Element Cards Data Probability and Statistics
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{{BACK TO|[[Element Cards]]}} | {{BACK TO|[[Element Cards]]}} | ||
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=Teaching Data, Probability, and Statistics= | =Teaching Data, Probability, and Statistics= | ||
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[http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | [http://www.ncpublicschools.org/acre/standards/common-core-tools/ http://www.ncpublicschools.org/acre/standards/common-core-tools/] | ||
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=CCC Mathematics: Data, Probability and Statistics= | =CCC Mathematics: Data, Probability and Statistics= | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 1.MD.C.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: Formulate Questions/Plan research''' | | style="background-color:#C2D69B;" colspan=2|'''Family: Formulate Questions/Plan research''' | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Match an object or representation to the exact replica. | * Match an object or representation to the exact replica. | ||
− | | | + | ||'''Representation:''' |
* Match a question with a set of data (e.g., match the question about counting bears to the set of counting bears). | * Match a question with a set of data (e.g., match the question about counting bears to the set of counting bears). | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model selecting questions and creating categories. | * Model selecting questions and creating categories. | ||
* Task analysis | * Task analysis | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Graphic organizer with steps of task analysis | * Graphic organizer with steps of task analysis | ||
* Photos representing topics that can be the focus of the research questions (e.g., 1. ice cream, 2. animals in a zoo, 3. movies) | * Photos representing topics that can be the focus of the research questions (e.g., 1. ice cream, 2. animals in a zoo, 3. movies) | ||
* Photos representing categories for topics (e.g., 1. chocolate, vanilla, strawberry ice cream; 2. lions, monkeys, elephants; 3. Shrek, Spiderman, Journey to the Center of the Earth) | * Photos representing categories for topics (e.g., 1. chocolate, vanilla, strawberry ice cream; 2. lions, monkeys, elephants; 3. Shrek, Spiderman, Journey to the Center of the Earth) | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 1.MD.C.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: Represent and Interpret Data''' | | style="background-color:#C2D69B;" colspan=2|'''Family: Represent and Interpret Data''' | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:''''' E.DPS.1c Collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Understand how data is organized on a picture graph. | * Understand how data is organized on a picture graph. | ||
* Can match to correct category (match to same) | * Can match to correct category (match to same) | ||
− | | | + | ||'''Representation:''' |
* Understand that each person can only represent one piece of data. | * Understand that each person can only represent one piece of data. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis | * Task analysis | ||
** Use established categories (e.g., flavors of ice cream from CCC 1.DPS.1a2). | ** Use established categories (e.g., flavors of ice cream from CCC 1.DPS.1a2). | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Assistive technology (e.g., voice output) | * Assistive technology (e.g., voice output) | ||
* Interactive whiteboard | * Interactive whiteboard | ||
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* Object representations to use on graph as opposed to picture representations | * Object representations to use on graph as opposed to picture representations | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 1.MD.C.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''' ''' |
| style="background-color:#D6E3BC;" colspan=2|'''Family: Draw Conclusions from Data Collection''' | | style="background-color:#D6E3BC;" colspan=2|'''Family: Draw Conclusions from Data Collection''' | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Can identify groups of objects in terms of more and less | * Can identify groups of objects in terms of more and less | ||
* Can match numbers from a graph to numbers on a number line | * Can match numbers from a graph to numbers on a number line | ||
− | | | + | ||'''Representation:''' |
* Identify and use the symbols for <, >, =. | * Identify and use the symbols for <, >, =. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach the concept of more or less using example, non-example; apply to data on graph. | * Teach the concept of more or less using example, non-example; apply to data on graph. | ||
* Use or create a graph that provides a visual of the values in each category such as a bar graph. | * Use or create a graph that provides a visual of the values in each category such as a bar graph. | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Number line | * Number line | ||
* Snap cubes to create a concrete bar graph | * Snap cubes to create a concrete bar graph | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 2.MD.D.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: Represent and Interpret Data''' | | style="background-color:#C2D69B;" colspan=2|'''Family: Represent and Interpret Data''' | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:''''' E.DPS.1c Collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs)'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Identify a picture or bar graph. | * Identify a picture or bar graph. | ||
