1. science
2. mathematics

Current Developments:
Sample Mathematics Items and Tasks
Being Developed by Smarter Balanced
Item and Performance Task Development
Theory Of Action
and CCSS
Item Piloting,
Alignment, Bias
Review
Large Scale Item
Writing
Content
Specifications
Initial Item Writing
Alignment and
Bias Review
Large Scale
Alignment and
Bias Review
Item and Test
Specifications
Cognitive Labs
and Prototyping
Field Testing and
Scaling
Item and Performance Task Development
• Just started item
development for the pilot
• If the the pilot is 100%
successful than we likely
didn’t reach far enough
• We are planning for change
• Assessments will include
Selected Response,
Constructed Response and
Performance Tasks.
• Any of the above items may
be “technology enhanced”
Smarter Balanced is Building a System,
Not a Test
Formative, Interim or Summative?
Formative, Interim or Summative?
Three frogs sit on a log and
18 flies in the air,
How many flies should each
frog get if each frog gets a
fair share?
Show your work or explain
how you found your answer.
Sixteen frogs sit on a log
and 139 flies in the air,
How many flies should each
frog get if each frog gets a
fair share?
How many flies are still in
the air after each frog
receives an equal number?
Show your work or explain
how you found your answer.
4
Assessment Claims for Mathematics
Overall Claim (Gr. 3-8)
“Students can demonstrate progress toward college and
career readiness in mathematics.”
Overall Claim (High School)
“Students can demonstrate college and career readiness in
mathematics.”
Concepts and Procedures
“Students can explain and apply mathematical concepts
and interpret and carry out mathematical procedures with
precision and fluency.”
Problem Solving
“Students can solve a range of complex well-posed problems in
pure and applied mathematics, making productive use of
knowledge and problem solving strategies.”
Communicating Reasoning
“Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique
the reasoning of others.”
Modeling and Data
Analysis
“Students can analyze complex, real-world scenarios and
can construct and use mathematical models to interpret
and solve problems.”
Assessment Claims for Mathematics
Overall Claim
(Gr. 3-8)
Overall Claim
“Students can demonstrate
progress toward college and
career readiness in
mathematics.”
“Students can demonstrate
college and career readiness
(High School)
Overall Claim (High in mathematics.”
School)
Modeling and Data
Analysis
Mathematics Claim 1
Overall Claim (Gr.
3-8)
Concepts and
Procedures
Students can explain and
apply mathematical
concepts and interpret and
carry out mathematical
procedures with precision
and fluency.”
Claim 1: Concepts and Procedures
Technology Enhanced (Grades 3 – 5)
The
numbers
0
and
3/5
are
shown
on
the
number
line.
Put
a
point
on
the
line
to
represent
the
number
1.
0
3/5
Claim 1: Concepts and Procedures
Technology Enhanced (Grades 5 – 7)
1 2/7 - 5 3/8 = ?
Enter a key
sequence to
perform this
operation on
the calculator.
Assessing Fluency
• 
• 
The standards require speed and accuracy in
calculation.
Fluency is called for explicitly in certain standards.
Grade
Standard
K
K.OA.5
Add/subtract
within
5
1
1.OA.6
2.OA.2
Add/subtract
within
10
Add/subtract
within
20
(know
single‐digit
sums
from
memory)
2.NBT.5
3.OA.7
Add/subtract
within
100
MulKply/divide
within
100
(know
single‐digit
products
from
memory)
4
3.NBT.2
4.NBT.4
Add/subtract
within
1000
Add/subtract
within
1,000,000
5
5.NBT.5
6
6.NS.2,3
MulK‐digit
mulKplicaKon
MulK‐digit
division
2
3
Required
Fluency
MulK‐digit
decimal
operaKons
10
MeeKng
DraQ
‐
05/29/12
Assessing Fluency
(Grade 3)
Mark each equation True or False.
Standards
Addressed:
____
3 x 8 = 10 + 10 + 4
3.OA.7
Mul:ply/divide
within
100
____
6 x 2 = 15 – 3
2.OA.2
Fluently
add
and
subtract
within
20
using
mental
strategies.
By
end
of
Grade
2,
know
from
memory
all
sums
of
two
one‐digit
numbers.
____
42 ÷ 7 = 24 ÷ 6
1.OA.7
Understand
the
meaning
of
the
equal
sign,
and
determine
if
equa:ons
involving
addi:on
and
subtrac:on
are
true
or
false.
