__Modified documents (after parcc)Lin’s Bike Ride: Illustrative Math w/Student Achievement Partners Prototype MachineScorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
6.RP.2
6.RP.3b
Understand the concept of a unit rate a/b associated with a ratio a:b
with b≠0, and use rate language in the context of a ratio
relationship. For example, “This recipe has a ratio of 3 cups of
flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of
sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per
hamburger.”
Use ratio and rate reasoning to solve real-world and mathematical
problems, e.g., by reasoning about tables of equivalent ratios, tape
diagrams, double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing
and constant speed. For example, if it took 7 hours to mow 4 lawns,
then at that rate, how many lawns could be mowed in 35 hours? At
what rate were lawns being mowed?
Level 5: Distinguished Command
Uses ratio and rate reasoning to
solve real-world and mathematical
problems, including ratio, unit rate
percent and unit conversion
problems.
Uses and connects a variety of
representations and strategies to
solve these problems.
i) Expectations for unit rates in this grade are
limited to non-complex fractions. (See footnote,
CCSS p 42.)
i) See ITN Appendix F, Table F.c, “Minimizing or
avoiding common drawbacks of selected
response,” specifically, Illustration 1 (in contrast to
the problem “A bird flew 20 miles in 100 minutes.
At that speed, how long would it take the bird to
fly 6 miles?”) Instead ask:“A bird flew 20 miles in
100 minutes at constant speed. At that speed: (a)
How long would it take the bird to fly 6 miles? (b)
How far would the bird fly in 15 minutes? (c) How
fast is the bird flying in miles per hour? (d) What is
the bird’s pace in minutes per mile?”
ii) Expectations for unit rates in this grade are
limited to non-complex fractions. (See footnote,
CCSS p 42)
Addressed Portion of the PLDs: Grade 6, Sub-claim A, Ratios
Level 4: Strong Command Level 3: Moderate Command
Uses ratio and rate
Uses ratio and rate reasoning to
reasoning to solve realsolve real-world and
world and mathematical
mathematical problems,
problems, including ratio,
including ratio, unit rate,
unit rate, percent and unit
percent and unit conversion
conversion problems.
problems.
Uses a variety of
representations and
strategies to solve these
problems.
Uses a limited variety of
representations and strategies to
solve these problems.
2
No
2, 8, 5
Yes
Level 2: Partial Command
Uses ratio and rate reasoning to
solve mathematical problems,
including ratio, unit rate, percent
and unit conversion problems.
Uses a limited variety of
representations and strategies to
solve these problems.
Illustrative Math w/Student Achievement Partners Prototype
Machine-Scorable Assessment Item
Cognitive Complexity
Rate each of the following as: low, moderate, or high. Explain.
Lin rode a bike 20 miles in 150 minutes. If she rode at a constant
speed,
a. How far did she ride in 15 minutes?
20 miles in 150 minutes, divide each by 10, so 2 miles in 15
minutes
or
1 mile in 7.5 minutes, so 2 miles in 15 minutes.
b. How long did it take her to ride 6 miles?
20 mi
6 mi
, x  45 min

150 min
x
or
She rides
7.5
150 min
min
which is 7.5
, so it would take her
20 mi
mi
min
 6 mi  45 min
mi
c. How fast did she ride in miles per hour?
2 mi
x mi
8 mi
mi