* Identify a data set represented with pictorial representations (e.g., pictures of apples, pictures of oranges). | * Identify a data set represented with pictorial representations (e.g., pictures of apples, pictures of oranges). | ||
− | | | + | ||'''Representation:''' |
* Know parts of a picture or bar graph. | * Know parts of a picture or bar graph. | ||
* Identify a data set represented with numbers. | * Identify a data set represented with numbers. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis | * Task analysis | ||
** Use established categories (e.g., flavors of ice cream from CCC 1.DPS.1a2). | ** Use established categories (e.g., flavors of ice cream from CCC 1.DPS.1a2). | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Assistive technology (e.g., voice output) | * Assistive technology (e.g., voice output) | ||
* Interactive whiteboard | * Interactive whiteboard | ||
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* Object representations to use on graph as opposed to picture representations | * Object representations to use on graph as opposed to picture representations | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 2.MD.D.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 |
| style="background-color:#D6E3BC;" colspan=2|'''Family: Draw Conclusions from Data Collection''' | | style="background-color:#D6E3BC;" colspan=2|'''Family: Draw Conclusions from Data Collection''' | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Identify the categories in a graph. | * Identify the categories in a graph. | ||
* Understand the concept of more and less. | * Understand the concept of more and less. | ||
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* Can match to correct category (match to same) | * Can match to correct category (match to same) | ||
− | | | + | ||'''Representation:''' |
* Understand that each person can only represent on piece of data. | * Understand that each person can only represent on piece of data. | ||
* Identify data set with some number (e.g., bar graph representing 5 pencils). | * Identify data set with some number (e.g., bar graph representing 5 pencils). | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Teach the concept of more or less using example, non-example; apply to data on graph. | * Teach the concept of more or less using example, non-example; apply to data on graph. | ||
* Use or create a graph that provides a visual of the values in each category such as a bar graph. | * Use or create a graph that provides a visual of the values in each category such as a bar graph. | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Number line | * Number line | ||
* Concrete objects for graph | * Concrete objects for graph | ||
* Graphic organizer with number line and question to be answered | * Graphic organizer with number line and question to be answered | ||
− | |||
|} | |} | ||
− | [[File:Element Cards Data Probability and Statistics1.jpg]] | + | [[File:Element Cards Data Probability and Statistics1.jpg|An equation prompt. Can be read as blank plus or minus blank equals blank.]] |
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 3.MD.B.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:''''' E.DPS.1g Collecting data and representing data (e.g., bar graphs, frequency tables, line plots) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Identify data set based on a single attribute (e.g., pencils vs. markers). | * Identify data set based on a single attribute (e.g., pencils vs. markers). | ||
* Identify data set with more or less (e.g., this bar represents a set with more). | * Identify data set with more or less (e.g., this bar represents a set with more). | ||
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* Properly label graph (e.g., axes on bar graph). | * Properly label graph (e.g., axes on bar graph). | ||
− | | | + | ||'''Representation:''' |
* Identify data set with some number (e.g., bar graph representing 5 pencils). | * Identify data set with some number (e.g., bar graph representing 5 pencils). | ||
* Identify a picture and bar graph. | * Identify a picture and bar graph. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis (e.g., Decide on your question, create categories, decide on source of data, collect data based on categories, count data sets, organize data, create graph) | * Task analysis (e.g., Decide on your question, create categories, decide on source of data, collect data based on categories, count data sets, organize data, create graph) | ||
* Match to same | * Match to same | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Template (e.g., graphic organizer) or structure for collecting and organizing data | * Template (e.g., graphic organizer) or structure for collecting and organizing data | ||
* Velcro numbers on a graph | * Velcro numbers on a graph | ||
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* Self-monitoring task analysis for student independence | * Self-monitoring task analysis for student independence | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 3.MD.B.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:''''' E.DPS.1g Collecting data and representing data (e.g., bar graphs, frequency tables, line plots) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Identify data set based on a single attribute (e.g., pencils vs. markers). | * Identify data set based on a single attribute (e.g., pencils vs. markers). | ||
* Identify data set with more of less (e.g., this bar represents a set with more). | * Identify data set with more of less (e.g., this bar represents a set with more). | ||
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* Properly label graph (e.g., axes on bar graph). | * Properly label graph (e.g., axes on bar graph). | ||
