Arkansas

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Skills available for Arkansas high school math standards

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Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics
Arkansas Curriculum Framework: Algebra I Arkansas Curriculum Framework: Algebra I
Arkansas Curriculum Framework: Algebra I Part A Arkansas Curriculum Framework: Algebra I Part A
Arkansas Curriculum Framework: Algebra I Part B Arkansas Curriculum Framework: Algebra I Part B
Arkansas Curriculum Framework: Algebra II/Advanced Algebra Arkansas Curriculum Framework: Algebra II/Advanced Algebra
Arkansas Curriculum Framework: Algebra III Arkansas Curriculum Framework: Algebra III
Arkansas Curriculum Framework: Bridge to Algebra II Arkansas Curriculum Framework: Bridge to Algebra II
Arkansas Curriculum Framework: Calculus Arkansas Curriculum Framework: Calculus
Arkansas Curriculum Framework: Computer Science and Mathematics Arkansas Curriculum Framework: Computer Science and Mathematics
Arkansas Curriculum Framework: Geometry Arkansas Curriculum Framework: Geometry
Arkansas Curriculum Framework: Geometry A Arkansas Curriculum Framework: Geometry A
Arkansas Curriculum Framework: Geometry B Arkansas Curriculum Framework: Geometry B
Arkansas Curriculum Framework: Mathematical Applications and Algorithms Arkansas Curriculum Framework: Mathematical Applications and Algorithms
Arkansas Curriculum Framework: Precalculus Arkansas Curriculum Framework: Precalculus
Arkansas Curriculum Framework: Statistics Arkansas Curriculum Framework: Statistics

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IC Making Inferences and Justifying Conclusions

IC.1.S Make inferences and justify conclusions from sample surveys, experiments, and observational studies
- IC.1.S.1 Use data from a sample survey to estimate a population mean or proportion. Develop a margin of error through the use of simulation models for random sampling.
  - Find confidence intervals for population means (PC-Z.12)
  - Find confidence intervals for population proportions (PC-Z.13)
- IC.1.S.2 Use data from a randomized experiment to compare two treatments. Use simulations to decide if differences between parameters are significant.
  - Analyze the results of an experiment using simulations (PC-Z.16)

CP Conditional Probability and the Rules of Probability

CP.2.S Understand independence and conditional probability and use them to interpret data
- CP.2.S.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
  - Calculate probabilities of events (PC-X.2)
- CP.2.S.2 Understand that two events A andb are independent if the probability of A andb occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
  - Probability of independent and dependent events (A2-DD.8)
  - Identify independent events (PC-X.6)
- CP.2.S.3 Understand the conditional probability of A givenb as P(A and B)/P(B), and interpret independence of A andb as saying that the conditional probability of A givenb is the same as the probability of A, and the conditional probability ofb given A is the same as the probability of B.
  - Find conditional probabilities (PC-X.7)
  - Independence and conditional probability (PC-X.8)
- CP.2.S.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
  - Find probabilities using two-way frequency tables (PC-X.5)
  - Find conditional probabilities using two-way frequency tables (PC-X.9)
- CP.2.S.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
CP.3.S Use the rules of probability to compute probabilities of compound events
- CP.3.S.1 Find the conditional probability of A given B.
- CP.3.S.2 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
  - Find probabilities using the addition rule (PC-X.10)
- CP.3.S.3 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
  - Find conditional probabilities (PC-X.7)
- CP.3.S.4 Use permutations and combinations to compute probabilities of compound events and solve problems.
  - Combinations and permutations (PC-X.3)
  - Find probabilities using combinations and permutations (PC-X.4)
- CP.3.S.5 Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to: Venn Diagrams, Tree Diagrams.

MD Using Probability to Make Decisions

MD.4.S Calculate expected values and use them to solve problems
- MD.4.S.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
  - Write a discrete probability distribution (PC-Y.2)
  - Graph a discrete probability distribution (PC-Y.3)
- MD.4.S.2 Calculate the expected value of a random variable. Interpret the expected value of a random variable as the mean of the probability distribution.
  - Expected values of random variables (PC-Y.4)
- MD.4.S.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.
  - Write the probability distribution for a game of chance (PC-Y.7)
  - Expected values for a game of chance (PC-Y.8)
- MD.4.S.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.
MD.5.S Use probability to evaluate outcomes of decisions
- MD.5.S.1 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. Evaluate and compare strategies on the basis of expected values.
- MD.5.S.2 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- MD.5.S.3 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
  - Choose the better bet (PC-Y.9)

Arkansas

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IC Making Inferences and Justifying Conclusions

IC.1.S Make inferences and justify conclusions from sample surveys, experiments, and observational studies

IC.1.S.1 Use data from a sample survey to estimate a population mean or proportion. Develop a margin of error through the use of simulation models for random sampling.

IC.1.S.2 Use data from a randomized experiment to compare two treatments. Use simulations to decide if differences between parameters are significant.

CP Conditional Probability and the Rules of Probability

CP.2.S Understand independence and conditional probability and use them to interpret data

CP.2.S.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CP.2.S.2 Understand that two events A andb are independent if the probability of A andb occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

CP.2.S.3 Understand the conditional probability of A givenb as P(A and B)/P(B), and interpret independence of A andb as saying that the conditional probability of A givenb is the same as the probability of A, and the conditional probability ofb given A is the same as the probability of B.

CP.2.S.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

CP.2.S.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

CP.3.S Use the rules of probability to compute probabilities of compound events

CP.3.S.1 Find the conditional probability of A given B.

CP.3.S.2 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

CP.3.S.3 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

CP.3.S.4 Use permutations and combinations to compute probabilities of compound events and solve problems.

CP.3.S.5 Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to: Venn Diagrams, Tree Diagrams.

MD Using Probability to Make Decisions

MD.4.S Calculate expected values and use them to solve problems

MD.4.S.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

MD.4.S.2 Calculate the expected value of a random variable. Interpret the expected value of a random variable as the mean of the probability distribution.

MD.4.S.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.

MD.4.S.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

MD.5.S Use probability to evaluate outcomes of decisions

MD.5.S.1 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. Evaluate and compare strategies on the basis of expected values.

MD.5.S.2 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

MD.5.S.3 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).