Common Core Essential Elements Alternate...
Transcript of Common Core Essential Elements Alternate...
&Common Core Essential ElementsAlternate Achievement Descriptors
Kindergarten - 5 GradeInstructional Guide
Mathematics
West Virginia Board of education
2012-2013
L. Wade Linger Jr., PresidentGayle C. Manchin, Vice President
Robert W. Dunlevy, Secretary
Michael I. Green, MemberPriscilla M. Haden, MemberLloyd G. Jackson II, MemberLowell E. Johnson, MemberJenny N. Phillips, MemberWilliam M. White, Member
Paul L. Hill, Ex OfficioChancellor
West Virginia Higher Education Policy Commission
James L. Skidmore, Ex OfficioChancellor
West Virginia Council for Community and Technical College Education
Jorea M. Marple, Ex OfficioState Superintendent of Schools
Math | Kindergarten-5 Grade i
ACKNOWLEDGEMENTS ......................................................................................................... iii
INTRODUCTION ...................................................................................................................... 1
NCLB GUIDANCE ..................................................................................................................... 2
ACCESS TO INSTRUCTION AND ASSESSMENT ................................................................ 3
ACCESSING THE GENERAL CURRICULUM ........................................................................ 4Model Symbol Use Throughout Instruction ............................................................................. 4Use Partner-Assisted Scanning Across the Day......................................................................... 4Use First-Letter Cueing as a Communication Strategy Whenever Possible .............................. 4
GUIDANCE AND SUPPORT .................................................................................................... 5
RELATIONSHIP TO THE DYNAMIC LEARNING MAPS ASSESSMENT ........................... 6
SYSTEM ALIGNMENT .............................................................................................................. 6Levels of Performance .............................................................................................................. 7
DOCUMENT ORGANIZATION ............................................................................................... 8Directions for Interpreting Essential Elements ......................................................................... 9
COMMON CORE ESSENTIAL ELEMENTS AND ACHIEVEMENT DESCRIPTORS
Kindergarten Mathematics StandardsCounting and Cardinality .................................................................................................... 10Operations and Algebraic Thinking ..................................................................................... 14Number and Operations in Base Ten .................................................................................. 16Measurement and Data ...................................................................................................... 17Geometry ........................................................................................................................... 18
First Grade Mathematics StandardsOperations and Algebraic Thinking ..................................................................................... 20Number and Operations in Base Ten .................................................................................. 27Measurement and Data ...................................................................................................... 33Geometry ........................................................................................................................... 39
Second Grade Mathematics StandardsOperations and Algebraic Thinking ..................................................................................... 41Number and Operations in Base Ten .................................................................................. 44Measurement and Data ...................................................................................................... 52Geometry ........................................................................................................................... 59
Third Grade Mathematics StandardsOperations and Algebraic Thinking ..................................................................................... 61Number and Operations in Base Ten .................................................................................. 67Number and Operations--Fractions .................................................................................... 70Measurement and Data ...................................................................................................... 72Geometry ........................................................................................................................... 78
TABLE OF CONTENTS
ii Common Core Essential Elements
Fourth Grade Mathematics StandardsOperations and Algebraic Thinking ..................................................................................... 80Numbers and Operations in Base Ten ................................................................................ 84Number and Operations--Fractions .................................................................................... 89Measurement and Data ...................................................................................................... 93Geometry ......................................................................................................................... 103
Fifth Grade Mathematics StandardsOperation and Algebraic Thinking .................................................................................... 106Number and Operations in Base Ten ................................................................................ 108Number and Operations--Fractions .................................................................................. 114Measurement and Data .................................................................................................... 119Geometry ......................................................................................................................... 124
GLOSSARY AND EXAMPLES OF MATHEMATICS TERMS.............................................. 125
GLOSSARY OF SPECIAL EDUCATION TERMS ................................................................ 131
BIBLIOGRAPHY OF DEVELOPMENT PROCESS .............................................................. 135
BIBLIOGRAPHY FOR MATHEMATICS CONTENT .......................................................... 137
APPENDIX A: SEA/STAKEHOLDER DEMOGRAPHICS ................................................... 141
Math | Kindergarten-5 Grade iii
ACKNOWLEDGEMENTS*For stakeholder demographics, See Appendix A.
