Welcome to Sections 1-2 and 1-5!

Hello, Professor Baker's Math Class! This page contains the notes and assignments for Sections 1-2 and 1-5. These sections are designed to help you develop crucial critical thinking skills, understand logical arguments, recognize common fallacies, and become more comfortable working with numbers in everyday life.

Section 1-2: Logic and Fallacies

In this section, we explore the fundamentals of logic and common fallacies that can weaken arguments. Understanding these concepts will make you a more discerning thinker and a better communicator. Here's what we'll cover:

  • Logic: The study of methods and principles used to distinguish correct from incorrect reasoning. A logical argument consists of premises (hypotheses) and a conclusion. A valid argument is one where the premises justify the conclusion.
  • Fallacies: An argument that appears correct on the surface but is, in fact, incorrect.
  • Informal Fallacies: Fallacies that arise from the content of an argument. It's incorrect because of what is said, not how it is said.
  • Formal Fallacies: Fallacies that arise from the form or structure of an argument.

Common Informal Fallacies:

  • Fallacies of Relevance: Premises are logically irrelevant to the conclusion.
    • Appeal to Ignorance: Arguing that a statement is true because it hasn't been proven false (or vice-versa).
    • Dismissal based on Personal Attack: Rejecting an argument based on the person making it, rather than the argument itself.
    • False Authority: Claiming that something is true because an unqualified "expert" said so.
    • Straw Man: Misrepresenting an opponent's argument to make it easier to attack.
    • Appeal to Common Practice: Arguing that something is acceptable because it's commonly done.
  • Fallacies of Presumption: False or misleading assumptions form the basis of the conclusion.
    • False Dilemma: Presenting only two options when more exist.
    • False Cause: Assuming that because two events are related, one causes the other.
    • Circular Reasoning (Begging the Question): Restating the argument as the conclusion.
    • Hasty Generalization: Drawing a conclusion based on insufficient evidence.

Here are the links to the section 1-2 materials:

Section 1-5: Critical Thinking and Number Sense

This section focuses on developing your number sense and applying critical thinking to numerical data. We will learn to cope with the myriad of measurements the average consumer encounters every day.

  • Magnitudes: Understanding the relative sizes of numbers and using powers of 10.
  • Taming large and small numbers: Working with large and small numbers using scientific notation.
  • Estimation: Using estimation to avoid complicated computations.

Powers of 10

  • Positive powers of 10:
    • $10^3 = 1,000$ (thousand)
    • $10^6 = 1,000,000$ (million)
    • $10^9 = 1,000,000,000$ (billion)
    • $10^{12} = 1,000,000,000,000$ (trillion)
  • Negative powers of 10:
    • $10^{-2} = 0.01$ (hundredth)
    • $10^{-3} = 0.001$ (thousandth)
    • $10^{-6} = 0.000001$ (millionth)
    • $10^{-9} = 0.000000001$ (billionth)

Remember these basic properties of exponents:

  • $a^p a^q = a^{p+q}$
  • $\frac{a^p}{a^q} = a^{p-q}$
  • $(a^p)^q = a^{pq}$

And here are the section 1-5 materials:

Unit Conversion

Here's a brief explanation on how to set up conversion problems. The key is to ensure that the units you want to cancel out are in opposite positions (numerator vs. denominator). Remember, the conversion factor must equal one in order to not change the problem.

Example: Converting Inches to Miles:

$$ Inches \times \frac{1 \text{ foot}}{12 \text{ inches}} \times \frac{1 \text{ mile}}{5280 \text{ feet}} = \text{ Miles} $$

Remember to multiply across the top and bottom, then divide for your final answer.

Good luck with the material. Keep practicing, and don't hesitate to ask questions!