This is the powerpoint presentation presented by Shelbi Cole, Director of Mathematics at Smarter Balanced. Please contact Jill Bessette, April Schultz or Jackie Walsh if you would like to meet for an overview or a PLC session on the contents.

1. Preparing K-5 Students for the Focus,
Coherence and Rigor of the Common Core
State Standards for Mathematics
1
Shelbi K. Cole, Ph.D.
Smarter Balanced Director of Mathematics
September 24, 2013

2. "The world is small now, and we're not just competing
with students in our county or across the state. We
are competing with the world," said Robert Kosicki,
who graduated from a Georgia high school this year
after transferring from Connecticut and having to
repeat classes because the curriculum was so
different. "This is a move away from the time when a
student can be punished for the location of his home
or the depth of his father's pockets."
Excerpt from Fox News, Associated Press. (June 2, 2010) States join to establish 'Common Core' standards for high school graduation.

3. Common Core State Standards
• Define the
knowledge and
skills students need
for college and
career
• Developed
voluntarily and
cooperatively by
states; more than
40 states have
adopted
• Provide clear,
consistent
standards in
English language
arts/literacy and
mathematics
Source: www.corestandards.org

4. What questions will we try to answer today?
• How can teachers plan lessons that take
into account the shifts in the CCSS-M and
meet the needs of all learners?
• How will the new assessment system help
educators understand what students have
learned and how to support their future
learning?
4

5. The Three Shifts:
What do they really mean?
5

6. The Background of the Common Core
Initiated by the National Governors Association
(NGA) and Council of Chief State School Officers
(CCSSO) with the following design principles:
• Result in college and career readiness
• Based on solid research and practice evidence
• Focused, coherent and rigorous
6

7. The CCSSM Requires Three Shifts in Mathematics
• Focus strongly where the
standards focus
• Coherence: Think across
grades and link to major
topics within grades
• Rigor: In major topics,
pursue conceptual
understanding, procedural
skill and fluency, and
application with equal
intensity
7

8. Mathematics
topics
intended at
each grade by
at least two-
thirds of A+
countries
Mathematics
topics
intended at
each grade by
at least two-
thirds of 21
U.S. states
Shift #1: Focus Strongly where the Standards Focus
The shape of math in A+ countries
1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 8

9. 9
Shift #1: Focus
Traditional U.S. Approach
K 12
Number and
Operations
Measurement
and
Geometry
Algebra and
Functions
Statistics and
Probability

10. 10
Grade
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual
Understanding
K–2
Addition and subtraction - concepts, skills, and
problem solving and place value
3–5
Multiplication and division of whole numbers and
fractions – concepts, skills, and problem solving
6
Ratios and proportional reasoning; early expressions
and equations
7
Ratios and proportional reasoning; arithmetic of
rational numbers
8 Linear algebra and linear functions
Shift #1: Focus
Key Areas of Focus in Mathematics

11. Shift #1: Focus
Content Emphases by Cluster
11
The Smarter Balanced Content Specifications help support
focus by identifying the content emphasis by cluster. The
notation [m] indicates content that is major and [a/s] indicates
content that is additional or supporting.

12. 12
Shift #2: Coherence
Think Across Grades, and Link to Major Topics Within
Grades
• Carefully connect the learning within and across
grades so that students can build new
understanding on foundations built in previous
years.
• Begin to count on solid conceptual
understanding of core content and build on it.
Each standard is not a new event, but an
extension of previous learning.

13. Shift #2: Coherence
Think Across Grades
Example: Fractions
“The coherence and sequential nature of mathematics
dictate the foundational skills that are necessary for
the learning of algebra. The most important
foundational skill not presently developed appears to
be proficiency with fractions (including decimals,
percents, and negative fractions). The teaching of
fractions must be acknowledged as critically
important and improved before an increase in
student achievement in algebra can be
expected.”
13
Source: Final Report of the National Mathematics Advisory Panel (2008, p. 18)

14. 14
Shift #2: Coherence
Think Across Grades
4.NF.4. Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number.
5.NF.4. Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a
fraction.
5.NF.7. Apply and extend previous understandings of
division to divide unit fractions by whole numbers and
whole numbers by unit fractions.
6.NS. Apply and extend previous understandings of
multiplication and division to divide fractions by fractions.
6.NS.1. Interpret and compute quotients of fractions, and
solve word problems involving division of fractions by
fractions, e.g., by using visual fraction models and
equations to represent the problem.
Grade 4
Grade 5
Grade 6

15. 15
Shift #2: Coherence
Link to major work within grade
Example: Data
Representation
Standard 3.MD.3

16. Shift #3: Rigor
In Major Topics, Pursue Conceptual Understanding,
Procedural Skill and Fluency, and Application
16
• The CCSSM require a balance of:
 Solid conceptual understanding
 Procedural skill and fluency
 Application of skills in problem solving
situations
• Pursuit of all threes requires equal intensity in
time, activities, and resources.

