CH1 – 3 REVIEWSummary

CHAPTER 1: 1A RECOGNIZING FALLACIESKEY TERMS AND KEY IDEAS AND SKILLS

Key Terms Logic

Argument – premises, conclusions

Fallacy

Key Ideas and Skills Identify an argument’s premises and conclusions.

Recognize fallacious arguments, which contain logical flaws so that their conclusions are not well supported by their premises

1B: PROPOSITIONS AND TRUTH VALUESKEY TERMS

Key Terms Proposition

Truth values, truth tables

Negation: not p

Conjunction: p and q

Disjunction: p or q

Conditional: if p, then q

Logical equivalence

1B: PROPOSITIONS AND TRUTH VALUESKEY IDEAS AND SKILLS

Understand truth tables for negation, conjunction, disjunction, conditional.

Inclusive vs. exclusive: Inclusive (or) means either or both; exclusive or means one or the other, but not both

Variations on the conditional: if p, then q Converse: if q, then p

Inverse: if not p then not q

Contrapositive: if not q, then not p

1C: SETS AND VENN DIAGRAMSKEY TERMS

Key Terms: Set Categorical Propositions Venn diagrams

1C: SETS AND VENN DIAGRAMSKEY IDEAS AND SKILLS

Set Relationships Subsets, disjoint sets, overlapping sets

Four categorical propositions All S are P;

No S are P;

Some S are P;

Some S are not P

Uses of Venn diagrams Illustrating set relationships

Organizing information

ID: ANALYZING ARGUMENTSKEY TERMS

Inductive argument Strength

Deductive argument Validity Soundness

1D: ANALYZING ARGUMENTSKEY IDEAS AND SKILLS

Evaluating arguments Inductive arguments in terms of strength

Deductive arguments in terms of validity and soundness

Venn diagram tests of validity

Chains of conditionals

Induction and deduction in mathematics Propose a theorem inductively

Prove a theorem deductively

1E: CRITICAL THINKING IN EVERYDAY LIFEKEY TERMS AND KEY IDEAS AND SKILLS

Key Terms Critical thinking

Key ideas and skills 1. Read (listen) carefully

2. look for hidden assumptions

3. Identify the real issue

4. Understand the options

5. Watch for fine print and missing information

6. Are other conclusions possible

CHAPTER 2: 2A PROBLEM SOLVING POWER OF UNITSKEY TERMS AND KEY IDEAS AND SKILLS

Key Terms Units

Conversion factor

Currency conversions

Key ideas and skills Identify units with key words per, square, or cube or with hyphens

Write conversion factors in three equivalent forms

Work with units to check answers and help solve problems

2B: MORE PROBLEM SOLVING POWER OF UNITSKEY TERMS

US customary system (USCS)

Metric system (SI)

Celsius, Fahrenheit, Kelvin

Absolute zero

Energy units: Calorie, Joule, Kilowatt-hour

Power units: 1 watt = 1 joule/s

Density

Concentration Blood alcohol

content

2B: MORE PROBLEM SOLVING POWER OF UNITSKEY IDEAS AND SKILLS

Understand and convert basic USCS and metric units

Know metric prefixes

Know temperature units and convert between °F, °C, and Kelvin

Understand energy units and power units Energy is what makes matter move or heat up

Power is the rate at which energy is used

Apply the concept of density to materials, population, and information

Apply the concept of concentration to pollution and blood alcohol content

2C: PROBLEM-SOLVING GUIELINES AND HINTSKEY TERMS AND KEY IDEAS AND SKILLS

Key Terms Four-step problem-solving process

Key ideas and skills Apply eight strategic hints for problem

solving

3A: USES AND ABUSES OF PERCENTAGESKEY TERMS

Key ideas Absolute change Relative Change Absolute difference Relative difference

3A: USES AND ABUSES OF PERCENTAGESKEY IDEAS AND SKILLS

Absolute change=new value-reference value

Relative change (formula)

Absolute difference (formula)

Relative difference (formula)

Understand the of versus more than rule

Understand percentage points versus %

Solve percentage problems

Identify common abuses of percentages

3B: PUTTING NUMBERS IN PERSPECTIVE

Key terms Scientific notation

Order of magnitude

Key ideas and skills Write and interpret numbers in scientific notation

Put numbers in perspective through

Estimation, including order of magnitude estimates Comparisons

Scaling

3C: DEALING WITH UNCERTAINTYKEY TERMS

Significant digits

Random error

Systematic error

Absolute error

Relative error

Accuracy

Precision

3C: DEALING WITH UNCERTAINTYKEY IDEAS AND SKILLS

Distinguish significant digits from non significant zeros

Identify and distinguish between random and systematic errors

Absolute error

Relative error

Distinguish between accuracy and precision

Apply rounding rules for combining approximate numbers Add/subtract – round to the precision of the least precise number

in the problem

Mult./division – round to the same number of significant digits as in the number in the problem with the fewest significant digits

3D: INDEX NUMBERS: THE CPI AND BEYOND

Key terms

Index number

Reference value

Consumer price index (CPI)

Inflation

Key ideas and skills

Understand index numbers and how they are useful for comparisons

Understand how the CPI is used to measure inflation

Adjust prices for inflation with the CPI (formula)

3E: HOW NUMBERS DECEIVE: POLYGRAPHS, MAMMOGRAMS, AND MORE

Key terms Simpson’s paradox

Test results: false +, true +, false -, true –

Key Ideas and skills Understand and give examples of Simpson’s paradox

Understand and give examples of how mammograms and polygraphs can lead to surprising results

Understand and give examples of how Democrats and Republicans can make different claims about the same data even if neither side is lying