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MAT-12.DPS.03

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.03 Evaluate reports based on data.
  • Evaluate articles, reports, or websites based on data published in the media by identifying sources of the data, the design of the study, and the way the data are analyzed and displayed.
  • Identify and explain misleading use of data and recognize when claims based on data confuse correlation and causation.
  • Recognize and describe how graphs and data can be distorted to support different points of view.

proficiency scale iconProficiency Scale

Progressions

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.04

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • Fit the function to the data (with or without technology) and interpret the special features (e.g., meaning of a and b in the exponential function y = abx) of the function in context.
  • Use functions fitted to data to solve problems in the context of the data.

proficiency scale iconProficiency Scale

Progressions

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.05

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.

proficiency scale iconProficiency Scale

Progressions

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.06

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.06 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.

proficiency scale iconProficiency Scale

Progressions

Data Collection

  • MAT-00.DPS.D.01 Sort and classify objects (up to 10) based on attributes and explain the reasoning used.
  • MAT-01.DPS.D.01 Collect, organize and represent data with up to three categories using picture and bar graphs.
  • MAT-02.DPS.D.01 Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.
  • MAT-03.DPS.D.01 Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.
  • MAT-04.DPS.D.01 Formulate questions to collect, organize, and represent data to reason with math and across disciplines.
  • MAT-06.DPS.DA.01 Write a statistical question that can be answered using measures of center or variability of a data set.
  • MAT-07.DPS.DA.01 Identify the strengths and weaknesses of a population sample, including possible bias in the process of the data collection.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.09 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.07

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.

proficiency scale iconProficiency Scale

Progressions

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.08

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

proficiency scale iconProficiency Scale

Progressions

Data Analysis

  • MAT-01.DPS.D.02 Analyze data by answering descriptive questions.
  • MAT-02.DPS.D.03 Analyze data and interpret the results to solve one-step comparison problems using information from the graphs.
  • MAT-03.DPS.D.03 Analyze data and make simple statements to solve one- and two-step problems using information from the graphs.
  • MAT-04.DPS.D.02 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
  • MAT-04.DPS.D.03 Utilize graphs and diagrams to represent and solve word problems using the four operations involving whole numbers, benchmark fractions, and decimals.
  • MAT-05.DPS.D.01 Generate data and create line plots to display a data set of fractions of a unit (1/2, 1/4, 1/8). Use grade-level operations for fractions to solve problems involving information presented in line plots.
  • MAT-05.DPS.D.02 Utilize graphs and diagrams to represent, analyze, and solve authentic problems using information presented in one or more tables or line plots, including whole numbers, fractions, and decimals.
  • MAT-06.DPS.DA.02 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  • MAT-06.DPS.DA.03 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
  • MAT-06.DPS.DA.04 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
  • MAT-07.DPS.DA.02 Analyze and draw inferences about a population using single and multiple random samples by using given measures of center and variability for the numerical data set.
  • MAT-08.DPS.DA.01 Interpret scatter plots for bivariate measurement data to investigate patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • MAT-08.DPS.DA.02 Draw a trend line on a given scatter plot with a linear association and justify its fit by describing the closeness of the data points to the line.
  • MAT-08.DPS.DA.03 Solve authentic problems in the context of bivariate measurement data by interpreting the slope and intercept(s) and making predictions using a linear model.
  • MAT-08.DPS.DA.04 Construct and interpret a two-way table summarizing bivariate categorical data collected from the same subjects.
  • MAT-10.DPS.02 Compare the center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets using statistics appropriate to the shape of the data distribution.
  • MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • MAT-10.DPS.04 Distinguish between correlation and causation.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.01 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • MAT-12.DPS.02 Use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.
  • MAT-12.DPS.03 Evaluate reports based on data.
  • MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.
  • MAT-12.DPS.05 Informally assess the fit of a function by plotting and analyzing residuals.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.07 Understand the process of making inferences about population parameters based on a random sample from that population.
  • MAT-12.DPS.08 Decide if a specified model is consistent with results from a given data-generating process (e.g., using simulation).

