Title
The 26^{th} Degree/FOIL Frenzy
Problem Statement
What is
(xa)(xb)(xc)...(xy)(xz)? Explain how you found the answer.
Problem setup
When I first looked at this problem I thought I
would have to multiply 26 variables together. After thinking about the problem and
listening to class discussion I felt there must be a pattern that would
help solve the problem. I
looked up the definition of a mathematical pattern and looked for
regularity.
Plans to
Solve/Investigate the Problem
Problem solving strategies including reading the
problem, recalling and discussing terminology and functions, using trial
and error computations, making tables or charts, looking for a simpler
problem and generalizing would be employed. Definitions of unknown terminology
were looked up on the Intermath dictionary.
Prior to beginning I looked up the definition
of a mathematical pattern in the Intermath dictionary. The
definition of a mathematical pattern per the Intermath dictionaly is
“a mathematical pattern involves regularity. This regularity may
manifest itself in shape, direction, orientation, size, or number
relationships, among other things. The key to being a pattern is that there
is some regularity that can be repeated, extended, or built upon.”
Investigation/Exploration
of the Problem
The problem was approached by
brainstorming as a class. Then
individually and collectively, the class applied foil to the first terms
(xa) * (xb).
Extensions of the Problem
What would the constant be in
the final problem?
Author & Contact
Susan R. Kelly
skelly.rockdale.k12.ga.us
Link(s) to resources, references, lesson plans, and/or other
materials
Link 1
Link 2
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