Element Cards Data Probability and Statistics
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=CCC Mathematics \| Data, Probability and Statistics= | =CCC Mathematics \| Data, Probability and Statistics= | ||
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 2.MD.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.MD.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to four categories. Solve simple put‐together, take apart, and compare problems using information presented in a bar graph. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to four categories. Solve simple put‐together, take apart, and compare problems using information presented in a bar graph. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. ''For example, draw a bar graph in which each square in the bar graph might represent 5 pets.'' | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. ''For example, draw a bar graph in which each square in the bar graph might represent 5 pets.'' |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. ''For example, draw a bar graph in which each square in the bar graph might represent 5 pets.'' | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. ''For example, draw a bar graph in which each square in the bar graph might represent 5 pets.'' |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 6.SP.5 Summarize numerical data sets in relations to their context such as by: | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 6.SP.5 Summarize numerical data sets in relations to their context such as by: |
Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered. | Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered. | ||
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the two populations. ''For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.'' | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the two populations. ''For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.'' |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 8.SP.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 non linear association. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 8.SP.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 non linear association. |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' 8.SP.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 tows or columns to describe possible association between the two variables. ''For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?'' | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 8.SP.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 tows or columns to describe possible association between the two variables. ''For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?'' |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). |
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− | |width = "33%" style="background-color:#FFFFFF;"|'''CCSS:''' S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. | + | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. |
S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. | ||
S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data. | S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data. |
Revision as of 14:53, 13 November 2013
Contents |
Teaching Data, Probability, and Statistics
All of the CCCs in this document relate to teaching Data, Probability, and Statistics. Below are some additional resources that may be helpful: NCSC Curriculum Resource Guide: Data Analysis
Websites
http://www.teachingideas.co.uk/maths/contents.htm http://www.mathsisfun.com/ http://www.mathplayground.com/ https://www.khanacademy.org/ http://www.mathhelp.com/
Other Resources
http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf http://www.ncpublicschools.org/acre/standards/common-core-tools/
CCC Mathematics \| Data, Probability and Statistics
CCSS: 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | ||
CCC: | 1.DPS.1a2 | Select questions that ask about "How many" and represent up to three categories that can be concretely represented. |
Strand: Data, Probability and Statistics | Family: Formulate Questions/Plan research | |
Progress Indicator: E.DPS.1a Posing questions of interest that can be answered by counting or collecting data (e.g., concrete comparisons about students, classroom materials, science topics) with teacher guidance | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | ||
CCC: | 1.DPS.1c1 | Using a picture graph, represent each object/person counted on the graph (1:1 correspondence) for 2 or more categories. |
Strand: Data, Probability and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: E.DPS.1c Collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
What is the favorite flavor of ice cream? Chocolate
What is the favorite flavor of ice cream? Chocolate 5 Vanilla 5 Strawberry 2
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Supports and Scaffolds:
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CCSS: 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | ||
CCC: | 1.DPS.1e1 | Compare the values of the 2 categories of data in terms of more or less. |
Strand: Data, Probability and Statistics | Family: Draw Conclusions from Data Collection | |
Progress Indicator: E.DPS.1e Describing and comparing data and beginning to identify what the data do or do not show (e.g., bar graphs, line plots, picture graphs) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: 2.MD.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. | ||
CCC: | 2.DPS.1c2 | Organize data by representing categorical data on a pictorial graph or bar graph. |
Strand: Data, Probability and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: E.DPS.1c Collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
What is the favorite flavor of ice cream? Chocolate
What is the favorite flavor of ice cream? Chocolate 5 Vanilla 5 Strawberry 2
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Supports and Scaffolds:
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CCSS: 2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to four categories. Solve simple put‐together, take apart, and compare problems using information presented in a bar graph. | ||
CCC: | 2.DPS.1e2 | Compare the information shown in a bar graph or picture graph with up to four categories. Solve simple comparisons of how many more or how many less. |
Strand: Data, Probability and Statistics | Family: Draw Conclusions from Data Collection | |
Progress Indicator: E.DPS.1e Describing and comparing data and beginning to identify what the data do or do not show (e.g., bar graphs, line plots, picture graphs) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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File:Insert Picture here.jpg From "Teaching to standards – math," by K. Trela, B. Jimenez, & D. Browder, 2008, Verona, WI: Attainment Co. Copyright 2009 by Attainment Company. Reprinted with permission.
CCSS: 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. | ||
CCC: | 3.DPS.1g1 | Collect data and organize it into picture or bar graph. |
Strand: Data, Probability and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: E.DPS.1g Collecting data and representing data (e.g., bar graphs, frequency tables, line plots) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. | ||
CCC: | 4.DPS.1g3 | Collect data and organize it into a graph (e.g. picture graph, line plot, bar graph). |
Strand: Data, Probability and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: E.DPS.1g Collecting data and representing data (e.g., bar graphs, frequency tables, line plots) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: 6.SP.5 Summarize numerical data sets in relations to their context such as by:
Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered. | ||
CCC: | 6.DPS.1d3 | Select statement that matches mean, mode, and spread of data for 1 measure of central tendency for given data set. |
Strand: Data, Probability, and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: M.DPS.1d Identifying the range, three common measures of central tendency (mean, median, and mode) and interpreting the mean as a fair share and a center of balance | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. | ||
CCC: | 7.DPS.1k1 | Analyze graphs to determine or select appropriate comparative inferences about two samples or populations. |
Strand: Data, Probability and Statistics | Family: Draw Conclusions from Data Collection | |
Progress Indicator: M.DPS.1k Supporting claims about the results of investigations (e.g., coordinating among the measures of central tendency and variability) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.SP.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 non linear association. | ||
CCC: | 8.DPS.1h1 | Graph bivariate data using scatter plots and identify possible associations between the variables. |
Strand: Data, Probability and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: M.DPS.1h Displaying data in scatter plots and investigating the association between the variables | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.SP.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 tows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? | ||
CCC: | 8.DPS.1k2 | Analyze displays of bivariate data to develop or select appropriate claims about those data |
Strand: Data, Probability and Statistics | Family: Draw Conclusions from Data Collection | |
Progress Indicator: M.DPS.1k Supporting claims about the results of investigations (e.g., coordinating among the measures of central tendency and variability) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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CCSS: S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). | ||
CCC: | H.DPS.1b1 | Complete a graph given the data, using dot plots, histograms, or box plots |
Strand: Data, Probability, and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: H.DPS.1b Representing data with plots on the real number line (dot plots, histograms, box plots) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
S.ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data. | ||
CCC: | H.DPS.1c1 | Use descriptive stats including range, median, mode, mean, outliers/ gaps to describe data set. |
Strand: Data, Probability, and Statistics | Family: Represent and Interpret Data | |
Progress Indicator: H.DPS.1c Analyzing and summarizing the data resulting from studies using statistical measures appropriate to shape of the data (median, mean) and spread (interquartile range, standard deviation), and using data to support inferences (population parameters, sample size) or explain possible outliers | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.