Edvantia FacilitatorsJan Sheinker, Sheinker Educational Services, Inc.
Beth Judy, Director, Assessment, Alignment, and Accountability ServicesNathan Davis, Information Technology Specialist
Kristen Deitrick, Corporate Communications SpecialistLinda Jones, Executive Assistant
Dynamic Learning Maps (DLM) Staff and ConsultantsNeal Kingston, Project Director
Alan Sheinker, Associate Project DirectorLaura Kramer, Test Development Lead
Karthick Palaniswamy, Technology Development LeadKelli Thomas, Mathematics Learning Map Team Lead
Carrie Mark, English Language Arts Learning Map Team LeadPatti Whetstone, Research Associate
Sue Bechard, ConsultantKaren Erickson, Consultant
Chris Cain, Consultant
Dynamic Learning Maps (DLM) Consortia StatesIowa
KansasMichigan
MississippiMissouri
New JerseyNorth Carolina
OklahomaUtah
VirginiaWashington
West VirginiaWisconsin
iv Common Core Essential Elements
Mathematics State Education Agency (SEA)/Stakeholder Representatives
IOWASEA Representatives: Tom Deeter, Emily Thatcher
Stakeholders: Barbara Adams, John Butz, Laurel Cakinberk, Dagny FidlerKANSAS
SEA Representatives: Sidney Cooley, Debbie MatthewsStakeholders: DiRae Boyd, Teresa Kraft, Michele Luksa, Mona Tjaden
MICHIGANSEA Representatives: Linda Howley, Joanne Winkelman
Stakeholders: Tamara Barrientos, Roula AlMouabbi, Brian Pianosi, Larry TimmMISSOURI
SEA Representatives: Lin Everett, Sara King, Jane VanDeZandeStakeholders: Sharon Campione, Emily Combs, Karen Pace
NEW JERSEYSEA Representatives: Shirley Cooper, MaryAnn Joseph
Stakeholders: Sue Burger, Tracey Lank, Katie SlaneNORTH CAROLINA
SEA Representative: Robin BarbourStakeholders: Ronda Layman, Janet Sockwell
OKLAHOMASEA Representatives: Jennifer Burnes, Amy Daugherty
Stakeholder: Christie StephensonUTAH
SEA Representatives: Wendy Carver, Jennie DeFriezStakeholders: Lynda Brown, Kim Fratto, Lisa Seipert, Nicole Warren
VIRGINIASEA Representatives: John Eisenberg, Deborah Wickham
Stakeholders: Diane Lucas, Laura Scearce, Joyce Viscomi, Roslynn WebbWASHINGTON
SEA Representatives: Debra Hawkins, Janice TornowStakeholders: Jeff Crawford, John DeBenedetti, Kirsten Dlugo, Angelita Jagla
WEST VIRGINIASEA Representatives: Melissa Gholson, Beth Cipoletti
Stakeholders: Wes Lilly, Melissa Mobley, Lisa New, Deena SwainWISCONSIN
SEA Representative: Brian JohnsonStakeholders: Amber Eckes, Rosemary Gardner, Mary Richards, Jeff Ziegler
Math | Kindergarten-5 Grade 1
The Common Core Essential Elements (EEs) are linked to the Common Core State Standards (CCSS) for Mathematics. A group of general educators, special educators, and content specialists from member states in the Dynamic Learning Maps (DLM) Consortium gathered to determine the essence of the CCSS.
This document provides a high-level view of the relationship between the CCSS and the links to performance for students with significant cognitive disabilities. It is intended to provide a beginning structure for the design of a summative alternate assessment. The document is not intended as a stand-alone guide to instruction, nor is it intended to contain all the steps in a complete learning progression or detailed curriculum. The DLM and associated professional development will provide greater detail than described in this document.
