MIDTERM L1 Problem Solving and Reasoning

Inductive Reasoning

is the process of reaching a general conclusion by examining specific examples

Example 1: Use Inductive Reasoning to Predict a Number:

3,6,9,12,15, ?

Example 2: Use ____ to Make a Conjecture: Original number: 5, Multiply by 8: 8 × 5 = 40, Add 6: 40 + 6 = 46, Divide by 2: 46 ÷ 2 = 23, Subtract 3: 23 − 3 = 20

Inductive Reasoning

Galileo Galilei

used inductive reasoning to discover that the time required for a pendulum to complete one swing, called the period of the pendulum, depends on the length of the pendulum. Galileo did not have a clock, so he measured the periods of pendulums in "heart-beats."

Date of Birth of Galileo Galilei ?

(1564-1642)

True

Scientists often use inductive reasoning

Deductive Reasoning

is the process of reaching a conclusion by applying general assumptions, procedures, or principles.

Logic Puzzles

can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner.

George Polya (1877-1985).

He developed Polya's Problem Solving Strategy

He was born in Hungary and moved to the United States in 1940. The basic problem-solving strategy that Polya advocated considered of the following four (4) steps.

George Polya

1.Understand the problem.

2.Devise a plan.

3.Carry out the plan.

4.Review the solution.

Polya's Four-Step Problem Solving Strategy

Understand the Problem

This part of Polya's four-step strategy is often overlooked. You must have a clear understanding of the problem.

Devise a Plan.

Successful problem solvers use a variety of techniques when they attempt to solve a problem.

Carry Out the Plan.

Once you have devised a plan, you must carry it out.

Review the Solution

1. Ensure that the solution is consistent with the facts of the problem,

2. Interpret the solution in the context of the problem,

3. Ask yourself if there are generalizations of the solution that could apply to other problems

Term of a Sequence

An ordered list of numbers such as 5,14,27,44,65

True

𝑎𝑛 represents the 𝑛𝑡ℎ term of a sequence.

𝑎1 represents the first term of a sequence.

True

"nth" term is a formula with "n"

in it which enables you to find any term of a sequence without having to go up from one term to the next. "n" stands for the term number, so to find the 50th term, we would just substitute 50 in the formula in place of "n".

Difference Table

1. Sequence

2. First Difference

3. Second Difference

4. Third Difference

shows the differences between successive terms of the sequence.

Difference Table