− | | | + | ||'''Representation:''' |
* Identify components of graphs (picture, line, plot, bar). | * Identify components of graphs (picture, line, plot, bar). | ||
* Identify data set with some number (e.g., bar graph with 5 pencils). | * Identify data set with some number (e.g., bar graph with 5 pencils). | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for categorical data (e.g., Decide on your question, create categories, decide on source of data, collect data based on categories, count data sets, organize data, select best graph for data, create graph) | * Task analysis for categorical data (e.g., Decide on your question, create categories, decide on source of data, collect data based on categories, count data sets, organize data, select best graph for data, create graph) | ||
* Task analysis for continuous data (e.g., Decide you topic for data collection, collect data, identify the least and greatest numbers within the data set, create line graph using the least to greatest range, plot each number on the line graph) | * Task analysis for continuous data (e.g., Decide you topic for data collection, collect data, identify the least and greatest numbers within the data set, create line graph using the least to greatest range, plot each number on the line graph) | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Template (e.g., graphic organizer) or structure for collecting and organizing data | * Template (e.g., graphic organizer) or structure for collecting and organizing data | ||
* Velcro numbers on a graph | * Velcro numbers on a graph | ||
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* Self-monitoring task analysis for student independence | * Self-monitoring task analysis for student independence | ||
− | |||
|} | |} | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 6.SP.B.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. | ||
|- | |- | ||
− | | | + | ||'''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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Identify the lowest to highest value in a data set given a number line and matching symbols. | * Identify the lowest to highest value in a data set given a number line and matching symbols. | ||
* Arrange data from lowest to highest. | * Arrange data from lowest to highest. | ||
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* Use concrete materials to produce the mean (leveled plastic snap cubes). | * Use concrete materials to produce the mean (leveled plastic snap cubes). | ||
− | | | + | ||'''Representation:''' |
* Identify the mode and the spread of the data using a line drawing of the distribution. | * Identify the mode and the spread of the data using a line drawing of the distribution. | ||
* Calculate the mean using pre-slugged template of data points. | * Calculate the mean using pre-slugged template of data points. | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis using template (e.g., steps to find the mean) | * Task analysis using template (e.g., steps to find the mean) | ||
* Task analysis for the spread of the data | * Task analysis for the spread of the data | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Calculator | * Calculator | ||
* Graphic organizer for mode | * Graphic organizer for mode | ||
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* Self-monitoring task analysis for student independence | * Self-monitoring task analysis for student independence | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 7.SP.B.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 |
| style="background-color:#D6E3BC;" colspan=2|'''Family: '''Draw Conclusions from Data Collection | | style="background-color:#D6E3BC;" colspan=2|'''Family: '''Draw Conclusions from Data Collection | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Understand basic information from simple graphs (e.g., interpret a bar graph using the understanding that the taller column on a graph has a higher frequency, the shorter column on a graph has a lower frequency). | * Understand basic information from simple graphs (e.g., interpret a bar graph using the understanding that the taller column on a graph has a higher frequency, the shorter column on a graph has a lower frequency). | ||
* Identify a representation of two bar graphs (one category apiece) as having greater or less frequency of members/events related to a single variable (e.g.,'' Example, compare number of boys in soccer to girls in two graphs).'' | * Identify a representation of two bar graphs (one category apiece) as having greater or less frequency of members/events related to a single variable (e.g.,'' Example, compare number of boys in soccer to girls in two graphs).'' | ||
* Make a comparison between two graphs. | * Make a comparison between two graphs. | ||
− | | | + | ||'''Representation:''' |
* Identify a pictorial representation of two bar graphs (one category apiece) as having greater or less frequency of members/events related to a single variable (e.g.'', compare number of boys in soccer to girls in two graphs).'' | * Identify a pictorial representation of two bar graphs (one category apiece) as having greater or less frequency of members/events related to a single variable (e.g.'', compare number of boys in soccer to girls in two graphs).'' | ||
* Understand the concept, symbols and vocabulary for: more, less, higher, lower. | * Understand the concept, symbols and vocabulary for: more, less, higher, lower. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis to analyze graph (e.g., look at 1<sup>st</sup> graph, identify the column of interest, mark, look at 2<sup>nd</sup> graph | * Task analysis to analyze graph (e.g., look at 1<sup>st</sup> graph, identify the column of interest, mark, look at 2<sup>nd</sup> graph | ||