Beginning with the Mathematics CCSS, stakeholders defined links to illuminate the precursors for the essential content and skills contained in the grade level CCSS clusters and indicators. These EEs are not intended as a redefinition of the standards. Rather, they are intended to describe challenging expectations for students with significant cognitive disabilities in relation to the CCSS. The EEs clarify the bridge between grade level achievement expectations for students with significant cognitive disabilities who participate in alternate assessments and the CCSS.
Neither are the EEs intended to prescribe the beginning or end of instruction on the content and skills they represent; rather, they indicate the grade level at which initial mastery would be the target to be assessed. Students should begin instruction in content and skills at the earliest point possible and continue instruction until mastery is attained.
The stakeholder group, consisting of state education agency (SEA) representatives and SEA-selected content teachers of students with significant cognitive disabilities, developed instructional achievement level descriptors (IALDs) for each of the EEs. IALDs were defined for four performance levels: I, II, III, and IV. Level III IALDs are aligned with the EEs. The target content and skills for each level of achievement, from Level I to Level IV, were then defined. For each target skill, the stakeholder group developed examples to illustrate how students might demonstrate achievement of the performance level. The IALDs are intended to provide an achievement ladder for students working toward achievement (Level III) of the EEs and onward (Level IV) and toward greater participation in the grade level CCSS to which the EEs are linked. The provided examples are intended to assist teachers to envision how the broad range of students with significant cognitive disabilities might perform the same content, despite the different challenges their disabilities might present. The examples are not exhaustive and do not represent the full range of possibilities in which the highly diverse population of students with significant cognitive disabilities might access the EEs or demonstrate the achievement of those elements. However, the examples do provide some of the ways that performance might be elicited and demonstrated across the spectrum of students with significant cognitive disabilities.
Finally, the stakeholder group developed alternate assessment achievement descriptors for each grade level -- from third grade through high school -- where summative assessments might be required. The alternate assessment achievement descriptors will provide a bridge between the EEs and a summative alternate assessment aligned to them. The descriptors are intended to provide one element to guide development of the test blueprint, development of items and
INTRODUCTION
2 Common Core Essential Elements
tasks that measure the full range of achievement, and the setting of cut scores during standard setting for the assessment. The focus of an alternate assessment in a standards-based system is based on the achievement that aligns with EEs linked to grade level content.
Together, the system of standards and descriptors is designed to allow students with significant cognitive disabilities to progress toward the achievement of state standards linked to grade level expectations. The relationship of standards and assessment to teaching and learning are depicted for use by teachers, assessment designers, and users of alternate assessment results.
NCLB GUIDANCEThe stakeholder group’s work was guided by the U. S. Department of Education’s Peer Review Guidance (Standards and Assessments Peer Review Guidance: Information and Examples for Meeting Requirements of the No Child Left Behind Act of 2001 [NCLB]), which requires that alternate academic achievement standards align with the alternate assessment. They must• include knowledge and skills that link to grade level expectations,• promote access to the general curriculum, and• reflect professional judgment of the highest learning standards possible for the group of
students with the most significant cognitive disabilities.
Although the grade-level content may be reduced in complexity or adjusted to reflect prerequisite skills, the link to grade-level standards must be clear. The Peer Review Guidance notes that the concept of alternate achievement standards related to grade level may be ambiguous. According to the Guidance, the descriptors• should be defined in a way that supports individual growth because of their linkage to
different content across grades;• are not likely to show the same clearly defined advances in cognitive complexity as the
general education standards when examined across grade levels;• should rely on the judgment of experienced special educators and administrators, higher
education representatives, and parents of students with disabilities as they define alternate achievement standards; and
• should provide an appropriate challenge for students with the most significant cognitive disabilities as they move through their schooling.
The Guidance requires links to grade-level standards. The EEs were developed by DLM consortium states to differentiate knowledge and skills by grade level. This differentiation is intended to clarify the link between the grade-level EEs and the grade-level CCSS and to show a forward progression across grades. The progression of content and skills across years of instruction reflect the changing priorities for instruction and learning as students move from grade to grade. The differences from grade level to grade level are often subtle and progression is sometimes more horizontal than vertical. For example, the grade-to-grade level differences may consist of added skills that are not of obvious increasing rigor compared to the differences found in the CCSS across grade levels. To the degree possible, skills escalate in complexity or rigor at Levels III and IV across the grades, with clear links to the shifting emphasis at each grade level in the CCSS.
