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The journal provides a source of modern problem solving for students and teachers from grade school through grad school and beyond in all subjects that use mathematics for problem solving.

Last update: July 19, 2003.
Copyright 1994-2003, Howard C. McAllister.
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Frequently asked questions.
About these problems
Craven Community College, Dan Bellittiere
Fermi problems 2/5/96
GOAL-Oriented Problem Solving
Interactive problem solution 4/5/96
Pathway problem solving 9/14/96
Problems from The Mathematics Teacher . 1/29/97
Problems from Quest 2000, Addison-Wesley, 1995
Unit Conversions

Algebra (Return to Contents)

The problems are partially organized into problem types. This is for convenience only. The problem solving process is independent of the type of problem.

Introductory problems and ideas.
Mary's Apples. The solution to all problems . 1/9/96
Use Mary's Apples to find out about Harold's money .1/27/96
Use Mary's Apples to find Ronald's and Dolores's ages . 1/28/96
Use Mary's Apples to go on a picnic with the Andersons . 1/28/96
The photographer and the council . Contributed by Rana Taji 9/15/96
Bill, Will and Jill weigh in . 6/24/96
The fireman works the ladder . 6/24/96
The great gold robbery . 6/24/96
The great train robbery . 6/24/96

If you are here to learn/teach problem
solving see the following 5 problems
Mary's Apples from grade school through grad school.
A must for 5th grade (and earlier) through grad school .
Mary's Apples 1 . 1/30/96
Mary's Apples 2 . 1/31/96
Mary's Apples 3 . 1/30/96
Mary's Apples 4 . 1/30/96
Mary's Apples 5 . 1/30/96

Algebra exercises. Learn/teach reliable problem solving early
Introduce reliable story problem skills at an early age . 1/24/96
Learning about substitution. A basic problem solving skill . 1/24/96
Where story problems start. Learn problem solving from scratch . 1/24/96
What is the value of (a + b) 2 if ab = 10 and a 2 + b 2 = 30. 1/24/96

Age Problems
John's Age. Illustrates some fundamental problem solving principles . 1/21/96
The age of Jim, David and Tom . 1/7/96
The age of A, B and C if ... . 1/8/96
Once in a lifetime . 5/5/96
The age of Paul's Sons . 3/17/97
The age of Paul's daughters . 7/5/99

Cubic (Return to Contents)
Evaluate a3- 1/a 3 if (a + 1/a) 2 = 1. - - 6/21/97
The solution of the cubic equation . 10/9/97
Determine the roots of z3 + 6z2 - 4z - 24 = 0 . 2/2/99
Geometric shapes. Triangles, rectangles, areas, angles, etc.
Distance between two points using the Pythagorean theorem . 3/21/97
Translating coordinates. Shifted triangle example. . 3/21/97
Sides of a right triangle of given perimeter if ... 1/2/96
Sides of two squares of different areas . 1/4/96
The perimeter and area of a rectangle . 5/31/97
What is the area of the red square ? 1/8/97
What is the size of a square inscribed in a triangle ? 5/28/97

Once you have learned to solve simple problems you can solve all problems . 1/24/96

Mixture Problems (Return to Contents)
Ok! So it's partly chlorine. How much of the stuff is there ? 1/9/96
Mr. Biggs and his pencils and pens . Contributed by Greg Hall 9/12/96
Solving the problem is a cinch. But what in the world is assonance ? 1/10/96
The solution of three simultaneous equations . 1/11/96
Preparing a diluted mixture of disinfectant . 1/17/96
Hiding places for xenophobes . 1/17/96
Mixing two concentrations of acid to get a desired concentration . 1/18/96
A problem from a June 1996 SAT . . 6/13/97
A SAT mixture problem . . 6/20/97
Let's see how many stamps she bought . 1/21/96
How many nickels, dimes and quarters are there in the piggy bank ? 1/18/96
Brushes and rollers in painting a room . 1/21/96
Tom, Harry and Dick mowing lawns . 3/20/97
Mixtures by the barrelfull. . 9/15/97

