Math 114 Module 1: Critical Thinking and Introductory Math Concepts

Name: ___________________________________

1. Critical Thinking and Logical Fallacies

Logic: The study of methods and principles of reasoning. Arguments use facts or assumptions (premises) to support a conclusion.

Argument vs. Fallacy: An argument uses premises to support a conclusion. A fallacy is a deceptive argument where the conclusion is not truly supported by the premises.

Common Fallacies

Appeal to Popularity: Claiming something is true because many believe it.
False Cause: Mistaking a prior event for the cause of a subsequent event.
Appeal to Ignorance: Assuming something is false because it has not been proven true.
Hasty Generalization: Drawing broad conclusions from too few or unrepresentative cases.
Limited Choice (False Dilemma): Presenting a narrow set of options and ignoring other possibilities.
Appeal to Emotion: Persuading by eliciting strong emotional reactions rather than providing evidence.
Personal Attack (Ad Hominem): Attacking the individual instead of examining the argument.
Circular Reasoning: Restating the conclusion as a premise, offering no new support.
Diversion (Red Herring): Introducing a related but irrelevant topic to shift focus.
Straw Man: Misrepresenting an argument to make it easier to refute.

2. Identifying “Fake News”

When evaluating media information, follow these steps:

Check the source for credibility.
Check the date to ensure relevance.
Validate accuracy with multiple sources.
Watch for hidden agendas that might bias the presentation.
Keep the big picture in mind and consider consistency with known facts.

3. Numerical Skills Review

Simplifying Fractions

Reduce numerator and denominator by their greatest common divisor (GCD).
Or use prime factorization to find and cancel shared prime factors.
Example: 36/27 → 4/3.

Rounding Decimals

Identify the digit at the place value to be rounded (e.g., tenths, hundredths).
If the next digit is 5 or greater, round up; otherwise, keep the digit as is and drop the rest.

Evaluating Algebraic Expressions

Substitute given values for the variables.
Simplify step by step.
Example: If a = 4 and b = 35, then b - 5a = 35 - 20 = 15.

Translating Phrases Into Algebraic Expressions

Addition: sum, plus, added to, more than
Subtraction: minus, difference, less than, decreased by
Multiplication: product, times, of, multiplied by
Division: quotient, divided by, shared among

Example: “Three times the difference of a number and ten” → 3(x - 10).

4. Suggested Module 1 Practice Focus

Homework or guided practice on answer entry, logic, fraction simplification, and decimal rounding.
A short quiz or check-in on rounding, fractions, logical statements, and critical thinking.
Any current-term due dates or submission links should be checked in Canvas.

5. Learning Outcomes

Apply logical reasoning to evaluate statements and detect fallacies.
Use critical thinking to solve logical and numerical puzzles.
Master basic fraction simplification and decimal rounding.
Translate verbal descriptions into algebraic expressions accurately.