MMW REVIEWER

Inductive reasoning

The process of reaching a general conclusion by examining specific examples or patterns (moving from specific to general).

Deductive reasoning

The process of reaching a conclusion by applying established general assumptions, procedures, or principles (moving from general to specific).

Conjecture

An educated guess or conclusion formed by observing patterns in specific examples that may or may not be correct.

Logic puzzle

A problem designed to be solved deductively through clues, often with the aid of an elimination chart or grid.

Problem-solving strategy

A systematic method used to solve a problem.

Polya's four steps in problem solving

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Review the solution

Polya's Step 1: Understand the problem

The phase where one identifies the given information, what is being asked, and the overall conditions.

Polya's Step 2: Devise a plan

The phase where a suitable strategy, formula, or procedure is chosen to solve the problem.

Polya's Step 3: Carry out the plan

The phase where the selected strategy is executed and the steps to the solution are systematically completed.

Polya's Step 4: Review the solution

The phase where the result is checked to ensure it makes sense, is accurate, and aligns with the original problem statement.

Organized list

A systematic method of recording and arranging data, outcomes, or combinations in a structured order to ensure all possibilities are accounted for without omissions or duplicates.

Sequence

An ordered list of numbers governed by a specific rule or pattern.

Term

A number that is part of a sequence.

nth term

A formula containing n that allows any term of a sequence to be found.

a₁

Rhe first term of a sequence.

$$a_n$$

The mathematical notation representing the $n^{\text{th}}$ term of a sequence.

First difference

The set of values found by subtracting each term of a sequence from the term that immediately follows it.

Second difference

The set of values found by computing the differences between consecutive first differences.

Third difference

The difference between consecutive second differences.

Difference table

A tabular arrangement used to show successive orders of differences between consecutive terms in a sequence.

Constant first difference

- A sequence whose first differences are all equal. constant second difference

- A sequence whose second differences are all equal.