; x
8
15 min 60 min
60 min
hr
or
If she rides 2 miles in 15 minutes, then she can ride 8 miles in 60
minutes which is the same as 1 hour.
d. What was her pace in minutes per mile?
min
7.5
mi
Mathematical Content: moderate
requires students to attend to both ratios 20/150 and 150/20 and both
associated unit rates 20/150 and 150/20 that are implicit in the given
context
Mathematical Practice: moderate
MP.6 – attend to precision
cognitive load associated with making sense of units in proportional
relationships is heavy
Processing Demand: low
simple short stem
Stimulus Material: low
no stimulus material
Response Mode: low
students type in numerical answers only
Ty’s Elevator Ride: Illustrative Math w/Student Achievement Partners Prototype Machine-Scorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
6.RP.1 Understand the concept of a ratio and use ratio language i) Expectations for ratios in this grade are
2
No
to describe a ratio relationship between two quantities.
limited to ratios of positive whole
For example, “The ratio of wings to beaks in the bird
numbers. (Cf. footnote, CCSS p. 42.)
house at the zoo was 2:1, because for every 2 wings
there was 1 beak.” “For every vote candidate A
received, candidate C received nearly three votes.”
6.RP.2 Understand the concept of a unit rate a/b associated
i) Expectations for unit rates in this grade
2
No
with a ratio a:b with b≠0, and use rate language in the
are limited to non-complex fractions. (See
context of a ratio relationship. For example, “This
footnote, CCSS p 42.)
recipe has a ratio of 3 cups of flour to 4 cups of sugar,
so there is 3/4 cup of flour for each cup of sugar.” “We
paid $75 for 15 hamburgers, which is a rate of $5 per
hamburger.”
Level 5: Distinguished Command
Uses ratio and rate reasoning to
solve real-world and mathematical
problems, including ratio, unit rate
percent and unit conversion
problems.
Addressed Portion of the PLDs: Grade 6, Sub-claim A, Ratios
Level 4: Strong Command
Level 3: Moderate Command
Uses ratio and rate
Uses ratio and rate reasoning to
reasoning to solve realsolve real-world and
world and mathematical
mathematical problems, including
problems, including ratio,
ratio, unit rate, percent and unit
unit rate, percent and unit
conversion problems.
conversion problems.
Level 2: Partial Command
Uses ratio and rate reasoning
to solve mathematical
problems, including ratio, unit
rate, percent and unit
conversion problems.
Illustrative Math w/Student Achievement Partners
Prototype Machine-Scorable Assessment Item
Cognitive Complexity
Rate each of the following as: low, moderate, or high. Explain.
Ty took the escalator to the second floor. The escalator is 12
meters long, and he rode the escalator for 30 seconds. Which
statements are true? Select all that apply.
a. He traveled 2 meters every 5 seconds. True
12 m
2m

30 sec 5 sec
b. Every 10 seconds he traveled 4 meters. True
12 m
4m

30 sec 10 sec
c. He traveled 2.5 meters per second. False
12 m
2.5 m

30 sec 1 sec
d. He traveled 0.4 meters per second. True
12 m
m
 0.4
30 sec
sec
e. Every 25 seconds, he traveled 7 meters. False
12 m
7m

30 sec 25 sec
f. None of the above. False
Mathematical Content: moderate
more complex than it appears; the distractors are placed in a
particular order; students might choose (c) after correctly choosing
(a) because they look similar; the three correct answers are
purposely interrupted by an incorrect choice, and (e) is included for
students who subtract rather than divide
Mathematical Practice: moderate
MP.6-attend to precision
the cognitive load associated with making sense of units in
proportional relationships is heavy
Processing Demand: low
simple short stem
Stimulus Material: low
no stimulus material
Response Mode: low
students select all that apply
Molly’s Run: Illustrative Math w/Student Achievement Partners Prototype Machine-Scorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
7.RP.1 Compute unit rates associated with ratios of fractions,
i) Tasks have a context.
2, 6, 4
Yes
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.
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command Level 3: Moderate Command
Analyzes and uses proportional
Analyzes and uses
Analyzes and uses
relationships to solve real-world and
proportional relationships to proportional relationships to
mathematical problems, including
solve real-world and
solve real-world and
multi-step ratio/percent problems.
mathematical problems,
mathematical problems,
including multi-step
including simple ratio/percent
ratio/percent problems.
problems.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of
quantities associated with
ratios of fractions.
Computes unit rates of
quantities associated with
ratios of fractions.
Level 2: Partial Command
Uses proportional relationships
to solve real-world and
mathematical problems,
including simple ratio/percent
problems.
Computes unit rates of
quantities associated with ratios
of fractions.
Illustrative Math w/Student Achievement Partners
Prototype Machine-Scorable Assessment Item
2
Molly ran of a mile in 8 minutes. If Molly runs at that speed,
3
how long will it take her to run one mile? [_____]
2
mi
1 mi
3

