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Problem Solving
by Christina Bird
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Problem Solving

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Introduction to Problem Solving

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draw sketches and diagrams.

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trial-and-error procedures.

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list some or all of the possibilities

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use a model to aid in visualizing the problem.

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work backward.

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Patterns and Problem Solving

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Compare and Contrast

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Fibonacci numbers

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Pascal's Triangle-triangular pattern of numbers.

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Arithmetic Sequence

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Geometric Sequence

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Triangular Numbers

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Problem Solving with Algebra

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Properties of Equality

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Properties of Inequality

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Sets, Functions, and Reasoning

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Sets and Venn Diagrams

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Functions, Coordinates, and Graphs

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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.

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.

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

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.

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

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

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

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.