Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing |

S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots) . | What are the qualities of each of the following types of graphs and when should they be used? (dot plots, histograms, box plots) | -Conduct an informal survey about issues relevant to you and express your results in dot plots, histograms, and box plots. | -Data points -Dot plots -Histograms -Box plots | 3 days |

S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. | Why could the centers be different when considering data? What is the benefit of determining the inter-quartile range? | -Differentiate when to consider the median of a set of data and the mean value of a set of data. -Analyze a given set of data by gathering statistics on measures of central tendency, interquartile range, and standard deviation. | -Data distribution -Measures of central tendency -Mean -Median -Mode -Spread -Interquartile range -Standard deviation | 3 days |

S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). | How could outlier information skew the results of a data set? | -Consider data with outliers and support when to include extreme data points and when not to. | -Center -Outliers -Extreme data points | 3 days |

S.ID.4 Use the mean and standard deviation of a data set to fit in to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | How would the U.S. Census use standard deviation when considering population? | -Choose a population set to research; Go to the U.S. Census information site; compare the data from the 2000 census with the 2010 census; display your results in a method of your choosing | -Mean -Standard deviation -Normal distribution -Population | 3 days |

S.ID.5 Summarize categorical data for two categories in two-way frequency tables, interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | How are joint, marginal, and relative frequencies determined when looking at a two-way frequency table? What methods could be used to summarize large amounts of data? | - Compare the data presented in a two-way frequency table - Evaluate the information in two similar contingency tables using measures of central tendency. | -Categorical data -Two-way frequency table -Contingency table -Relative frequency -Joint frequency -Marginal frequency -Conditional frequency -Trend | 3 days |

S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | How does a line of best fit assist in interpreting the data displayed on a scatter plot? | -Design and conduct a study which includes two variables. -Create a visual representation of your results including a scatter plot, line of best fit, and description of the data. | -Positive correlation -Negative correlation -No correlation | 3 days |

S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. | How are graphing calculators and certain programs available on the internet useful in determining the function which best fits the data? | - Formulate a line of best fit given data presented in a table or in a graph. -Analyze the line of best fit to determine qualities of the data. | -Line of best fit | 3 days |

S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals. | How are residuals useful in determining the accuracy of a line of best fit? | -Analyze a line of best using residuals to determine the accuracy of the function. | -Residuals | 3 days |

S.ID.6c Fit a linear function for a scatter plot that suggest a linear association. | What is true about the scatter plots above and below a fitted linear function? | -Support the visual determination of the correlation of a set of data with its computed correlation coefficient. | -Correlation coefficient | 3 days |

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. | What information can be determined when considering the equation of a function? | -Analyze the equation of a line of best fit to determine the rate of change and intercept. | -Slope -Rate of change -Intercept | 3 days |

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. | How could technology be utilized to provide information pertaining to the qualities of a line of best fit? | -Experiment with different equations to determine the relationship between the correlation coefficient and the graph. | -Correlation coefficient | 3 days |

S.ID.9 Distinguish between correlation and causation. | How does correlation differ from causation? If it is determined that one variable causes another variable, what is also implied? | -Evaluate the usage of the term causation to determine if it is an accurate representation of the data | -Causation -Correlation | 3 days |

Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing |

S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. | Why do most polls include a (+/-) number? | -View the U.S. Census page on Center of Population, (http://2010.census.gov/2010census/data/center-of-population.php) investigate why the center moved over the years | -Statistics -Inference -Random sample | 2 days |

S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls head up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model? | What role does statistics play in market research? | -From Common Core: a model says a spinning coin falls head up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model? -Create your own model. | -Model -Data-generating process | 2 days |

S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | How does the television industry utilize sample surveys in developing programming? | -Create a Venn Diagram to compare and contrast: Sample surveys, experiments, and observational studies | -Sample surveys -Experiments -Observational studies -Randomization | 3 days |