8 min
x
x  12 min
Cognitive Complexity
Rate each of the following as: low, moderate, or high. Explain.
Mathematical Content: low
a straight-forward extension of the work in 6th grade; the only
difference is that students now work with ratios defined by fractions
rather than just whole numbers, thus, this task in not mathematically
complex except for students who still struggle with fractions
Mathematical Practice: low
none
or
8 min
min
 12
, so 12 min
2
mi
mi
3
or
2
1
mile in 8 minutes; needs to go mile more to go 1 miles total;
3
3
1 1
2
1
since is of mile, it will take of 8 minutes more time, so
3 2
3
2
4 more minutes for a total of 12 minutes.
Processing Demand: low
simple short stem
Stimulus Material: low
no stimulus material
Response Mode: low
students type in numerical answers only
Spicy Vegetables: PARCC prototype (Dana Center)
ES Key
Evidence Statement Text
Clarifications
7.RP.1 Compute unit rates associated with ratios of fractions,
i) Tasks have a context.
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
MP
2, 6, 4
Calculator
Yes
miles per hour,
equivalently 2 miles per hour.
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command Level 3: Moderate Command
Analyzes and uses proportional
Analyzes and uses
Analyzes and uses proportional
relationships to solve real-world and
proportional relationships to relationships to solve real-world
mathematical problems, including
solve real-world and
and mathematical problems,
multi-step ratio/percent problems.
mathematical problems,
including simple ratio/percent
including multi-step
problems.
ratio/percent problems.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of
quantities associated with
ratios of fractions.
Computes unit rates of
quantities associated with ratios
of fractions.
Level 2: Partial Command
Uses proportional relationships
to solve real-world and
mathematical problems,
including simple ratio/percent
problems.
Computes unit rates of
quantities associated with
ratios of fractions.
PARCC prototype (Dana Center)
Cognitive Complexity
Rate each of the following as: low, moderate, or
high. Explain.
Mathematical Content: low/moderate
students must use proportional reasoning with
fractions rather than simple reliance on rules; they
must reason about how the quantities relate to a
specified whole
Mathematical Practice: low
none
2
1
2
1
4
6
3
1
1
2
1
1
2
4
2
1
2
1
2
Processing Demand: moderate
lengthy stem but no difficult words or phrases
Stimulus Material: low
the text provides the information and answers are in a
single table
Response Mode: low
students type in numerical answers only
Mrs. Baca’s Art Class: Illustrative Math w/Student Achievement Partners Prototype Machine-Scorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
7.RP.2a Recognize and represent proportional relationships
i) Tasks have “thin context” or no context.
2, 5
Yes
between quantities.
ii) Tasks may offer opportunities for
a. Decide whether two quantities are in a proportional
students to investigate a relationship by
relationship, e.g., by testing for equivalent ratios in a
constructing graphs or tables; however,
table or graphing on a coordinate plane and observing
students can opt not to use these tools.
whether the graph is a straight line through the origin.
iii) Tasks are not limited to ratios of whole
numbers.
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command Level 3: Moderate Command
Level 2: Partial Command
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including multistep ratio/percent problems.
Analyzes and uses proportional
relationships to solve real-world
and mathematical problems,
including multi-step
ratio/percent problems.
Analyzes and uses proportional
relationships to solve real-world
and mathematical problems,
including simple ratio/percent
problems.
Uses proportional relationships to
solve real-world and mathematical
problems, including simple
ratio/percent problems.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of
fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Decides whether two quantities are in a
proportional relationship and identifies
the constant of proportionality (unit rate)
in tables, equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities
are in a proportional relationship
and identifies the constant of
proportionality (unit rate) in
tables, equations, diagrams,
verbal descriptions and graphs.
Decides whether two quantities
are in a proportional relationship
and identifies the constant of
proportionality (unit rate) in
tables, equations, diagrams,
verbal descriptions and graphs.
Decides whether two quantities are
in a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Represents proportional relationships by
equations and uses them to solve
mathematical and real-world problems,
including multi-step ratio and percent
problems.
Represents proportional
relationships by equations and
uses them to solve mathematical
and real-world problems,
including multi-step ratio and
percent problems.
Represents proportional
relationships by equations and
uses them to solve mathematical
and real-world problems,
including simple ratio and percent
problems.
Uses equations representing a
proportional relationship to solve
simple mathematical and realworld problems, including simple
ratio and percent problems.
Illustrative Math w/Student Achievement Partners
Prototype Machine-Scorable Assessment Item
The students in Ms.Baca’s art class were mixing yellow and blue paint. She told
them that two mixtures will be the same shade of green if the blue and yellow
paint are in the same ratio. The table show the different mixtures of paint that the
students made.
Amount of Yellow Paint (cups)
Amount of Blue Paint (cups)
A
0.5
0.75
B
1
2
C
1.5
3
D
2
3
E
3
4.5
1
2
0.5 50 2
1
1.5 1
2
3
6 2
A : 2  or

 ; B: ; C:
 ; D: ; E:
 
