The Comparisons. Grade Levels Comparisons. Focal PSSM K-8. Points PSSM CCSS 9-12 PSSM CCSS. Color Coding Legend. Not Identified in the Grade Band

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1 Comparison of NCTM to Dr. Jim Bohan, Ed.D Intelligent Education, LLC The Comparisons Grade Levels Comparisons Focal K-8 Points 9-12 pre-k through 12 Instructional programs from prekindergarten through grade 12 should enable all students to Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Select and use appropriate statistical methods to analyze data Develop and evaluate inferences and predictions that are based on data Understand and apply basic concepts of probability Color Coding Legend Identified in the Grade Band Not Identified in the Grade Band Comparison of to Focal Points pre-k through 2 Comparison of NCTM to FOCAL POINTS Comparison of to Focal Points Comparison of to Focal Points Continued Comparison of to Focal Points Continued 1

2 Comparison of to Focal Points Grades 6 through 8 Comparison of NCTM to pre-k through 12 Instructional programs from prekindergarten through grade 12 should enable all students to Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Select and use appropriate statistical methods to analyze data Develop and evaluate inferences and predictions that are based on data Understand and apply basic concepts of probability Pre-K through Grade 2 pose questions and gather data about K themselves and their surroundings; sort and classify objects according to 1 their attributes and organize data Organize, represent, and interpret about the objects; data with up to three categories represent data using concrete objects, pictures, and graphs. 2 describe parts of the data and the set Generate measurement data by of data as a whole to determine what measuring lengths of several objects the data show. to the nearest whole unit, or by making discuss events related to students' repeated measurements of the same experiences as likely or unlikely. object. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. design investigations to address a use measures of center, question and consider how datacollection methods affect the nature of focusing on the median, and the data set; understand what each does collect data using observations, and does not indicate about surveys, and experiments; represent data using tables and graphs the data set; such as line plots, bar graphs, and line compare different graphs; representations of the same recognize the differences in representing categorical and numerical data and evaluate how well data. each representation shows describe the shape and important important aspects of the features of a set of data and compare related data sets, with an emphasis on data. how the data are distributed; Compare different representations of the Understand that the measure of the same data and evaluate how well each likelihood of an event can be representation shows important aspects represented by a number from 0 to 1. of the data. Propose and justify conclusions and Propose and justify conclusions and predictions that are based on data and predictions that are based on data and design studies to further investigate the design studied to further investigate the conclusions or predictions. conclusions or prediction. Describe events as likely or unlikely and Describe events as likely or unlikely and discuss the degree of likelihood using discuss the degree of likelihood using such words as certain, equally likely, and such words as certain, equally likely, and impossible; impossible Predict the probability of outcomes of Predict the probability of outcomes of simple experiments and test the simple experiments and test the predictions; predictions. Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1. Grade Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Generate measurement data by measuring lengths. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. Make a line plot to display a data set of measurements in 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. 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. 2

