Overview of CCSS Statistics and Probability Math Alliance September 2011

CCSS Focus Key ideas, understandings, and skills are identified. Deep learning of concepts is emphasized. –That is, adequate time is devoted to a topic to counter the “mile wide, inch deep” criticism leveled at most current U.S. standards.

CCSS Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

NCTM Process StandardsCCSS Mathematical Practices Problem SolvingMake sense of problems and persevere in solving them. Use appropriate tools strategically Reasoning and ProofReason abstractly and quantitatively. Critique the reasoning of others. Look for and express regularity in repeated reasoning CommunicationConstruct viable arguments ConnectionsAttend to precision. Look for and make use of structure RepresentationsModel with mathematics. NCTM Process Standards and the CCSS Mathematical Practice Standards

Common Core Organization High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (No pre-K Common Core Standards)

Common Core - Domain Overarching “big ideas” that connect topics across the grades Descriptions of the mathematical content to be learned, elaborated through clusters and standards

Common Core - Clusters May appear in multiple grade levels with increasing developmental standards as the grade levels progress Indicate WHAT students should know and be able to do at each grade level Reflect both mathematical understandings and skills, which are equally important

Common Core - Standards Content statements Progressions of increasing complexity from grade to grade

CCSSM Domains CCSSM-Grade 6 CCSSM-Grade 7CCSSM-Grade 8 1. Ratio and proportional Relationships 2. The Number System 3. Expressions & Equations 4. Geometry 5. Statistics and Probability 1. Ratio and proportional Relationships 2. The Number System 3. Expressions & Equations 4. Geometry 5. Statistics and Probability 1. Functions 2. The Number System 3. Expressions & Equations 4. Geometry 5. Statistics and Probability

Grade 5 Measurement & Data Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Grade 6 Statistics & Probability Develop understanding of statistical variability. 1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Grade 6 Statistics & Probability Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 5. Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Grade 7 Statistics & Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.

8 th Grade Statistics Domain Investigate patterns of association in bivariate data. 1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8 th Grade Statistics Domain 2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8 th Grade Statistics Domain 3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8 th Grade Statistics Domain 4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.