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Curriculum and Instruction – Mathematics
Quarter 3
Grade 7
Introduction
In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is
committed to these goals, as further described in our strategic plan, Destination 2025. By 2025,
 80% of our students will graduate from high school college or career ready
 90% of students will graduate on time
 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity
In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The
Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness
is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in
mathematics instruction: focus, coherence and rigor.
Focus
• The Standards call for a greater focus in mathematics. Rather
than racing to cover topics in a mile-wide, inch-deep curriculum,
the Standards require us to significantly narrow and deepen the
way time and energy is spent in the math classroom. We focus
deeply on the major work of each grade so that students can
gain strong foundations: solid conceptual understanding, a high
degree of procedural skill and fluency, and the ability to apply the
math they know to solve problems inside and outside the math
classroom.
• For grades K–8, each grade's time spent in instruction must
meet or exceed the following percentages for the major work of
the grade.
• 85% or more time spent in instruction in each grade
Kindergarten, 1, and 2 align exclusively to the major work of
the grade.
• For grade 7, more than 65% of instructional time is spent on the
major focus standards.
• Supporting Content - informaiont that supports the
understanding and implementation of the major work of the
grade.
• Additional Content - content that does not explicitly connect to
the major work of the grade yet it is required for proficiency.
Major Content
Coherence
• Thinking across grades:
• The Standards are designed around coherent
progressions from grade to grade. Learning is carefully
connected across grades so that students can build new
understanding on to foundations built in previous years.
Each standard is not a new event, but an extension of
previous learning.
• Linking to major topics:
• Instead of allowing additional or supporting topics to
detract from the focus of the grade, these concepts serve
the grade level focus. For example, instead of data
displays as an end in themselves, they are an opportunity
to do grade-level word problems.
 Supporting Content
Rigor
• Conceptual understanding:
• The Standards call for conceptual understanding of key
concepts, such as place value and ratios. Students must
be able to access concepts from a number of
perspectives so that they are able to see math as more
than a set of mnemonics or discrete procedures.
• Procedural skill and fluency:
• The Standards call for speed and accuracy in calculation.
Students are given opportunities to practice core
functions such as single-digit multiplication so that they
have access to more complex concepts and procedures.
• Application:
• The Standards call for students to use math flexibly for
applications in problem-solving contexts. In content areas
outside of math, particularly science, students are given
the opportunity to use math to make meaning of and
access content.

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
8. Look for and
express regularity
in repeated
reasoning
7. Look for and
make use of
structure
Grade 7
1. Make sense of
problems and
persevere in
solving them
2. Reason
abstractly and
quatitatively
Mathematical
Practices(MP)
6. Attend to
precision
3. Construct viable
arguments and
crituqe the
reasoning of
others
4. Model with
mathematics
5. Use appropriate
tools strategically
The Standards for Mathematical Practice describe varieties of expertise, habits of
minds and productive dispositions that mathematics educators at all levels should seek to
develop in their students. These practices rest on important National Council of Teachers
of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in
mathematics education. Throughout the year, students should continue to develop
proficiency with the eight Standards for Mathematical Practice.
This curriculum map is designed to help teachers make effective decisions about what
mathematical content to teach so that, ultimately our students, can reach Destination
2025. To reach our collective student achievement goals, we know that teachers must
change their practice so that it is in alignment with the three mathematics instructional
shifts.
Throughout this curriculum map, you will see resources as well as links to tasks that will
support you in ensuring that students are able to reach the demands of the standards in
your classroom. In addition to the resources embedded in the map, there are some highleverage resources around the content standards and mathematical practice standards
that teachers should consistently access:
The TN Mathematics Standards
The Tennessee Mathematics Standards:
Teachers can access the Tennessee State standards, which are featured
https://www.tn.gov/education/article/mathematics-standards
throughout this curriculum map and represent college and career ready
learning at reach respective grade level.
