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Learning Math Home
Patterns, Functions, and Algebra
Session 3 Part A Part B Part C Part D Part E Homework
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Session 3 Materials:

Session 3:
Other Kinds of Functions

In This Part: Functions and More Functions | More Functions | A Geometric Function

Sometimes, functions can be based on an algorithm but still not use numbers as inputs. Here's an algorithm; let's call it Algorithm M: Note 10


Start with a polygon


Find the midpoint of each side of the polygon


Connect each midpoint to the two midpoints on either side of it

Here's what the algorithm does to a pentagon:

pentagon algorithm

Take it Further

Problem E13


Try Algorithm M on three different triangles. Describe in words how the output is related to the input.

Be sure to select triangles that are different in a significant way: acute, obtuse, scalene, isosceles.   Close Tip


Problem E14


How does any new triangle created by Algorithm M relate to the original, in size and in shape?


Problem E15


Try Algorithm M on several different quadrilaterals. Describe anything you notice about the outputs.

As with Problem E13, select quadrilaterals that are different in a significant way. You might also concentrate on a specific type of special quadrilateral to determine if Algorithm M does something similar to all quadrilaterals of that type.   Close Tip


Problem E16


Does Algorithm M describe a function? Explain how you know.


Problems in Part E taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000).

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