The activity begins with an applet demo showing the hands of a clock
moving in various positions while a number appears on the alarm bell
at the top of the clock. The user is asked to determine what this number
represents.
The next page allows the user to control the speed of the hands and
to choose the base of the clock face. The following page allows the
user to set the clock manually by clicking and dragging each hand. Whenever
a time is set, a number appears on the alarm bell. Suggestions are given
to help the viewer determine the relation between the time and the number
on the alarm bell. Eventually the viewer discovers that the number on
the alarm bell is the sum of the digits enclosed between the hands on
the clock, starting from the hour hand and proceeding clockwise to the
minute hand.
The next page allows the user to enter a number on the alarm bell
(a candidate for the sum) and the computer automatically shows all positions
of the hands corresponding to this number (if any exist), or announces
that there are no solutions.
The next page presents a Clock Game. A number appears at random on
the clock face, and the player's challenge is to place the hands in
such a position that the sum of the digits enclosed between the hands
is equal to the number on the clock face. The game can be played at
different levels of difficulty. At level k the clock hands surround
k clock digits. For example, at level 3 the number shown on a base 12
clock face could be 24, and there are two solutions: 7+8+9 and 11+12+1.
The player will soon learn that the first solution can be obtained by
averaging, because onethird of 24 is 8.
The ultimate goal of this activity is to have the user discover (with
the help of tutorials) properties of sums of integers in arithmetic
progression. Sometimes the numbers being added are consecutive, as in
the foregoing example 7+8+9 = 24. The game becomes more interesting
when the numbers being added overlap the clock base, as in the example
11+12+1 = 24.
Several variations of the Clock Game are also being considered. For
example, the numbers on the clock face need not be consecutive but can
be in any arithmetic progression.
