Content Standard(s):
Mathematics 18 ) Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7-SP2]
Example: Estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
NAEP Framework
NAEP Statement::
NAEP Statement::
NAEP Statement::
NAEP Statement::
English Language Arts 35 ) Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information. [SL.6.5]
English Language Arts 34 ) Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points. [SL.7.5]
Digital Literacy and Computer Science R5) Locate and curate information from digital sources to answer research questions.
Unpacked Content
Evidence Of Student Attainment:
Students will:
locate and curate information from digital sources to answer given research questions. Teacher Vocabulary:
Knowledge:
Students know:
how to find valid sources to answer a given research topic.
how to cite sources. Skills:
Students are able to:
locate valid digital resources to answer given research questions. Understanding:
Students understand that:
a great deal of information is available, so it is important to validate the information and to cite the source of the information.
Digital Literacy and Computer Science R6) Produce, review, and revise authentic artifacts that include multimedia using appropriate digital tools.
Unpacked Content
Evidence Of Student Attainment:
Students will:
produce a multimedia artifact.
review artifacts created by others.
revise an artifact based on peer or teacher feedback. Knowledge:
Students know:
feedback is important in a design process. Skills:
Students are able to:
create a multimedia artifact.
critique the work of others.
revise their work based on feedback received. Understanding:
Students understand that:
much like the writing process, design of a multimedia artifact nets the best results when creators have the opportunity to be given feedback and revise as needed.
Digital Literacy and Computer Science 23) Discuss how digital devices may be used to collect, analyze, and present information.
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Evidence Of Student Attainment:
Students will:
discuss various methods for using digital devices to collect, analyze, and present information. Knowledge:
Students know:
that information can be presented in many ways. Skills:
Students are able to:
identify ways to collect, analyze, and present information. Understanding:
Students understand that:
devices can be used to collect, analyze, and present information.
Digital Literacy and Computer Science R6) Produce, review, and revise authentic artifacts that include multimedia using appropriate digital tools.
Unpacked Content
Evidence Of Student Attainment:
Students will:
produce a multimedia artifact.
review artifacts created by others.
revise an artifact based on peer or teacher feedback. Knowledge:
Students know:
feedback is important in a design process. Skills:
Students are able to:
create a multimedia artifact.
critique the work of others.
revise their work based on feedback received. Understanding:
Students understand that:
much like the writing process, design of a multimedia artifact nets the best results when creators have the opportunity to be given feedback and revise as needed.
Digital Literacy and Computer Science 16) Construct content designed for specific audiences through an appropriate medium.
Examples: Design a multi-media children's e-book with an appropriate readability level.
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Evidence Of Student Attainment:
Students will:
construct content designed for specific audiences through an appropriate medium. Knowledge:
Students know:
how to select and design an appropriate medium to display designed content. Skills:
Students are able to:
select the best medium for the content design. Understanding:
Students understand that:
while many mediums exist, it is best to select the one most appropriate to your intended audience.
Digital Literacy and Computer Science 23) Demonstrate the use of a variety of digital devices individually and collaboratively to collect, analyze, and present information for content-related problems.
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Evidence Of Student Attainment:
Students will:
use any devices available for data collection and research to present on an assigned or chosen content related issue. Knowledge:
Students know:
that often there exists a devices that will be better for a task than another device. Skills:
Students are able to:
use multiple devices to research and collect data to compile a presentation. Understanding:
Students understand that:
in research, the tool used is less important than the information gathered.
Mathematics 23. Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.
a. Determine which measure of center best represents a real-world data set.
b. Interpret the measures of center and variability in the context of a problem.
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Evidence Of Student Attainment:
Students:
Given a set of numerical data, summarize the data by,
Reporting the number of observations (n).
Describing the nature of the attribute under investigation.
Calculating, interpreting, and comparing the measures of center (median/mean/mode) in a real-world data set,
Calculating, interpreting and comparing the measures of variability (interquartile range and range) in a real-world data set.
Given a set of numerical data interpret the measures of center and variability in the context of a problem.
Justify their choice of measures of center and variability to describe the data based on the data distribution and the context in which the data were gathered. Teacher Vocabulary:
Data distribution
Measures of center
Measures of variability
Mean
Median
Mode
Interquartile range
Range Knowledge:
Students know:
Measures of center and how they are affected by the data distribution and context.
Measures of variability and how they are affected by the data distribution and context.
Methods of determining mean, median, mode, interquartile range, and range. Skills:
Students are able to:
Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
Determine measures of center and variability for a set of numerical data.
Use characteristics of measures of center and variability to justify choices for summarizing and describing data. Understanding:
Students understand that:
Measures of center for a set of data summarize the values in the set in a single number and are affected by the distribution of the data.
Measures of variability for a set of data describe how the values vary in a single number and are affected by the distribution of the data. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.6.23.1: Define numerical data set, measure of variation, and measure of center.
M.6.23.2: Relate the measure of variation, of a data set, with the concept of range.
M.6.23.3: Relate the measure of the center for a numerical data set with the concept of measure of center.
M.6.23.4: Define numerical data set, quantitative, measure of center, median, frequency distribution, and attribute.
M.6.23.5: Compare and contrast the center and variation.
M.6.23.6: Collect the data.
M.6.23.7: Organize the data.
M.6.23.8: Describe how attribute was measured including units of measurement.
