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.
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.
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.
Vocabulary






Ratio
Complex
fraction
Unit rate
Rate
Proportion
equivalent
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.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Divide two fractions by taking the reciprocal of the
divisor.
Compute the unit rate.
SAMPLE TASKS
I.
If 5 tomatoes cost $2.00, what is the unit price of the tomatoes? How much would a dozen tomatoes cost?
II.
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?
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
III.
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.
IV.
An artist made purple paint by mixing ½ quart of red paint and ¾ quart of blue paint. What is the ratio of red paint to blue paint in
simplest form.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
V.
Franklin walked ½ mile in 8 ½ minutes. What is the unit rate in miles per minute.
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
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Write and solve proportions.
SAMPLE TASKS
I.
A
Is ∆ABC similar to ∆DEF? Use the constant of proportionality in your reasoning.
D
6 cm
10 cm
B
C
8 cm
12cm
E
20 cm
16cm
F
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Height of Rockets
A) Which rocket is traveling at a proportional speed?
How can you tell?
80
Height (ft.)
70
60
KEY
50
Rocket A
40
Rocket B
30
B) What is the constant of proportionality of that
rocket?
20
10
0
________________
0
1
2
3
4
5
Time after launch (sec.)
6
7
8
C) After how many seconds are the rockets at the
same height? How can you tell? How high are they?
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.
Use the graph at the left to help you answer the following
questions.
7
6
1. Explain why it is or is not a proportional relationship.
Cost (in Dollars
5
4
2. What is the constant of proportionality? ____________
3
2
3. Write the equation of the line?_____________________
1
4. How would you determine how much it would cost for 7
roses?
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? How do you know?
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
Concepts
Embedded Skills
Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
Proportional
relationships
and equations
Write an equation from a proportional relationship.

Solve equations created from proportional
relationships.



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.
Vocabulary
proportional
relationships
equation
rate
ratio
SAMPLE TASKS
I.
Raffle tickets cost $3 each. Write an equation that shows the total cost c of buying r raffle tickets.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II.
The speed limit on a highway is 65 miles per hour. Write an equation that shows the number of miles driven, d , in t hours.
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
Concepts
Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
Relationships
and
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.
Embedded Skills
Define the rate of proportionality from a graph.
Explain the meaning of a point on a graph y=mx of a
real life situation.
Vocabulary



Calculate the unit rate by identifying that on a graph 
when the x-coordinate is 1, the y-coordinate is the
unit rate.
rate of
proportionalit
y
x-coordinate
y-coordinate
unit rate
SAMPLE TASKS
A) Describe in a sentence what point A (10,12)
represents on this graph?
A (10,12)
B) Identify the unit rate and describe what it means?
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
Onds Analyze proportional
relationships 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.
Concepts
ratios,
percents, and
proportions
Embedded Skills
Solve multistep ratio problems using proportions.
Focus on simple interest, tax, markups/downs,
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.
Vocabulary



Ratio
Proportion
Percent
SAMPLE TASKS
I. Dan takes a loan for $2000 for two years. If the interest rate is 6%, determine how much money will be paid back in total.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
ii. A car costs $21,949. If the tax rate is 7.5%, find the total cost of the car.
III. KIx sneakers are sold at two different stores. At The Sneaker Outlet, the cost is $60.00 but they are on sale for 15% off.
At The Sneaker Barn, the cost is $66.00 but they are on sale for 25% off. Determine which pair of sneakers is cheaper and how much would
saved compared to the other store.
IV. A group of 4 friends went to a restaurant. The bill came to a total of $75.00 . If a gratuity is 20% is added to the bill, how much would each
person pay if the bill was split evenly.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
V. The price of a Barry Bonds baseball card in 2001 was $50. It is now being sold for $30. Find the percent decrease in the cost of the card.
VI. The 2010 census of Buffalo was estimated to be 400,000 residents. The actual count was 376,908. Find the relative error to the nearest
tenth of a percent.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.