Standards for Mathematical Practice
Mathematical Practice Standards
Teachers can access the Mathematical Practice Standards, which are
https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view featured throughout this curriculum map. This link contains more a more
detailed explanation of each practice along with implications for instructions.
Major Content
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
Grade 7
Purpose of the Mathematics Curriculum Maps
This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready
(CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach
and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the
grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools.
Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching
for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with
colleagues to continuously improve practice and best meet the needs of their students.
The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional
practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of
the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and
assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected-with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective
instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each
teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—highquality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.
Additional Instructional Support
Shelby County Schools adopted our current math textbooks for grades 6-8 in 2010-2011. The textbook adoption process at that time followed the requirements set
forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards; therefore,
the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief
State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of
conceptual knowledge development and application of these concepts), of our current materials.
The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still
incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and
external/supplemental resources (e.g., engageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.
Major Content
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
Grade 7
How to Use the Mathematics Curriculum Maps
Overview
An overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the
students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.
Tennessee State Standards
The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a
key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that
supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s
responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
Content
Teachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related
best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.).
Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture”
of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best
practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.
Instructional Support and Resources
District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, iReady lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as
needed for content support and differentiation.
Major Content
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
Grade 7
Topics Addressed in Quarter
Random Sampling
Comparative Inferences
Probability Models
Scale Drawings
Constructing Triangles
Overview
In quarter 3 students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities by
conducting experiments and observations (7.SP.C.5, 6), calculate probabilities of compound events using lists, tables, tree diagrams, and simulations (7.SP.C.8) and learn to use probabilities to
make decisions and to determine whether or not a given probability model is plausible (7.SP.C.7). Additionally, students build on their knowledge of data distributions that they studied in Grade 6,
compare data distributions of two or more populations (7.SP.B.3, 7.SP.B.4), and are introduced to the idea of drawing informal inferences based on data from random samples (7.SP.A.1,
7.SP.A.2). Up to 7th grade, almost all of students’ statistical topics and investigations have dealt with univariate data, e.g., collections of counts or measurements of one characteristic. During eighth
grade students will extend their work to bivariate data, applying their experience with the coordinate plane and linear functions in the study of association between two variables related to a question
of interest. Near the end of the quarter, students will bring their experience with proportional relationships to the context of scale drawings (7.RP.2b, 7.G.1). Given a scale drawing, students should
rely on their background in working with side lengths and areas of polygons (6.G.1, 6.G.3) as they identify the scale factor as the constant of proportionality, calculate the actual lengths and areas of
objects in the drawing, and create their own scale drawings of a two-dimensional figure. Students will also construct geometric shapes, mainly triangles provided given conditions, side length and the
measurement of the included angle (7.G.A.2) and learn two new concepts about unique triangles. Students develop an intuitive understanding of the structure of a triangle.
Year at a Glance Document
Grade Level Standard
Type of Rigor
Foundational Standards
7.SP.1
Conceptual Understanding
6.SP.1, 6.SP.2
7.SP.2
7.SP.3
7.SP.4
7.SP.5
7.SP.6
7.SP.7
7.SP.8
7.SP.1
5.NF.4, 6.NS.1, 6.SP.2
7.SP.2, 7.SP.3
7.G.1, 7.RP.2b
Conceptual Understanding
Conceptual Understanding
Conceptual Understanding
Conceptual Understanding
Conceptual Understanding
Application
Conceptual Understanding,
Procedural Skill & Fluency, Application
Procedural Skill & Fluency
7.G.2
Conceptual Understanding
Major Content
Sample Assessment Items
Inside Mathematics Performance Assessment
Task 7.SP.1 & 4: Ducklings
Math Shell: Counting Trees
Orglib.com Assessment Items 7.SP.3
Learnzillion: 7.SP.1-4
Learnzillion: 7.SP.5-7
Orglib.com Assessment Items 7.SP.5
Math Shell: Lottery
Inside Mathematics Performance Task: Fair
Game?