3 3
0.75 75 3
2
3
2
3
4.5 9 3
4
a. How many different shades of paint did the students make? 2
b. Which mixture(s) make the same shade as mixture A? D & E
c. How many cups of yellow paint would a student add to one cup of blue paint to
2
make a mixture that is the same shade as mixture A?
3
d. Let b represent the number of cups of blue paint and y represent the number of
cups of yellow paint in a paint mixture. Write an equation that shows the
relationship between the number of cups of yellow paint, y, and the number of
2
cups of blue paint, b, in mixture E. y  b
3
Cognitive Complexity
Rate each of the following as: low, moderate, or
high. Explain.
Mathematical Content: low/moderate
students must work with ratios of whole numbers and
common decimals between 0-5; ratios involving only whole
numbers were introduced in the 6th grade; additionally, this
task addresses the transition between working with ratios in
isolation to thinking of ratios as defining proportional
relationships
Mathematical Practice: moderate
MP.1-Make sense of the problem and persevere in solving it
while it is possible that students have thought about what
makes one paint mixture the same shade as another, it is
unlikely they have thought about this from a mathematical
perspective
MP.7-look for and make use of structure
convert all five ratios into unit ratios and then group the
ratios that have the same unit ratio; find equivalent ratios
with the same amount of one kind of paint or the same total
amount of paint
MP.2-reaosn abstractly and quantitatively
decontextualize and contextualize
Processing Demand: low/moderate
there are three sentences with approximately 50 words; two
of the sentences are simple, and the other is conditional; the
first two questions are simple while the third is more
complex (29 words); the set up and question in Part D is
longer than the stem (approximately 60 words); there are
not unfamiliar words in the stem (mixture and represent are
Grade 4 words and relate is Grade 6
Stimulus Material: low
the text describes the ideas about paint ratios and the
information in the table organizes ten amounts into the five
ratios that the student must consider; there is no extraneous
information in the stem
Response Mode: low
students select their answers from drop-down menus, so it is
not complex
Buying Bananas: Illustrative Math w/Student Achievement Partners Prototype Machine-Scorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
7.RP.2a
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.
7.RP.2c
Recognize and represent proportional relationships between
quantities.
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 total the total cost and
the number of items can be expressed as t  pn.
i) Tasks have “thin context” or no context.
ii) Tasks may offer opportunities for students to
investigate a relationship by constructing graphs or
tables; however, students can opt not to use these
tools.
iii) Tasks are not limited to ratios of whole
numbers
i) Tasks have a context
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command
Level 3: Moderate Command
2, 5
Yes
2, 8
No
Level 2: Partial Command
Analyzes and uses proportional relationships
to solve real-world and mathematical
problems, including multi-step ratio/percent
problems.
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including
multi-step ratio/percent problems.
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including
simple ratio/percent problems.
Uses proportional relationships to
solve real-world and
mathematical problems, including
simple ratio/percent problems.
Computes unit rates of quantities associated
with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Decides whether two quantities are in a
proportional relationship and identifies the
constant of proportionality (unit rate) in
tables, equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities are in
a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities are in
a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities
are in a proportional relationship
and identifies the constant of
proportionality (unit rate) in
tables, equations, diagrams,
verbal descriptions and graphs.
Interprets a point (x, y) on the graph of a
proportional relationship in terms of the
situation, with special attention to the points
(0, 0) and (1, r) where r is the unit rate.
Interprets a point (x, y) on the graph of
a proportional relationship in terms of
the situation, with special attention to
the points (0, 0) and (1, r) where r is
the unit rate.
.
Interprets a point (x, y) on the
graph of a proportional relationship
in terms of the situation, with
special attention to the points (0, 0)
and (1, r) where r is the unit rate.
Illustrative Math w/Student Achievement Partners
Prototype Machine-Scorable Assessment Item
1
Carlos bought 6 pounds of bananas for $5.20.
2
a. What is the price per pound of the bananas that Carlos
bought?[_____]
$5.20 $0.80

; $0.80
6.5 lbs
lbs
b. What quantity of bananas would one dollar buy?[_____]
pounds
$0.80 $1
5
 ; x  lbs
1 lb
x
4
c. Which of the points in the coordinate plane shown below
correspond to a quantity of bananas that cost the same price
per pound as the bananas Carlos bought? (Select all that
apply.)
i. A
ii. B
iii. C
iv. D
v. (10.4, 13)
vi. (13, 10.4)
vii.There is not
enough information
to determine this.
Cognitive Complexity
Rate each of the following as: low, moderate, or high. Explain.
Mathematical Content: moderate/high
Part (c) assesses students’ understanding of proportional relationships on two
different levels. Concretely, it asks them to recognize that 13 pounds of bananas
for $10.40 is proportional to 6.5 pounds of bananas for $5.20, which can be
determined without thinking about the geometric representation of proportional
relationships; however, for students to recognize that C and D are also in the
same proportional relationship, they must be able to draw on the fact that
quantities that are in a proportional relationship determine a line through the
origin.
Mathematical Practice: moderate
MP.1-make sense of problems and persevere in solving them
students will have very likely been to the grocery store and bought items that
cost a certain price per pound, but it is unlikely they will have seen his kind of
information represented graphically outside of math class; furthermore, the
number of different lines represented in the coordinate plane will likely be an
unfamiliar setup for students and there are lines that present relationships that
would be difficult to make sense in context which means that students will need
to decide which lines do make sense and what they mean as well as which ones
do not.
MP. 2-reason abstractly and quantitatively
in part c, students must recognize that points C and D correspond to bananas that
have the same cost per pound
MP.6-attend to precision
students need to specify the units in part a and attend carefully to the way the
axes are labeled in part c
Processing Demand: moderate
the question contains a complex sentence as well as a more complex
mathematical request
Stimulus Material: moderate
student must connect a verbal description of a context to a graphical
representation of the relationship described; the distractors in the graph make it
moderately complex; students typically see one or at most two graphs on the
same coordinate plane; there is no extraneous information in the stem
Response Mode: low;
students type in the answers for the first two and select all that apply for the third
(a variant of the familiar multiple choice); this interface is not complex
Lines and Proportional Relationships: PARCC Sample Item
ES Key
Evidence Statement Text
Clarifications
7.C.4
Base explanations/reasoning on a coordinate plane
none
diagram (whether provided in the prompt or constructed
by the student in her response).
Content Scope: Knowledge and skills articulated in
7.RP.A
MP
2, 3,
5, 6
Calculator
Yes
Addressed Portion of the PLDs: Grade 7, Sub-C, Concrete Referents and Diagrams (7.C.4)
Level 5: Distinguished Command Level 4: Strong Command
Level 3: Moderate Command
Level 2: Partial Command
Clearly constructs and communicates a
complete response based on concrete
referents provided in the prompt or
constructed by the student such as
diagrams that are connected to a written
(symbolic) method, number line diagrams
or coordinate plane diagrams, including:

a logical approach based on a
conjecture and/or stated assumptions

a logical and complete progression of
steps
precision of calculation
correct use of grade-level vocabulary,
symbols and labels





complete justification of a conclusion
generalization of an argument or
conclusion
evaluating, interpreting and critiquing
the validity and efficiency of other’s
responses, approaches, conclusions
and reasoning, and providing a
counter-example where applicable.
Clearly constructs and
communicates a complete
response based on concrete
referents provided in the prompt
or constructed by the student
such as: diagrams that are
connected to a written
(symbolic) method, number line
diagrams or coordinate plane
diagrams, including:
 a logical approach based on
a conjecture and/or stated
assumptions
 a logical and complete
progression of steps
 precision of calculation
 correct use of grade-level
vocabulary, symbols and
labels
 complete justification of a
conclusion
Constructs and communicates an
incomplete response based on concrete
referents provided in the prompt or in
simple cases, constructed by the
student such as: diagrams that are
connected to a written (symbolic)
method, number line diagrams or
coordinate plane diagrams, including:
Constructs and communicates an
incomplete response based on
concrete referents provided in the
prompt such as: diagrams, number
line diagrams or coordinate plane
diagrams, which may include:

a logical approach based on a
conjecture and/or stated
assumptions
a logical, but incomplete,
progression of steps
minor calculation errors
some use of grade-level
vocabulary, symbols and labels


partial justification of a conclusion



evaluating the validity of other’s
approaches and conclusions.
evaluating, interpreting
and critiquing the validity
of other’s responses,
approaches, conclusions
and reasoning.






a faulty approach based on a
conjecture and/or stated
assumptions
an illogical and incomplete
progression of steps
major calculation errors
limited use of grade-level
vocabulary, symbols and labels
partial justification of a
conclusion
PARCC Sample Item (3 point task)
Part A
Each row of the table identifies a line containing a pair of points. Indicate whether each
line represents a proportional relationship between x and y.
Be sure to indicate whether each line represents a proportional relationship or not by
selecting the appropriate box in the table.
Line
Proportional
Relationship
Not a Proportional
Relationship
Line 1 containing (1, 3) and (2, 3)
Line 2 containing (1, 2) and (2, 4)
Line 3 containing (3, 1) and (6, 2)
Line 4 containing (0, 2) and (5, 4)
Line 5 containing (4, 4) and (5, 5)
Part B
For the lines in Part A that do not represent a proportional relationship, explain why they
do not.
Lines 1 and 4 do not represent a proportional relationship because in both lines, the x and y
values of the two given points are in different ratios. (Or, another valid response, such as,
the lines do not contain the origin.)
For each line in Part A that does not represent a proportional relationship, describe how
you would change the coordinates of one of the two given points on the line to create a
proportional relationship.
For line 1 to become a proportional relationship, either:
 the second point can be changed so that its y-coordinate is 3 times its x-coordinate
1 
(solutions include, but are not limited to (0, 0); (2, 6); (3, 9); and  , 1  OR
3 
3
 the first point can be changed so that its y-coordinate is
of its x-coordinate
2
(solutions include, but are not limited to (0, 0); (4, 6); (6, 9); and (1, 1.5).
For line 4 to become a proportional relationship, the only option is to change the first point,
because it is on the y-axis
4
 The first point can be changed so that its y-coordinate is
of its x-coordinate
5
5 
(solution include, but are not limited to (0, 0); (10, 8); (15, 12); and  , 1  .
4 
Cognitive Complexity
Rate each of the following as: low, moderate,
or high. Explain.
Mathematical Content: moderate
this conceptual understanding task illustrates
how students can test for equivalent ratios using
a graphing tool and explain their reasoning with
precision required at Grade 7; students first show
that they understand proportional relationships
by deciding whether five lines are proportional;
if they wish, there is graphing technology
available that they could use to expedite the
process; then students confirm their
understanding by explaining how the two lines
that do not represent proportional relationships
could be changed so that they become
proportional relationships; there are an infinite
number of possible points that could satisfy this
requirement and students must justify their new
points using correct mathematical descriptors
Mathematical Practice: moderate
MP.3-Consturct viable arguments and critique
the reasoning of others and MP.6-Attend to
precisions
students are asked to explain how to make the
non-proportional relationships into proportional
relationships; the rubric requires students to use
precise language in order to receive full credit for
Part B; students who use the graphing tool
(MP.5) may look for structure to expedite the
analysis of the five lines in Part A (MP.7)
Processing Demand: moderate
complex sentences as well as a more complex
mathematical request
Stimulus Material: moderate
table with an online tool
Response Mode: moderate
multiple response modes including a
combination of selected responses and short
constructed responses
Speed: PARCC prototype (Dana Center)
ES Key
Evidence Statement Text
Clarifications
7.RP.2b Recognize and represent proportional relationships
i) Pool should contain tasks with and
between quantities.
without context.
b. Identify the constant of proportionality (unit rate) in
ii) Tasks sample equally across the listed
tables, graphs, equations, diagrams, and verbal
representations (graphs, equations,
descriptions of proportional relationships.
diagrams, and verbal descriptions).
Level 5: Distinguished Command
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 4: Strong Command
Level 3: Moderate Command
MP
2, 8, 5
Calculator
No
Level 2: Partial Command
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including multistep ratio/percent problems.
Analyzes and uses proportional
relationships to solve realworld and mathematical
problems, including multi-step
ratio/percent problems.
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including
simple ratio/percent problems.
Uses proportional relationships to
solve real-world and mathematical
problems, including simple
ratio/percent problems.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of
quantities associated with
ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Decides whether two quantities are in a
proportional relationship and identifies
the constant of proportionality (unit rate)
in tables, equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities
are in a proportional
relationship and identifies the
constant of proportionality
(unit rate) in tables, equations,
diagrams, verbal descriptions
and graphs.
Decides whether two quantities are
in a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities are in
a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Interprets a point (x, y) on the graph
of a proportional relationship in terms
of the situation, with special attention
to the points (0, 0) and (1, r) where r
is the unit rate.
Interprets a point (x, y) on
the graph of a proportional
relationship in terms of the
situation, with special
attention to the points (0, 0)
and (1, r) where r is the unit
rate.
Interprets a point (x, y) on the
graph of a proportional relationship
in terms of the situation, with
special attention to the points (0,
0) and (1, r) where r is the unit
rate.
Compares proportional relationships
given in different forms (tables,
equations, diagrams, verbal, graphs).
PARCC prototype (Dana Center)
The speed of an object is defined as the change in distance divided by the change in time.
Information about objects A, B, C, and D are shown. Objects C and D both have constant
speed.
Cognitive Complexity
Rate each of the following as: low, moderate, or high.
Explain.
Mathematical Content: low/moderate
students must read unit rates from both a table and a
graph as stated in the standard but in context of the
situation
Mathematical Practice: moderate
MP.2-reason abstractly and quantitatively
students must relate the graphs and tables to each
other via the unit rate and then to the context
Processing Demand: moderate
stem is over 25 words long; definition of speed is
provided
Stimulus Material: moderate
information is provided verbally, graphically, and
numerically in a table and a drag and drop tool is used
Response Mode: :low
students drag and drop objects in correct order
Based on the information given, drag and drop the object names in order from greatest
100 m 600 m
speed to least speed in the table provided.
Object A:
;

5 sec
30 sec
A
Object B:
100 m 300 m

10 sec 30 sec
Object C:
10 m 100 m
;