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The EEs and Achievement Descriptors developed by the DLM consortium states are intended to create the maximum possible access to the CCSS for students with significant cognitive disabilities. The way in which information is presented for instruction and assessment and the manner in which students demonstrate achievement is in no way intended to be limited by statements of EEs or Achievement Descriptors. To that end, modes of communication, both for presentation or response, are not stated in either the EEs or Achievement Descriptors unless a specific mode is an expectation. Where no limitation has been stated, no limitation should be inferred. Students’ opportunities to learn and to demonstrate learning should be maximized by providing whatever communication, assistive technologies, augmentative and alternative communication (AAC) devices, or other access tools that are necessary and routinely used by the student during instruction.
Students with significant cognitive disabilities include a broad range of students with diverse disabilities and communication needs. For some students with significant cognitive disabilities, graphic organizers similar to those used by students without disabilities provide useful access to content and are adequate to maximize opportunities to learn and demonstrate achievement. Other students require a range of assistive technologies to access content and demonstrate achievement. For some students, AAC devices and accommodations for hearing and visual impairments will be needed. As with other physical disabilities, students with visual impairments may perform some expectations using modified items, presentations, or response formats. A few items may not lend themselves to such modifications. Decisions about the appropriate modifications for visual impairments are accounted for in the design of the assessments.
The access challenge for some is compounded by the presence of multiple disabilities. All of these needs, as well as the impact of levels of alertness due to medication and other physical disabilities which may affect opportunities to respond appropriately, need to be considered.
Most presentation and response access conditions do not constitute accommodations as they are understood for students who take the general assessment. Methods of presentation that do not violate the intended construct by aiding or directing the students’ response allow the student to perceive what knowledge or skill is expected. Aids to responding that do not constitute a violation of the intended construct allow the student to demonstrate the expected knowledge and skills. Examples of acceptable access technologies include the following:• communication devices that compensate for a students’ physical inability to produce
independent speech.• devices that compensate for a students’ physical inability to manipulate objects or
materials, point to responses, turn pages in a book, or use a pencil or keyboard to answer questions or produce writing.
• tools that maximize a students’ ability to acquire knowledge and skills and to demonstrate the products of their learning.
ACCESS TO INSTRUCTION AND ASSESSMENT
4 Common Core Essential Elements
Technology is also of particular importance to students with significant cognitive disabilities to access the general curriculum and achieve the EEs. Although educators have traditionally viewed technology as hardware and software, assistive technology tenets provide a broader view of the applications of low, medium, and high levels of technology use. Assistive technology tools can be vital to a student in acquiring and demonstrating learning unimpeded by the barriers that the disability presents.
Model Symbol Use Throughout Instruction
Many students with significant cognitive disabilities have difficulty with or cannot use speech to communicate and/or are supported by the use of communication symbols (e.g., communication boards, speech generating devices, voice output communication devices) and supports to augment their speech and other means of communication. Students who require symbols and other AAC supports require frequent modeling in the use of those symbols to interact and respond during instruction. Students who use symbols and other communication supports need as much modeling as children who use speech to communicate. Modeling in this way is not viewed as a means of prompting, guidance, or support, just as having a teacher talk serves those purposes for a student who communicates using speech.
When modeling the use of symbols and other communication supports, teachers use the symbols and supports themselves, hand them to students without communication impairments to use, and involve the students who need to use them every day. Each of these steps can play an important role in validating the use of symbols and communication supports and demonstrating multiple levels of expertise in their use.
Use Partner-Assisted Scanning Across the Day
Making a choice from the items on a list, symbols, tactuals, or a communication board can be difficult for some students because they lack the ability to point, cannot see or read the choices, or are positioned too far away (as in group activities). Partner-assisted scanning addresses these issues by asking the communication partner (a teacher, paraprofessional, or peer) to point to each of the options pausing long enough at each for the students with physical and communication impairments to respond “yes” if the item is their desired choice. Depending on the needs of an individual child, the partner can name each option when pointing or simply point.
Throughout the IALDS, examples are provided that require students to select, identify, recognize, and so forth from a number of options. It is suggested that teachers use partner-assisted scanning to support these modes of responding and communicating whenever it appears that the act of directly pointing to a response is too difficult for a particular student.
Use First-Letter Cueing as a Communication Strategy Whenever Possible
Students with communication impairments who are beginning to read, write, and communicate regularly face the challenge of not having access to the words or symbols they want or need to communicate effectively. When attempting to provide them with every possible word they might need, the result is an unmanageable communication system. When guessing what will be most important, it is inevitable that some guesses will be wrong. Until students can spell well enough to communicate their own thoughts, it is important to rely on cueing strategies. First-letter cueing is one such strategy. Students can use an alphabet display to point to the
ACCESSING THE GENERAL CURRICULUM
Math | Kindergarten-5 Grade 5
first letter (or try to spell more) of the word they are trying to communicate. Teachers can use this strategy to help students respond efficiently to questions that involve known choices. Teachers can also model the use of first-letter cueing in their day-to-day interactions with the class. Natural opportunities to incorporate this strategy occur when the teacher is prompting students to recall a specific word (e.g., “I am thinking of a new word we learned yesterday that started with the letter ‘t’”.) or concept (e.g., “Who remembers the big word we learned to describe when we put things together to find out how many we have in all? It begins with the letter ‘a’”.). There are times every school day when the adults in the class can model the use of first-letter cueing.
GUIDANCE AND SUPPORTThe authors of the CCSS use the words, “prompting and support” at the earliest grade levels to indicate when students were not expected to achieve standards completely independently. Generally, “prompting” refers to “the action of saying something to persuade, encourage, or remind someone to do or say something” (McKean, 2005). However, in special education, prompting is often used to mean a system of structured cues to elicit desired behaviors that otherwise would not occur. In order to communicate clearly that teacher assistance is permitted during instruction of the EEs, and is not limited to structured prompting procedures, the decision was made by the stakeholder group to use the more general term guidance throughout the EEs and alternate achievement descriptors.
Guidance and support during instruction should be interpreted as teacher encouragement, general assistance, and informative feedback to support the student in learning. Some examples of the kinds of teacher behaviors that would be considered guidance and support include• getting the student started (e.g., “Tell me what to do first”),• providing a hint in the right direction without revealing the answer (e.g., Student wants to
write dog but is unsure how, the teacher might say, “See if you can write the first letter in the word, /d/og.”),
• narrowing the field of choices as a student provides an inaccurate response,• using structured technologies such as task specific word banks, or• providing the structured cues such as those found in prompting procedures (e.g., least-to-
most prompts, simultaneous prompting, and graduated guidance).
Guidance and support as described above apply to instruction per the examples provided in the IALDS. The IALDs are intended to provide an idea of how students might perform the EEs at the threshold to various achievement levels as they work toward independent mastery.
Alternate assessments measure the degree to which students with significant cognitive disabilities have mastered the EEs. During any assessment, accommodation(s) allowed on the assessment must have been used and practiced during instruction; however, some accommodations that are permissible during instruction would compromise the integrity of the assessments, thereby yielding invalid and unreliable results and cannot be used for assessment purposes. Some guidance and support strategies may not be allowed for assessment purposes when variance in teacher assistance, cues, and prompts could compromise judgments about mastery of the EEs and comparability of administration.
6 Common Core Essential Elements
The EEs and Achievement Descriptors developed by the DLM consortium states and their stakeholder representatives serve two functions. Instructionally, they provide teachers with information about the level of knowledge and skills expected of their students. Second, they provide elaboration that teachers can use to help guide instruction toward achievement expectations. IALDs were developed for each of the EEs. Each IALD is further clarified by a range of examples. Teachers may find these examples useful for envisioning how their students might perform as they progress toward the expected achievement, as long as they keep in mind that they are examples only and cannot represent the full range of ways in which students might demonstrate their achievement.
Assessment Achievement Level Descriptors (AALDs) will emerge as drafts from the IALDS. The AALDs are content and grade specific, but summarize across the EEs the key performance differences across levels of achievement and across grade levels. While draft AALDs will be used in the initial stages of standard setting to help guide that process, final AALDs will emerge from the standard setting process. Standard setting will take into account the overall degree of accuracy with which a student would need to perform in order to achieve at a particular level. Just as on a general education assessment, no individual student will be expected to perform proficiently on every EE in order to be considered Level III.
For purposes of the DLM assessments under development, the achievement descriptors provide a useful link between the EEs and the DLM assessments. The descriptors, along with DLM developed from the CCSS, provide guidance to the development of the alternate assessment so that a full range of performance is measured and the setting of score ranges within each level rests on a defined frame of reference. The grade level EEs and alternate achievement standards• standardize meaning for the content and skill expectations,• create consistency in expected performance,• emphasize skill similarities for all students participating in the alternate assessments,• accommodate diverse disabilities, and• ground alternate assessments in a consistent set of expectations.
Achievement descriptors are used to categorize and explain student performance both in the course of instruction and on the alternate assessment.
SYSTEM ALIGNMENTThe EEs and alternate achievement descriptors are intended to contribute to a fully aligned system of standards, curriculum, teaching, learning, technology, and assessment that optimize equity of opportunity for all students in each classroom, school, and local education agency to access and learn the standards. To the degree possible, the grade level EEs are vertically aligned and linked to the grade level CCSS.
The linkages provided by the EEs to the CCSS are intended to increase access to the general curriculum for all students with disabilities. Examples provided for IALDs at each level of achievement are designed for special education and general education classroom teachers to
RELATIONSHIP TO THE DYNAMIC LEARNING MAPS ASSESSMENT
Math | Kindergarten-5 Grade 7
use in working with special education students who have significant cognitive disabilities. The examples are designed to help teachers evaluate students’ progress toward achievement of the EEs as well as illuminate the kinds of performances that indicate various levels of achievement.
Just as the EEs and IALDS are designed to guide teaching practices toward achievement in academic content areas, the standards reframe the expectations for foundational skills in pre-academic and academic areas. Precursor/prerequisite and the unique enabling skills related to mathematics content is specified in the context of their roles as a foundation for students with significant cognitive disabilities to achieve skills related to academic content.
Levels of Performance
Within this document, each grade level EE is cross-referenced to one or several CCSS.
Four performance levels have been proposed for the DLM’s alternate academic achievement standards: I, II, III, and IV. Mastery is considered to be demonstrated at Level III and Level IV and is identified as meeting the Level III level on an alternate assessment as specified in the NCLB. A general description of each of these levels is included below:
Level I - A student at this level attempts to perform tasks with support.
Level II - A student at this level demonstrates some content knowledge and skills from the extended grade level standards.
Level III - A student at this level demonstrates content knowledge and skills at a level aligned with the complexity of the EEs.
Level IV - A student at this level demonstrates content knowledge and skills at a higher level of complexity than those described for Level III. Typically, this complexity includes the routine use of symbol systems as applied to mathematics.
For each performance level, specific descriptions of content and skills are bulleted and examples of each level of performance are provided. The EEs, IALDS, and examples are intended as a resource for developing individualized education plan (IEP) goals, benchmarks, and curricular materials in reading, language arts, and mathematics. Students may need goals and benchmarks in areas other than academic content domains (e.g., self-care/living skills, mobility). As always, IEPs address the individual needs of each student to make progress toward the standards.
8 Common Core Essential Elements
Common Core Grade-Level Clusters are the Cluster titles and Grade-Level Indicators as they appear in the CCSS for Mathematics (Common Core State Standards Initiative, 2010).
Common Core Essential Elements (EEs) describe links to the CCSS for access by students with significant cognitive disabilities.
Instructional Achievement Level Descriptors (IALDs) describe performance at four achievement levels based on the EEs and are accompanied by examples at each achievement level.
CCSS Grade-Level Clusters
Common Core Essential Elements
Instructional Achievement Level Descriptor
Represent and solve problems involving addition and subtraction.
