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MAT-10.DPS

MAT-10.DPS Domain

(DPS) Data Probability and Statistics

Sub-Categories

• (D) Data
Learners will represent and interpret data.
• (DA) Data Analysis
Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, and making predictions.
• (P) Probability
Learners will understand and apply basic concepts of probability.

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-10.DPS.01

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (DA) Data Analysis Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, and making predictions.

Progressions

Displaying Data

• 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-02.DPS.D.02 Generate data and create line plots marked in whole number units.
• MAT-03.DPS.D.02 Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.
• 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-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-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-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-10.DPS.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• 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.NO.04 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

MAT-10.DPS.02

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (DA) Data Analysis Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, and making predictions.

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-10.DPS.03

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (DA) Data Analysis Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, and making predictions.

Progressions

Displaying Data

• 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-02.DPS.D.02 Generate data and create line plots marked in whole number units.
• MAT-03.DPS.D.02 Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.
• 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-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-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-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-10.DPS.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• 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.NO.04 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

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-10.DPS.04

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (DA) Data Analysis Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences and conclusions, and making predictions.

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-10.DPS.05

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (P) Probability Learners will understand and apply basic concepts of probability.

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-10.DPS.06

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (P) Probability Learners will understand and apply basic concepts of probability.

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-10.DPS.07

 10th 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 and making predictions; and understanding and applying basic concepts of probability.

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-10.DPS.08

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (P) Probability Learners will understand and apply basic concepts of probability.

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-10.DPS.09

 10th Grade (MAT) Targeted Standard     (DPS) Data Probability and Statistics (P) Probability Learners will understand and apply basic concepts of probability.

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-10.DPS.10

 10th 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 and making predictions; and understanding and applying basic concepts of probability.

Progressions

Displaying Data

• 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-02.DPS.D.02 Generate data and create line plots marked in whole number units.
• MAT-03.DPS.D.02 Generate data and create line plots marked in whole numbers, halves, and fourths of a unit.
• 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-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-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-09.NO.03 Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.05 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.
• MAT-10.DPS.01 Represent data with plots on the real number line (dot plots, histograms, and box plots).
• MAT-10.DPS.03 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.
• 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.NO.04 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the units in graphs and data displays.
• MAT-12.DPS.04 Represent data on a scatter plot for two quantitative variables and describe how the variables are related.

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).

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-10.GM

MAT-10.GM Domain

(GM) Geometry and Measurement

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-10.GM.00

 10th 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.

Progressions

PASTE

• LIST

MAT-10.GM.01

 10th 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.

Progressions

Two-Dimensional Shapes

• MAT-00.GM.G.01 Name shapes and identify them as two-dimensional (squares, circles, triangles, rectangles)regardless of their orientations or overall size.
• MAT-00.GM.G.03 Compare and classify two-dimensional shapes to describe their similarities, differences, and attributes (squares, circles, triangles, rectangles).
• MAT-01.GM.G.01 Name shapes and identify them as two-dimensional (trapezoids, rhombuses, pentagons, hexagons, octagons).
• MAT-01.GM.G.03 Determine geometric attributes of two-dimensional and three-dimensional shapes.
• MAT-02.GM.G.01 Identify two-dimensional shapes (parallelograms and quadrilaterals).
• MAT-02.GM.G.03 Compose geometric shapes having specified geometric attributes, such as a given number of edges, angles, faces, vertices, and/or sides.
• MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.
• MAT-03.GM.G.02 Sort quadrilaterals into categories based on attributes.
• MAT-04.GM.G.01 Identify, label, and draw points, lines, line segments, rays, and angles (right, acute, obtuse).
• MAT-04.GM.G.02 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size.
• MAT-05.GM.G.01 Classify two-dimensional figures in a hierarchy based on properties.
• 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.11 Prove and apply theorems about parallelograms.
• MAT-10.GM.34 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects.

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-10.GM.02

 10th 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.

