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Lesson Plans for Problem Solving

CONTENT: This file contains a sequence of lesson plans designed to help your students learn to solve problems logically in all subjects that use mathematics for problem solving.

Grade Level: Grades 3-4 and up


Teaching logical problem solving.
The lessons provide the teacher with a systematic approach to introducing logical problem solving. Examples are used to illustrate the concepts involved in logical problem solving. These concepts are introduce in a logical order starting with the most basic ideas and evolving to a complete description of the tools of logical problem solving. They are applicable in all subjects at all grade levels that use mathematics for problem solving.


(1) Regardless of grade level use the lessons in order presented starting with Lesson 1.
The lessons provide students in early grades with problem solving methods which will last a life time.

More advanced students can correct ineffective problem solving habits. This becomes increasingly important at the highschool and college level since inadequate problem solving habits have become firmly embedded.

(2) Provide adequate time and practice with each lesson.
Strive to embed the problem solving idea of each lesson so well that use of the idea is automatic.

Focus on the problem solving concepts involved in each lesson not on the problem used to illustrate the concept involved..

(3) Maintain a global view by reviewing previous lessons before starting a new lesson.
Each of the successive lessons builds on the ideas presented in preceding lessons.

Lesson 1.

This lesson introduces the basic element of problem solving, Request-Response-Result, to solve problems involving a single variable. The concept involved will be expanded in successive lessons.

See the lesson plan .

Lesson 2.

Request-Response-Result is applied to a problems involving sequential variables. The left-right processing of an equation is introduced.

See the lesson plan .

Lesson 3

A response to a request can also make requests. This lesson introduces the nested nature of problem solution steps that arise in this case. Nested requests are very common in problem solving.

See the lesson plan .

Lesson 4

Responding to sequential and nested requests in an orderly manner generates a logically sound problem solution. The solutions so obtained have an hierarchical structure. Hierarchical organization of information is an effective, widely used, means of communication.

See the lesson plan .

Lesson 5

Successfully teaching students to solve problems depends on inducing awareness of the basic ideas involved in problem solving. This lesson provides an overview of the principles involved.

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Lesson 6

An interactive lesson in modelling a problem solution. Learn that problems are self-solving by simply using the everyday method of responding to what is asked for.

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Lesson 7

The lesson discusses some aspects of the substitution process in problem solving

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Lesson 8

An example of problem solving. The lesson also shows the open ended nature of most problems. Multiple solution paths are common.

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Lesson plans are presented in a form that are useful for producing manipulatives for activity centered learning. This provides a hands-on, minds-on approach to learning modern problem solving.

See the lesson plan

Lesson Plans at the Apple Learning Interchange

Addition, Problem Solving, & Algebra, Grades 2 and up
Subtraction, Problem Solving, & Algebra , Grades 2 and up
Equations Talk!
Solving Problems Logically, Grades 4 and up
Problem Solving Techniques
Factorials & Recursion
Fibonacci Series and Recursion
Roots of a Quadratic Equation

To be continued

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Home Page To physics To algebra
Copyright . Howard C. McAllister, 1998.
See permitted use of this material .