17. 17
Grade Standard Required Fluency
K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2
2.OA.2
2.NBT.5
Add/subtract within 20 (know single-digit sums
from memory)
Add/subtract within 100
3
3.OA.7
3.NBT.2
Multiply/divide within 100 (know single-digit
products from memory)
Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3
Multi-digit division
Multi-digit decimal operations
Shift #3: Rigor
Required Fluencies for Grades K-6

18. • Students can use appropriate concepts and
procedures for application even when not prompted
to do so.
• Teachers provide opportunities at all grade levels
for students to apply math concepts in “real world”
situations, recognizing this means different things in
K-5, 6-8, and HS.
• Teachers in content areas outside of math,
particularly science, ensure that students are using
grade-level-appropriate math to make meaning of
and access science content.
18
Shift #3: Rigor
Application

19. Resources
• www.achievethecore.org
• http://corestandards.org/assets/Math_Publishers_Criteria_K-
8_Summer%202012_FINAL.pdf
• www.illustrativemathematics.org
• www.pta.org/4446.htm
• commoncoretools.me
• www.corestandards.org
• http://math.arizona.edu/~ime/progressions/#products
• http://www.smarterbalanced.org/k-12-education/common-core-
state-standards-tools-resources/
19

20. Five Basic Characteristics to Support
Quality Mathematics Teaching
• Precision: Mathematical statements are clear and
unambiguous. At any moment, it is clear what is known and
what is not known.
• Definitions: They are the bedrock of the mathematical
structure. They are the platform that supports reasoning. No
definitions, no mathematics.
• Reasoning: The lifeblood of mathematics. The engine that
drives problem solving. Its absence is the root cause of
teaching and learning by rote.
• Coherence: Mathematics is a tapestry in which all the
concepts and skills are interwoven.
• Purposefulness: Mathematics is goal-oriented, and every
concept or skill is therefore a purpose. Mathematics is not
just fun and games.
(Wu, 2011)
20

21. “Just as technicians in any kind of
engineering must have a „feel‟ for their
profession in order to avert disasters in the
myriad of unexpected situations they are
thrust into, mathematics teachers need to
know something about the essence of
mathematics in order to successfully carry
out their duties in the classroom.”
(Wu, 2011)
21

22. 22
Topic 1: Fractions
The Progression Across Grades 3-5

23. Definition of “fraction”
23

24. 3.NF.A Develop understanding of
fractions as numbers.
• On a piece of paper, draw a line segment that is 6
inches long.
• Label the left endpoint 0 and the right endpoint 3.
• Locate and label the numbers 1 and 2 on the
number line with respect to locations of 0 and 3.
• Locate and label the numbers 1/3, 5/3, and 9/3.
If you were doing this with Grade 3 students,
would you change any direction above? What
additional support may be needed? Why?
24

25. 3.NF.A Develop understanding of
fractions as numbers.
• Next, label all fractions with denominator
3 along the part of the number line you
have drawn.
– How many fractions with denominator 3 do
you have labeled?
• Discuss with your table: What parallels
are there between how whole numbers
are introduced in kindergarten and this
introduction to fractions?
25

26. Which standards were addressed in the
activity so far?
• 3.NF.A Develop understanding of fractions as numbers.
• 3.NF.A.1. Understand a fraction 1/b as the quantity formed
by 1 part when a whole is partitioned into b equal parts;
understand a fraction a/b as the quantity formed by a parts of
size 1/b.
• 3.NF.A.2. Understand a fraction as a number on the number
line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size 1/b
and that the endpoint of the part based at 0 locates the
number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the resulting
interval has size a/b and that its endpoint locates the number
a/b on the number line.
26

27. Which aspects of this standard have
been addressed so far?
• 3.NF.A.3. Explain equivalence of fractions in special cases, and
compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the
same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 =
2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by
using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions
that are equivalent to whole numbers. Examples: Express 3 in the
form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same
point of a number line diagram.
d. Compare two fractions with the same numerator or the same
denominator by reasoning about their size. Recognize that
comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with the symbols >, =, or
<, and justify the conclusions, e.g., by using a visual fraction model.
27

28. 28
A Brief Detour
The Parallel Curriculum Model

29. What is the Parallel Curriculum Model?
The Parallel Curriculum Model is a set
of four interrelated designs that can be
used singly, or in combination, to create
or revise existing curriculum units,
lessons, or tasks. Each of the four
parallels offers a unique approach for
organizing content, teaching, and
learning that is closely aligned to the
special purpose of each parallel.

30. The Parallel Curriculum Model
CURRICULUM
OF CONNECTIONS
CURRICULUM OF
PRACTICE
CURRICULUM
OF
IDENTITY
CORE
CURRICULUM

31. Why Four Parallels?
• Qualitatively differentiated
curriculum isn‟t achieved by
doing only one thing or one
kind of thing.
• Students are different.
• Students have different
needs at different times in
their lives.
• Students‟ styles, talents,
interests, environments and
opportunities are different.
• Students have different
levels of expertise.