Inside Mathematics Performance Task: Which is
Bigger?
Inside Mathematics Performance Assessment
Task 7.G.2 & 7.G.6 Parallelogram
7.RP.3, 7.SP.5
7.RP.3, 7.SP.6
7.RP.3, 7.SP.7
6.G.1, 7.RP.2
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
Grade 7
Fluency
NCTM Position
Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to
transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is
more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar
procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used
procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.
The fluency standards for 7th grade listed below should be incorporated throughout your instruction over the course of the school year. Click engageny Fluency
Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.




7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
References:
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


https://www.engageny.org/
http://www.corestandards.org/
http://www.nctm.org/
http://achievethecore.org/
Major Content
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Grade 7
CONTENT
Domain: Statistics and Probability
Cluster(s): Use random sampling to draw
inferences about a population. Draw informal
comparative inferences about two populations.
 7. SP.A.1 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.
 7. SP.A.2Use 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.SP.B.3 Informally assess the degree of
visual overlap of two numerical data
distributions with similar variabilities,
measuring the difference between the
centers by expressing it as a multiple of a
measure of variability.
 7.SP.B.4 Use measures of center and
measures of variability for numerical data
from random samples to draw informal
comparative inferences about two
populations.
INSTRUCTIONAL SUPPORT & RESOURCES
Statistics
(Allow approximately 3.5 weeks for instruction, review and assessment)
Enduring Understandings:
Focus on the Real-World Examples,
Problem Solving and H.O.T. exercises from
 The rules of probability can lead to more
the following book lessons.
valid and reliable predictions about the
likelihood of an event occurring.
Glencoe
8-3E Use Data to Predict (pp. 468-471)
Essential Questions:
9-1B Measures of Central Tendency (pp.491 How is probability used to make informed
496)
decisions about uncertain events?
9-2A Measures of Variation (pp. 498-503)
9-2B Box-and-Whisker Plots (pp. 504-509)
Objectives:
9-3E Stem-and-Leaf Plots (pp. 526-531)
 Students will predict actions of a larger
Additional Lesson 14 Multiple Samples of Data
group by using a sample.
 Students will analyze the variation in multiple p. 807
Additional Lesson 15 Visual Overlap of Data
samples of data.
Distribution p. 809
 Students will calculate measures of center.
Additional Lesson 16 Compare Populations 9.
 Students will determine and describe how
811
changes in data values impact measures of
central tendency.
Holt
7-2
Mean,
Median,
Mode
& Range (pp. 385Additional Information: (7.SP.1-2)
389)
 Students will recognize that it is difficult to
7-5 Box-and-Whisker Plots (pp.398-401)
gather statistics on an entire population.
7-8 Populations and Samples (pp.418-421)
Instead a random sample can be
representative of the total population and will
generate valid predictions.
 Students collect and use multiple samples of
data to make generalizations about a
population.
Example(s):
 The school food service wants to increase
the number of students who eat hot lunch in
the cafeteria. The student council has been
asked to conduct a survey of the student
body to determine the students’ preferences
Major Content
Building Conceptual Understanding:
engageny: Random Sampling/Estimating
Population Characteristics (Lessons 13-20)
Math Shell Lesson: Comparing Data using
Statistical Measures
Vocabulary: Survey, variability,
biased/unbiased sample, sample population,
random sampling, mean absolute deviation
inferences
Writing in Math:
Students will explain the possible ways to use
statistics to gain information about a sample set
of a population.
Students will explain their knowledge of
measures of center.
Graphic Organizer: Students can create
Frayer Model for the following terms using a
variety of resources available in your
classroom (textbook, newspapers, internet
resources, prior knowledge, information
printed by teacher in advance):
 Measures of Center
 Measures of Variation
 Measures of Spread (note to teacher –
students should discover that measures
of spread are the same as measures of
variation)
 Outliers
 Mean absolute deviation
Choose from the following resources and
use them to deepen students' conceptual
understanding of mathematical content and
develop their ability to apply that
knowledge to non-routine problems.
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Grade 7
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
for hot lunch. They have determined two
ways to do the survey. The two methods are
listed below. Identify the type of sampling
used in each survey option. Which survey
option should the student council use and
why?
1. Write all of the students’ names on cards
and pull them out in a draw to determine who
will complete the survey.
2. Survey the first 20 students that enter the
lunch room.
3. Survey every 3rd student who gets off a bus.
 Below is the data collected from two random
samples of 100 students regarding students’
school lunch preferences. Make at least two
inferences based on the results.
Suggested Additional Lessons:
engageny: Comparing Populations Lessons 2123
Better Lesson: 7.SP.3 & 4
Math Shell Concept Development Lesson:
Comparing Data Using Statistical Measures
Suggested Tasks:
Illustrative Math: Mr. Briggs's Class Likes
7.SP.1
Illustrative Math Task: Valentine Marbles
7.SP.2
Illustrative Math Task: College Athletes
7.SP.3-4
Illustrative Math Task: Offensive Lineman
7.SP.3-4
Math Shell Task: Temperatures 7.SP.A.2
Math Shell Task: Candy Bars 7.SP.A.2
Suggested Additional Resources:
Khan Academy: Mean Absolute Deviation
Solution:
Most students prefer pizza
More people prefer pizza than hamburgers
and tacos combined.
Additional Information: (7.SP.3-4)
 This is the students’ first experience with
comparing two data sets. Students build on
their understanding of graphs, mean,
median, Mean Absolute Deviation (MAD)
and inter-quartile range from 6th grade.
Students understand that:
1. a full understanding of the data requires
Major Content
Correlated iReady Lesson(s): The iReady
program includes a variety of resources that
can be used to support teacher-led instruction
in Tier 1 and guided small-group Tier 1, 2 or 3
instruction.
 Random Samples
 Making Statistical Inferences
 Using Mean and Mean Absolute
Deviation to Compare Data (Related
lesson)
 Using Measures of Center to
Compare Data (Related lesson)
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Grade 7
CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
consideration of the measures of variability as
well as mean or median,
2. variability is responsible for the overlap of
two data sets and that an increase in variability
can increase the overlap, and
3. The median is paired with the inter-quartile
range and mean is paired with the mean
absolute deviation. Mean Deviation
 Measures of center include mean, median,
and mode. The measures of variability
include range, mean absolute deviation, and
inter-quartile range.
Example(s):
 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?
Company A {1.2 million, 242000, 265500,
140000, 281000, 265000, 211000}
Company B {5million, 154000, 250000,
250000, 200000, 160000, 190000}
Solution:
The median would be the most accurate
measure since both companies have one
value in the million that is far from the other
values and would affect the mean.
Major Content
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Grade 7
CONTENT
Domain: Statistics and Probability
Cluster: Investigate chance processes and
develop, use and evaluate probability models.
 7.SP.C.5 Understand that the probability of
a chance event is a number between 0 and
1 that expresses the likelihood of the event
occurring.
 7.SP.C.6 Approximate the probability of a
chance event by collecting data on the
chance process that produces it and
observing its long-run relative frequency,
and predict the approximate relative
frequency given the probability.
 7.SP.C.7 Develop a probability model and
use it to find probabilities of events.
Compare probabilities from a model to
observed frequencies; if the agreement is
not good, explain possible sources of the
discrepancy.
 7.SP.C.7a Develop a uniform probability
model by assigning equal probability to all
outcomes, and use the model to determine
probabilities of events.
 7.SP.C.7b Develop a probability model
(which may not be uniform) by observing
frequencies in data generated from a
chance process. For example: find the
approximate probability that a spinning
penny will land heads up or that a tossed
paper cup will land open-end down. Do the
outcomes for the spinning penny appear to
INSTRUCTIONAL SUPPORT & RESOURCES
Probability
(Allow approximately 3.5 weeks for instruction, review and assessment)
Enduring Understanding(s):
Focus on Real-World Examples, Problem
Solving and H.O.T. Exercises from the
 The rules of probability can lead to more
following book lessons.
valid and reliable predictions about the
likelihood of an event occurring.