* Identify the column of interest, mark, determine the facts that the graph shoes) | * Identify the column of interest, mark, determine the facts that the graph shoes) | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Raised line around the distribution of the data (e.g., wiki sticks) | * Raised line around the distribution of the data (e.g., wiki sticks) | ||
* Assistive technology/voice output devices | * Assistive technology/voice output devices | ||
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* Templates with sentence starters | * Templates with sentence starters | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 8.SP.A.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:'' '''M.DPS.1h''' '''Displaying data in scatter plots and investigating the association between the variables '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Locate points on the x-axis and y-axis an adapted grid (not necessarily numeric). | * Locate points on the x-axis and y-axis an adapted grid (not necessarily numeric). | ||
* Identify a similar distribution when given a choice of three (e.g., when shown a normal distribution, can select a second example of a normal distribution from three choices). | * Identify a similar distribution when given a choice of three (e.g., when shown a normal distribution, can select a second example of a normal distribution from three choices). | ||
− | | | + | ||'''Representation:''' |
* Graph a series of data points on a coordinate grid. | * Graph a series of data points on a coordinate grid. | ||
* Identify the associations between the variables using supports. | * Identify the associations between the variables using supports. | ||
Line 596: | Line 593: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for graphing bivariate data | * Task analysis for graphing bivariate data | ||
* Student adds points to data table (number of ice cream cones sold compared to outside temperature). | * Student adds points to data table (number of ice cream cones sold compared to outside temperature). | ||
Line 612: | Line 609: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Color coded grid (e.g., uses colors rather numbers) | * Color coded grid (e.g., uses colors rather numbers) | ||
* Raised grid | * Raised grid | ||
Line 622: | Line 619: | ||
* Assistive technology | * Assistive technology | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' 8.SP.A.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 |
| style="background-color:#D6E3BC;" colspan=2|'''Family: '''Draw Conclusions from Data Collection | | style="background-color:#D6E3BC;" colspan=2|'''Family: '''Draw Conclusions from Data Collection | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Identify a similar distribution when given a choice of three (e.g., when shown a normal distribution, the student can select a second example of a normal distribution from three choices). | * Identify a similar distribution when given a choice of three (e.g., when shown a normal distribution, the student can select a second example of a normal distribution from three choices). | ||
* Identify the appropriate statement when given a relationship between two variables (may use graphic supports such as highlighted transparency of an association). | * Identify the appropriate statement when given a relationship between two variables (may use graphic supports such as highlighted transparency of an association). | ||
− | | | + | ||'''Representation:''' |
* Explain the associations between the variables using supports (e.g., the selection of the highlighted transparency and make a statement). | * Explain the associations between the variables using supports (e.g., the selection of the highlighted transparency and make a statement). | ||
* Understand the following concepts and vocabulary: variable, claim | * Understand the following concepts and vocabulary: variable, claim | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Model-Lead-Test using different associations<nowiki>*</nowiki> | * Model-Lead-Test using different associations<nowiki>*</nowiki> | ||
* Guiding questions (e.g., How close is the fit? How sure can you be?) | * Guiding questions (e.g., How close is the fit? How sure can you be?) | ||
Line 664: | Line 661: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Use manipulatives to show relationships (e.g., transparencies that highlight relationships, straight line object such as spaghetti to find best fit line). | * Use manipulatives to show relationships (e.g., transparencies that highlight relationships, straight line object such as spaghetti to find best fit line). | ||
* Interactive whiteboard | * Interactive whiteboard | ||
Line 671: | Line 668: | ||
* Templates with sentence starters | * Templates with sentence starters | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' HS-ID.A.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 |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:''''' H.DPS.1b Representing data with plots on the real number line (dot plots, histograms, box plots) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Match the source of the values at the bottom of the x-axis with the appropriate category of the related data table. | * Match the source of the values at the bottom of the x-axis with the appropriate category of the related data table. | ||