M.6.23.9: Identify the attribute used to create the numerical set.
Prior Knowledge Skills:
Identify a numerical data set.
Calculate the range of data.
Organize numbers in a ordered list.
Calculate the mean, median, and mean of a data set.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 24. Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.
a. Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).
b. Use graphical representations of real-world data to describe the context from which they were collected.
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Evidence Of Student Attainment:
Students:
Given a set of numerical data,
Analyze graphical representation of data by describing the center, spread, and shape including approx. symmetric or skewed.
Reporting significant features in the shape of data including striking deviations, (e.g., extreme values, outliers, gaps, and clusters).
Organize and display the data using plots on line plots, dot plots, stem and leaf plots, histograms, and box plots. Teacher Vocabulary:
Dot plots
Histograms
Box plots
Stem and leaf plots
Line plots
Extreme values
Outliers
Gaps
Clusters
Symmetric
Skewed
Center
Spread
peaks
5 number summary
Minimum
Maximum
Median
lower quartile
Upper quartile Knowledge:
Students know:
How to use graphical representations of real-world data to describe context, center, spread and shape from which they were collected.
Techniques for constructing line plots, stem and leaf plots, dot plots, histograms, and box plots. Skills:
Students are able to:
Organize and display data using dot plots, line plots, stem and leaf plots, histograms, and box plots.
Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
Describe the shape of numerical data distribution including patterns and extreme values.
Use graphical representations of real-world data to describe and summarize the context from which they were collected. Understanding:
Students understand that:
Sets of data can be organized and displayed in a variety of ways, each of which provides unique perspectives of the data set.
Data displays help in conceptualizing ideas and in solving problems.
The overall shape and other significant features of a set of data, (e.g., gaps, peaks, clusters and extreme values) are important in summarizing numerical data sets. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.6.24.1: Define dot plots, line plot, stem and leaf plots, upper quartile, lower quartile, median, histograms, and box plots.
M.6.24.2: Recall how to read a graph or table.
M.6.24.3: Calculate upper quartile median, lower quartile median, overall median, greatest value, and lowest value.
M.6.24.4: Create box plot using calculations.
M.6.24.5: Plot data on dot plots and histograms.
M.6.24.6: Construct and label the display.
M.6.24.7: Recognize the different types of displays.
M.6.24.8: Define distribution and skew.
M.6.24.9: Describe the shape of a set of data in a given distribution.
M.6.24.10: Describe the spread of a set of data in a given distribution.
M.6.24.11: Describe the center of a set of data in a given distribution.
Prior Knowledge Skills:
Identify different types of graphs.
Create a bar graph and box plot.
Organize data in an ordered list.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 10. Examine a sample of a population to generalize information about the population.
a. Differentiate between a sample and a population.
b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.
c. Determine whether conclusions and generalizations can be made about a population based on a sample.
d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.
e. Informally explain situations in which statistical bias may exist.
Unpacked Content
Evidence Of Student Attainment:
Students:
distinguish between a population and a sample population, and identify both for statistical questions.
Understand that a population characteristic is determined using data from the entire population, whereas a sample statistic is determined using data from a sample of the population.
Describe different ways that data can be collected to answer a statistical question.
Understand why a sample of a population may be useful or necessary to answer a statistical question. Teacher Vocabulary:
Population Sample biased Unbiased Sampling techniques Random sampling Representative samples Inferences Knowledge:
Students know:
a random sample can be found by various methods, including simulations or a random number generator.
Samples should be the same size in order to compare the variation in estimates or predictions. Skills:
Students are able to:
determine whether a sample is random or not and justify their reasoning.
Use the center and variability of data collected from multiple same-size samples to estimate parameters of a population.
Make inferences about a population from random sampling of that population.
Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets. Understanding:
Students understand that:
statistics can be used to gain information about a population by examining a sample of the populations.
Generalizations about a population from a sample are valid only if the sample is representative of that population.
Random sampling tends to produce representative samples and support valid inferences
The way that data is collected, organized and displayed influences interpretation. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.10.1: Recall how to calculate range, outlier, ratio, and proportion.
M.7.10.2: Define sample, data, variation, prediction, estimation, validity, population, inference, random sampling, statistic, and generalization.
M.7.10.3: Explain the validity of random sampling.
M.7.10.4: Differentiate the appropriate sampling method.
M.7.10.5: Analyze attributes of sample size.
M.7.10.6: Compare and contrast the random sampling data to the population.
M.7.10.7: Compare sample size with population to check for validity.
M.7.10.8: Analyze conclusions of the sample to determine its appropriateness for the population.
M.7.10.9: Predict an outcome of the entire population based on random samplings.
M.7.10.10: Discuss real-world examples of valid sampling and generalizations.
M.7.10.11: Recall the nature of the attribute, how it was measured, and its unit of measure.
M.7.10.12: Collect data from population randomly, choosing same size samples. (Ex. If population is your school, different random samplings should be same number of students).
M.7.10.13: Define and discuss bias.
M.7.10.14: Compare and contrast statistical situations to determine if statistical bias exists.
Prior Knowledge Skills:
Define statistical question.
Calculate the range, mean, median, and mode of a numerical data set.
Recognize the difference between population and sample.
Identify bias from real-world context.
Alabama Alternate Achievement Standards
AAS Standard:
