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Table 12.2 (continued)
Worksheet: toward the leap of faith approach
First task: A recursive description of a visual figure (binary tree) is given. Draw the
described figure for level 3.
The basic binary tree is of level 1, and it looks like a V-shape.
A binary tree of level N is a V-shape with a smaller binary tree at each edge of the
V-shape.
Second task: A recursive description of a valid expression is given. Write as many valid
expressions as you can.
The basic valid expression is the letter C.
A valid expression begins with the letter A, proceeds with a shorter valid expression,
and ends with the letter B.
Third task: Represent the following sand clocks by a recursive description, similar to the
two descriptions presented above.
Fourth task: A series of numbers is given. Write two formulas for the n th element of the
series: one formula should be recursive; the other formula—not recursive.
$
$ =
O
Q
=
Worksheet, part B: Design similar tasks
What is the structure of a recursive description?
Design at least one additional task for each kind of the four tasks presented in part A.
The first task: translating a recursive description into a visual figure
The second task: translating a recursive description into a textual (nonvisual) expression
The third task: translating a visual figure into a recursive description
The fourth task: representing a series of numbers by a recursive formula and by a nonre-
cursive formula
Design a new kind of tasks that deal with recursive descriptions and are different from
those presented in part A
• Stage B: Class discussion
• Once the students finish working on the two parts of the worksheet, it is
recommended to facilitate a whole class discussion, which clarifies the
purposes of the tasks presented in part A, that is, getting familiarity with
 
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