EMAT 6600
Problem Solving in Mathematics
Summer, 2008
This
is the web site page devoted to EMAT 6600 Problem Solving in Mathematics, at
the University of Georgia, as led by Jim Wilson.
Last
modified on July 21, 2008
Send
e-mail to jwilson@uga.edu
Back
to Jim
Wilson's Home Page
EMAT 6600 Documentation
EMAT
6600 Syllabus - General
information about the objectives and operation of the course.
PAPERS:
Synthesis of
Research on Problem Solving. This paper was published as Chapter 4 in
Wilson, P. S. (Ed.)
(1993). Research Ideas for the Classroom:
High School Mathematics. New
York: MacMillan.
The book was part of
the National Council of Teacher of Mathematics Research Interpretation Project,
directed by Sigrid Wagner.
The bibliographic
reference for the published version is
Wilson, J. W.,
Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P.
S. Wilson (Ed.), Research Ideas for the
Classroom: High School Mathematics
(pp. 57-78). New York: MacMillan.
Squares. X What is the ratio of
areas of the two squares? 
This is a discussion of some exploration and extensions of this problem.
Roots 2
and 5. This paper examines sets of equations that have graphs crossing
the x-axis only at 2 and 5. For a preview on one family of such graphs, click here.
Problem Solving
with Heron's Formula. X This is a paper on the development and demonstration of
Heron's formula for the area of a triangle given the lengths of its three
sides. Problems and explorations are included for using Heron's formula.
An
Investigation with Parametric Equations. This paper examines the movement
of triangles when one vertex is moved along the x-asis and another is moved
along the y-axis. We trace trace the movement of the third vertex.
Extended
Concurrencies of the Triangle
PROBLEMS:
X-- Problems discussed/introduced in class
Project InterMath
Project InterMath has a web site with many investigations
deemed appropriate for Middle School mathematics teachers. I believe secondary
mathematics teachers may find some challenges here as well. Please access the
site: Project INTERMATH
Environment Problems
Volume of an
Irregular Solid X
The Three
Point Problem from Geology
Volume of a
curved trench, Trapezoid Cross-section
Geometry Problems
Angle
Bisector of two line non-intersecting line segments X
Arc Length
equal to a given segment
Bisector of an
angle of a triangle X
Bisectors Problem in 120 degree Obtuse
Triangle X
Circles of
Apollonius for a Triangle ABC X
Color a Circle
Coloring Circles
Equilateral
Triangle Altitude Theorem
Find
Inscribed Square for Given Triangle X
Find
Inscribed Rectangle with Maximum Area for Given Triangle X
Folding a sheet
of paper into equal areas X
Half the Area
of a Triangle: A Line Parallel to a Side
Half the
Area of a Triangle: A line Through a Point on the Side
Inscribed
Equilateral Triangle in a Square – Construction X
Inscribed Equilateral Triangle in a Square – Problem X
Inscribed
Triangle in a given triangle X
Isosceles
Right Triangles--Path of the Mid-Point
Isosceles Right
Triangles With a Common Vertex
Isosceles
Trapezoid -- Equal areas X
Kite X
Lines
of Symmetry in a Polygon
Locus
of intersection of two secants
Pairs of
Segments with the Same Sum of Lengths
Parallelogram with Integer Sides and
Integer Diagonals
Partition
Square into Acute Triangles X
Perpendicular
Chords in a Circle
Points closer to the Centroid than the
Sides
Quadrilateral
Inscribed in a Semicircle
Quadrilateral
with Maximum area
Quadrilateral
with Squares on the Sides
Ratio on a line
segment -- Something Golden
Ratio: Segments
cut off by an angle bisector to the adjacent sides
Right
Triangle with perimeter 60, altitude to hypotenuse 12
Square
Inscribed along a base of any Triangle X
Squares
Inscribed in a Right Triangle X
Squares on the
Sides of a Parallelogram
Tangent
Lines Common to Two Given Circles
Trapezoid
Inscribed in a Semicircle
Triangle
areas/Triangle Built on Outside of a Given Triangle
Triangle Area
and the Circumcircle
Triangles
with Integer Area and Integer Sides
Volume of Holes
Left by Tree Spade
Algebra Problems
Solve
by iteration.
Comparision of Two Radical Expressions
Linear
functions tangent to their product function