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Problem Solving by Mind Map: Problem Solving
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Problem Solving

Understanding the Problem-reread the statement of the problem, draw a sketch or diagram, restate the problem in your own words, make a reasonable guess at the solution. Devising a Plan-come up with a plan on how you are going to solve your problem. Carrying Out the Plan-write your thoughts down. Looking back-verify or check your results by referring to the original problem.  

Introduction to Problem Solving

draw sketches and diagrams.

trial-and-error procedures.

list some or all of the possibilities

use a model to aid in visualizing the problem.

work backward.

Patterns and Problem Solving

Compare and Contrast: compare to find features that remain constant and contrast to find those that are changing. Inductive Reasoning: the process of forming conclusions on the basis of patterns, observations, examples, or experiments. Counterexample: an example that shows a statement to be false.  

Compare and Contrast

Number patterns, geometric patterns, word patterns, and letter patterns.  

Fibonacci numbers

  After the first two numbers of this sequence, which are 1 and 1, each successive number can be obtained by adding the two previous numbers.

Pascal's Triangle-triangular pattern of numbers.

Arithmetic Sequence

Each new number is obtained from the previous number in the sequence by adding a selected number throughout.

Geometric Sequence

Each new number is obtained by multiplying the previous number by a selected number.

Triangular Numbers

Called triangular because of the arrangement of dots that is associated with each number.

Problem Solving with Algebra

Introduce variables with geometric shapes. Use a balance scale for introducing equations in the elementary school. Find all the replacements for the variable that make the equation true.    

Properties of Equality

Addition or Subtraction Property of Equality

Multiplication or Division Property of Equality


Properties of Inequality

Addition or Subtraction Property of Inequality

Multiplication or Division Property of Inequality


Sets, Functions, and Reasoning

Sets and Venn Diagrams

Sets And Their Elements

Attribute Pieces

Relationships Between Sets

Intersection of Sets

Union of Sets

Complement of a Set

Functions, Coordinates, and Graphs


Rectangular Coordinates

Linear Functions and Slope

Deductive Reasoning