32. Four Facets of Qualitatively Differentiated
Curriculum
• Core: The essential nature of a discipline
• Connections: The relationships among
knowledge
• Practice: The applications of facts,
concepts, principles, skills, and methods as
scholars, researchers, developers, or
practitioners
• Identity: Developing students‟ interests and
expertise, strengths, values, and character
32

33. Concepts, Principles and Skills
• Concepts: A general idea or
understanding, especially a generalized
idea of a thing or class of things; a
category or classification
• Principles: Fundamental truths, laws,
doctrines, or rules, that explain the
relationship between two or more
concepts
• Skills: Proficiency, ability, or technique,
strategy, method or tool
33

34. Building a CCSS-Aligned Lesson
• Discuss the number line activity.
– How would you implement a similar activity
with students in a grade 3 classroom?
– How can you determine if students are
successful on individual standards while still
building important connections across
standards?
– Should there be something that precedes the
number line activity in introducing fractions to
grade 3 students? If so, what does it look
like?
34

35. Learning from the Group
DON‟T start filling in the lesson template
before hearing the GOOD IDEAS of other
educators working on the SAME THING.
The Common Core State Standards offer
new opportunity for collaboration so that
TOGETHER we can build and gather the
BEST RESOURCES for students.
35

36. Work Time
• Begin to populate the template with some
of the ideas we‟ve heard that represent
important learning opportunities for
students.
• But first, let‟s take a look at the lesson
plan template.
36

37. Increasing Engagement, Thinking Across
Grades
• Grade 1 – 1.OA.A (standards 5&6)
• Grade 2 – 2.MD.B (standards 5&6)
• Grade 3 – 3.NF.A (standard 3)
• Grade 4 – 4.NF.A (standards 1&2)
• Grade 4 – 4.NF.C (standards 5-7)
• Grade 5 – 5.NF.B (standards 3&4)
Create a task or learning opportunity that
relates the content of the indicated standards to
the number line.
Materials allowed: Ruler, Sidewalk chalk
37

38. • And the number line remains relevant
even after grade 5…
38

39. Grade 3
3.NF.A.3b Express whole numbers as fractions, and recognize fractions that are
equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that
6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

40. Grade 7

41. Grade 8

42. Beyond the Number Line: Other
Representations that Support Student
Understanding of Fractions
• What fraction is represented by the
shaded area?
42

43. Notice the use of “represented.” The
shaded area is not “equal” to a fraction.
• The fraction represented by the shaded area
is ¾. Based on this:
– Draw an area that represents ¼.
– Draw an area that represents 1.
• The fraction represented by the shaded area
is equal to 3/2. Based on this:
– Draw an area that represents ½.
– Draw an area that represents 1.
43

44. Linking Operations with Fractions to
Operations with Whole Numbers
“Children must adopt new rules for
fractions that often conflict with well-
established ideas about whole number”
(p.156)
Bezuk & Cramer, 1989
44

45. Fractions Example
The shaded area represents 3/2. Drag the figures below to
make a model that represents 3 x 3/2.
BA C D

46. Slide 46
Student A drags three of shape B, which is equal in area to the shaded region. This
student probably has good understanding of cluster 5.NF.B he knows that 3 x 3/2 is
equal to 3 iterations of 3/2. Calculation of the product is not necessary because of the
sophisticated understanding of multiplication.
Apply and extend previous understandings of multiplication and division to multiply
and divide fractions.

47. Slide 47
Student B reasons that 3 x 3/2 = 9/2 = 4 ½. She correctly reasons that since
the shaded area is equal to 3/2, the square is equal to one whole, and drags
4 wholes plus half of one whole to represent the mixed number.
Apply and extend previous understandings of multiplication and division to
multiply and divide fractions.
Note that unlike the previous chain
of reasoning, this requires that the
student determines how much of
the shaded area is equal to 1.

48. Slide 48
Student C multiplies 3 x 3/2 = 9/2. She reasons that since the shaded area is 3/2,
this is equal to 3 pieces of size ½. Since 9/2 is 9 pieces of size ½, she drags nine of
the smallest figure to create her model.
Apply and extend previous understandings of multiplication and division to
multiply and divide fractions.
This chain of reasoning links nicely back
to the initial development of 3/2 in
3.NF.1 “understand a fraction a/b as the
quantity formed by a parts of size 1/b,
illustrating the coherence in the
standards across grades 3-5.

49. How can K-2 work on operations with whole numbers
and work on fractions in grade 3 support students’
thinking about these problems in grades 4 & 5?
49
4
5
2
? 4
5
2
?
Even before learning the
exact sum, can students
tell you between which
two whole numbers the
answer lies?
Even before learning the
exact product, what can
students tell you about
the value of the product?

50. At what grade should students be able to
solve these problems?
1
3
1
3
1
?
1
3
2
5
2
3
1
10
4
6
?
?

51. Explain the flaw in the chain of reasoning.
In the first group, 3/5 of the cats have spots. In the second group,
1/3 of the cats have spots. All together, 4/8 of the cats have spots.
Therefore, 3/5 + 1/3 = 4/8.

