7th Grade Mathematics
UNIT 2: RATIOS AND PROPORTIONAL RELATIONSHIPS
Unit Description/ Topic Length: This 5-week unit focuses on the concept of ratios and
proportional relationships. Students will extend their understanding of ratios and develop
understanding of proportionality to solve real-world and mathematical problems. They will engage
in instructional tasks that provide them with opportunities to recognize and represent proportional
relationships between quantities.
Big Ideas/Enduring Understandings
 A ratio is a multiplicative comparison
of two quantities, or it is a joining of
two quantities in a composed unit.
 Forming a ratio as a measure if a realworld attribute involves isolating that
attribute from other attributes and
understanding the effect of changing
each quantity on the attribute of
interest.
 A number of mathematical
connections link ratios and fractions:
o Ratios are often expressed in
fraction notation, although
ratios and fractions do not have
identical meaning.
o Ratios are often used to make
“part-part” comparisons, but
fractions are not.
o Ratios and fractions can be
thought of as overlapping sets.
o Ratios can often be
meaningfully reinterpreted as
fractions.
 Ratios can be meaningfully
reinterpreted as quotients.
 A proportion is a relationship of
equally between two ratios. In a
proportion, the ratio of two quantities
remains constant as the corresponding
values of the quantities change.
 Proportional reasoning is complex and
involves understanding that
o Equivalent ratios can be
created by iterating an/or
partitioning a composed unit:
o If one quantity in a ratio is
multiplied or divided by a
particular factor, then the other
quantity must be multiplied or
divided by the same factor to
Guiding Questions:
1. What is a ratio?
2. What is a ratio as a measure of an attribute in a
real-world situation?
3. How are ratios related to fractions and division?
4. What is a proportion?
5. What are the key aspects of proportional
reasoning?
6. What is a rate and how is it related to
proportional reasoning?
7. What is the relationship between the crossmultiplication algorithm and proportional
reasoning?
8. When is it appropriate to reason proportionally?
7th Grade Mathematics
maintain the proportional
relationship; and
o The two types of ratioscomposed units and
multiplicative comparisons are
related.
 A rate is a set of infinitely many
equivalent ratios.
 Several ways of reasoning, all
grounded in sense making, can be
generalized into algorithms for solving
proportions problems.
 Superficial cues present in the context
of a problem do not provide sufficient
evidence of proportional relationships
between quantities.
NYS Common Core Learning Standards for Mathematics:
Mathematical Content
7.RP. Analyze proportional relationships and use them to solve real-world and mathematical
problems.
1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and
other quantities measured in like or different units.
2. 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.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams,
and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is
proportional to the number 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.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of
the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
3. Use proportional relationships to solve multistep ratio and percent problems. Examples:
simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent
increase and decrease, percent error.
7th Grade Mathematics
Mathematical Practices
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.
b
Content
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Unit Rates
Recognizing Proportional Relationships
Representing Proportional Relationships
Constant of proportionality (unit rate)
Vocabulary/ Key Terms
Ratio
Rate
Unit rate
Proportion
Proportional Relationship
Constant of proportionality
Complex fractions
Skills
 Compute unit rates associated with
ratios of fractions in like or different
units
 Determine if two quantities are in a
proportional relationship from a table, a
graph, an equation and a verbal
description
 Represent a proportional relationship
using a table, a graph, and an equation
 Identify the constant of proportionality
(unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of
proportional relationships
 Explain what a point (x, y) on the graph
of a proportional relationship means in
terms of the situation, including the
points (0, 0) and (1, r) where r is the unit
rate
7th Grade Mathematics
ASSESSMENT EVIDENCE
Initial Assessment
Formative Assessments:
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Checks for Understanding
Short- and Extended-Response questions used throughout the unit.
Reflections
Formative Assessment Tasks
Summative Assessments:
1. Quizzes
2. Interim assessments
3. Unit test
4. Performance Tasks
TEACHING PLAN
Teaching and Learning Activities:
1. Administer the initial assessment for the unit.
2. Pose this question: “How does ratio reasoning differ from proportional reasoning?”
Have students brainstorm based on previous knowledge.
3. Review ratios.
4. Discuss rate and unit rate. Then have students work in pairs to complete the instructional
task/s.
5. Think-Pair-Share: “What is a proportion?”
6. Have students work on instructional tasks to help them learn the key aspects of
proportional reasoning.
7. Check for understanding: How is rate related to proportional reasoning?
8. Conduct the formative assessment lesson from MARS: Developing a Sense of Scale.
(Please see attachment)
9. Use unit guiding questions to do lessons on how to calculate with rational numbers and
solve real-life and mathematical problems involving rational numbers.
10. Have students work in groups to complete the authentic task for the unit.
11. Read informational text together.
12. Use essential question as a post-assessment. (individual journal entry)
13. Have students self-select pieces for the portfolio, reflect on selections and set goals for
improvement.
7th Grade Mathematics
14. Administer the unit test.
Please emphasize the following:
 Compute unit rates associated with ratios of fractions in like or different units
 Determine if two quantities are in a proportional relationship from a table, a graph, an
equation and a verbal description
 Represent a proportional relationship using a table, a graph, and an equation
 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships
 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
situation, including the points (0, 0) and (1, r) where r is the unit rate
Resources Needed:
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IMPACT Curriculum
GLENCOE Math
Chart Paper
http://www.projectpaced.com/index.html
NYC Common Core Library
CALENDAR
Time
Spent on
Standard
5 days
Standards
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.
Topics To Cover
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Ratios of Fractions
Unit Rates
7th Grade Mathematics
3 days
7.RP.2a 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.
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4 days
7.RP.2b Identify the constant of proportionality
(unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of
proportional relationships.
6 days
7.RP.2c Represent proportional relationships by 
equations. For example, if total cost t is
proportional to the number 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.
Equivalent ratios
Proportional Relationships
Graphing a proportional
relationship, with special
attention to the points (0, 0)
and (1, r) where r is the unit
rate
Recognizing proportional
relationships in a table and
graphs on a coordinate plane
Unit Rate and the Constant of
Proportionality
Representing proportional
relationships by equations
7.RP.2d Explain what a point (x, y) on the
graph of a proportional relationship means in
terms of the situation, with special attention to
the points (0, 0) and (1, r) where r is the unit
rate.
10 days
7.RP.3 Use proportional relationships to solve
multistep ratio and percent problems.
Examples: simple interest, tax, markups and
markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.

Percents