7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Math Florida Standards
Unit C: Overview
Content Standards
Students build on their previous work with single data distributions to compare two data distributions and address
questions about difference between populations. They begin informal work with random sampling to generate data
sets and learn about the importance of representative samples for drawing inferences.
MAFS.7.SP.1.1
(Assessed by SP.1.2)
MAFS.7.SP.1.2
In 6th grade students learned to:
 Recognize a statistical question as one that anticipates variability in the data related to the question and
accounts for it in the answers.
 Understand that a set of data collected to answer a statistical question has a distribution, which can be
described by its center, spread, and overall shape.
 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number,
while a measure of variation describes how its values vary with a single number.
 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
 Summarize numerical data sets in relation to their context, such as:
o Reporting the number of observations.
o Describing the nature of the attribute under investigation, including how it was measured and its
units of measurement.
o Giving quantitative measures of center (median and/or mean) and variability (interquartile range
and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations
from the overall pattern with reference to the context in which the data were gathered.
o Relating the choice of measures of center and variability to the shape of the data distribution and the
context in which the data were gathered.
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MAFS.7.SP.2.3
(Assessed by SP.2.4)
MAFS.7.SP.2.4
Standards for
Mathematical Practice
MP 1: Make sense
of problems and
preserver in solving
them.
MP 3:Construct
Viable Arguments
and Critique the
Reasoning of Others
MP 4 Model with
Mathematics
Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Textbook Resources
MH FL Math
Chapter Lesson: 10.1-10.5
Inquiry Lab: Multiple Samples of Data, Collect Data, Visual Overlap of Data
Distributions
Problem Solving Investigation: Use a Graph
College & Career Readiness: Market Research
Real-World Link Video: 10.2
Lesson Video: 10.1
HMH GO MATH
Unit 5: Statistics
Module 10: Random Samples and Population: Lessons 10.1 – 10.3
Module 11: Analyzing and Comparing Data: Lessons 11.1 – 11.3
Real-World Videos: Frequency Tags pg. 307, Scientific Data pg. 331
Explore Activities:
* Random and Non-Ransom Sampling pg. 311
* Using Dot Plots to Make Inferences pg. 317
* Using Box Plots to Make Inferences pg. 318
* Generating a Random Sample Using Technology pg. 323
* Generating a Random Sample without Technology pg. 325
* Analyzing Dot Plots pg. 335
* Analyzing Box Plots pg. 341
“Power Up” Performance Task: Class Evaluation
Mathematics Formative Assessment System Tasks
The system includes tasks or problems that teachers can implement with their
students, and rubrics that help the teacher interpret students' responses.
Teachers using MFAS ask students to perform mathematical tasks, explain
their reasoning, and justify their solutions. Rubrics for interpreting and
evaluating student responses are included so that teachers can differentiate
instruction based on students' strategies instead of relying solely on correct or
incorrect answers. The objective is to understand student thinking so that
teaching can be adapted to improve student achievement of mathematical
goals related to the standards. Like all formative assessment, MFAS is a
process rather than a test. Research suggests that well-designed and
implemented formative assessment is an effective strategy for enhancing
student learning.
Animated Math: 10.2, 11.1
Performance Task: Entomologist
Other Resources
Mathematics Assessment Project
CPALMS
Secondary Canvas:
https://pasco.instructure.com/courses/846/pages/mathematics-6-12
http://www.cpalms.org/resource/mfas.aspx
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for
measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1,
“What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps
students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the
academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and
declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
4.0
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these
standards. Examples:

3.0
Collect, display, and compare data using various measures of central tendencies and justify which measure is the most appropriate.
The Student will:
 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a
population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce
representative samples and support valid inferences. (MAFS.7.SP.1.1)

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. For 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. (MAFS.7.SP.1.2)

Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers
by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean
height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two
distributions of heights is noticeable. (MAFS.7.SP.2.3)

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about 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. (MAFS.7.SP.2.4)
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
2.0
The student will recognize or recall specific vocabulary, such as:
 data, data distribution, hypothesis, statistics, biased sample, inferences, population, random sample, sample, sample size, lower extreme (minimum)
lower quartile, measures of variability, deviation, similar variability, mean, upper extreme (maximum) standard deviation, upper quartile, variance
The student will perform basic processes, such as:
 Ability to solve problems involving statistics but has difficulty pulling necessary components to set up proportion problems.
1.0

Ability to use data from a random sample to draw inferences when the problem is presented, however has difficulty pulling necessary components to set
up proportion problems.