Glencoe
8-2A Independent and Dependent Events
Essential Question(s):
(pp.450-455)
 How is probability used to make informed
8-3A Theoretical & Experimental Probability
decisions about uncertain events?
(pg.458-462)
8-3B Extend Simulations (pg. 463)
Objective(s):
8-3C Problem Solving (pg.466-467)
 Students will compute or estimate
8-3E Use Data to Predict (pp. 468-471)
probabilities using a variety of methods,
including collecting data, using tree
IMPACT Math Unit G, Inv. 2, pp. 108-111
diagrams, and using simulations.
 Students will find and compare theoretical
Holt
and experimental probabilities.
11-1 Probability (pp. 640-643)
 Students will predict actions of a larger
11-2 Experimental Probability (pp. 644-647)
group by using a sample.
11-4 Theoretical Probability (pp. 652-655)
11-5 Making Predictions (pp. 658-661)
Additional Information: 7.SP.5
Experimental and Theoretical Probability Lab
Students need multiple opportunities to
(pp. 662-663)
perform probability experiments and compare
11-6 Probability of Independent and
these results to theoretical probabilities.
Dependent Events (pp. 666-669)
Example:
The container below contains 2 gray, 1 white,
and 4 black marbles. Without looking, if you
choose a marble from the container, will the
probability be closer to 0 or to 1 that you will
select a white marble? A gray marble? A black
marble? Justify each of your predictions.
Major Content
Vocabulary: Probability, event outcome,
theoretical probability, experimental
probability, relative frequency, simple event,
compound event, tree diagram
Writing in Math:
Compare and contrast experimental probability
and theoretical probability.
Have students explain the difference between
independent events and dependent events.
Building Conceptual Understanding:
Math Shell Lesson: Analyzing Games of
Chance 7.SP.C.6-7
engageny: Module 5 Topic A Lessons for
7.SP.C.5
engageny : Module 5 Topic B Lessons 8-10 for
7.SP.C.6-8
Choose from the following resources and
use them to deepen students' conceptual
understanding of mathematical content and
 Supporting Content

Additional Content
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Major Content
Curriculum and Instruction – Mathematics
Quarter 3
TN STATE STANDARDS
Grade 7
CONTENT
be equally likely based on the observed
frequencies?
7.RP.A.3 Use proportional
relationships to solve multistep ratio
and percent problems. (This standard
was covered in Q1 but it is repeated
here because of the strong
application of percent in probability.)
 7.SP.C.8 Find probabilities of compound
events using organized lists, tables, tree
diagrams, and simulation.
 7.SP.C.8a Understand that, just as with
simple events, the probability of a
compound event is the fraction of outcomes
in the sample space for which the
compound event occurs
 7.SP.C.8b Represent sample spaces for
compound events using methods such as
organized lists, tables and tree diagrams.
For an event described in everyday
language (e.g., “rolling double sixes”),
identify the outcomes in the sample space
which compose the event.
 7.SP.C.8c Design and use a simulation to
generate frequencies for compound events.
For example, use random digits as a
simulation tool to approximate the answer to
the question: If 40% of donors have type A
blood, what is the probability that it will take
at least 4 donors to find one with type A
blood.
INSTRUCTIONAL SUPPORT & RESOURCES
Solution:
White marble: Closer to 0
Gray marble: Closer to 0
Black marble: Closer to 1
develop their ability to apply that
knowledge to non-routine problems.
Students can use simulations such as Marble
Mania on AAAS or the Random Drawing Tool
on NCTM’s Illuminations to generate data and
examine patterns.
Marble Mania
Random Drawing Tool
Additional Information: 7.SP.6
Students can collect data using physical
objects or graphing calculator or web-based
simulations. Students can perform
experiments multiple times, pool data with
other groups, or increase the number of trials
in a simulation to look at the long-run relative
frequencies.
