Download Algebra 1 Unit 3: Systems of Equations

Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
Enduring understanding (Big Idea): Students will understand that data analysis involves describing data using graphs
and numerical summaries which helps us see and understand the most important features of a set of data.
Essential Questions:
1. What type of graph would be best used with this data?
2. What can be concluded from this graph?
3. What is the five number summary for this data?
BY THE END OF THIS UNIT:
Students will know…
 how to create a variety of graphs to represent data and
how to choose the best one
 how to calculate single variable statistics.
Vocabulary: (in the order they appear) Distribution, Pie
Chart, Bar Graph, Dotplot, Stemplot, Histogram, Overall Pattern,
Deviations, Outliers, Shape, Center, Spread, Symmetric, Skewed,
Five-Number Summary, Mean, Standard Deviation, Median,
Interquartile Range, Boxplot, Line Graph, Trend, Seasonal
Variation, Pictograms
Unit Resources
www.onlinestatbook.com (II. Graphing Distributions, III.
Summarizing Distributions)
http://www.learner.org/resources/series65.html (2.
Picturing Distributions, 3. Describing Distributions)
Decisions Through Data (Unit 2: Stemplots, Unit 3: Histograms
and Distributions, Unit 4: Measures of Center, Unit 5: Box Plots,
Unit 6: The Standard Deviation)
Students will be able to…
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Create a pie chart, bar graph, line graph, dotplot, and stemplot.
Look for the overall pattern of a dotplot and stemplot and for major
deviations from the pattern.
Create a histogram
Look for the overall pattern of a histogram and for major deviations
from the pattern.
Assess from a dotplot, stemplot, or histogram whether the shape of a
distribution is roughly symmetric, distinctly skewed, or neither.
Find the five-number summary and draw a boxplot; use boxplots to
compare distributions.
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated resoning
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable
Standard: S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
Concepts and Skills to Master
 Graph numerical data on a real number line using dot plots, histograms, and box plots
 Describe and give a simple interpretation of a graphical representation of data
 Determine which type of data plot would be most appropriate for a specific situation
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Know how to compute a median
 Find the lower extreme (minimum), upper extreme (maximum), and quartiles
Academic Vocabulary
Dot plot, histogram, box plot, quartiles, lower extreme (minimum), upper extreme (maximum), median, outlier
Suggested Instructional Strategies
Resources
 The case studies at
 Textbook Correlation:
http://www.onlinestatbook.com/2/case_studies/case.html
 Statistics Through Applications
 Gather or provide data and have students plot each
 Chapter 2
type of graph
 MARS Concept Development Lesson: (S.ID.1 through
 Analyze the strengths and weaknesses inherent in
S.ID.4)
each type of plot by comparing different plots of the
Representing Data Using Frequency Graphs
same data
 Have students collect their own data and choose a
 MARS Concept Development Lesson: (S.ID.1 through
graph to represent it.
S.ID.4) Representing Data Using Box Plots
 Data sets: http://www.freestatistics.info
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
Skill-based task
The following data set shows the number of songs
downloaded in one week by each student in Mrs. Jones’
class: 10, 20, 12, 14, 12, 27, 88, 2, 7, 30, 16, 16, 32, 15,
25, 15, 4, 0, 15, 6.
Choose and create a plot to represent the data
Problem Task
On the midterm math exam, students had the following scores: 95,
45, 37, 82, 90, 100, 91, 78, 67, 84, 85, 85, 82, 91, 92, 93, 92, 73,
84, 100, 59, 92, 77, 68, 88.
What are the strengths and weaknesses of presenting this data in a
certain type of plot for:
 Students in a class?
 Parents?
 The school board?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable
Standard: S-ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and
spread (interquartile range, standard deviation) of two or more different data sets.
Concepts and Skills to Master
 Given two sets of data or two graphs, identify similarities and differences in shape, center and spread.
 Compare data sets and be able to summarize the similarities and differences between the shape, and measures of centers
and spreads of the data sets.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Know how to compute the mean, median, interquartile range, and standard deviation by hand in simple cases and using
technology with larger data sets.
 Create a graphical representation of a data set
Academic Vocabulary
Mean, median, interquartiles range, standard deviation, center, spread, shape
Suggested Instructional Strategies
Resources
 The case studies at
 Textbook Correlation:
http://www.onlinestatbook.com/2/case_studies/case.html
 Statistics Through Applications
 Chapter 2
 Use technology to manipulate plots of dats sets to
explore how changing data affects the measures of
 Data sets: http://www.freestatistics.info
center and spread.
 Discuss what it means when related data sets have
differing centers of spreads in relation to the
context.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
Sample Formative Assessment Tasks
Skill-based task
The boxplots show the
distribution of scores on a
district writing test in two fifth
grade classes at a school.
Compare the range and
Medians of the scores from
the two classes.
Problem Task
 Plot data based on populations of European countries. Plot
data based on populations of Asian countries. Compare and
discuss differences in center and spread.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
CORE CONTENT
Cluster Title: Summarize, represent, and interpret data on a single count or measurement variable
Standard:
S-ID.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of
extreme data points (outliers).
Concepts and Skills to Master
 Given two sets of data or two graphs, identify similarities and differences in shape, center and spread.
 Interpret similaritieses and differences between the shape and measure of centers and spread of data sets.
 State the effects of any existing outliers.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Know how to compute the mean, median, interquartiles range, and standard deviation by hand in simple cases and using
technology with larger data sets.
 Create a graphical representation of a data set.
Academic Vocabulary
Extreme data point (outliers), skewed, center, spread
Suggested Instructional Strategies
Resources
 The case studies at
 Textbook Correlation:
http://www.onlinestatbook.com/2/case_studies/case.html
 Statistics Through Applications
 Chapter 2
 Use data from multiple sources to interpret
differences in shape, center and spread
 Data sets: http://www.freestatistics.info
 Use data that includes outliers and explore what
happens when outliers are removed.
 Discuss the effect of outliers on measures of center
and spread and the effect on the shape
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
Regular Statistics Unit 2: Displaying and Interpreting Univariate Data
Sample Formative Assessment Tasks
Skill-based task
The boxplots show the
distribution of scores on a
district writing test in two fifth
grade classes at a school.
Which class performed better
and why?
Problem Task
 Find two similar data sets A and B (use textbook or internet
resources). What changes would need to be made to data set
A to make it look like the graph of set B?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.