MAT-12.DPS.09

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.09 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

proficiency scale iconProficiency Scale

Progressions

Data Collection

  • MAT-00.DPS.D.01 Sort and classify objects (up to 10) based on attributes and explain the reasoning used.
  • MAT-01.DPS.D.01 Collect, organize and represent data with up to three categories using picture and bar graphs.
  • MAT-02.DPS.D.01 Formulate questions and collect, organize, and represent data, with up to four categories using single unit scaled pictures and bar graphs.
  • MAT-03.DPS.D.01 Formulate questions to collect, organize, and represent data with more than four categories using scaled pictures and bar graphs.
  • MAT-04.DPS.D.01 Formulate questions to collect, organize, and represent data to reason with math and across disciplines.
  • MAT-06.DPS.DA.01 Write a statistical question that can be answered using measures of center or variability of a data set.
  • MAT-07.DPS.DA.01 Identify the strengths and weaknesses of a population sample, including possible bias in the process of the data collection.
  • MAT-12.DPS.06 Use data from a sample survey to estimate a population means or proportion; develop a margin of error through the use of simulation models for random sampling.
  • MAT-12.DPS.09 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

MAT-12.DPS.10

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, “or” (union), or “and” (intersection), and determine the probability of an event.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.11

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.

proficiency scale iconProficiency Scale

Progressions

Counting Patterns

  • MAT-00.NO.CC.05 Count and tell how many objects up to 20 are in an arranged pattern or up to 10 objects in a scattered configuration. Represent a quantity of up to 20 with a numeral.
  • MAT-01.NO.CC.05 Skip count forward and backward by 5s and 10s from multiples and recognize the patterns of up to 10 skip counts.
  • MAT-02.NO.CC.04 Skip count forward and backward by 2s and 100s and recognize the patterns of skip counts.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.12

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.12 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.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.13

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.14

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.15

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities are calculated; find the expected value.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.16

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.17

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.17 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.DPS.18

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (DPS) Data Probability and Statistics
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, making predictions, and understanding and applying basic concepts of probability
MAT-12.DPS.18 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

proficiency scale iconProficiency Scale

Progressions

Probability

  • MAT-07.DPS.P.01 Develop a probability model to find probabilities of theoretical events and contrast probabilities from an experimental model.
  • MAT-07.DPS.P.02 Develop a probability model to find theoretical probabilities of independent compound events.
  • MAT-10.DPS.05 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").
  • MAT-10.DPS.06 Recognize that event A is independent of event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A)·P(B) given that events A and B are independent.
  • MAT-10.DPS.07 Recognize the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Calculate the conditional probability of A given B and interpret the answer in context.
  • MAT-10.DPS.08 Apply the formula P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in context.
  • MAT-10.DPS.09 Determine the number of outcomes using permutations and combinations in context.
  • MAT-10.DPS.10 Construct and interpret two-way frequency tables of data for two categorical variables. Use the two-way table as a sample space to decide if events are independent and approximate conditional probabilities.
  • MAT-12.DPS.10 Determine when the order in counting matters and use permutations and combinations to compute probabilities of events accordingly. Determine probability situations as conditional, "or" (union), or "and" (intersection), and determine the probability of an event.
  • MAT-12.DPS.11 Use permutations and combinations to compute probabilities of compound events and solve problems.
  • MAT-12.DPS.12 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.
  • MAT-12.DPS.13 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • MAT-12.DPS.14 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
  • MAT-12.DPS.15 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • MAT-12.DPS.16 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • MAT-12.DPS.17 Use probabilities to make fair decisions.
  • MAT-12.DPS.18 Analyze decisions and strategies using probability concepts.

MAT-12.GM

BPSS-MAT-GM logo  MAT-12.GM Domain 
BPSS-MAT-GM logo

(GM) Geometry and Measurement 

Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.


Sub-Categories

  • (G) Geometry 
    Learners will compose and classify figures and shapes based on attributes and properties; represent and solve problems using a coordinate plane.
  • (M) Measurement 
    Learners will represent and calculate measurement data, including time, money, and geometric measurement, and convert like measurement units within a given system.
  • (AV) Area and Volume 
    Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.
  • (GF) Geometric Figures
    Learners will use visualization, spatial reasoning, and geometric modeling to investigate the characteristics of figures, perform transformations, and construct logical arguments.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.


MAT-12.GM.01

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.

proficiency scale iconProficiency Scale

Progressions

Equivalent Expressions
  • MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.
  • MAT-07.AR.EE.01 Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.
  • MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  • MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  • MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
  • MAT-09.AR.02 Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.
  • MAT-09.AR.07 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.NO.02 Perform operations on complex radical expressions to write a simplified equivalent expression.
  • MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.
  • MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
  • MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
  • MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
  • MAT-12.NO.12 Extend polynomial identities to the complex numbers.

Circle Measurements

  • MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply the given formula to calculate the area and circumference of a circle, including in authentic problems.
  • MAT-10.GM.22 Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents, and chords to find unknown lengths or angles.
  • MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
  • MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  • MAT-10.GM.31 Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
  • MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
  • MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
  • MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

MAT-12.GM.02

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.

proficiency scale iconProficiency Scale

Progressions

Equivalent Expressions
  • MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.
  • MAT-07.AR.EE.01 Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.
  • MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  • MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  • MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
  • MAT-09.AR.02 Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.
  • MAT-09.AR.07 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.NO.02 Perform operations on complex radical expressions to write a simplified equivalent expression.
  • MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.
  • MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
  • MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
  • MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
  • MAT-12.NO.12 Extend polynomial identities to the complex numbers.

Circle Measurements

  • MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply the given formula to calculate the area and circumference of a circle, including in authentic problems.
  • MAT-10.GM.22 Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents, and chords to find unknown lengths or angles.
  • MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
  • MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  • MAT-10.GM.31 Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
  • MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
  • MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
  • MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

MAT-12.GM.03

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context.

proficiency scale iconProficiency Scale

Progressions

Ratio and Proportional Relationships
  • MAT-06.AR.RP.01 Describe the concept of a ratio relationship between two quantities using ratio language and visual models.
  • MAT-06.AR.RP.03 Make and use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios, rates, and unit rates.
  • MAT-07.AR.RP.02 Analyze the relationships between the dependent and independent variables of a proportional relationship using graphs and tables. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, k) where k is the unit rate.
  • MAT-07.AR.RP.03 Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by an equation of the form y = kx, where k is the constant of proportionality, and describe the meaning of each variable (y, k, x) in the context of the situation.
  • MAT-07.AR.RP.04 Use proportional relationships to solve multi-step problems involving ratios, percents, and scale drawings of geometric figures, including authentic problems.
  • MAT-08.AR.EE.03 Explain the characteristics of a linear relationship, including identifying the slope and yintercept in tables, graphs, equations, and descriptions.
  • MAT-08.AR.EE.04 Represent linear relationships using tables, graphs, equations, and descriptions when given a relationship in one of these forms.
  • MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.
  • MAT-10.GM.15 Use transformations to decide if two given figures are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • MAT-10.GM.16 Prove similarity theorems about triangles.
  • MAT-10.GM.18 Recognize how the properties of similar right triangles allow the trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
  • MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30°-60°-90° and 45°-45°-90°).
  • MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
  • MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  • MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  • MAT-10.GM.36 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; scaling a model).
  • MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context.

Angles/Triangles

  • MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
  • MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
  • MAT-04.GM.M.07 Recognize angle measures as additive and solve addition and subtraction problems to find unknown angles on a diagram.
  • MAT-07.GM.GF.01 Draw triangles from given conditions using appropriate tools. Defend whether a unique triangle, multiple triangles, or no triangle can be constructed when given three measures of angles or sides.
  • MAT-07.GM.GF.02 Describe the angle-pair relationships: supplementary angles, complementary angles, vertical angles, and adjacent angles. Solve for an unknown angle in a figure by applying facts about these angles.
  • MAT-08.GM.GF.04 Describe the following angle-pair relationships: interior and exterior angles of triangles and angles formed when a transversal cuts parallel lines or intersecting lines. Solve for an unknown angle in a figure by applying facts about these angles.
  • MAT-08.GM.GF.05 Describe the relationship between the leg length and the hypotenuse length of a right triangle. Determine whether a triangle is a right triangle using this relationship.
  • MAT-08.GM.GF.06 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions on and off a coordinate plane, including authentic problems.
  • MAT-10.GM.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, and plane.
  • MAT-10.GM.09 Prove and apply theorems about lines and angles.
  • MAT-10.GM.10 Prove and apply theorems about triangles.
  • MAT-10.GM.18 Recognize how the properties of similar right triangles allow for trigonometric ratios to be defined and determine the sine, cosine, and tangent of an acute angle in a right triangle.
  • MAT-10.GM.19 Explain and use the relationship between the sine and cosine of complementary angles.
  • MAT-10.GM.20 Solve applied problems involving right triangles using trigonometric ratios, the Pythagorean Theorem, and special right triangles (30º, -60º, -90º, and 45º-45º-90º).
  • MAT-10.GM.21 Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
  • MAT-10.GM.23 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
  • MAT-10.GM.24 Construct a tangent line from a point outside a given circle to the circle.
  • MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  • MAT-12.AR.F.16 Extend right triangle trigonometry and apply knowledge of the unit circle to determine values of sine, cosine, and tangent for multiples of π/3, π/4, and π/6.
  • MAT-12.AR.F.17 Use the Pythagorean Identity sin² (θ) + cos² (θ) = 1 to find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant of the angle.
  • MAT-12.GM.03 Determine and apply appropriate formulas to solve right and non-right triangle problems in context