52. Closing Task – Fractions
• You have 4 strips of paper each 1 foot in
length.
– Partition one into thirds.
– Partition one into fifths.
– Partition one into eighths.
– Use the ruler as needed.
– How can the strips be used to compare fractions?
– What is the length, in inches, of each partition?
Assume that the strip is exactly one foot and each
of your partitions is exactly equal.
52

53. 53
Topic 2: Whole Numbers

54. 0
3/2
1 + 3 = ?
Operations with fractions should be a natural
extension of operations with whole numbers
54
2 4 5
0
1 3
1
2
3
2
?
1/2 2/2 4/2

55. 55

56. Future impact
1.OA.B Understand and apply properties of
operations and the relationship between
addition and subtraction.
1.OA.B.3. Apply properties of operations as
strategies to add and subtract.3 Examples: If 8 + 3
= 11 is known, then 3 + 8 = 11 is also known.
(Commutative property of addition.) To add 2 + 6
+ 4, the second two numbers can be added to
make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
(Associative property of addition.)
1.OA.B.4. Understand subtraction as an
unknown-addend problem. For example, subtract
10 – 8 by finding the number that makes 10 when
added to 8.
.

57. Future impact
1.OA.C Work with addition and subtraction
equations.
1.OA.C.7. Understand the meaning of the equal sign,
and determine if equations involving addition and
subtraction are true or false. For example, which of
the following equations are true and which are false?
6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.C.8. Determine the unknown whole number in
an addition or subtraction equation relating to three
whole numbers. For example, determine the unknown
number that makes the equation true in each of the
equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?

58. Within grade impact
• Look at the grade 2 standards in the
domains NBT and OA. Discuss how the
standards in NBT might be integrated with
the standards for OA to create problems that
challenge mathematically talented students.
• Develop a problem that integrates concepts
and skills from the two domains to increase
the level of challenge. (You may use online
resources such as Illustrative Math to find a
base task and then further differentiate.)
58

59. Smarter Balanced Assessment Consortium
An Assessment System to Support Teaching and Learning

60. The Assessment Challenge
How do we get from here... ...to here?
All students
leave high school
college and
career ready
Common Core
State Standards
specify K-12
expectations for
college and
career readiness
...and what can an
assessment system
do to help?

61. Concerns with Today's Statewide Assessments
• Each state bears the burden of test development;
no economies of scale
Each state pays for its own
assessments
• Students in many states leave high school
unprepared for college or career
Based on state standards
• Inadequate measures of complex skills and deep
understanding
Heavy use of multiple choice
• Tests cannot be used to inform instruction or
affect program decisions
Results delivered long after tests
are given
• Difficult to interpret meaning of scores; concerns
about access and fairness
Accommodations for special
education and ELL students vary
• Costly, time consuming, and challenging to
maintain security
Most administered on paper

62. The Purpose of the Consortium
• To develop a comprehensive and innovative
assessment system for grades 3-8 and high school in
English language arts and mathematics aligned to the
Common Core State Standards, so that...
• ...students leave high school prepared for
postsecondary success in college or a career through
increased student learning and improved teaching
[The assessments shall be operational across Consortium
states in the 2014-15 school year]

63. • 26 member
states and
territories
representing
39% of K-12
students
• 22 Governing
States, 3
Advisory States,
1 Affiliate
Member
• Washington
state is fiscal
agent
• WestEd provides
project
management
services
A National Consortium of States

64. Theory of Action Built on Seven Key
Principles
1. An integrated system
2. Evidence-based approach
3. Teacher involvement
4. State-led with transparent governance
5. Focus: improving teaching and learning
6. Actionable information – multiple
measures
7. Established professional standards

65. A Balanced Assessment System
Common
Core State
Standards
specify
K-12
expectations
for college
and career
readiness
All students
leave
high school
college
and career
ready
Teachers and
schools have
information and
tools they need
to improve
teaching and
learning
Interim assessments
Flexible, open, used
for actionable
feedback
Summative
assessments
Benchmarked to
college and career
readiness
Teacher resources for
formative
assessment
practices
to improve instruction

66. A Balanced Assessment System
School Year Last 12 weeks of the year*
DIGITAL LIBRARY of formative tools, processes and exemplars; released items and tasks; model
curriculum units; educator training; professional development tools and resources; scorer training modules;
and teacher collaboration tools.
ELA/Literacy and Mathematics, Grades 3-8 and High School
Computer Adaptive
Assessment and
Performance Tasks
Computer Adaptive
Assessment and
Performance Tasks
Scope, sequence, number and timing of interim assessments
locally determined
*Time windows may be adjusted based on results from the research agenda and final implementation decisions.
Performance
Tasks
• ELA/literacy
• Mathematics
Computer
Adaptive
Assessment
• ELA/literacy
• Mathematics
Optional Interim
Assessment
Optional Interim
Assessment
Re-take option available
Summative Assessment for
Accountability

67. Using Computer Adaptive Technology for
Summative and Interim Assessments
• Provides accurate measurements of student growth over
timeIncreased precision
• Item difficulty based on student responses
Tailored for Each
Student
• Larger item banks mean that not all students receive the
same questionsIncreased Security
• Fewer questions compared to fixed form testsShorter Test Length
• Turnaround time is significantly reducedFaster Results
• GMAT, GRE, COMPASS (ACT), Measures of Academic
Progress (MAP)Mature Technology

68. What is CAT?
Administered by computer, a
Computerized Adaptive Test (CAT)
dynamically adjusts to the trait level of
each examinee as the test is being
administered.

