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Problem Solving
by Christina Bird
# Problem Solving

## 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

### Fibonacci numbers

### Pascal's Triangle-triangular
pattern of numbers.

### Arithmetic Sequence

### Geometric Sequence

### Triangular Numbers

## Problem Solving with Algebra

### Properties of Equality

### Properties of Inequality

## Sets, Functions, and Reasoning

### Sets and Venn Diagrams

### 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.

Addition or Subtraction Property of Equality

Multiplication or Division Property of Equality

Simplification

Addition or Subtraction Property of Inequality

Multiplication or Division Property of Inequality

Simplification

Sets And Their Elements

Attribute Pieces

Relationships Between Sets

Intersection of Sets

Union of Sets

Complement of a Set

Function

Rectangular Coordinates

Linear Functions and Slope

Deductive Reasoning