MAT-12.GM.04

BPSS-MAT-GM logo 12th Grade (MAT) Targeted Standard  
  (GM) Geometry and Measurement
Learners will use visualization, spatial reasoning, geometric modeling, and measurement to investigate the characteristics of figures, perform transformations, and construct logical arguments.
MAT-12.GM.04 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

proficiency scale iconProficiency Scale

Progressions

Area/Surface Area

  • MAT-03.GM.M.07 Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • MAT-03.GM.M.08 Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as found by multiplying the side lengths.
  • MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
  • MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
  • MAT-06.GM.AV.01 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals in authentic and mathematical problems by composing and/or decomposing them into rectangles and triangles.
  • MAT-06.GM.GF.03 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets. Apply these techniques in the context of solving authentic and mathematical problems.
  • MAT-07.GM.AV.02 Calculate areas of polygons by composing and/or decomposing them into rectangles and triangles, including in authentic problems. Solve problems involving the surface area of prisms and right pyramids using nets, including authentic problems.
  • MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.
  • MAT-12.GM.04 Derive the formula A=1 ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

MAT-12.NO

BPSS-MAT-GM logo  MAT-12.NO Domain 
BPSS-MAT-NO logo

(NO) Number and Operations 

Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.


Sub-Categories

  • (CC) Counting and Cardinality 
    Learners will understand the relationship between numerical symbols, names, quantities, and counting sequences.
  • (NBT) Number Base Ten 
    Learners will understand the place value structure of the base-ten number system and represent, compare, and perform operations with multi-digit whole numbers and decimals.
  • (NF) Number Fractions 
    Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.
  • (NS) Number System 
    Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.
  • (O) Operations
    Learners will expand their computational fluency to create connections and solve problems within and across concepts.

Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.


MAT-12.NO.01

BPSS-MAT-NO logo 12th Grade (MAT) Targeted Standard  
 (NO) Number and Operations 
Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.
MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.

proficiency scale iconProficiency Scale

Progressions

None listed

  • LIST

MAT-12.NO.02

BPSS-MAT-NO logo 12th Grade (MAT) Targeted Standard  
 (NO) Number and Operations 
Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.
MAT-12.NO.02 Perform operations on complex radical expressions and simplify radicals to write equivalent expressions.

proficiency scale iconProficiency Scale

Progressions

Exponents

  • MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
  • MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.
  • MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  • MAT-09.NO.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
  • MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  • MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.
  • MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.
  • MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-0.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays. 
  • MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.
  • MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.
  • MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
  • MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  • MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
  • MAT-12.AR.F.15 Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.
Equivalent Expressions
  • MAT-06.AR.EE.03 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.
  • MAT-07.AR.EE.01 Apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions involving variables, integers, and/or non-negative fractions and decimals with an emphasis on writing equivalent expressions.
  • MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.
  • MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.
  • MAT-09.AR.01 Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
  • MAT-09.AR.02 Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.
  • MAT-09.AR.07 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.NO.02 Perform operations on complex radical expressions to write a simplified equivalent expression.
  • MAT-12.AR.01 Rearrange multi-variable formulas to highlight a quantity of interest.
  • MAT-12.AR.02 Use the structure of an expression (to extend to polynomial and rational expressions) to identify ways to rewrite it.
  • MAT-12.AR.04 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
  • MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
  • MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
  • MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
  • MAT-12.NO.12 Extend polynomial identities to the complex numbers.


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