Claim 1 – Mathematical Practices Still Matter!
How CAT Works (Binet’s Test)
13
Adap:ve
Versioning
of
Items
Easier
than
Level
1
–
Item
mapped
to
5.MD.5a
Level
1
(CCSS
6.G.2)
Mike
is
using
cubes
that
measure
½
inch
on
each
side
to
fill
a
box
that
has
a
height
of
5
½
inches,
width
of
3
inches,
and
length
of
2
½
inches.
How
many
½
inch
cubes
will
Mike
need
to
fill
the
box?
Level
2
(CCSS
6.G.2)
Mike
is
using
cubes
that
measure
¼
inch
on
each
side
to
fill
a
box
that
has
a
height
of
5
¼
inches,
width
of
3
inches,
and
length
of
2
½
inches.
How
many
¼
inch
cubes
will
Mike
need
to
fill
the
box?
Level
3
(CCSS
6.G.2)
Mike
is
using
cubes
that
measure
¾
inch
on
each
side
to
fill
a
box
that
has
a
height
of
5
¼
inches,
width
of
3
¾
inches,
and
length
of
7
½
inches.
How
many
¾
inch
cubes
will
Mike
need
to
fill
the
box?
14
Mathematics Claim 2
Overall Claim (Gr.
3-8)
Problem Solving
“Students can solve a range
of complex well-posed
problems in pure and
applied mathematics,
making productive use of
knowledge and problem
solving strategies.”
Claim 2: Problem Solving
(Grades 9 – 11)
The figure below is made up of a square with
height, h units, and a right triangle with height, h
units, and base length, b units.
The area of this figure is 80 square units.
Write an equation for the height, h, in terms of b.
Show all work necessary to justify your answer.
Mathematics Claim 3
Overall Claim (Gr.
3-8)
Communicating
Reasoning
“Students can clearly and
precisely construct viable
arguments to support their
own reasoning and to
critique the reasoning of
others.”
Claim 3: Communicating Reasoning
Constructed Response (Grades 3 – 5)
A tent is 8 feet by 10 feet. A sleeping bag is 3 feet
by 6 feet. A camper says that 4 sleeping bags will
fit in the tent because 18 + 18 + 18 + 18 = 72. The
tent is 80 square feet, so there is enough space.
a. Is the camper correct? ______________
b. Explain.
Gavin,
M.
K.,
Casa,
T.
M.,
Chapin,
S.,
Copley,
J.
V.,
&
Sheffield,
L.
J.
(2008).
Project
M2:
Using
Everyday
Measures:
Measuring
with
the
Meerkats
from
Project
M2:
Mentoring
Young
MathemaOcians
series.
Claim 3: Communicating Reasoning
Constructed Response (Grades 3 – 5)
Mathematics Claim 4
Overall Claim (Gr.
“Students can analyze
3-8)
complex, real-world
Modeling and Data scenarios and can construct
and use mathematical
Analysis
models to interpret and
solve problems.”
Claim 4: Modeling and Data Analysis
(Grades 8 – 11)
Great white sharks are about 12 to 16 feet
long on average. How many great white
sharks laid end-to-end would surround the
circumference of Earth?
The volume of the earth is approximately
10.83 x 1011 km3. 5 km ≈ 3.1 miles.
A Sample High School
Performance Task:
“What is the Cost of Speeding?”
Sample Task Stimulus
Stimulus/Information Source for Task
Massachusetts
(http://www.sudbury.ma.us/services/individual_faq.asp?id=69)
The initial 10MPH over the speed limit is assessed a $50 fine. In
other words, there is a flat fee for the first 10MPH. Each MPH
above the initial 10MPH is then calculated at $10 per MPH
thereafter. In addition to the fines established relative to the speed
traveled, there is a $50 assessment applied to the fine schedule
which goes to a Head Injury Fund established by the state.
Example: 46MPH in a 30MPH zone = 16MPH over the speed limit
Fine = $50 Head Injury Fund assessment + $50 (first 10MPH over
the speed limit) + $60 (next 6MPH) = $160
Sample Task Stimulus (cont.)