3 sec 30 sec
Object D:
20 m 200 m

3sec 30 sec
B
D
C
Robot Races: Illustrative Math w/Student Achievement Partners Prototype Machine-Scorable Assessment Item
ES Key
Evidence Statement Text
Clarifications
MP
Calculator
7.RP.2d Recognize and represent proportional relationships
i) Tasks require students to interpret a
2, 4
No
between quantities.
point ( x, y ) on the graph of a proportional
d. Explain what a point ( x, y ) on the graph of a
relationship in terms of the situation, with
proportional relationship means in terms of the
special attention to the points (0, 0) and
situation, with special attention to the points (0, 0) and
(1, r ) where r is the unit rate.
(1, r ) where r is the unit rate.
Level 5: Distinguished Command
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 4: Strong Command
Level 3: Moderate Command
Level 2: Partial Command
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including multistep ratio/percent problems.
Analyzes and uses proportional
relationships to solve real-world
and mathematical problems,
including multi-step ratio/percent
problems.
Analyzes and uses proportional
relationships to solve real-world and
mathematical problems, including simple
ratio/percent problems.
Uses proportional relationships to
solve real-world and mathematical
problems, including simple
ratio/percent problems.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of
fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Computes unit rates of quantities
associated with ratios of fractions.
Decides whether two quantities are in a
proportional relationship and identifies the
constant of proportionality (unit rate) in
tables, equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities
are in a proportional relationship
and identifies the constant of
proportionality (unit rate) in
tables, equations, diagrams,
verbal descriptions and graphs.
Decides whether two quantities are in a
proportional relationship and identifies the
constant of proportionality (unit rate) in
tables, equations, diagrams, verbal
descriptions and graphs.
Decides whether two quantities are in
a proportional relationship and
identifies the constant of
proportionality (unit rate) in tables,
equations, diagrams, verbal
descriptions and graphs.
Interprets a point (x, y) on the graph of a
proportional relationship in terms of the
situation, with special attention to the
points (0, 0) and (1, r) where r is the unit
rate.
Interprets a point (x, y) on the
graph of a proportional
relationship in terms of the
situation, with special attention to
the points (0, 0) and (1, r) where r
is the unit rate.
.
Interprets a point (x, y) on the graph of a
proportional relationship in terms of the
situation, with special attention to the
points (0, 0) and (1, r) where r is the unit
rate.
Illustrative Math w/Student Achievement Partners
Cognitive Complexity
Prototype Machine-Scorable Assessment Item
After the race, Carli drew the graphs shown below to represent the distance, in Rate each of the following as: low, moderate, or high.
meters, that each of three robots A, B, and C traveled after seconds.
Explain.
Mathematical Content: moderate
students are introduced to constant speed in 6th grade but they are
not asked to interpret graphs that represent objects moving at a
constant speed until 7th grade; the first option under part a reflects
a common student error where they interpret graphs as position
graphs even when they aren’t; correctly interpreting the point on
the graph and computing the unit rate are straight-forward
applications of the math described in 7.RP.A and comparing the
speeds in part b is only slightly more complex
Mathematical Practice: low
none
a. Which of the following statements about Robot B are true? (Select all that
apply.)
m
7.5 m
m
2m
m
Robot A: 5
; Robot B:
; Robot C:
 1.5
 0.4
5 sec
sec
5 sec
sec
sec
i. Robot B traveled in a different direction than the other two robots. False
ii. Robot B traveled 5 meters in 7.5 seconds. False
iii. Robot B traveled 7.5 meters in 5 seconds. True
2
iv. Robot B traveled meters per second. False
3
3
v. Robot B traveled meters per second. True
2
vi. None of these are true. False
b. How do the speeds of the robots compare? (Choose one.)
i. The Robots all traveled at the same speed, they just left at different times.
ii. Robot A is the fastest and Robot C is the slowest.
iii. There is not enough information given to compare how fast the robots
traveled.
Processing Demand: low
the context of racing solar-powered robots will not be familiar to
all students, so a brief video clip showing a robot moving at a
constant speed removes some of the linguistic complexity
introduced by making sense of a verbal description in an
unfamiliar context.; the language structure for this task in not
very complex
Stimulus Material: moderate
there is a verbal description of the context and a short video clip
meant to decrease the linguistic complexity, although it increases
the stimulus complexity; students have to connect a verbal
description of a context to a graphical representation of the
relationships described.; the racing setup is meant to help
motivate the graphical representation of the information, although
it increases the complexity in the sense that students could simply
be given the graphs
Response Mode: low
students are asked to select all that apply for the first part, a
variant of the familiar multiple choice, and to choose one and fill
in blanks if they select the correct one; this type of interface is
not complex.
ES Key
7.RP.3-1
Book Reading Rate: PARCC Sample Item
Evidence Statement Text
Clarifications
Use proportional relationships to solve multi-step ratio
problems.
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command Level 3: Moderate Command
Analyzes and uses proportional
Analyzes and uses
Analyzes and uses proportional
relationships to solve real-world and proportional relationships to relationships to solve real-world
mathematical problems, including
solve real-world and
and mathematical problems,
multi-step ratio/percent problems.
mathematical problems,
including simple ratio/percent
including multi-step
problems.
ratio/percent problems.
MP
1, 2, 6
Calculator
Yes
Level 2: Partial Command
Uses proportional relationships
to solve real-world and
mathematical problems,
including simple ratio/percent
problems.
PARCC Sample Item (2 point task)
On Friday, three friends shared how much they read during the week.
 Barbara read the first 100 pages from a 320-page book in the last 4 days.
 Colleen read the first 54 pages from a 260-page book in the last 3 days.
 Nancy read the first 160 pages from a 480-page book in the last 5 days.
Part A
A person’s average reading rate can be defined as the number of pages read divided
by the number of days. Place the three friends’ reading rates in order from greatest to
least by clicking on the names and dragging them to the appropriate boxes.
Greatest Rate
(pages per day)
 160
pages 
 32
Nancy 