Recognize and calculate mean, median, mode, and range and understand how an outlier affects data.
With help, partial success at 2.0 content but not at score 3.0 content
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question
#1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what
student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional
scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are
essential for mastery.
Domain: Statistics & Probability
Cluster: Draw informal comparative inferences about two populations
Standard: MAFS.7.SP.2.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the
centers by expressing it as a multiple of a measure of variability
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.



Measures of Center: mean, median, mode
Measures of Variability: Mean absolute deviation, range
Multiples of variability
Know
Declarative knowledge: Facts, vocab., information



Measures of Center: mean, median,
mode
Measures of Variability: Mean absolute
deviation, range
Multiples of variability
Do
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.




Find the measures of variability of a set of data.
Compare the differences between the measures of center and variability between multiple sets of data.
Use measures of center and variability to visually analyze the overlap of data set displayed on a graph.
Express the measure of center as a multiple of the measure of variability.
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
Addition, Division, Ordering on a number line,
Learning Goals:
Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a
multiple of a measure of variability.
Moving Beyond:
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of
knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown
below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to
further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1,
“Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the
actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level,
not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
Standard: MAFS.7.SP.2.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the
centers by expressing it as a multiple of a measure of variability
Score
Learning Progression
I can…
 Collect, display, and compare data using various measures of central
tendencies and variability of data, and justify which measure is the
most appropriate to my class.
Sample Tasks
You want to compare the average amounts of time students
sixth, seventh, and eighth grade spend on homework each
week.
a. Design an experiment involving random sampling that can
help you make a comparison.
4.0
Perform the experiment and display the data in a way that
allows you to make conclusions about how much time
students spend on homework? Explain your reasoning.
3.5
3.0
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
 Compare and contrast the measure of central tendency (mean, median, and
mode) in two numerical data distributions. 
The double box-and-whisker plot shows the points scored
per game by two football teams during the regular season.
 Determine the variability of data (range, mean deviation, variance, and
standard deviation). 
a. Compare the populations using measures of center and
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
variation.
Express the difference in the measure of central as a
multiple of measure of variation.
2.5
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
 Find the measures of central tendency (mean, median, and mode) in a
data distribution. 

The tables show the numbers of baskets made by two
basketball teams.
Find the measures of variation including upper quartile, lower
quartile, upper extreme (maximum), lower extreme (minimum),
range, interquartile range, and mean deviation. 
2.0
a. Find the mean, median, mode, range, interquartile range,
and mean absolute deviation for each data set.
Compare the data sets.
1.0
I need prompting and/or support to complete 2.0 tasks.
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Pasco County Schools, 2014-2015
7th Grade Advanced Mathematics Unit C: Measures of Central Tendencies
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply
demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them
as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and
common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?”
and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New
Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
Design Question 1; Element 1
MAFS.7.SP.2.3 Informally assess the degree of visual overlap of two numerical data distributions with similar
variability, measuring the difference between the centers by expressing it as a multiple of a measure of
variability.
MAFS Mathematical Practice(s)
MAFS.K12.MP.6.1– Attend to precision
Design Question 1; Element 1
MAFS.K12.MP.2.1 – Reason abstractly and quantitatively
Marzano’s Taxonomy
Level 3 Procedures with Connections
Teacher Notes
This lesson is designed to be used to introduce box-and-whisker plots to discover students understanding. You
might have to adjust your lessons according to student observations and conversations.
MAFS Mathematical Content Standard(s)
Questions to develop mathematical thinking,
possible misconceptions/misunderstandings,
how to differentiate/scaffold instruction,
anticipate student problem solving strategies
Task
The double box-and whisker plot shows the number of eggs laid by random sampels of two species of snakes.
The number of eggs produced at a single time is called a clutch.
*These tasks can either be teacher created or
modified from a resource to promote higher
order thinking skills. Please cite the source for
any tasks.
Compare the data sets and make three observations with justification.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015