How the Classroom-Based Portion
Supports Accessibility to the Task
• 
• 
• 
Teacher clarifies some of the everyday and
mathematical language in the task (e.g., Head
Injury Fund Assessment, mph)
Teacher presents different ways that “speed zones”
are marked (e.g., by showing visuals of the signs
used to indicate allowable speeds and discussing
what they mean) and relate this to the information
presented in the stimuli
Teacher demonstrates a simpler version of a
speeding ticket cost function to ensure even
understanding of the variables that students will
encounter
Student Products
•  Develop graphical and tabular
representations of speeding costs in MA
•  Determine which representation is most
effective and explain why
•  Compare the MA method of assigning
tickets to the NY method
•  Develop a “more fair” system for
assigning tickets in NY based on given
constraints
Contextually Linked Item
The function f(x) = 5(x – 65) + 120 is used to
calculate a speeding ticket for a driver going
x mph in a 65 mph speed zone.
Explain what the difference (x – 65) means
in the context of this problem.
Contextually Linked Item
The function f(x) = 5(x – 65) + 120 is used
to calculate a speeding ticket for a driver
going x mph in a 65 mph speed zone.
If the “5” in the function is changed to “4”
and the “120” is changed to “180,” for
what values of x would ticket costs be
greater than before the change?
Contextually Linked Item
Ticket
Cost
800
700
600
500
400
300
200
100
0
MPH
Over
Limit
The graph shows the relationship between the number of miles over the speed limit
a person is traveling and the cost of a speeding ticket.
Explain how the graph supports or refutes the statement below:
“As driving speeds become more reckless, the penalties are more severe.”
English Language Arts Items
Assessment Claims for ELA
Overall Claim (Gr. 3-8)
“Students can demonstrate progress toward college and
career readiness in English language/Arts.”
Overall Claim (High School)
“Students can demonstrate college and career readiness in
English language/Arts.”
Reading
“Students can read closely and analytically to comprehend
a range of increasingly complex literary and informational
texts”
Writing
Speaking/Listening
Research
“Students can produce effective and well-grounded writing for a
range of purposes and audiences.”
“Students can employ effective speaking and listening
skills for a range of purposes and audiences”
“Students can engage in research/inquiry to investigate
topics, and to analyze, integrate, and present information.
Assessment Claims for ELA
Overall Claim (Gr.
3-8)
Overall Claim
“Students can demonstrate
progress toward college and
career readiness in English
language/Arts.”
“Students can demonstrate
college and career readiness
(High School)
Overall Claim (High in English language/Arts.”
School)
Modeling and Data
Analysis
ELA Claim 1
Overall Claim (Gr.
3-8)
Reading
“Students can read closely
and analytically to
comprehend a range of
increasingly complex literary
and informational texts”
Claim 1: Reading -- Using Supporting
Evidence (Grade 4)
SKmulus
Text…
Rightly Unfair
Janie frowned as Chandra left the room. “What’s wrong, Janie?” Ms.
Simpson asked.
“Every day at 3:00 Chandra’s mother picks her up from school,” Janie
explained. “Even though she gets to go home when class is over, I have
to wait until 3:20 just like everyone else before I’m allowed to leave.”
Ms. Simpson smiled at Janie. “Have you talked with Chandra about it?”
“No,” Janie admitted. “But she should have to wait like everyone else,
no matter what.”
“I think it would be best if you told her how you feel,” Ms. Simpson said.
“Then maybe you’d think differently about the situation.”
Janie kept frowning and sat in her seat until the bell rang at 3:20 and
she left the room. The next day, she sat next to Chandra at lunch.
“So why do you get to leave early every day while the rest of us have
to wait?” Janie asked immediately.
“What?” Chandra asked.
“At 3:00” Janie explained. “Your mom picks you up every day.”
“Oh!” Chandra exclaimed. “My mom gets me early so I can go with her
to read to the kids at the library. Every day from 3:15 until 5:15, kids visit
the library for story time. We read for a half hour to each age group,
three-year-olds, four-year-olds, five-year-olds, and six-year-olds. The kids
love it. I love it, too.”
“Oh, I didn’t know that,” Janie said.
“It’s great to be able to read to the younger kids,” Chandra continued.
“It makes me feel so good to do that for them. I’ll admit, though, it’s not
easy finding interesting stories for them every day. The three-year-olds
get bored very easily.”
“Well, I have a few great stories at home that I read when I was that
age,” Janie said. “Do you want me to give them to you to read to the
kids? I’m sure they would find them interesting. I could bring them to you
tomorrow during lunch.”
“That would be great!” Chandra replied.