day 
 5
 100
pages 
 25
Barbara 

day 
 4
Least Rate
(pages per day)
 54
pages 
Colleen   18

day 
 3
Part B
If the three friends continue to read every day at their rates, who will finish reading
her book first, Second? Third? Order the students from the first one who is predicted
to finish her book to the third one who is predicted to finish her book.
First


 (320  100)pages

 8.8 days 
Barbara 
pages
 25

day


Second


 (480  160)pages

 10.0 days 
Nancy 
pages
 32

day


Third


 (260  54)pages

 11.4 days 
Colleen 
pages
 18

day


Cognitive Complexity
Rate each of the following as: low, moderate, or high. Explain.
Mathematical Content: moderate
this two-point task starts with students engaging in the important
procedural skills of calculating and comparing unit rates; students
take information presented through the context to order the unit
rates from greatest to least; then, students use those rates to solve
an application problem; using ratios to solve problems is a critical
skill for Grade 7 student that builds on their earlier work with
ratios in Grade 6 to set the stage for important Grade 8 work with
functions; the use of technology in this task makes it difficult to
guess the correct answer or use a choice-elimination strategy;
acalculation aid will be available
Mathematical Practice: moderate
this task has some features of Modeling (MP.4) because a
mathematical quantity (pages per day) is being defined to capture
a real-world notion, “reading rate,” that does not come from the
real world with a mathematical definition already associated with
it
Processing Demand: moderate
stem is over 25 words
Stimulus Material: low
single online tool (incremental-drag and drop)
Response Mode: low
multiple selection drag and drop
ES Key
7.RP.3-2
T.V. Sales: PARCC prototype (Dana Center)
Evidence Statement Text
Clarifications
Use proportional relationships to solve multi-step
percent problems. Examples: simple interest, markups
and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.
Addressed Portion of the PLDs: Grade 7, Sub-claim A, Ratios
Level 5: Distinguished Command
Level 4: Strong Command
Level 3: Moderate Command
Analyzes and uses proportional
Analyzes and uses proportional Analyzes and uses proportional
relationships to solve real-world and relationships to solve real-world relationships to solve real-world
mathematical problems, including
and mathematical problems,
and mathematical problems,
multi-step ratio/percent problems.
including multi-step
including simple ratio/percent
ratio/percent problems.
problems.
Represents proportional
relationships by equations and uses
them to solve mathematical and realworld problems, including multi-step
ratio and percent problems.
Represents proportional
relationships by equations and
uses them to solve
mathematical and real-world
problems, including multi-step
ratio and percent problems.
Represents proportional
relationships by equations and
uses them to solve mathematical
and real-world problems,
including simple ratio and
percent problems.
MP
1, 2,
5, 6
Calculator
Yes
Level 2: Partial Command
Uses proportional
relationships to solve realworld and mathematical
problems, including simple
ratio/percent problems.
Uses equations representing
a proportional relationship
to solve simple
mathematical and realworld problems, including
simple ratio and percent
problems.
PARCC prototype (Dana Center)
A store is advertixing a sale with 10% off all items in the store. Sales tax is 5%.
A 32-inch television is regularly priced at $295.00. What is the total price of the
television, including sales tax, if it was purchased on sale? Round your answer to the
nearest cent.
$295  $29.5  $265.50; $265.50(1.05)  $278.78
Cognitive Complexity
Rate each of the following as: low, moderate, or
high. Explain.
Mathematical Content: low
typical multi-step percent problem
Mathematical Practice: : moderate
MP.3-Construct viable arguments and critique
the reasoning of others
students must justify if Adam’s and Brandi’s
processes will both result in the correct answer
using properties of operations
Processing Demand: moderate
stem is over 25 words long
Stimulus Material: moderate;
words and student work
Response Mode: low/moderate;
students type in numerical answers and short
explanation with equation
Yes, both equations simplify to: T  0.945 p