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Topic: Reasoning and predicting from data 

Mathematics

 Standard 6.  Understands and applies basic and advanced concepts of statistics and data analysis
  Level III (Grade 6-8)
   Benchmark 4.Reads and interprets data in charts, tables, and plots (e.g., stem-and-leaf, box-and-whiskers, scatter)
    Knowledge/skill statements
     1.Reads scatter plots
     2.Interprets box-and-whisker plots
     3.Reads box-and-whisker plots
     4.Interprets stem-and-leaf plots
     5.Reads stem-and-leaf plots
     6.Interprets data in tables
   Benchmark 5.Uses data and statistical measures for a variety of purposes (e.g., formulating hypotheses, making predictions, testing conjectures)
    Knowledge/skill statements
     1.Test conjectures using data
     2. Makes predictions using data
     3. Formulates hypotheses using data
  Level IV (Grade 9-12)
   Benchmark 3.Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated)
    Knowledge/skill statements
     1.Understands the relationship between causality and correlation
     2.Understands the concept of spurious correlation
     3. Understands the concept of correlation
   Benchmark 6.Understands how the reader’s bias, measurement error, and display distortion can affect the interpretation of data
    Knowledge/skill statements
     1.Understands how reader bias can affect data interpretation
     2.Understands how measurement errors can affect data interpretation
     3.Understands how display errors can affect data interpretation
   Benchmark 9.Understands that making an inference about a population from a sample always involves uncertainty and the role of statistics is to estimate the size of that uncertainty
    Knowledge/skill statements
     1. Understands the concept of statistical inference
  Level V (Grade (College Readiness))
   Benchmark 3.Identifies patterns in graphical displays of data
    Knowledge/skill statements
     1.Understands graphical displays of data
     2.Identifies trends in graphical displays of data
 Standard 7.  Understands and applies basic and advanced concepts of probability
  Level I (Grade K-2)
   Benchmark 2.Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event
    Knowledge/skill statements
     1.Understands that the more that is known about something the better the prediction
     2.Understands that some things can be predicted better than others
  Level II (Grade 3-5)
   Benchmark 3.Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event
    Knowledge/skill statements
     1.Understands that predictions assume that things will stay the same
     2.Understands that predictions apply to the frequency of occurrence better than to specific events
   Benchmark 4.Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents) rather than which individuals within the group will experience something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur
    Knowledge/skill statements
     1.Understands that predictions apply to proportions of groups better than individuals
     2.Understands that predictions apply to how often events will occur better than when events will occur
   Benchmark 5.Uses basic sample spaces (i.e., the set of all possible outcomes) to describe and predict events
    Knowledge/skill statements
     1.Understands the concept of sample space
     2.Uses basic sample spaces (set of all outcomes) to describe events
     3.Uses basic sample spaces (set of all outcomes) to predict events
  Level III (Grade 6-8)
   Benchmark 3.Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability)
    Knowledge/skill statements
     1.Understands predictions based on experimental probability
     2.Understands predictions based on theoretical probability
     3.Contrasts predictions based on theoretical vs experimental 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
  Level IV (Grade 9-12)
   Benchmark 5.Understands the properties of the normal curve (i.e., the graph used to approximate the distribution of data for many real-world phenomena) and how the normal curve can be used to answer questions about sets of data
    Knowledge/skill statements
     1.Understands how the normal curve can be used to answers questions about data
     2.Understands the properties of the normal curve