Area Problems
Fitting a receiver on a ship . Submitted by Daniel Baldwin. 3/4/96
The overlapping area of two congruent squares . Contributed by Anonymous. 4/20/96

Money problems
Total cost of two articles if ... . 1/2/96
A shares his money with B so... 1/2/96
Mr. Brown's conservative investments . 1/4/96
The number of dollars, quarters and dimes . 1/4/96
The pay rate of a plumber and his helper (years ago) . 1/5/96
The nonprofit tennis racket caper . 1/21/96
The overlapping area of two congruent squares . Contributed by Anonymous. 4/20/96

Motion problems in introductory algebra
Distance between two cars traveling at different speeds . 1/3/96
The round trip of the intrepid truck driver . 3/5/97
The speeds of Sarah and Rick 3/6/97 .
Jean couldn't have driven that fast. Must have used a small plane . 1/9/96
A day's work for Tuna fishers . 1/19/96
How long would it take for an express train to catch up with a milk train ? 1/24/96

Number Problems
Find the larger and smaller of two numbers if... 1/4/96
Find two numbers from their ratio if... 1/5/96
Find a two digit number. 11/11/96
Find two numbers if ... 1/5/96
Find three consecutive odd numbers such that ... 1/7/96
Find three consecutive numbers if ... 1/7/96
A simple numerical exercise and the reason why . 1/2/96
An exercise in reading and numerical operations . 1/8/96
Find a sequence of even integers if ... 1/5/96
Position of four holes in a steel plate . 1/5/97
A number problem involving use of the quadratic formula . 1/20/96

Quadratic equations (Return to Contents)
Solving a quadratic using the quadratic formulae . 9/29/96
Use of the quadratic formulae . 4/14/97
Solving a quadratic by completing the square . 9/14/96
A number problem involving use of the quadratic formula . 1/20/96
Algebra problems using quadratic equations . Contributed by Kelly D. Buttler. 3/1/96
Exploring a quadratic equation to find it's roots . Contributed by Angelo Ricotta 10/20/96
More about quadratic equations. . A different approach to the preceding problem. Contributed by Angelo Ricotta 1/3/97
Formal development of completing the square . Contributed by Angelo Ricotta 11/20/96

Systems of Equations
Two Examples of the solution of systems of two equations . 1/23/96

More Algebra



Business (Return to Contents)

Chemistry (Return to Contents)

Find the mole fraction of water mixed with some other things. if... 1/25/96
Determine the number of carbon dioxide molecules if ... 1/25/96
A problem involving Dalton's law. Three solution paths are shown . 1/25/96
Earth sciences

Fermi Problems (Return to Contents)

Grains of sand on beaches of the earth .
Physics (Return to Contents)

The number of electrons in a given amount of charge . 1/21/96
The amount of positive charge in a glass of water . 1/21/96
Three connected charges. Find the tension in the strings . 1/21/96
Force on a charge due to two other charges . 11/25/96
Let's remove some electrons from one penny and put them on another. What happens? 1/22/96
Electric flux through a butterfly net . 1/22/96

Faraday's Law
Problems using Faraday's Law . 7/20/96
The acceleration of a fast car compared with the acceleration due to gravity . 1/22/96
Acceleration of an elevator with given cable tension and.... 1/3/96
Eddy and his motor scooter . 1/21/96
How long would it take for an express train to catch up with a milk train ? 1/24/96
To catch a baseball you need to be at the same place as the ball . 1/22/96
About lifting a box if... 1/24/96
Pulling a sled. . 1/23/96
How fast can you go around the curve ? 6/6/96
A variation of the incline plane problem . 6/25/97
A variation of the incline plane problem. Energy method. . 7/8/97

Magnetic field
Friction to maintain constant angular velocity of a rotating disk in a uniform magnetic field .

Quantum mechanics

Young's experiment in water . 5/18/96
Interference of television waves by reflection from an airplane . 5/18/96
A modification of Young's experiment . 5/18/96
Special Relativity. Lorentz transformations . 8/28/96
Tension in the wires supporting a picture . 1/22/96
When will a stack of bricks topple ? 4/27/96

Statistical mechanics

More Physics

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