1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
EE1.OA.1.a. Use language to describe putting together and taking apart, aspects of addition and subtraction.
Level IV AA Students will:EE1.OA.1.a. Use words like take away, subtract, give, add, more, and same quantity, when putting together and taking apart.Ex. When gathering and distributing classroom supplies, appropriately use words like “more” and “take away” (handing out paper, pencils, or other tools used in a lesson).Ex. When picking teams for P.E., use the language of “I need one more student” or “I need to take away one more from my team.”Ex. Request “one more” or “take away” one or more when the teacher has set up an activity where there is an uneven number of supplies.Ex. During an activity, use “add,” “more,” “less,” etc. to indicate when a different amount is needed.
Level III AA Students will:EE1.OA.1.a. Use language to describe putting together and taking apart, aspects of addition and subtraction.Ex. After the teacher shows six blocks and removes two, label the action as “take away” or informal language with the same meaning.Ex. Appropriately use “more” and “give” to express desire for more snacks or blocks.Ex. Use one-to-one correspondence to line up two sets of objects and ask which group has more/less.Ex. During practice of adding __ more to a numeral, show correct flashcard when asked, “I have two; who has two more (4)?”
Level II AA Students will:EE1.OA.1.a. Put together or take away.Ex. Take away one crayon from the box.Ex. Put together red blocks and green blocks when asked.Ex. Give coins to purchase an item or take change at end of purchase.Ex. Give the teacher two blocks and then two more blocks.
Level I AA Students will:EE1.OA.1.a. Follow directions to put together or take away an object with a verbal prompt.Ex. In a classroom routine and when presented with a component needed for the routine, give component(s) when asked to put together for the activity.Ex. Take a paper or object from peer when passed out.Ex. Offer paper or object to peer to put together with group’s work when collected at the end of the lesson.
DOCUMENT ORGANIZATION
Math | Kindergarten-5 Grade 9
Directions for Interpreting Essential Elements
Essential Elements (EEs). The EEs are statements that provide links for students with significant cognitive disabilities to the essential content and skills defined in the grade-level clusters of the CCSS. The EEs provide a bridge for students with significant cognitive disabilities to the CCSS. The EEs are not intended as a reinterpretation of the CCSS; rather, they were developed to create a bridge between the CCSS and challenging achievement expectations for students with significant cognitive disabilities. The order in which the EEs are listed is a direct reflection of the order in which the CCSS are listed. The order is not intended to convey a sequence for instruction; rather, it illustrates progress across years. In the tables, the left column contains the CCSS grade-level clusters and indicators, the middle column contains the EE linked to them, and the right column contains the IALDs for each EE and examples for each IALD (as demonstrated by the example provided on the previous page). Each EE and IALD completes the phrase “Students will . . . .”
CCSS marked with an (+) are advanced standards and are not included in this document as it was determined by the stakeholder group that students of this population would not be accessing the curriculum at this advanced level and writing Essential Elements to this level would be unnecessary. Also, if it appears that a standard has been omitted in the high school grades, it is an advanced standard.
NOTE: N/A is used instead of a descriptor under Level IV, if it was determined by the stakeholder group that the content of the CCSS could not be addressed.
Bullets under instructional achievement levels denote descriptions of achievement at that level for the content related to the essential element.
Examples clarify certain components of EEs. The provided examples are illustrative, not exhaustive. They are intended to provide a range of ways in which a student may demonstrate progress toward the essential element and beyond.
10 Common Core Essential Elements
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pend
ent o
f obj
ects
, pic
ture
s, o
r thi
ngs
as a
stud
ent w
ould
reci
te th
e al
phab
et o
r by
poin
ting.
Ex. C
ount
with
out o
ne-t
o-on
e co
rres
pond
ence
to fi
ve.
Ex. S
eque
ntial
ly si
ng n
umbe
rs to
five
.Ex
. Sin
g al
ong
to c
ounti
ng so
ng.
Leve
l I A
A S
tude
nts
will
:EE
K.CC
.1. C
ount
with
teac
her f
rom
one
to tw
o.Ex
. Cou
nt w
ith th
e te
ache
r to
two.
