Course Name: 7th Grade Math
Unit # 8
Unit Title:
Data Distribution
Enduring understanding (Big Idea): Students will determine strategies for collecting, analyzing data and interpreting
statistical data. Students will learn to explain variability in categorical and numerical data as well as the difference
between collecting data by counting and by measuring. Students will develop a variety of representations to display
distributions and make effective use of the data.
Essential Questions: Is there anything surprising about the data and their distribution? Where do the data cluster in the
distribution? How can I use the mean or median and range to help me understand and describe a data distribution? What
strategies can I use to compare two different data sets? What are the sources of variability impacting the data?
BY THE END OF THIS UNIT:
Students will know…
 How to pose a question to explore and determine
what data to collect.
 How to collected necessary data and orchestrate
displays which will allow students to interpret the
collection of data
 How to organize, represent, summarize, and describe
the data and look for patterns.
 How to predict, compare, and identify relationships
and use the results from the analysis to make
decisions about the original question.
Vocabulary
Attribute
Ordered value of bar graph
Counts
Range
Distribution
Value of an attribute graph
Measures
Value of a graph
Measures of Center
Variability of a set of
numerical data
Unit Resources
Learning Task: Additional Practice Investigation 1 – 4,
Mathematical Reflection
Performance Task: Check-Up(s)/Partner Quiz
Project: Unit Project from CMP2 textbook
Students will be able to…
 Recognize that variability occurs whenever data are
collected.
 Describe the variability in the distribution of a data set.
 Identify sources of variability.
 Determine whether to use the mean or median to
describe a distribution.
 Use the shape of a distribution to estimate the location
of the mean and the median.
 Use a variety of representations, including tables, bar
graphs, and line plots, to display distributions.
 Understand and use counts or percents to report
frequencies of occurrence of data.
 Compare the distributions of data sets using their
centers, variability and shape.
 Develop and use strategies to compare data sets to
solve problems.
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 reasoning
Vocabulary:
CCSS-M Included:
7.SP.3, 7.SP.4
Suggested Pacing: 10 days
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: 7th Grade Math
Unit Plans
Standards: 6.SP.1; 6.SP.2; 6.SP.3
These standards are a review from the
previous year.
Investigation 1: Making Sense of
Variability
Standards: 7.SP.3; 7.SP.4
Investigation 2: Making Sense of
Measures of center
Standards: 7.SP.4
Investigation 3: Comparing
Distributions: Equal Numbers of
Data Value
Standards: 7.SP. 4
Investigation 4: Comparing
Distribution: Unequal Numbers of
Data Values
Unit # 8
Unit Title:
Data Distribution
Investigation
1.1 Variability in Categorical Data
1.2 Variability in Numerical Counts
1.3 Variability in Numerical Measurements
1.4 Two Kinds of Variability
Mathematical Reflections: Making Sense of Variability
Suggested ACE Questions
ACE 1, 2, 14, 15
ACE 8 – 11, 16, 17
ACE 3 – 7, 18
ACE 12, 13, 19 - 23
2.1 The Mean as a Equal Share
2.2 The Mean as a Balance Point in a Distribution
2.3 Repeated Values in a Distribution
2.4 Measures of Center and Shapes of Distributions
Mathematical Reflections: Making Sense of Measures of
Center
ACE
ACE
ACE
ACE
3.1 Measuring and Describing Reaction Times
3.2 Comparing Reaction Times
3.3 Comparing More Than a Few Students
3.4 Comparing Fastest and Slowest Trials
Mathematical Reflections: Comparing Distributions
4.1 Representing Survey Data
4.2 Are Steel Coasters Faster Than Wood Coasters?
Mathematical Reflections: Comparing Distributions:
Unequal Numbers of Data Values
ACE 1, 2, 9 – 13
ACE 3, 4, 14 – 17
ACE 5, 6, 18 – 22
ACE 7 – 8, 23 – 29
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
1, 2, 13, 17
3, 14, 15
4 – 6, 16
7 – 12, 18, 19
ACE 1, 8 – 16
ACE 2 – 7, 17
Course Name: 7th Grade Math
Unit # 8
Unit Title:
Data Distribution
CORE CONTENT
Cluster Title:
Standard: 7.SP.3 Use informal methods to evaluate the degree of visual overlap of two numerical data distributions with similar
variability’s, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
Concepts and Skills to Master:


Ability to describe and identify deviation, standard deviation, absolute deviation, measures of central tendency, and
measures of variability.
Ability to build on prior experience with dot plots to compare/contrast data displayed on two dot plots and to make inferences
from the data.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understand and read bar graphs and line plots to display data distributions.
 Understand and use an equal share model to make sense of the mean.
 Understand and use properties of distribution to describe the variability in a given data set.
 Understand and use a balance model to make sense of the mean.
 Understand and decide when to use the mean, median, or mode to describe a distribution.
 Understand when and how changes in data values in a distribution affect the median or the mean.
Procedural
 Recognize that variability occurs whenever data are collected.
 Recognize and decide the difference among data values and/or summary measure matters.
 Develop and use strategies for comparing equal-size and unequal-size data sets to solve problems.
 Relate the shape of the distribution to the location of the mean and the median.
Academic Vocabulary
Distribution, measures of center, variability of a set of numerical data
Suggested Instructional Strategies:
Before beginning review with students their understanding of
graphs, mean, median, and inter quartile range from 6th grade.
To introduce students to variability, review the three measures of
central tendency with them: mean, median, and mode. Remind
students that a measure of central tendency tells about how the
data is centered. Ask students if mean, median, or mode gives
any indication of how a set of data is spread out. Tell students
that the topic of the new lesson will address how a data set is
spread out.
Resources:
 Textbook Correlation: Investigation 2
 MARS Short Task
Statistics and Probability Assessment
Sample Assessment Task
Skill-based task
Problem Task
A student wrote that the data set of 22, 16, 45, 17, 18, 29, 22,
14, 32, 54 has a range of 32. What’s the error?
The time in minutes that it took 5 students to complete a math test
was 35, 27, 30, 25, and 38. What is the absolute deviation of the
times? Does the value of the mean absolute deviation indicate
that the data were spread out or close together? Explain your
answer.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: 7th Grade Math
Unit # 8
Unit Title:
Data Distribution
CORE CONTENT
Cluster Title:
Standard: 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw
informal comparative inferences about two populations.
Concepts and Skills to Master:
 Ability to determine which measure of central tendency is most appropriate for a given situation.
 Ability to use statistical findings to draw inferences about populations.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understand and use properties of distribution to describe the variability in a given data set.
 Understand and read bar graphs and line plots to display data distributions.
 Understand and use properties of distribution to describe the variability in a given data set.
 Understand and decide when to use the mean, median, or mode to describe a distribution.
 Understand and use counts or percents to report frequencies of occurrence of data.
Procedural
 Recognize that variability occurs whenever data are collected.
 Recognize and decide the difference among data values and/or summary measure matters.
 Recognize the importance of having the same scales on graphs that are used to compare data distributions.
 Develop and use strategies for comparing equal-size and unequal-size data sets to solve problems.
Academic Vocabulary
Distribution, measures of center, variability of a set of numerical data
Suggested Instructional Strategies:
Resources:
 Textbook Correlation: Investigations 3 and 4
Introduce students to the concept of sampling by asking them to  MARS Task: A26 Temperatures
think of a question that they would like to ask people at school.
A26 Temperatures
Discuss how long it would take them to pose the question to
 Other Resources:
everyone in the school. Have students hypothesize different
TinkerPlots - http://www.keycurriculum.com/eventways that they could conduct a fair survey that would not include
product/tinkerplots
every student at the school.
Sample Assessment Tasks
Skill-based task
The two data sets below depict random samples of the
management salaries in two companies. Based on the salaries
below which measure of center will provide the most accurate
estimation of the salaries for each company?
265,000, 211,000
Company B: 5 million, 154,000, 250,000, 250,000, 200,000,
160,000, 190,000
Problem Task
Do honors students read more over the summer? Serena’s class
asked 30 parents to estimate how many pages their child read
over the summer. They collected the following data.
Honors students: 10 30 230 130 110 240 150 260 60 230 100 20
50 160 90 pages
Regular students: 210 100 0 40 260 240 200 220 190 150 50 100
12 140 40 pages
a. Make parallel box plots and compare the center, shape,
spread, and outliers.
b. Do honors students read more? How many more (use the box
plots to estimate)?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.