Fractions, Ratios, and Probability

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Essential Questions: 
  • How do fractions relate to percents and ratios
  • How do ratios relate to probability?
  • How does probability relate to the "fairness" of a game or situation?
Content: 
  • Compare two fractions with different denominators
  • Define: fraction, lowest terms, improper fraction, numerator, denominator, equivalent fractions
  • Theoretical and experimental probability
  • Relationship between P(A) and the P(not A)
  • Logical operators affect counting
  • Percent
  • Factors that may influence a game or experiment
Skills and Processes: 
  • Perform probability experiments, collect and analyze results to determine experimental probability
  • Calculate theoretical probability for a given situation, including the use of logical (and, or, not) operators
  • Create systematic lists as a method for counting possibilities
  • Perform fraction arithmetic operations on fractions and mixed numbers, also be able to reduce fractions, convert to/from mixed numbers, and compare fractions
  • Convert between fractions, decimals, and percents
  • Determine a definition for fairness
  • Decide whether a game or situation is fair (consider probability, value, influences)
  • Calculate the probability of dartboards using area
Assessment: 

*Test: Fraction arithmetic, reducing, comparing fractions, definitions
*Test: Probability and Percents. Convert between fraction/decimal/percent, calculate probabilities, list factors that may affect the experimental probability of a game
*Create a game in which the theoretical and experimental probabilities are the same (i.e., eliminate the external influences)

Resources: 

Fraction arithmetic worksheets
Probability books: handouts, games, worksheets
What is Fair? activity
Crossing the River with Dogs - Problem Solving