“I guess it is fair that you get to leave early,” Janie said. “I never
realized that you had such a good reason.”
Item
Stem:
Read the sentences below. Select a sentence from the
passage that best supports each statement. Drag and drop
the sentence into the box below.
How Janie changes in the story
Janie is jealous in the beginning of the story.
Janie is helpful by the end of the story.
Scoring
Key:
(Note: No text is highlighted in the passage when presented to
students; highlighting is for scoring rules only. Any sentence in the
passage can be selected and dragged into a response block.)
2-Point Response: Student selects any of the first three highlighted
sentences for Block 1 and either of the last two highlighted
sentences for Block 2
1-Point Response: Student selects only one correct sentence –
either for Block 1 or for Block 2
0-Points: Student does not select a correct sentence for Block 1
and for Block 2
ELA Claim 2
Overall Claim (Gr.
3-8)
Writing
“Students can produce
effective and well-grounded
writing for a range of
purposes and audiences.”
Claim 2: Writing – Composing Full Texts
(Grade 6)
Claim 2: Writing – Composing Full Texts
(Grade 6)
Task
Title:
GeneKcally
Modified
Food
(105
total
minutes):
Part
1
(35
minutes):
UlKmately
tasked
with
wriKng
an
argumentaKve
essay
on
geneKcally
modified
food,
students
will
first
view
a
brief
video
explaining
gene:c
modifica:on
and
some
of
the
ways
it
relates
to
food
producKon.
Students
will
then
read
a
text
arguing
for
the
producKon
of
geneKcally
modified
food,
and
view
a
second
video
in
which
several
experts
present
evidence
against
the
producKon
of
geneKcally
modified
food.
Students
will
take
notes
on
both
of
these
sources.
They
will
then
respond
to
three
constructed‐response
items
focused
on
research
skills.
All
work
will
be
completed
independently.
Claim 2: Writing – Composing Full Texts
(Grade 6)
Part
2
(70
minutes):
Students
will
work
individually
to
compose
a
full‐length
argumenta:ve
essay
either
supporKng
or
opposing
the
producKon
of
geneKcally
modified
food,
referring
to
their
notes
as
needed.
Students
will
be
allowed
access
to
the
sources
they
read/viewed
during
Part
1.
Pre‐wriKng,
draQing,
revising,
and
ediKng
will
be
involved.
Scorable
Products:
Student
responses
to
the
research
quesKons
and
the
essay
will
be
scored.
Claim 2: Writing – Composing Full Texts
(Grade 6)
Part
1
Ques>ons
for
Students
to
Respond
to:
1.
Explain
why
most
people
have
strong
feelings
about
geneKcally
modified
food.
Use
details
from
the
sources
to
support
your
answer.
2.
Which
piece
of
informaKon
from
the
arKcle
you
read
could
be
used
as
the
strongest,
most
convincing
supporKng
evidence
for
the
producKon
of
geneKcally
modified
food?
Use
details
from
the
arKcle
to
explain
your
answer.
3.
Which
piece
of
informaKon
from
the
second
video
you
viewed
could
be
used
as
the
strongest,
most
convincing
supporKng
evidence
against
the
producKon
of
geneKcally
modified
food?
Use
details
from
the
video
to
explain
your
answer.
Claim 2: Writing – Composing Full Texts
(Grade 6)
Part
2
Ques>on
for
Students
to
Respond
to:
Your
science
class
is
creaKng
a
website
on
recent
scienKfic
discoveries.
Your
assignment
is
to
write
an
argumentaKve
essay
about
geneKcally
modified
food
for
the
website.
In
the
essay,
you
should
briefly
explain
what
geneKcally
modified
food
is
and
argue
either
for
or
against
its
producKon,
including
specific
details
and
evidence
from
the
sources
you
read/viewed
during
part
1.
The
audience
for
your
essay
will
be
your
teacher
and
classmates,
as
well
as
parents
and
friends
who
visit
the
website
where
your
essay
will
be
published.
ELA Claim 3
Overall Claim (Gr.
3-8)
“Students can employ
effective speaking and
Speaking/Listening listening skills for a range of
purposes and audiences”
ELA Claim 4
Overall Claim (Gr.
3-8)
Research
“Students can engage in
research/inquiry to
investigate topics, and to
analyze, integrate, and
present information.
Keep in Touch
Smarter Balanced can be found online at:
www.smarterbalanced.org