Example:
Each group receives a bag that contains 4
green marbles, 6 red marbles, and 10 blue
marbles. Each group performs 50 pulls,
recording the color of marble drawn and
replacing the marble into the bag before the
next draw. Students compile their data as a
group and then as a class. They summarize
their data as experimental probabilities and
make conjectures about theoretical
probabilities (How many green draws would
are expected if 1000 pulls are conducted?
10,000 pulls?).
Additional Information: 7.SP.7
Students need multiple opportunities to
perform probability experiments and compare
Major Content
Suggested Additional Lessons:
engageny : Module 5 Topic B Lessons 11-12
for 7.SP.C.8
Better Lesson: Simple Events
Better Lesson: Experimental vs Theoretical
Probability
Better Lesson: Probability Lab
Suggested Tasks:
Math Shell Assessment Task: Spinner Bingo
7.SP.C.6-7
Math Shell Task: Analyzing Games of Chance
7.SP.C.6
Math Shell Task: Charity Fair 7.SP.C.6-7
Illustrative Math Task: Red, Blue or Green?
7.SP.C.8
Illustrative Math Task: Rolling Twice 7.SP.8.C
Illustrative Math Task: Waiting Times 7.SP.8.C
Illustrative Math Task: Sitting across from
Each Other 7.SP.C.8.a & b
Illustrative Math Task: Tetrahedral Dice
7.SP.C.8.a & b
Shmoop: Simulation of Compound Event
7.SP.C.8.c
Suggested Additional Resources:
Learnzillion: Making predictions using
proportional reasoning- Probability fair prizes
Learnzillion: Analyze independent and
dependent events
Correlated iReady Lesson: The iReady
program includes a variety of resources that
can be used to support teacher-led instruction
 Supporting Content

Additional Content
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CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
these results to theoretical probabilities.
Critical components of the experiment process
are making predictions about the outcomes by
applying the principles of theoretical
probability, comparing the predictions to the
outcomes of the experiments, and replicating
the experiment to compare results.
in Tier 1 and guided small-group Tier 1, 2 or 3
instruction.
 Probability Concepts
 Experimental Probability
 Probability of Compound Events
 Simulations of Compound Events
Example:
Devise an experiment using a coin to
determine whether a baby is a boy or a girl.
Conduct the experiment ten times to determine
the gender of ten births. How could a number
cube be used to simulate whether a baby is a
girl or a boy or girl?
Example:
Conduct an experiment using a Styrofoam cup
by tossing the cup and recording how it lands.
• How many trials were conducted?
• How many times did it land right side up?
• How many times did it land upside down/
• How many times did it land on its side?
• Determine the probability for each of the
above results.
Additional Information: 7.SP.8
Students can use tree diagrams, frequency
tables, and organized lists, and simulations to
determine the probability of compound events.
Example:
How many ways could the 3 students, Amy,
Brenda, and Carla, come in 1st, 2nd and 3rd
place?
Solution:
Making an organized list will identify that there
Major Content
 Supporting Content

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CONTENT
INSTRUCTIONAL SUPPORT & RESOURCES
are 6 ways for the students to win a race
A, B, C
A, C, B
B, C, A
B, A, C
C, A, B
C, B, A
Example: Students conduct a bag pull
experiment. A bag contains 5 marbles. There
is one red marble, two blue marbles and two
purple marbles. Students will draw one marble
without replacement and then draw another.
What is the sample space for this situation?
Explain how the sample space was
determined and how it is used to find the
probability of drawing one blue marble
followed by another blue marble.
Example: A fair coin will be tossed three
times. What is the probability that two heads
and one tail in any order will results?
Solution:
HHT, HTH and THH so the probability would
be 3/8.
Domain: Geometry
Cluster: Draw, construct and describe
geometrical figures and describe the
relationships between them.