69. How CAT Works (Binet’s Test)

70. Rating Item Difficulty
A) 9 x 4 = 2 x □
B) 9 x 4 = □ x 9
C) 4 x □ = 40 – 8
D) 8 x 5 = □
E) 8 x □ = 4 x □
Give two different pairs of numbers that could fill the boxes to
make a true equation.
F) 8 x □ = 40

71. 0
3/2
Put a point at the number 1.
Some Important “Constraints” in the
Smarter Balanced Summative
71
2 4
0 3
0
0
3/5

72. Grade 1
Add and subtract within 20.
6. Add and subtract within 20,
demonstrating fluency for addition and
subtraction within 10. Use strategies
such as counting on; making ten (e.g., 8
+ 6 = 8 + 2 + 4 = 10 + 4 = 14);
decomposing a number leading to a ten
(e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9);
using the relationship between addition
and subtraction (e.g., knowing that 8 + 4
= 12, one knows 12 – 8 = 4); and
creating equivalent but easier or known
sums (e.g., adding 6 + 7 by creating the
known equivalent 6 + 6 + 1 = 12 + 1 =
13).
Work with addition and subtraction
equations.
7. Understand the meaning of the equal
sign, and determine if equations
involving addition and subtraction are
true or false. For example, which of the
following equations are true and which
are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5,
4 + 1 = 5 + 2.
8. Determine the unknown whole number
in an addition or subtraction equation
relating to three whole numbers. For
example, determine the unknown
number that makes the equation true in
each of the equations 8 + ? = 11, 5 = ? –
3, 6 + 6 = ?.
Grade 4
Understand decimal notation for
fractions, and compare decimal
fractions.
5. Express a fraction with denominator 10
as an equivalent fraction with
denominator 100, and use this technique
to add two fractions with respective
denominators 10 and 100.4 For example,
express 3/10 as 30/100, and add 3/10 +
4/100 = 34/100.
6. Use decimal notation for fractions with
denominators 10 or 100. For example,
rewrite 0.62 as 62/100; describe a
length as 0.62 meters; locate 0.62 on a
number line diagram.
7. Compare two decimals to hundredths
by reasoning about their size.
Recognize that comparisons are valid
only when the two decimals refer to the
same whole. Record the results of
comparisons with the symbols >, =, or
<, and justify the conclusions, e.g., by
using a visual model.

73. K-12 Teacher Involvement
• Support for implementation of the
Common Core State Standards
(2011-12)
• Write and review items/tasks for the pilot
test (2012-13) and field test (2013-14)
• Development of teacher leader teams in
each state (2012-14)
• Evaluate formative assessment practices
and curriculum tools for inclusion in digital
library (2013-14)
• Score portions of the interim and
summative assessments (2014-15 and
beyond)

74. Higher Education Collaboration
• Involved 175 public and 13 private
systems/institutions of higher education
in application
• Two higher education representatives
on the Executive Committee
• Higher education lead in each state
and higher education faculty
participating in work groups
• Goal: The high school assessment
qualifies students for entry-level, credit-
bearing coursework in college or
university

75. Assessment System Components
Summative Assessment (Computer Adaptive)
• Assesses the full range of Common Core in English
language arts and mathematics for students in grades 3–8
and 11 (interim assessments can be used in grades 9 and 10)
• Measures current student achievement and growth across
time, showing progress toward college and career readiness
• Can be given once or twice a year (mandatory testing
window within the last 12 weeks of the instructional year)
• Includes a variety of question types: selected response,
short constructed response, extended constructed response,
technology enhanced, and performance tasks

76. Assessment System Components
Interim Assessment (Computer Adaptive)
• Optional comprehensive and content-cluster assessment to
help identify specific needs of each student
• Can be administered throughout the year
• Provides clear examples of expected performance on
Common Core standards
• Includes a variety of question types: selected response,
short constructed response, extended constructed response,
technology enhanced, and performance tasks
• Aligned to and reported on the same scale as the
summative assessments
• Fully accessible for instruction and professional development

77. Assessment System Components
• Extended projects demonstrate
real-world writing and analytical
skills
• May include online research,
group projects, presentations
• Require 1-2 class periods to
complete
• Included in both interim and
summative assessments
• Applicable in all grades being
assessed
• Evaluated by teachers using
consistent scoring rubrics
The use of performance
measures has been found
to increase the intellectual
challenge in classrooms
and to support higher-
quality teaching.
- Linda Darling-Hammond
and Frank Adamson,
Stanford University
“
”
Performance Tasks

78. Assessment System Components
Few initiatives are
backed by evidence
that they raise
achievement.
Formative assessment
is one of the few
approaches proven to
make a difference.
- Stephanie Hirsh,
Learning Forward
Formative Assessment Practices
• Research-based, on-
demand tools and
resources for teachers
• Aligned to Common Core,
focused on increasing
student learning and enabling
differentiation of
instruction
• Professional development
materials include model units
of instruction and publicly
released assessment items,
formative strategies
“
”