* Describe the elements within a graph (e.g., in a box plot, the line is the median, the line extending from each box is the lower and upper extreme, and the box shows the lower quartile and the upper quartile). | * Describe the elements within a graph (e.g., in a box plot, the line is the median, the line extending from each box is the lower and upper extreme, and the box shows the lower quartile and the upper quartile). | ||
− | | | + | ||'''Representation:''' |
* Complete the steps of the task analysis to complete a box plot. | * Complete the steps of the task analysis to complete a box plot. | ||
* Understand the following concepts and vocabulary: quartile, median, intervals, upper and lower extremes, box plot, histograms, dot plots. | * Understand the following concepts and vocabulary: quartile, median, intervals, upper and lower extremes, box plot, histograms, dot plots. | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Follow steps of task analysis to complete box plot, dot plots, or histograms (these can be found on internet or many calculators). | * Follow steps of task analysis to complete box plot, dot plots, or histograms (these can be found on internet or many calculators). | ||
* Model-Lead-Test<nowiki>*</nowiki> | * Model-Lead-Test<nowiki>*</nowiki> | ||
|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Technology (e.g., computers) | * Technology (e.g., computers) | ||
* Graphing calculators | * Graphing calculators | ||
* Self-monitoring task analysis for student independence | * Self-monitoring task analysis for student independence | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | ||
+ | |||
{|border=1 | {|border=1 | ||
− | |width = "33% | + | |width = "33%" colspan=3|'''CCSS:''' HS-ID.A.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. | ||
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||H.DPS.1c1 |
− | | | + | ||Use descriptive stats including range, median, mode, mean, outliers/ gaps to describe data set. |
|- | |- | ||
− | | | + | ||'''Strand:''' Data, Probability, and Statistics |
| style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | | style="background-color:#C2D69B;" colspan=2|'''Family: '''Represent and Interpret Data | ||
|- | |- | ||
− | | | + | | colspan=3|'''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:''' |
* Given a scatter plot, identify outliers in the data set. | * Given a scatter plot, identify outliers in the data set. | ||
* Identify the highest and lowest value in a data set given a number line and matching symbols (concept of range). | * Identify the highest and lowest value in a data set given a number line and matching symbols (concept of range). | ||
Line 749: | Line 745: | ||
* Find the mean using concrete materials. | * Find the mean using concrete materials. | ||
− | | | + | ||'''Representation:''' |
* Identify the mode and the spread of the data using a line drawing of the distribution. | * Identify the mode and the spread of the data using a line drawing of the distribution. | ||
* Calculate the mean using pre-slugged template of data points. | * Calculate the mean using pre-slugged template of data points. | ||
Line 756: | Line 752: | ||
|- | |- | ||
− | | | + | | colspan=3|'''Suggested Instructional Strategies:''' |
* Task analysis for finding range, median, mode, mean | * Task analysis for finding range, median, mode, mean | ||
* Explicit vocabulary instruction for outliers | * Explicit vocabulary instruction for outliers | ||
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|- | |- | ||
− | | | + | | colspan=3|'''Supports and Scaffolds:''' |
* Template for finding mean | * Template for finding mean | ||
* Assistive technology/voice output devices | * Assistive technology/voice output devices | ||
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* Manipulatives | * Manipulatives | ||
− | |||
|} | |} | ||
<nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | ||
− | [[Category: | + | |
+ | |||
+ | |||
+ | [[Category: Element Cards]] | ||
+ | [[Category: Math]] |
Latest revision as of 09:57, 16 September 2014
BACK TO Element Cards
Contents |
[edit] 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
[edit] Websites
http://www.teachingideas.co.uk/maths/contents.htm
http://www.mathplayground.com/
[edit] Other Resources
http://www.jstor.org/stable/10.5951/teacchilmath pdf
http://www.ncpublicschools.org/acre/standards/common-core-tools/
[edit] CCC Mathematics: Data, Probability and Statistics
CCSS: 1.MD.C.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.C.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:
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Supports and Scaffolds:
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CCSS: 1.MD.C.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:
|
Representation:
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Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: 2.MD.D.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:
| ||||||||||||||||
Suggested Instructional Strategies:
| ||||||||||||||||||
Supports and Scaffolds:
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CCSS: 2.MD.D.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: 3.MD.B.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:
|
Representation:
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Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: 3.MD.B.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: 6.SP.B.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: 7.SP.B.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.SP.A.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 8.SP.A.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
CCSS: HS-ID.A.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: HS-ID.A.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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.