60. You may put 0 on the right side of the radius alongside 60.

Cut out hour and minute hands of different lengths (and preferably different colors), and attach them to your clock face with a brad.
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The teacher should have her (large) picture ready to stick to the blackboard.

Activity 1.
When is the hour hand at a given time (1 am, 2 pm, quarter past 4 pm, just now)?
Children should indicate a radius or estimate in which part of a sector the hand would be.

Activity 2.
The minute hand moves all the way around in 1 hour, so it covers one of 12 sectors in 60/12 = 5 minutes.
Where it is going to be at 5, 15, 25, ... minutes after an hour?
(Show the radius.)
Where is it going to be at 2, 19, 47, ... minutes after an hour?
(Show the sector and estimate the position.)

Activity 3.
Show the position of BOTH hands at a given time.

Remark 1.
Children work with their clock faces, and they show the answer to the rest of the class on the teacher's clock.

Remark 2.
Their clock faces MUST be correctly drawn. If this is a problem, children should work in groups and have a correct clock face (only one) for two or three or even four children.

Remark 3.
Do not discuss seconds. They make the picture too complex without adding much to the concept.

Remark 4.
Working with angles (and measuring them in degrees), and not just talking about dividing the circumference of the circle into 12 even parts, is important for future introductions of angles of more than 360 degrees.

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Telling Time

This activity requires a clock in the classroom visible to all children. The activity is planned for two days. During the first day a "log" of activities is created. The next day, early in the morning, it is analyzed during the math lesson.

1. First day.
Each activity starts, and ends, with the question, "What time is it now?" Children read the clock, in hours and minutes. The time is written on the blackboard. And a sentence or two, such as, "We finished reading Peter Rabbit," is written next to it.

Example:

______________________________________________________
Time: What happened:

8:15 am We started our art lesson. We painted flowers.
8:45 am We finished painting.
9:03 am We finished cleaning up.
9:05 am Math lesson started.
______________________________________________________

Comments about what happened can be very brief. They will act as reminders the next morning.

2. Second day.
Start with a discussion, "What did we do yesterday?" with the log on the blackboard as a reminder, prompting children with questions, "At what time....?"

The real work starts with questions, "For how long did we ... ?"
Example of an answer:
We painted for 30 minutes, and there were 20 minutes between when we finished painting and when we started our math lesson.

Comments.
In this lesson, do not concentrate on any specific way of computing time. Children may use any method, with or without a calculator. The "time table" (see How much time has elapsed?) is recommended.

This (two-day) activity may be repeated several times, as long as children find it interesting and challenging.

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How much time has elapsed?

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In this lesson students learn how to answer questions such as "How much time elapsed between 6:24 am and 4:15 pm?" It was very successfully used in a third grade class!

Props: Each student should have the attached table. The whole table should form one long page (2 1/2 normal pages glued together). Or, one enlarged (at least 4 times in each direction) copy should be hung on a blackboard. Making it into a long "linear clock" is very effective.

LINEAR CLOCK FILES

Example of a short problem with a solution.
A bus left the San Francisco bus station at 7:13 am and arrived at the Los Angeles bus station at 4:32 pm. How long was the trip?
Solution: Locate 7:13 am and 4:32 pm in the table.
From 7:13 to 8 am is 60 - 13 = 47 min;
from 8 am to 12 noon is 12 - 8 = 4 h;
from 12 noon to 4 pm is 4 h;
finally, from 4 pm to 4:32 pm is 32 min.
The number of minutes is 47 + 32 = 79 = 60 + 19, which is 1 h and 19 min.
4 + 4 + 1 = 9 hours, so the trip lasted 4 + 4 + 1 = 9 hours and 19 minutes.

Remark 1. Calculators may be used for additions and subtractions.

Remark 2. Other methods should also be discussed. For example, finding the time between 7 am and 4 pm, and later adding 32 minutes and subtracting 13 minutes.
Again, 12 - 7 + 4 = 9 hours and 32 - 13 = 19 minutes.

Remark 3.
Some problems in which a bus (or train) leaves in the afternoon and arrives the next morning should be given.

A longer problem.
Jim is working in a Ford plant. He punches the clock every time he comes to the plant, and again when he leaves. Here are his working hours during one week.