3 Formulate questions, design studies, Discuss and understand the and collect data about a correspondence between data sets characteristic shared by two and their graphical representations, populations or different especially histograms, stem-and-leaf characteristics within one plots, box plots, and scatterplots. population; Use observations about differences Select, create, and use appropriate between two or more samples to graphical representations of data, make conjectures about the including histograms, box plots, and populations from which the samples scatterplots. were taken; Find, use, and interpret measures of Make conjectures about possible center and spread, including mean relationships between two and interquartile range; characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit; cont. Use conjectures to formulate new Use proportionality and a basic questions and plan new studies to understanding of probability to answer them. make and test conjectures about Understand and use appropriate the results of experiments and terminology to describe simulations; complementary and mutually Compute probabilities for simple exclusive events; compound events, using such methods as organized lists, tree diagrams, and area models. Grade Develop understanding of statistical variability. Summarize and describe distributions. Use random sampling to draw inferences about a population. Understand that random sampling tends to produce representative samples and support valid inferences. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Investigate patterns of association in bivariate data. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. High School Understand the differences among For univariate measurement data, be various kinds of studies and which types able to display the distribution, describe of inferences can legitimately be drawn its shape, and select and calculate from each; summary statistics; Know the characteristics of well-designed For bivariate measurement data, be able studies, including the role of to display a scatterplot, describe its randomization in surveys and shape, and determine regression experiments; coefficients, regression equations, and Understand the meaning of correlation coefficients using measurement data and categorical data, technological tools; of univariate and bivariate data, and of Display and discuss bivariate data where the term variable; at least one variable is categorical; Understand histograms, parallel box recognize how linear transformations of plots, and scatterplots and use them to univariate data affect shape, center, and display data; spread; Compute basic statistics and understand Identify trends in bivariate data and find the distinction between a statistic and a functions that model the data or parameter. transform the data so that they can be modeled High School cont. Use simulations to explore the variability Understand the concepts of sample of sample statistics from a known space and probability distribution and population and to construct sampling construct sample spaces and distributions; distributions in simple cases; Understand how sample statistics reflect Use simulations to construct empirical the values of population parameters and probability distributions; use sampling distributions as the basis Compute and interpret the expected for informal inference; value of random variables in simple Evaluate published reports that are based cases; on data by examining the design of the Understand the concepts of conditional study, the appropriateness of the data probability and independent events; analysis, and the validity of conclusions; Understand how to compute the Understand how basic statistical probability of a compound event. techniques are used to monitor process characteristics in the workplace. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models Making Inferences and Justifying Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Using Probability to Make Decisions Calculate expected values and use them to solve problems Use probability to evaluate outcomes of decisions So Now What????? 3

4 How About A Blend? Organization of the PA Common Core Development and Progression PA CC pre-k through 5 PA CC Grades 6 through 8 PA CC High School 2.4.PREK Grade PreK 2.4.K Grade K Grade Grade PREKAD K.A A A.4 Classify objects and Classify objects and Represent and Represent and count the number of count the number of interpret data using interpret data using objects in each objects in each tables/charts. line plots, picture category. category. graphs, and bar graphs Grade Grade Grade A A A.4 Represent and Represent and Solve problems interpret data using interpret data involving tally charts, tables, involving fractions computation of pictographs, line using information fractions using plots, and bar graphs. provided in a line plot information provided in a line plot Grade Grade Grade B B B.1 Use a set of numerical data Draw inferences about Analyze and/or interpret to develop an populations based on bivariate data displayed in understanding of and random sampling multiple representations. recognize statistical concepts. variability B B B.2 Use numerical data and Draw informal Understand that patterns of apply statistical properties comparative inferences association can be seen in to summarize and describe about two populations. bivariate data utilizing a distribution. frequencies. Intentionally Blank B.3 Investigate chance Intentionally Blank processes and develop, use, and evaluate probability models. 2.4.HS High School 2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. 2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. 2.4.HS.B.3 Analyze linear models to make interpretations based on the data. 2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. 2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. 2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data. 2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. Standards for Mathematical Practice in a Classroom McDonald s Claim Wikipedia reports that 8% of all Americans eat at McDonalds every day. 310 million Americans and 12,800 McDonalds Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position. 4

5 McDonald s Claim Problem Which mathematical practices are needed to complete the task? What mathematics content is needed to complete the task? Summary NCTM and agree that data analysis, statistics and probability are important NCTM and disagree about timing and ordering to some extent. But should we blend???? Consider The Structure is the Standards Phil Daro, Bill McCallum, Jason Zimba What we tend to do? You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. The Authors point! In the Common Core State Standards, individual statements of what students are expected to understand and be able to do are embedded within domain headings and cluster headings designed to convey the structure of the subject. The Standards refers to all elements of the design the wording of domain headings, cluster headings, and individual statements; the text of the grade level introductions and high school category descriptions; the placement of the standards for mathematical practice at each grade level. Their conclusion. Indeed, it is the nature of mathematics that much new learning is about extending knowledge from prior learning to new situations. For this reason, teachers need to understand the progressions in the standards so they can see where individual students and groups of students are coming from, and where they are heading. But progressions disappear when standards are torn out of context and taught as isolated events. SO WHAT SHOULD WE DO! Attempt to remain true to the vision of the Common Core Standards Use available resources from NCSM ( p.org) and other sources to inform your implementation Questions? Comments? 5

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