The Department of Mathematics
and Science Education
EMAT 4600/6600. J. Wilson
Problem Solving in Mathematics
Spring, 2012
This
is the web site page devoted to EMAT 4600/6600 Problem Solving in Mathematics, at
the University of Georgia, as led by Jim Wilson.
Last modified on January 8, 2012. Send e-mail to Jwilson@uga.edu. Back to Jim Wilson's Home Page
EMAT 4600/6600 Documentation
EMAT
4600/6600 Syllabus - General
information about the objectives and operation of the course.
Introductory
Remarks
Resources
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.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. 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:
Recently added
Three Mile Roadway -- Two line segments and an arc
Two Stamp Problem
Orthogonal Parabolas
Parallel Chords
Three Adjacent Squares
Check Cashing Problem
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
Distance
survey
Volume of a
curved trench, Trapezoid Cross-section
Volume of an
Irregular Solid
The Three
Point Problem from Geology
Geometry Problems
20-30-130 Triangle
100
degree isosceles triangle
Angle
Bisector of two line non-intersecting line segments
Angle
of View
Arc Length
equal to a given segment
Area and Side of a Rhombus Given its Diagonals
Areas
of a Rectangle
Bisector of an
angle of a triangle
Bisectors Problem in 120 degree Obtuse
Triangle
Bouncing Barney
Brahmagupta's
Formula
Carl's
Cone
Ceva's Theorem
Checkerboard
Problems
Circle
Theorems Review
Circles of
Apollonius for a Triangle ABC
Circular
Window
Concurrency
Theorems
Cone Half Full
Count
the Triangles -- I
Count
the Triangles -- II
Count
the Triangles -- III
Construct Equilateral Triangle with Vertices on Three Given Parallel Lines
Cutting the Cake
Cyclic Quadrilateral
Dissect a Square into a Set of Acute Triangles
Dissect a Triangle a form a Square
Equilateral
Triangle Altitude Theorem
Equiperimetric
Areas
Excircle
Problems
Find
Inscribed Square for Given Triangle
Find
Inscribed Rectangle with Maximum Area for Given Triangle
FlowingStream
Fly
and Spider
Folding a sheet
of paper into equal areas
Four
dogs
Goat Tethered in a Field
Goat Tethered to the Edge of a Square Field
Golden Ratio Calipers
Golden Ratio Construction
Golden Triangle (same as Sublime Triangle)
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
Heron's Formula
Incircle
Problems
Inequality
in a triangle
Inscribed
Equilateral Triangle in a Square -- Construction
Inscribed Equilateral Triangle in a Square -- Problem
Inscribed
Quadrilateral
Inscribed Trapezoids
Inscribed
Triangle in a given triangle
Island
Treasure
Isosceles
Right Triangles--Path of the Mid-Point
Isosceles Right
Triangles With a Common Vertex
Isosceles
trapezoid
Isosceles
Trapezoid -- Equal areas
Kite
Lines
of Symmetry in a Polygon
Lighthouse Problem: Three lighthouses
Locus
of intersection of two secants
Locus
Problems
Maximum
Quadrilateral
Medians of a Triangle
Menelaus's Theorem
Networks of
Minimal Length
Notch for Felling
a Tree
Obtuse
Triangle Relationship
Octagon Construction and Formulas
Orthogonal Parabolas
Pairs of
Segments with the Same Sum of Lengths
Parallelogram with Integer Sides and
Integer Diagonals
Partition
Square into Acute Triangles
Perfect
Triangles
Pappus
Areas
Path Problems
Perpendicular
Chords in a Circle
Points closer to the Centroid than the
Sides
Polya's
Problem 2.35.1
Problem of Apollonius
Projections: Homothetic Similarity
Ptolemy's
Theorem
Pyramids
in a Prism
Quadrilateral Determined by Intersecting Orthogonal Parabolas
Quadrilateral
Inscribed in a Semicircle
Quadrilateral
with Maximum area
Quadrilateral
with Squares on the Sides
Ratio
Sums from Orthocenter
Ratio on a line
segment -- Something Golden
Ratio: Segments
cut off by an angle bisector to the adjacent sides
Right
Triangle Constructions
Right
Triangle Relationships
Right
Triangle with perimeter 60, altitude to hypotenuse 12
