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Topic: Likelihood/chance/certainty 

Mathematics

 Standard 7.  Understands and applies basic and advanced concepts of probability
  Level I (Grade K-2)
   Benchmark 1.Understands that some events are more likely to happen than others
    Knowledge/skill statements
     1.Understands the basic concept of chance
     2.Understands that some events are more likely to happen than others
  Level II (Grade 3-5)
   Benchmark 1.Understands that the word "chance" refers to the likelihood of an event
    Knowledge/skill statements
     1.Understands the concept of "chance"
   Benchmark 2.Recognizes events that are sure to happen, events that are sure not to happen, and events that may or may not happen (e.g., in terms of "certain," "uncertain," "likely," "unlikely")
    Knowledge/skill statements
     1.Identifies events that are sure to happen
     2.Identifies events that may or may not happen
     3.Identifies events that are sure not to happen
     4.Understands the term "certain"
     5.Understands the term "uncertain"
     6. Understands the term "likely"
     7. Understands the term "unlikely"
  Level III (Grade 6-8)
   Benchmark 1.Determines probability using mathematical/theoretical models (e.g., table or tree diagram, area model, list, sample space)
    Knowledge/skill statements
     1. Uses tables to determine probability
     2. Uses tree diagrams to determine probability
     3. Understands the concept of tree diagrams
     4. Uses sample spaces to determine probability
     5.Understands the concept of area models
     7.Understands the concept of modeling probability
     8.Uses area models to determine probability
     9.Uses lists to determine probability
   Benchmark 2.Determines probability using simulations or experiments
    Knowledge/skill statements
     1.Understands the concept of a simulation
     2.Understands the concept of an experiment
     3.Uses simulations to determine probability
     4.Uses experiments to determine probability
   Benchmark 4.Understands that the measure of certainty in a given situation depends on a number of factors (e.g., amount of data collected, what is known about the situation, how current data are)
    Knowledge/skill statements
     1.Understands that the certainty of conclusion(s) depend upon many factors
     2.Understands that the certainty of conclusion(s) depends upon the currency of data
     3.Understands that the certainty of conclusion(s) depend upon what is known about a situation
     4.Understands that the certainty of conclusion(s) depend upon the amount of data
   Benchmark 5.Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers
    Knowledge/skill statements
     1.Understands the concept of percents representing probability
     2.Understands the concept of fractions representing probability
     3.Understands the concept of odds
     4.Understands the relationship between odds and probability
     5.Understands the concept of decimals representing probability
  Level IV (Grade 9-12)
   Benchmark 1.Knows that a random variable can be represented by a discrete or continuous probability distribution
    Knowledge/skill statements
     1.Understands concept of a random variable
     2.Knows that a random variable can be represented by a discrete probability distribution
     3.Knows that a random variable can be represented by a continuous probability distribution
   Benchmark 2.Understands the concepts of independent and dependent events and how they are related to compound events and conditional probability
    Knowledge/skill statements
     1.Understands the relationship between compound events and dependent events
     2.Understands the concept of compound events
     3.Understands the concept of independent events
     4.Understands the concept of dependent events
     5.Understands the concept of conditional probability
     6.Understands the relationship between compound events and independent events
     7.Understands the relationship between dependent events and conditional probability
     8.Understands the relationship between independent events and conditional probability
   Benchmark 3.Uses experimental and simulation methods (e.g., Monte Carlo simulations, statistical experiments, counting techniques) to determine probabilities
    Knowledge/skill statements
     1.Understands concept of Monte Carlo simulations
     2.Uses formulas to determine permutations
     3.Carries out a statistical experiment
     4.Uses Monte Carlo simulation to determine probability
     5.Understands the concept of a statistical experiment
     6.Uses formulas to determine combinations
     7.Uses counting principles to determine probability
     8.Uses permutations to determine probability
     9.Uses combinations to determine probability
  Level V (Grade (College Readiness))
   Benchmark 1.Calculates the probability for dependent, independent, and conditional events
    Knowledge/skill statements
     1.Calculates the probability of dependent events
     2.Calculates the probability of independent events
     3.Calculates the probability of conditional events
   Benchmark 2.Understands the relationship between the probability of an event and the probability of its complement
    Knowledge/skill statements
     1. Understands the concept of a complementary event
     2.Understands the concept of determining the probability of an event
   Benchmark 3.Uses Venn diagrams in probability situations
    Knowledge/skill statements
     1.Understands the concept of a Venn diagram
     2.Knows that Venn diagrams can be used to show relationships in probability situations