Course Name: 7th Grade Math
Unit #4
Unit Title: Comparing and Scaling
Enduring understanding (Big Idea): Students will understand how to use ratios, percents and fractions to determine the
relationship between quantities. Students will use scaling, proportions, and unit rate to find equivalent ratios and unknown quantities
in real world situations.
Essential Questions:
Which quantities should be compared?
Which comparison strategies should be used to make predictions about unknown quantities?
How can the comparison be expressed in different but useful ways?
BY THE END OF THIS UNIT:
Students will know…
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Students will be able to…
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How to use proportions, equations and tables to
compare quantitative data.
How to scale ratios, rates and fractions to make larger
or smaller objects relative to the characteristics of the
original.
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Analyze comparison statements made about
quantitative data
Use ratios, fractions, differences, and percents to form
comparison statements given various situations
Use tables, graphs and equations to make predictions
and useful comparisons
Determine point of view and judge the reasonableness
of comparison statements.
Vocabulary:
Proportion, unit rate, rate, rate table, ratio, scale, scaling
Unit Resources
Mathematical Practices in Focus:
Learning Task: Additional Practice Investigation 1- 4
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
Performance Task: CC Additional Investigations 1.2-3
Project: Paper Pool Investigation and Report
Unit Review Game: Proportions Trail
https://www.teachingchannel.org/videos/junior-high-mathlesson
MathForward: Just How Many Are There?
CCSS-M Included: 7.RP.1, 7.RP.2a, 7.RP.2b, 7.RP.2c,
7.G.1
Suggested Pacing: 18 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 Plan
Standard 7.RP.1
Investigation 1:
Making Comparisons
Standard 7.G.1, 7.RP.2a
Investigation 2:
Comparing Ratios, Percents, and
Fractions
Standard 7.RP.2b
Investigation 3:
Comparing and Scaling Rates
Standard 7.RP.2a, 7.RP.2c
Investigation 4:
Making Sense of Proportions
Unit #4
Unit Title: Comparing and Scaling
Investigation
1.1 Ads That Sell
1.2 Targeting and Audience
1.3 American Records
Math Reflection 1
Determine the Most Useful Comparison Strategies
Suggested ACE Questions
ACE 1-3, 11-16, 34
ACE 4-7, 17-33, 34
ACE 8-10, 36-41
2.1 Mixing Juice
2.2 Sharing Pizza
2.3 Finding Equivalent Ratios
Math Reflection 2
Compare the Use of Ratios, Decimals and Percents
ACE 1-3, 9-13
ACE 4, 5, 14-18, 22
ACE 6-8, 19-21, 23, 24
3.1 Technology on Sale
3.2 Time, Rate, Distance
3.3 Comparing CD Prices
3.4 What Does Dividing Tell You?
Math Reflection 3
Compare Rates Using Graphs, Tables and Equations
ACE1-3, 13-18, 33
ACE 4-8, 10, 19-23
ACE 9, 11, 24-26, 34
ACE 12, 27-32
4.1 Setting Up and Solving Proportions
4.2 Everyday Use of Proportions
4.3 Developing Strategies for Solving Proportions
Math Reflection 4
Create Multiple Proportions of Equivalence
Looking Back and Looking Ahead
1. Comparing Transportation Survey Results
2. Determining the Better Buy
3.Use Comparison Strategies to Interpret Data
ACE 1, 2, 15-17, 21-23
ACE 3-5, 18-20, 25, 26
ACE 6-14, 24, 27, 28
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 #4
Unit Title: Comparing and Scaling
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard: 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other
quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit
rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
Concepts and Skills to Master:

Ability to describe and identify complex fractions
Ability to recognize the difference between unit rate and ratio
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SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understand ratios as proportional relationships between quantities
 Understand fractions as a ratio, rate or as a part to whole relationship
 Understand the relationship between part to whole and part to part
 Understand the connection between decimals and fractions
Procedural
 Ability to convert fractions to decimals and percents
 Ability to determine fractional equivalence
 Ability to identify common factors or multiples of similar figures
Academic Vocabulary
Ratio, unit rate, compare, describe, explain, relate, quantities, equivalence
Suggested Instructional Strategies:
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Resources:
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Introduce the concept of ratios by requiring students to
write three ratios to represent a jar of marbles that has
two colors. This will help the students relate part to part,
part to whole and whole to part. Use several real world
examples such as boys to girls and girls to number of
students in the class.
Help students connect arithmetic ratios to algebraic
ratios by using variables to represent each quantity in
the ratios.