Progressions

Functional Relationships
• MAT-08.AR.F.01 Defend whether a relation is a function from various representations using appropriate function language.
• MAT-08.AR.F.02 Compare and contrast properties of two linear functions, each represented in a different way (algebraically, graphically, numerically in tables, and/or by descriptions).
• MAT-08.AR.F.03 Compare and contrast linear and non-linear functions represented in different ways (algebraically, graphically, numerically in tables, and/or by descriptions).
• MAT-08.AR.F.04 Model a linear relationship between two quantities by creating a table, graph, and equation. Interpret the rate of change and initial value of a linear function in terms of the situation it models.
• MAT-08.AR.F.05 Describe qualitatively the functional relationship between two quantities by analyzing a graph, including where the function is constant, increasing, or decreasing; linear or nonlinear; and discrete or continuous. Create a graph that exhibits the qualitative features of a function described.
• MAT-09.AR.F.01 Determine whether a relationship is a function given a table, graph, or words, identifying x as an element of the domain and f(x) as an element in the range. Determine the domain and range of a function in context.
• MAT-09.AR.F.02 Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of context.
• MAT-09.AR.F.03 Sketch key features (to include intercepts, maximums, minimums, and lines of symmetry, where applicable) of linear, exponential, and quadratic functions modeling the relationship between two quantities using tables, graphs, written descriptions, and equations.
• MAT-09.AR.F.04 Relate the domain of a linear, quadratic, or exponential function to its graph and, where applicable, to the quantitative relationship it describes.
• MAT-09.AR.F.05 Calculate and interpret the average rate of change of a linear, quadratic, or exponential function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
• 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-09.AR.F.07 Compare key features of two linear, exponential, or quadratic functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
• MAT-09.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions.
• MAT-09.AR.F.10 Find the inverse of a linear function and describe the relationship between the domain, range, and graph of the function and its inverse. Graph the inverse of a linear function.
• MAT-09.AR.F.11 Interpret the parameters of a linear, quadratic, or exponential function in terms of context.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• 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.01 Write a function that describes a relationship between two quantities.
• MAT-12.AR.F.02 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• 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.04 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.AR.F.05 Find inverse functions.
• MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.
• MAT-12.AR.F.07 Compare key features of two functions, each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
• MAT-12.AR.F.08 Use tables, graphs, verbal discussions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.
• MAT-12.AR.F.09 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
• MAT-12.AR.F.11 Analyze and graph functions expressed symbolically (by hand in simple cases and using technology for more complicated cases), identifying key features of the graph.
• MAT-12.AR.F.12 Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity.
• MAT-12.AR.F.13 Determine whether a linear, quadratic, polynomial, exponential, logarithmic, or trigonometric model fits the situation. Determine an appropriate mathematical model in context (with or without technology).
• MAT-12.AR.F.14 Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.
• 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.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.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.
• MAT-12.AR.F.20 Use the unit circle to explain the symmetry (odd and even) and the periodicity of trigonometric functions.
• MAT-12.AR.F.21 Create a trigonometric function to model periodic phenomena.
• MAT-12.AR.F.22 Restrict the domain of a trigonometric function to construct its inverse.
• MAT-12.AR.F.23 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in context.
• MAT-12.AR.F.24 Know and apply the addition and subtraction formulas for sine, cosine, and tangent to solve problems.

Transformations

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.
• MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),
• reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• 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 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.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.
• MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.NO.18 Multiply a vector by a scalar.

MAT-10.GM.03

 10th 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.

Progressions

Transformations

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.
• MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),
• reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• 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 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.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.
• MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.NO.18 Multiply a vector by a scalar.

MAT-10.GM.04

 10th 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.

Progressions

Transformations

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.
• MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),
• reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• 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 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.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.
• MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.NO.18 Multiply a vector by a scalar.

MAT-10.GM.05

 10th 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.

Progressions

Transformations

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.
• MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),
• reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• 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 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.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.
• MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.NO.18 Multiply a vector by a scalar.

MAT-10.GM.06

 10th 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.

Progressions

Transformations

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.
• MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative). Find the values of a, h, and k given the graph of the function.
• MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).
• MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.
• MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.
• MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),
• reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).
• MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.
• 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 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.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.
• MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and k given the graph of the function. Recognize even and odd functions from their graphs and equations.
• MAT-12.NO.18 Multiply a vector by a scalar.

MAT-10.GM.07

 10th 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.

Progressions

Congruence and Similarity

• MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.
• MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.
• MAT-10.GM.07 Use the definition of congruence, based on rigid motions, to show two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.
• MAT-10.GM.08 Prove two triangles are congruent using the congruence theorems.
• MAT-10.GM.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.

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