# Fractions, Ratios, and Probability

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