Inform the grade level teachers of the comparison
language needed for this unit and work together to
increase student ability to communicate effective
comparative statements.
Sample Assessment Tasks
Skill-based task
In 1990, there were approximately 141,542,000 babies born in
the world. About how many births was this per day? Per hour?
Per Minute?
Textbook Correlation: Investigation 1
MARS Task: E14: Best Buy
Graphing Calculator Task: Can You Walk 3 Miles Per
Hour?
Problem Task
Describe a method you could use to estimate how many times
your heartbeats in a day, a week, and in a year.
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 #4
Unit Title: Comparing and Scaling
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard: 7.RP.2.a Recognize and represent proportional relationships between quantities.
a) Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a
coordinate plane and observing whether the graph is a straight line through the origin.
Concepts and Skills to Master:
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Ability to graph coordinates interpreted from proportional context
Ability to recognize given proportional situations that the two “between ratios” and the two “within ratios” are the same
Ability to recognize that two equal ratios represent a proportion and can be represented using ordered pairs and linear
representations.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understand how to use equations, linear graphs, tables and ordered pairs to represent patterns
 Understand how to construct proportions to determine proportionality between multiple quantities
 Understand how to test for equivalence using multiple strategies
Procedural
 Ability to plot patterns in the form of linear representations on a coordinate grid
 Cross multiply to determine proportionality
 Ability to continue an arithmetic and geometric sequence
Academic Vocabulary
Linear, origin, equivalence, ordered pairs, proportional relationship
Suggested Instructional Strategies:
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Resources:
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Graphing Proportions: Allow students to discuss the
difference between inversely and directly proportional
prior to completing the problem task below. Assign the
students real world problems and solutions. Task:
Create, solve and describe a directly and inversely
proportional situation using a tables, graphs and
equations. Explain the difference between inversely
and directly proportional.
Performance Based Tasks with Rubrics: Complete
performance based tasks from the following link. Use
the sample response to help student understanding of
rubrics. #1 Amy’s Vacation
http://www.oercommons.org/courses/proportionalreasoning/view
Sample Assessment Tasks
Skill-based task
One of the pipes in your house broke. You are trying to decide
which plumbing company to call, Wizards or Easy Clean.
Wizards charges $75 to make a house call and then $25 per
hour until the job is finished. Easy Clean charges $60 to make a
house call and then $30 per hour until the job is finished. Using
the information above describe the meaning of each ordered
pair.
1. (2, 175)
2. (6, 240)
Textbook Correlation: Investigation 2, 4
MARS Task: E10: A Golden Crown
Graphing Calculator Task: Does the Hand Relate to
the Foot?
Problem Task
Photographs come in several standard print sizes. Some of the
most common print sizes are 4x6, 5x7, and 8x10. (Note: The
dimensions are given in inches.) Does a proportional relationship
exist between these print sizes? Justify your answer using a
graph, proportion and table.
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 #4
Unit Title: Comparing and Scaling
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard: 7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal
descriptions of proportional relationships.
Concepts and Skills to Master:

Ability to express unit rates using a variety of representations, given a contextual situation
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understands how to make connections between decimals, fractions and percents represented in real world situations
 Understands how to make inferences about quantities and develop strategies and techniques to solve for missing values
 Understands the purpose of expressing values in the form of unit rates
Procedural
 Ability to construct tables, graphs, equations and diagrams to demonstrate proportionality
 Ability to determine unit rate using proportions
 Ability to use division to determine unit rate and multiply to determine unknown data
Academic Vocabulary
Constant, diagrams, independent, dependent, rate tables
Suggested Instructional Strategies:
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Resources:
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If students are still having difficulty using fraction
equivalents rely upon the practice sheet “Ratios and
Fractions” to reinforce simplifying and comparing
fractions. This is recommended as a warm-up for
students that lack fraction foundations.
If students haven’t demonstrated mastery at writing
finding unit rates rely upon the skills practice sheet
“Finding and Using Rates.” Use this as a homework,
review or warm-up activity.
Go to this site for additional table and graph situations.
http://dooleymath.com/Algebra/SystemsOverview.html
Sample Assessment Tasks
Skill-based task
It takes Juan 80 steps on the elliptical machine to go 0.1 of a
mile. When his workout is done, he has gone 4 miles. How many
steps has she made on the machine?