 7.G.A.1 Solve problems involving scale
drawings of geometric figures, including
computing actual lengths and areas from a
scale drawing and reproducing a scale
Geometry: Draw, Construct & Describe Geometric Figures
( Allow approximately 2 weeks for instruction, review and assessment)
Enduring Understanding(s):
The following lessons only provide practice
to enhance procedural skill for solving
 Geometric properties can be used to
problems involving scale factor.
construct geometric figures.
 Everyday objects have a variety of
Glencoe
attributes which can be measured in many
5-2B Scale Drawings (pgs. 284-290)
ways.
5-2C Extend Scale Drawings (pg. 291)
 Scale factor is the constant ratio of each
IMPACT Math Unit D, Inv. 4 Map Scales, pp.
actual length to its corresponding length in
62-64; Inv. 5 Similarity pp. 65-66
a drawing.
Major Content
 Supporting Content

Vocabulary: dimensions, scale, scale factor,
scale drawings, scale models, triangle,
congruent segments, acute triangle, right
triangle, obtuse triangle, scalene triangle,
isosceles triangle, equilateral triangle
Writing in Math: Have students write a realworld problem that could be solved by making
a model. Then solve the problem.
Additional Content
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CONTENT
drawing at a different scale.
 7.RP.2.b Identify the constant of
proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions
of proportional relationships. (This standard
supports proportional reasoning needed to
calculate scale factors.)
INSTRUCTIONAL SUPPORT & RESOURCES
Essential Question(s):
 What is a scale factor?
 What is a scale drawing?
 How can measurements and information
about similar figures be used to solve
problems?
 7.G.A.2
Draw (freehand, with ruler and
protractor, and with technology) geometric
shapes with given conditions. Focus on
constructing triangles from three measures
of angles or sides, noticing when the
conditions determine a unique triangle,
more than one triangle, or no triangle.
Objective(s):
 Students will solve problems involving
scale drawings.
 Students will find the relationship between
perimeters and areas of similar figures.
 Students will determine how changes in
dimensions affect area.
 Students will use a compass, protractor,
and ruler to draw geometric shapes based
on given conditions.
 Students will determine whether a set of
given conditions for the measures of angle
and/or sides of a triangle describe a unique
triangle, more than one possible triangle or
do not describe a possible triangle.
Additional Information:

Students will determine the dimensions of
figures when given a scale and identify the
impact of a scale on actual length and area.

Example(s):
Julie showed you the scale drawing of her
room. If each 2 cm on the scale drawing
equals 5 ft, what are the actual dimensions of
Julie’s room? Reproduce the drawing at 3
times its current size.
5-3A Similar Figures (pgs.293-298) This
lesson focuses on how scale factor can be
used to determine if triangles are similar.
Remember the focus of 7.G.1 is not on
similar triangles.
5-3B Perimeter & Area of Similar Figures
(pgs.299-302)
Additional Lesson 23 Exploring Similarity
using Geometer’s Sketchpad pp. 832-833
5-3C Extend The Golden Rectangle (pgs. 303)
11-2A Make a Model (p. 651 # 3, 4, 6, 8 & 10)
11-2B Changes in Scale (p.652 Activity 1, # 12)
12-1B Explore Triangles
12-1CTriangles
Explain why it is impossible to draw an
equilateral triangle that is either right or obtuse.
Graphic Organizer(s):
Scale Drawing
Holt
4-8 Similar Figures (pp. 248-251) This
lesson focuses on proportionality of side
lengths.
4-9 Using Similar Figures (pp. 252-255) This
lesson focuses on indirect measurements.
4-10 Scale Drawing and Scale Models (pp.