Rotating
Triangle
Septagon
Spheres
Square
Inscribed along a base of any Triangle
Squares
Inscribed in a Right Triangle
Square Inscribed in a Semicircle -- find a ratio
Squares on the
Sides of a Parallelogram
Sum of Ratios
Sublime Triangle (Same as Golden Triangle)
Tangent and
Secant Problem
Tangent
Lines Common to Two Given Circles
The
Problem of Apollonius
Three Adjacent Squares
Three Circles Problem
Three Intersecting Circles
Trapezoid with Parallel through the Intersection of the Diagonals
Trapezoid Inscribed in a Semicircle
Triangle
areas/Steinhaus
Triangle
areas/Triangle Built on Outside of a Given Triangle
Triangle Area
and the Circumcircle
Triangle
Constructions
Triangle Inscribed in a Rectangle
Triangle
Loci
Triangle
Mid-Segment Theorem
Triangles and
Squares
Triangles
with Integer Area and Integer Sides
Triangle with Median Equal to the Base and Sides of Length 1 and 2
Trirectangular Vertex Problem
Two triangle
problems
Two
Squares
Volume of Holes
Left by Tree Spade
Algebra Problems
7-11 Problem
A Tangled Tale
Problem
Average
Rate
Big Tires
Calculator
sequence
Candy Problem
Combining Percentages
Comparision of Two Radical Expressions
Equiperimetric
Areas
Golden Ratio and Fibonacci Sequence I
Heart
to Bell
Iron Ball Floating in Vat of Mercury
Jordan's
Inequality
Linear
functions tangent to their product function
Maximum
Volume of a Cone
McNuggets
Minimal area
triangle
Orthogonal Parabolas
Phonograph groove
Pythagorean Triples
s(s-c) =
(s-a)(s-b)
Simultaneous
Quadratics
Square
Root Equation
Sum of Unit
Fractions
Three Mile Roadway -- Two line segments and an arc
Two Stamp Problem
Volume
of a Frustum
Conversion
Problems
Big Tires
Cubic Foot
Million Drops of
Water
Volume of a 12
ounce can
Cryptarhythm Problems
Cryptorithms
Nine
digit number
OCTOBER
Primes
"Mean" Problems
AM-GM Problems
Arithmetic Mean --
Geometric Mean Inequality
Arithmetic Mean -- Geometric Mean -- Harmonic Mean Inequality
Areas
in square of sides a+b
Area of a
Sector of a Circle
Box Problem
Combining Rates
Comparing
Segments in two circles
Comparison
of altitude and median in a right triangle
Equiperimetric
Areas
Harmonic Mean
Problems
Maximum area
-- rectangle
Maximum area
-- triangle
Maximum
and Minimum of 
Maximum of
f(x) = (1-x)(1+x)(1+x)
Mean Problem
Minimum of x +
1/x
Minimum
Surface area of a can of fixed volume
Phonograph groove
Trigonometry
Problems
Barn in a
square field
Bridge Expansion Problem
Closed Form for Some Values of Cosine and Sine
Cos 36
degrees
Navigation
Problems
Navigation Problems 2
Ratio of Sines
Sum of
Two Sines or Sum of Two Cosines
Segments in a Trig Drawing
Three Mile Roadway -- Two line segments and an arc
Mixture of all
7-11 Problem
Area of
Texas
A Sequence from Eudoxus
A Will to be
Interpreted
Area of Golfing Greens
Arithmetic
Mean Sequence
Bottles and
Cans
Census
Taker Problem
Change for a
Dollar
Coins
Compare
Radicals
David Rock's House Number
Distance to
Nearest Road
Fractions
Friday 13
Flowing Stream
Four
Number Challenge Problem
Grass
Consumption by Oxen
How Wide is the Alley?
Integer that is a Perfect Square, Cube, and Fifth Power
Ladder
and Box
Magic Square
Maximum
Volume of a Cone
Mirror Image
Oil
Tank Problems
Perfect Shuffle
Rational
or Irrational
Rolling Circle I -- Cycloids and Trochoids
Rolling Circle II -- Number of Revolutions
Rolling Circle III -- Cycloids, epitrochoids, hypocycloids, hypotrochoids
Rolling Circle IV -- When the ratio of circles is 2:1
Rolling Circle V -- When the ratio of circles is 3:2
Square
Root of 2
The
Salesperson's Journey
Triangular
Numbers
Sum of Cubes
Sum of Squares
Sums of Powers of Integers -- Derivations from summations
Finite Differences Instructions (Clay Kitchings)
Finite Differences Comments, Examples, and Problems
Where is
the store?
Final Project
Back
to Jim
Wilson's Home Page
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