# BPS District Mathematics Standards Book

## Math Domains/Progressions

### Data Probability and Statistics

#### (D) Data K-5

*Learners will represent and interpret data.*

#### (DA) Data Analysis MS

*Learners will ask and answer questions by collecting, organizing, and displaying relevant data, drawing inferences, conclusions, and making predictions.*

** 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.

** 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).

####
(P) Probability MS

*Learners will understand and apply basic concepts of probability.*

** 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.