Common Core Learning Standards
GRADE 7 Mathematics
RATIOS & PROPORTIONAL RELATIONSHIPS
Common Core Learning
Standards
Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
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
Unit Rate
Embedded Skills
Solve unit rate problems that have fractional
quantities. (Problems may require solving complex
fractions).
Solve ratio problems whose quantities are lengths
of the same unit and different units.
Solve ratio problems whose quantities are areas of
the same unit and different units.
Solve ratio problems of other quantities with the
same unit and different units.
Divide two fractions by taking the reciprocal of the
divisor.
Vocabulary






Ratio
Complex
fraction
Unit rate
Rate
Proportion
equivalent
Compute the unit rate.
SAMPLE TASKS
I.
II.
III.
IV.
V.
If 5 tomatoes cost $2.00, what is the unit price of the tomatoes? How much would a dozen tomatoes cost?
Whitney earns $206.25 for 25 hours of work. How much does Whitney earn per hour? At this rate, how much does Whitney earn
in 30 hours?
A trail mix recipe calls for 1/3 pound of mixed nuts, 4/15 pound of raisins, and 2/5 pounds of granola. What is the ratio of raisins
to mixed nuts in simplest form.
An artist made purple paint by mixing ½ quart of red paint and ¾ of blue paint. What is the ratio of red paint to blue paint in
simplest form.
Franklin walked ½ mile in 8 ½ minutes. What is the unit rate in miles per minute.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
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.
Concepts
Embedded Skills
Proportional
Relationships
Calculate the cross product to determine if the two
ratios are in proportion (equivalent).
Analyze ratios in a table to determine if the ratios
are equivalent by finding the constant of
proportionality (slope).
Graph ratios on a coordinate plane to determine if
the ratios are proportional by observing if the graph
is a straight line through the origin (y = mx, where m
is the slope/constant of proportionality).
Solve proportions by cross multiplication.
Vocabulary







constant of
proportionalit
y
rate of change
slope
cross product
equivalent
origin
quantities
Write and solve proportions.
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
7.RP.2b.
Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams,
and verbal descriptions of proportional
relationships.
Concepts
Embedded Skills
Constant of
Calculate the constant of proportionality/unit rate
proportionality from a table or diagram.
Compute the rate of change/slope from a graph
(rise over run) or equation (m in y=mx).
Calculate the constant of proportionality/unit rate
given a verbal description of a proportional
relationship.
Vocabulary
 constant of
proportionality
 unit rate
 slope
 proportional
relationship
 rate of change
 direct
proportional
relationship
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Identify the constant of proportion
x
1
2
y
8
16
3
24
4
32
7
Use the graph at the left to help you answer the
following questions.
6
Cost (in Dollars
5
4
1. Explain why it is or is not a proportional
relationship.
3
2. What is the constant of proportionality?
3. Write the equation of the line.
2
4. How much would it cost for 7 roses?
1
0
0
1
2
3
4
5
6
7
Number of Roses
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Use the graph at the left to help you answer the
following questions.
1. Explain why it is or is not a proportional
relationship.
2. What is the constant of proportionality?
3. Write the equation of the line.
4. How many times would the parrots heart beat in 10
minutes?
Common Core Learning
Standards
Analyze proportional relationships
Concepts
Proportional
Embedded Skills
Write an equation from a proportional relationship.
Vocabulary

proportional
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
and use them to solve real-world and
mathematical problems.
relationships
and equations
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.
Solve equations created from proportional
relationships.



relationships
equation
rate
ratio
SAMPLE TASKS
Common Core Learning
Standards
Analyze proportional relationships
Concepts
Relationships
and
Embedded Skills
Define the rate of proportionality from a graph.
Vocabulary

rate of
proportionalit
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
and use them to solve real-world and
mathematical problems.
proportional
relationships
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.
Explain the meaning of a point on a graph y=mx of a
real life situation.


Calculate the unit rate by identifying that on a graph 
when the x-coordinate is 1, the y-coordinate is the
unit rate.
y
x-coordinate
y-coordinate
unit rate
SAMPLE TASKS
Common Core Learning
Standards
Concepts
Analyze proportional relationships
ratios,
percents, and
Embedded Skills
Solve multistep ratio problems using proportions.
Focus on simple interest, tax, markups/downs,
Vocabulary


Ratio
Proportion
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
and use them to solve real-world and
mathematical problems.
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.
proportions
gratuities and commissions, fees, percent
increase/decrease, and percent error.
Solve multistep percent problems using
proportions. Focus on simple interest, tax,
markups/downs, gratuities and commissions, fees,
percent increase/decrease, and percent error.

Percent
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.