79. Assessment System Components
Data are only useful if
people are able to
access, understand and
use them… For
information to be useful,
it must be timely, readily
available, and easy to
understand.
- Data Quality Campaign
Online Reporting
• Static and dynamic reports,
secure and public views
• Individual states retain
jurisdiction over access and
appearance of online reports
• Dashboard gives parents, students,
practitioners, and policymakers
access to assessment
information
• Graphical display of learning
progression status (interim
assessment)
• Feedback and evaluation
mechanism provides surveys, open
feedback, and vetting of materials
“
”

80. Support for Special Populations
• Accurate measures of
progress for students
with disabilities and
English Language
Learners
• Accessibility and
Accommodations Work
Group engaged
throughout
development
• Outreach and
collaboration with
relevant associations
Common-
Core Tests
to Have Built-in
Accommodations
- June 8, 2011
“
”

81. “Students can demonstrate progress toward college and
career readiness in English Language arts and literacy.”
“Students can demonstrate college and career readiness in
English language arts and literacy.”
“Students can read closely and analytically to comprehend
a range of increasingly complex literary and informational
texts.”
“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 and inquiry to
investigate topics, and to analyze, integrate, and present
information.”
Overall Claim for Grades 3-8
Overall Claim for Grade 11
Claim #1 - Reading
Claim #2 - Writing
Claim #3 - Speaking and
Listening
Claim #4 - Research/Inquiry
Claims for the ELA/Literacy Summative Assessment

82. “Students can demonstrate progress toward college and career
readiness in mathematics.”
“Students can demonstrate college and career readiness in
mathematics.”
“Students can explain and apply mathematical concepts and
interpret and carry out mathematical procedures with precision and
fluency.”
“Students can solve a range of complex well-posed problems in pure
and applied mathematics, making productive use of knowledge and
problem solving strategies.”
“Students can clearly and precisely construct viable arguments to
support their own reasoning and to critique the reasoning of others.”
“Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and solve
problems.”
Overall Claim for Grades 3-8
Overall Claim for Grade 11
Claim #1 - Concepts &
Procedures
Claim #2 - Problem Solving
Claim #3 - Communicating
Reasoning
Claim #4 - Modeling and Data
Analysis
Claims for the Mathematics Summative Assessment

83. April 2012 Item/task specifications and guidelines v1.0 completed
May 2012 Training materials for writing & reviewing items/tasks completed
May-June 2012 Automated scoring models developed
June 2012 Engage students in “cognitive labs” for new and innovative items/tasks
June 2012 Recruit classrooms for small scale trials
Aug-Oct 2012 Conduct small scale trials
May 2012 Recruit teachers to write and review first ~10,000 items/tasks (“Pilot” Phase)
May-July 2012 Teachers trained and write pilot items/tasks
Sept-Oct 2012 Teachers review pilot items/tasks
Oct-Nov 2012 Solicit classrooms for pilot testing
Feb-Mar 2013 Pilot testing of items/tasks
May 2013 Recruit teachers to write/review next ~35,000 items/tasks (“Field Test” Phase)
May-July 2013 Teachers trained and write field test items/tasks
Sept-Oct 2013 Teachers review field test items/tasks
Oct-Nov 2013 Solicit classrooms for field testing
April-June 2014 Field testing of items/tasks
Development of Items and Tasks

84. Viewing Sample Items & Tasks
• Preliminary Sample Items
– http://sampleitems.smarterbalanced.org/itemp
review/sbac/
• Full Practice Tests Available
– http://sbac.portal.airast.org/practice-test/

85. 85
Usability, Accessibility,
Accommodations

86. Overall New Document
• Introduction
– Purpose and intended audience
– Briefly addresses Framework and ISAAP, includes
links
• Three main sections on supports
– Universal Accessibility Tools
– Designated Accommodations
– Documented Accommodations
• Resources (References)
• Appendices
– Summary of supports
– Research lessons

87. Speech-to-Text
• Available as a documented accommodation on
all math and ELA items:
– Available for students providing a response, as a
documented accommodation included in an IEP or
504.
– Available to students when taking notes in
preparation for a written response, included in an
IEP or 504.
• Students to use own Assistive Technology (AT)
device, with AT device certification
Note: Conventions not a challenge to the construct.

88. American Sign Language
• Available for students who are hard of
hearing or deaf as a documented
accommodation
• Available on math items
• Available on ELA listening items

89. Closed Captioning
• Available for students who are hard of
hearing or deaf as a documented
accommodation
• Available on ELA listening items

90. Calculator
• Universal embedded calculator: available on
items as per Smarter Balanced item
specifications and targets
• Non-embedded calculator is a documented
accommodation (i.e., Brailled calculator)
– Student can use own device
• Calculator is not allowed on non-calculator
items
– Decision based on intended construct to be
measured by assessment targets.

91. Survey Feedback—Participation
91

92. Universal Tools, Designated Supports,
and Accommodations
• Universal tools are access features of the assessment that
are either provided as digitally-delivered components of the
test administration system or separate from it. Universal tools
are available to all students based on student preference and
selection.
• Designated supports for the Smarter Balanced assessments
are those features that are available for use by any student
for whom the need has been indicated by an educator (or
team of educators with parent/guardian and student).
• Accommodations are changes in procedures or materials
that increase equitable access during the Smarter Balanced
assessments. They are available for students for whom there
is documentation of the need for the accommodations on an
Individualized Education Program (IEP) or 504
accommodation plan.

93. New Graphic

94. General Table, Appendix A

95. Text-to-Speech
• On Items
• Designated support for math items
• Designated support for ELA items
• On ELA Reading Passages
• Grades 3-5, TTS for passages is not available
• Grades 6-HS: for passages available
accommodation for students whose need is
documented in an IEP or 504 plan
95

96. Guidelines & Frameworks
• Smarter Balanced Usability, Accessibility
and Accommodations Guidelines
http://www.smarterbalanced.org/wordpres
s/wp-
content/uploads/2013/09/SmarterBalance
d_Guidelines_091113.pdf
• Smarter Balanced Translation Framework
• http://www.smarterbalanced.org/wordpres
s/wp-
content/uploads/2012/09/Translation-
Accommodations-Framework-for-Testing-
ELL-Math.pdf 96

97. 97
Making Items More Accessible

98. Drag and Drop

99. Equal to 5.42 NOT Equal to
5.42
2.36 + 3.06
1.80 x 3
2.16 + 3.36
9.53 – 4.11
2.71 x 2
8.01 – 2.69
Table

100. Translation

101. Translation

102. Translation

103. Translation

104. Embedded

105. Embedded

106. 106
Important Notes on Item
Development

107. 107
http://commoncoretools.me/2012/02/16/the-structure-is-the-standards/For an essay on similar themes, see
Features of CCSSM and Implications for Assessment
Assessing Individual Content Standards or Parts of Standards
Alignment in Context: Cluster, Domain, and Grade
3.c

108. What are progressions?
Many or most of the content standards in K-8 represent
steps or stages along a progression of learning and
performance.
Why are progressions important for item writers?
They are context for alignment questions. Progression-
sensitive tasks will help teachers implement the standards
with fidelity.
Where can I find more information?
Progressions documents are narratives of the standards
across grade levels, informed by research on children's
cognitive development and by the logical structure of
mathematics.
108
Features of CCSSM and Implications for Assessment
Assessing Individual Content Standards or Parts of Standards
Alignment in Context: Neighboring Grades and Progressions
http://math.arizona.edu/~ime/progressions/#products

109. 109
Features of CCSSM and Implications for Assessment
Assessing at All Levels of the Content Hierarchy
Standards in number and operations that involve place value of decimals
Items requiring procedural skill in expanded
form, reading/writing, and comparing
decimals, and rounding
Q Q
Q
How Standards and Tests Used To Be Designed: Tossing Items Into Buckets
Q

110. 110
Features of CCSSM and Implications for Assessment
Assessing at All Levels of the Content Hierarchy
Number and Operations in Base Ten—Understand the Place Value System
5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4
Q
Q QQ
Q
Q
Using the Design of CCSSM to Make Better Tests
Step 1: Better Buckets!
1) Standards complement procedural skill
with explicit expectations for conceptual
understanding of specific content, and
connections to practices such as
constructing mathematical arguments
(MP.3)
2) Individual standards make important
connections explicit and inescapable—
e.g., 3.MD.7 connects area to
multiplication, division, and the
distributive property. Buckets that
connect buckets.
3) Standards are given a
coherent context within
and across grades through
cluster headings

111. 111
Features of CCSSM and Implications for Assessment
Assessing at All Levels of the Content Hierarchy
5.NBT.1 5.NBT.2 5.NBT.3a 5.NBT.3b 5.NBT.4
Q
Q QQ
Q
Q
Using the Design of CCSSM to Make Better Tests
Step 2: Where Appropriate, Treat Headings As Buckets
Where appropriate, aim
some of the item
development at the
cluster level
Where appropriate,
aim some of the
item development
at the domain level
Q Q
5.NBT.A 5.NBT

112. • There are a finite set of key opportunities to assess at the
cluster, domain, and grade levels. Smarter Balanced is
exploring this feature of the Standards.
 Such opportunities should be identified carefully and must make
obvious educational and mathematical sense within the
framework of the standards. For example, the first two clusters in
NBT are often important to link; and doing simple word problems
to apply developing NBT skills requires some grade-level tasks
that blend OA and NBT.
 This is not a recommendation to make loose interpretations of the
standards or go beyond what is written in the standards. Rather, it
is an opportunity to measure plausible and immediate implications
of what is written in the standard, without ever slipping into the
imposition of additional requirements.
.
112
Features of CCSSM and Implications for Assessment
Assessing at All Levels of the Content Hierarchy

113. Features of CCSSM and Implications for Assessment
Assessing at All Levels of the Content Hierarchy
http://tinyurl.com/mathpubcrit
Coherent
Connections
113

114. 114
Features of CCSSM and Implications for Assessment
Minimizing pitfalls of traditional multiple choice
questions
• High-quality machine-scoreable tasks are critical.
• Some examples of how to do this in CBT that are
machine scored:
 Gridded response
 True/False with multiple options
 Drag and drop