256-259)
Hands-On Lab Make Scale Drawings and
Models (pp. 260-261)
8-6 Classifying Triangles
Building Conceptual Understanding:
Engage NY: Relating Scale Drawings to Ratios
and Rates
Engage NY: Drawing Geometric Shapes
Math Shell Lesson: Describing and Defining
Triangles
Achieve The Core: Identifying Proportional and
Non-proportional Relationships
Choose from the following resources and
Major Content
 Supporting Content

Additional Content
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INSTRUCTIONAL SUPPORT & RESOURCES
use them to deepen students' conceptual
understanding of mathematical content and
develop their ability to apply that
knowledge to non-routine problems.







Solution:
5.6 cm --- 14 ft
1.2 cm --- 3 ft
2.8 cm --- 7 ft
4.4 cm --- 11 ft
4 cm --- 10 ft
Suggested Additional Lesson(s):
engageny: Ratios of Scale Drawings
Connected Math: Stretching and Shrinking
Investigations 1-5
Similar Figures Lesson
Math Shell: Drawing to Scale - A Garden
engageny: Drawing Parallelograms
engageny: Drawing Triangles
If the rectangle below is enlarged using a scale
factor of 1.5, what will be the perimeter and
area of the new rectangle?
7 in.
2 in.
Suggested Task(s):
Illustrative Math: Floor Plan
Illustrative Math: Map Distance
Illustrative Math: Rescaling Washington Park
Illustrative Math: 7.G.2
Achieve the Core: Art Class Task
Solution:
The perimeter is linear or one-dimensional.
Multiply the perimeter of the given rectangle
(18 in.) by the scale factor (1.5) to give an
answer of 27 in.
Students could also increase the length and
width by the scale factor of 1.5 to get 10.5 in.
for the length and 3 in. for the width. The
perimeter could be found by adding 10.5 +
10.5 + 3 + 3 to get 27 in. The area is twodimensional so the scale factor must be
squared. The area of the new rectangle would
be 14 x 1.52 or 31.5 in2.
Additional Information: (7.G.2)
Students draw geometric shapes with given
parameters. Parameters could include parallel
Major Content
Suggested Additional Resources:
Illuminations: Scale Drawings Interactive
Illuminations: Making Triangles 7.G.2
Khan Academy: Constructing Triangles
Practice
Better Lessons 7.G.2
Correlated iReady Lesson(s): The iReady
program includes a variety of resources that
can be used to support teacher-led instruction
in Tier 1 and guided small-group Tier 1, 2 or 3
instruction.
 Scale Drawings
 Constructions of Triangles
 Supporting Content

Additional Content
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INSTRUCTIONAL SUPPORT & RESOURCES
lines, angles, perpendicular lines, line
segments, etc.
Example(s):
Is it possible to draw a triangle with a 90˚
angle and one leg that is 4 inches long and
one leg that is 3 inches long? If so, draw
one. Is there more than one such triangle?
Draw a triangle with angles that are 60
degrees. Is this a unique triangle? Why or
why not?
Draw an isosceles triangle with only one 80
degree angle. Is this the only possibility or can
you draw another triangle that will also meet
these conditions?
Through exploration, students recognize that
the sum of the angles of any triangle will be
180.
Major Content
 Supporting Content
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Additional Content
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Grade 7
RESOURCE TOOLBOX
The Resource Toolbox provides additional support for comprehension and mastery of grade-level skills and concepts. While some of these resources are imbedded in the map, the
use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.
NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources
will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)
https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.
Textbook Resources
www.myhrw.com
www.connected.mcgraw-hill.com
Standards Support
TNReady Math Standards
Achieve the Core
Edutoolbox
Videos
Khan Academy
Watch Know Learn
Learn Zillion
Virtual Nerd
Math Playground
Study Jams
Calculator
TI-73 Activities
CASIO Activities
TI-Inspire for Middle Grades
Interactive Manipulatives:
National Library of Virtual Manipulatives
Additional Sites:
PBS: Grades 6-8 Lesson Plans
AAA Math: Equations
Frayer Model Template
Grade 7 Flip Book (This book contains valuable resources that help develop the intent, the
understanding and the implementation of the state standards.)
Major Content
 Supporting Content

Additional Content
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