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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.

## 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.

### 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

Simplification

### Properties of Inequality

Addition or Subtraction Property of Inequality

Multiplication or Division Property of Inequality

Simplification

## 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

Function

Rectangular Coordinates

Linear Functions and Slope

Deductive Reasoning