S.IC.4 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. | How does margin of error affect the possible outcome of voting results? | -Using the internet research margin of error and political race; find an example when a poll could not predict an upcoming election; create a PowerPoint slide displaying your results | -Population mean -Population proportion -Margin of error | 3 days |

S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | What is the quality of a randomized study in regard to validity and reliability? | -Conduct a study of a topic of your choosing using 1) randomized approach and 2) targeted approach. How are your results different than if you used a targeted sample of the population? Display your results in a method of your choosing | -Data -Randomized experiment -Parameters -Significance -Validity -Reliability | 3 days |

S.IC.6 Evaluate reports based on data. | How does the medical industry utilize pilot studies in the development of new pharmaceuticals and treatments? | -Choose a product you are interested in purchasing on the internet with no less than 45 comments from other consumers; Conduct an analysis of the comments on the product, write a conclusion, and display your results | -Pilot study | 3 days |

Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing |

S.CP.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”). | Why are subsets relevant to areas beyond mathematics? | -Create and solve a word problem which uses unions and intersections of sets. | -Set -Subset -Union -Intersection -Sample space -Outcomes | 1 day |

S.CP.2 Understand that two events A and B are independent if the probability of A and B -occurring together is the product of the probabilities, and use this characterization to determine if they are independent | How can one check if two events are independent of each other? | -Compare and contrast the probabilities of two events to determine if the events are independent. | -Independent -Probabilities | 1 day |

S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of B given A is the same as the probability of B. | In what areas are conditional probabilities relative to everyday life? | -Create a Venn Diagram and determine the probabilities of each occurrence. | -Conditional probability -Venn diagram | 1 day |

S.CP.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. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. | How are frequency tables used to foresee possible election results? | From Common Core: Collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. | -Frequency Table | 1 day |

S.CP.5 Recognize and explain in the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. | How do meteorologists utilize probability to forecast weather? | From Common Core: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. | -Conditional probability -Independence of events | 1 day |

S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. | How does ratio relate to conditional probability? | Complete the following problem from Dartmouth College and create a similar problem: one finds that in a population of 100,000 females, 89.835% can expect to live to age 60, while 57.062% can expect to live to age 80. Given that a woman is 60, what is the probability that she lives to age 80? | -Conditional probability -Outcomes | 1 day |

S.CP.7 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 | What is the connection between intersection, union, and the Addition Rule? | Using a deck of cards, create a worksheet which requires the use of addition rule. Share your worksheet with your peers. | -Addition rule -Probability -Venn Diagram | 1 day |

S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BǀA) = P(B)P(AǀB), and interpret the answer in terms of the model. | How does the multiplication rule relate to independent and dependent events? | Using a bag of candy, create a worksheet utilizing the Multiplication Rule with seven examples of picking candy in a particular order. | -Multiplication Rule | 1 day |

S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. | What is the difference between a permutation and a combination? | Develop a worksheet in which your peers must determine if the question requires a permutation or a combination. | -Permutations -Combinations | 1 day |

Standard | Essential Question | Bloom’s Taxonomy Activities | Vocabulary | Pacing |

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S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). | When would it be appropriate to use a random number generator? | Explore the random calculators available on random.org and write a one paragraph reflection on any three tools. -Utilize an online Bingo caller to play Bingo as a class (http://www.bingoadvantage.com/online/bingo_caller.cfm) Evaluate how this method is different than if a Bingo tumbler was used or if numbers were chosen from cards off a table | -Random number generator | 1 day |

S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). | How does probability relate to drug-efficacy in patients? | Choose a form of testing which relates to probability. Read two articles related to your form of testing; write a one-page summary of your findings. and choose a sports team to follow for the entire unit. Given the team’s current status, make a hypothesis as to the team’s success over a month. Track the team each week and create a graph of the changes; at the end of the study, review your hypothesis and adjust it for the remainder of the season | -Strategies | 1 day |

### Statistics & Probability

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