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912.G.GMD.4 
12 
Geometry 
Visualize relationships between twodimensional and threedimensional objects. Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. 


912.G.MG.1 
9 
Geometry 
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 


912.G.MG.1 
10 
Geometry 
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 


912.G.MG.1 
11 
Geometry 
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 


912.G.MG.1 
12 
Geometry 
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 


912.G.MG.2 
9 
Geometry 
Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 


912.G.MG.2 
10 
Geometry 
Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 


912.G.MG.2 
11 
Geometry 
Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 


912.G.MG.2 
12 
Geometry 
Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 


912.G.MG.3 
9 
Geometry 
Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 


912.G.MG.3 
10 
Geometry 
Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 


912.G.MG.3 
11 
Geometry 
Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 


912.G.MG.3 
12 
Geometry 
Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 


912.S.ID.1 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots). 


912.S.ID.1 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots). 


912.S.ID.1 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots). 


912.S.ID.1 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots). 


912.S.ID.2 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. 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. 


912.S.ID.2 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. 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. 


912.S.ID.2 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. 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. 


912.S.ID.2 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. 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. 


912.S.ID.3 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 


912.S.ID.3 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 


912.S.ID.3 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 


912.S.ID.3 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 


912.S.ID.4 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it 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. 


912.S.ID.4 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it 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. 


912.S.ID.4 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it 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. 


912.S.ID.4 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it 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. 


912.S.ID.5 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway 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. 


912.S.ID.5 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway 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. 


912.S.ID.5 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway 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. 


912.S.ID.5 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Summarize categorical data for two categories in twoway 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. 


912.S.ID.6 
9 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 


912.S.ID.6 
10 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 


912.S.ID.6 
11 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 


912.S.ID.6 
12 
High School: Statistics and Probability 
Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 


912.S.ID.6a 
9 
High School: Statistics and Probability 
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. 


912.S.ID.6a 
10 
High School: Statistics and Probability 
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. 


912.S.ID.6a 
11 
High School: Statistics and Probability 
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. 


912.S.ID.6a 
12 
High School: Statistics and Probability 
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. 


912.S.ID.6b 
9 
High School: Statistics and Probability 
Informally assess the fit of a function by plotting and analyzing residuals. 


912.S.ID.6b 
10 
High School: Statistics and Probability 
Informally assess the fit of a function by plotting and analyzing residuals. 


912.S.ID.6b 
11 
High School: Statistics and Probability 
Informally assess the fit of a function by plotting and analyzing residuals. 


912.S.ID.6b 
12 
High School: Statistics and Probability 
Informally assess the fit of a function by plotting and analyzing residuals. 


912.S.ID.6c 
9 
High School: Statistics and Probability 
Fit a linear function for a scatter plot that suggests a linear association. 


912.S.ID.6c 
10 
High School: Statistics and Probability 
Fit a linear function for a scatter plot that suggests a linear association. 


912.S.ID.6c 
11 
High School: Statistics and Probability 
Fit a linear function for a scatter plot that suggests a linear association. 


912.S.ID.6c 
12 
High School: Statistics and Probability 
Fit a linear function for a scatter plot that suggests a linear association. 


912.S.ID.7 
9 
High School: Statistics and Probability 
Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 


912.S.ID.7 
10 
High School: Statistics and Probability 
Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 


912.S.ID.7 
11 
High School: Statistics and Probability 
Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 


912.S.ID.7 
12 
High School: Statistics and Probability 
Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 


912.S.ID.8 
9 
High School: Statistics and Probability 
Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit. 


912.S.ID.8 
10 
High School: Statistics and Probability 
Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit. 


912.S.ID.8 
11 
High School: Statistics and Probability 
Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit. 


912.S.ID.8 
12 
High School: Statistics and Probability 
Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit. 


912.S.ID.9 
9 
High School: Statistics and Probability 
Interpret linear models. Distinguish between correlation and causation. 


912.S.ID.9 
10 
High School: Statistics and Probability 
Interpret linear models. Distinguish between correlation and causation. 


912.S.ID.9 
11 
High School: Statistics and Probability 
Interpret linear models. Distinguish between correlation and causation. 


912.S.ID.9 
12 
High School: Statistics and Probability 
Interpret linear models. Distinguish between correlation and causation. 


912.S.IC.1 
9 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 


912.S.IC.1 
10 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 


912.S.IC.1 
11 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 


912.S.IC.1 
12 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 


912.S.IC.2 
9 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*. 


912.S.IC.2 
10 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*. 


912.S.IC.2 
11 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*. 


912.S.IC.2 
12 
High School: Statistics and Probability 
Understand and evaluate random processes underlying statistical experiments. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*. 


912.S.IC.3 
9 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 


912.S.IC.3 
10 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 


912.S.IC.3 
11 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 


912.S.IC.3 
12 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 


912.S.IC.4 
9 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. 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. 


912.S.IC.4 
10 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. 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. 


912.S.IC.4 
11 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. 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. 


912.S.IC.4 
12 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. 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. 


912.S.IC.5 
9 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 


912.S.IC.5 
10 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 


912.S.IC.5 
11 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 


912.S.IC.5 
12 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 


912.S.IC.6 
9 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data. 


912.S.IC.6 
10 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data. 


912.S.IC.6 
11 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data. 


912.S.IC.6 
12 
High School: Statistics and Probability 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data. 


912.S.CP.1 
9 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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). 


912.S.CP.1 
10 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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). 


912.S.CP.1 
11 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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). 


912.S.CP.1 
12 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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). 


912.S.CP.2 
9 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. 


912.S.CP.2 
10 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. 


912.S.CP.2 
11 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. 


912.S.CP.2 
12 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. 


912.S.CP.3 
9 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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 A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. 


912.S.CP.3 
10 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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 A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. 


912.S.CP.3 
11 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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 A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. 


912.S.CP.3 
12 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. 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 A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. 


912.S.CP.4 
9 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway 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. 


912.S.CP.4 
10 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway 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. 


912.S.CP.4 
11 
High School: Statistics and Probability 
Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway 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. 