115. Some considerations: Risks of technology in
assessing of the Standards.
• Technology for technology‟s sake - The construct should
drive the task design, not functionality
• Overuse of tech-friendly content - Technology can
threaten focus; consider how technology can support
focus and not dilute it
• Innovative does not equal more difficult. Many tasks
should give kids credit for learning the basics of the grade
• Need cognitive labs or other tryouts to make sure the
technology is adding value to the task
115
Features of CCSSM and Implications for Assessment

116. Grade 3

117. Grade 3

118. Grade 5

119. 119
Fluency as a special case of assessing individual
content standards.
• Fluent in the standards means fast and accurate.
• The word fluency was used judiciously in the Standards to
mark the endpoints of progressions of learning that begin
with solid underpinnings and then pass upward through
stages of growing maturity.
• Assessing the full range of the standards means
assessing fluency where it is called for in the standards.
 Some of these fluency expectations are meant to be mental and others
with “pencil and paper.” But for each of them, there should be no
hesitation in getting the answer with accuracy.
Features of CCSSM and Implications for Assessment

120. Topics for Discussion
1. Assessing individual content standards or parts of
standards
2. Assessing at all levels of the content hierarchy
3. Identifying ways in which technology can promote
quality assessment of the standards
4. Connecting mathematical practice standards and
content standards
120
Features of CCSSM and Implications for Assessment

121. “Designers of curricula, assessments, and
professional development should all attend to the
need to connect the mathematical practices to
mathematical content in mathematics
instruction.” (CCSSM, pg. 8)
121
Features of CCSSM and Implications for Assessment
Assessing through authentic connections of content and practices

122. Features of CCSSM and Implications for Assessment
Smarter Balanced’s Claims Embody Specific Mathematical
Practices in the Presence of Content Standards
Claim #2: 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 #3: Communicating Reasoning.
Students can clearly and precisely construct
viable arguments to support their own reasoning
and to critique the reasoning of others.
Claim #4: Modeling and Data Analysis.
Students can analyze complex, real-world
scenarios and can construct and use
mathematical models to interpret and solve
problems.
122

123. 123
A Closer Look at Claim #3: Communicating Reasoning
Students can clearly and precisely construct viable
arguments to support their own reasoning and to
critique the reasoning of others.
(Connection to MP.3: Construct viable arguments and critique the
reasoning of others)
Features of CCSSM and Implications for Assessment
Connecting Content Standards and Mathematical Practices in
Assessment

124. 124
Reasoning is a refrain in the content standards
Note generally such words as justify a conclusion, prove a statement,
explain the mathematics; also derive, assess, illustrate, and analyze.
Features of CCSSM and Implications for Assessment
Connecting Content Standards and Mathematical Practices in
Assessment

125. 125
Claim #3 tasks have fine “grain size.”
The Standards ask students not just to Reason, but to
“reason about X,” where X is key grade-level mathematics
such as properties of operations, relationships between
addition and subtraction or between multiplication and
division, fractions as numbers, variable expressions,
linear/nonlinear functions, etc.
Features of CCSSM and Implications for Assessment
Connecting Content Standards and Mathematical Practices in
Assessment

126. 126
A Closer Look at Claims #2 and #4
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.
Modeling & Data Analysis
Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and
solve problems.
Features of CCSSM and Implications for Assessment
Connecting Content Standards and Mathematical Practices in
Assessment

127. 127
Modeling is a mathematical practice (MP.4) – and in
high school, it is also a content category. Therefore
it is reasonable to say that modeling is enhanced in
high school as compared to K-8, with more
elements of the modeling cycle (CCSSM, p. 72, 73) –
and equivalently, that modeling builds more slowly
across K-8 and is less sophisticated there.
Features of CCSSM and Implications for Assessment
Connecting Content Standards and Mathematical Practices in
Assessment

128. 128
• Contextual word problems involving ideas that are currently at the
forefront of the student‟s developing mathematical knowledge.
• Multi-step contextual word problem in which the problem isn‟t broken
into steps or sub-parts
• Micro models: These tasks define goals that can be met by
autonomously apply a known technique from pure mathematics to a
real-world situation in which the technique yields valuable results
though it is obviously not applicable in a strict mathematical sense
• Reasoned estimates: these tasks require students to use reasonable
estimates of know quantities in a chain of reasoning that yield an
estimate of unknown quantity.
• Decisions from data: These tasks require students to select from a data
source, analyze the data and draw reasonable conclusions from it. This
will often result in an evaluation or recommendation.
• Full models: These tasks require execution of some or all of the
modeling cycle in high school.
Source: Excerpted from Smarter Balanced Content Specifications, PARCC Item Development ITN, Appendix F
Features of CCSSM and Implications for Assessment
Modeling and Problem Solving tasks may come in a variety of types

129. Grade 5

130. Grade 5

131. Grade 5

132. Grade 3

133. Find Out More
Smarter Balanced
can be found
online at:
SmarterBalanced.org
Contact Information:
shelbi.cole@smarterbalanced.org 133