Textbook Correlation: Investigation 3
MARS Task: A21: Sale
Graphing Calculator Task: Equations from Unit Rates
Problem Task
Surrounding the EPIC Center are several parking lots. Parking lot
A is charging $4.50 for the first hour and $1.50 for every after
following. Parking Lot B is charging $3.50 for the first hour and
$2.50 for every hour following. Create tables, graphs and
equations to determine which parking lot has the better rate for
customers. Write a paragraph to justify your final decision.
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 #4
Unit Title: Comparing and Scaling
CORE CONTENT
Cluster Title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard:
7.RP.2.c Recognize and represent proportional relationships between quantities.
c. Represent proportional relationships by equations.
Concepts and Skills to Master:
Ability to recognize that multiplicative relationships are proportional
For example, if total cost t is proportional to the number of n of items purchased at a constant price p, the relationship between the
total cost and the number of items can be expressed as t = pn.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understands how to relate corresponding units as fractions and ratios
 Understands how to interpret real life comparisons and translate the quantities into useful representations
 Understands which formulas to use when solving for unknown quantities
Procedural
 Ability to use cross products to determine proportionality
 Ability to use formulas to solve problems
 Ability to interpret patterns from tables and use the patterns to determine unknown values
Academic Vocabulary
Constant, relationship, correlation, rate, unit rate, rate table, compare, describe, inverse proportion, direct proportion
Suggested Instructional Strategies:
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Resources:
If students haven’t demonstrated mastery at setting up and
solving proportions rely upon the skills practice sheet
“Solving Proportions.” Use this as a homework or warmup activity.
Review formulas
Help students visually align corresponding sides, with
tracing paper if the figures are not angled in the same
direction. It may also be important to color code each
edge to help visual learners.
https://www.teachingchannel.org/videos/visualizinggeometry-lesson
Sample Assessment Tasks
Skill-based task
15 m
Textbook Correlation: Investigation 4
Graphing Calculator Task: The Golden Rectangles
Problem Task
Determine the missing measurements in the given similar triangles.
9m
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15 m
x
12 m
y
x = _______________ y = _______________
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.
The Iditarod is a 1,159-mile sled dog race from Anchorage,
Alaska to Nome, Alaska. Susan Bucher is a four-time winner
of the race. Her average time was about 11 days. Find her
average rate in miles per day. Use a diagram, formula,
substitution, and inverse operations to determine her average
rate per day.
Course Name: 7th Grade Math
Unit #4
Unit Title: Comparing and Scaling
CORE CONTENT
Cluster Title: Draw, construct and describe geometrical figures and describe the relationships between them.
Standard: 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a
scale drawing and reproducing a scale drawing at a different scale.
Concepts and Skills to Master:
• Ability to describe and identify ratios and proportions
• Ability to reproduce scale drawing at a different scale
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Conceptual
 Understands the difference between similar and congruent figures
 Understands the rules of angle relationships such as complementary and supplementary angles
 Understands the difference between area and perimeter and how the scale factor impacts dimensions of the image
Procedural
 Ability to determine corresponding parts of similar figures
 Ability to set up proportions and use cross products to determine missing values
 Ability to determine proportionality using ratios and cross products
 Ability to isolate the variable and solve two step equations
 Ability to construct geometric figures using ordered pairs
Academic Vocabulary
Scale drawing, scale factor, dilation, enlargement, reduction, congruence, similarity, corresponding parts
Suggested Instructional Strategies:
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Resources:
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Help students revisit the concept of similar figures and
proportionality using tools such as a protractor. Use
actual measurements to demonstrate the difference
between congruent and similar.
Revisit fraction equivalence to help students correlate
corresponding lengths, sides, widths, and parts. Use
cross products to demonstrate proportionality.
Students should know supplementary, vertical,
complementary, alternate interior and alternate exterior
angles. This will improve their ability to identify
corresponding parts of geometric figures.
Sample Assessment Tasks
Skill-based task
If you visit the Museum of Science and Industry in Chicago, you
are able to examine a scale model of a human heart that is large
enough to walk through. The height of the scale model is 16 feet.
The scale used is 1 ft: 9/32 in. What is the height of the actual
heart?
Textbook Correlation: Comparing and Scaling Labs
MARS Task: E09:Triangular Frameworks
Graphing Calculator Task: Scaling the Geometry
Problem Task
If given the dimensions of the builder’s floor plans and the actual
dimensions of the actual house, explain how you can determine
the scale factor. Design a sample floor plan and actual
dimensions to explain how you would determine the scale factor.
Use corresponding parts to create equations, tables and
proportions when possible as evidence of your understanding
how to scale ratios.
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.