K.CC
.2. C
ount
forw
ard
begi
nnin
g fr
om a
giv
en n
umbe
r with
in th
e kn
own
sequ
ence
(ins
tead
of
havi
ng to
beg
in a
t one
).
EEK.
CC.2
. N/A
K.CC
.3. W
rite
num
bers
from
0
to 2
0. R
epre
sent
a n
umbe
r of
obje
cts w
ith a
writt
en n
umer
al
0-20
(with
0 re
pres
entin
g a
coun
t of n
o ob
ject
s).
EEK.
CC.3
. N/A
Math | Kindergarten-5 Grade 11
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Es
senti
al E
lem
ents
Inst
ructi
onal
Ach
ieve
men
t Lev
el D
escr
ipto
r
Coun
t to
tell
the
num
ber
of
obje
cts.
K.CC
.4. U
nder
stan
d th
e re
latio
nshi
p be
twee
n nu
mbe
rs
and
quan
tities
; con
nect
cou
nting
to
car
dina
lity.
Whe
n co
untin
g ob
ject
s, sa
y th
e nu
mbe
r nam
es in
the
stan
dard
or
der,
pairi
ng e
ach
obje
ct w
ith
one
and
only
one
num
ber n
ame
and
each
num
ber n
ame
with
one
an
d on
ly o
ne o
bjec
t.
Und
erst
and
that
the
last
num
ber
nam
e sa
id te
lls th
e nu
mbe
r of
obje
cts c
ount
ed.
The
num
ber o
f ob
ject
s is t
he sa
me
rega
rdle
ss o
f th
eir a
rran
gem
ent o
r the
ord
er
in w
hich
they
wer
e co
unte
d.
Und
erst
and
that
eac
h su
cces
sive
num
ber n
ame
refe
rs to
a
quan
tity
that
is o
ne la
rger
.
EEK.
CC.4
. Dem
onst
rate
one
-to
-one
cor
resp
onde
nce
pairi
ng
each
obj
ect w
ith o
ne a
nd o
nly
one
num
ber a
nd e
ach
nam
e w
ith
only
one
obj
ect.
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
CC.4
. Dem
onst
rate
s one
-to-o
ne c
orre
spon
denc
e w
ith m
ore
than
one
.Ex
. Whe
n co
untin
g ob
ject
s, sa
y th
e nu
mbe
r nam
es in
stan
dard
ord
er a
nd p
air e
ach
obje
ct
with
one
and
onl
y on
e nu
mbe
r nam
e.Ex
. Pas
s pen
cils
out t
o cl
assm
ates
and
cou
nt th
e pe
ncils
as e
ach
clas
smat
e ge
ts a
pen
cil.
Ex. U
ses o
ne-to
-one
cor
resp
onde
nce
whe
n co
untin
g up
to 1
0 co
mm
on o
bjec
ts in
the
clas
sroo
m (c
rayo
ns, b
lock
s, b
utton
s).
Ex. C
ount
out
10
penn
ies t
o ex
chan
ge fo
r a d
ime.
Ex. S
ing
a co
untin
g so
ng a
nd ra
ise th
e co
rrec
t num
ber o
f fing
ers w
ith e
ach
num
ber.
Ex. C
ount
dot
s on
dice
and
mov
e fo
rwar
d co
rres
pond
ing
num
ber o
f spa
ces o
n ga
me
boar
d.Ex
. Rou
nd ro
bin
coun
t to
10.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
CC.4
. Dem
onst
rate
one
-to-o
ne c
orre
spon
denc
e pa
iring
eac
h ob
ject
with
one
and
onl
y on
e nu
mbe
r and
eac
h na
me
with
onl
y on
e ob
ject
.Ex
. Use
s one
-to-o
ne c
orre
spon
denc
e w
hen
coun
ting
up to
five
com
mon
obj
ects
in
clas
sroo
m (c
rayo
ns, b
lock
s, b
utton
s).
Ex. C
reat
e se
ts o
f obj
ects
to fi
ve.
Ex. P
lace
cor
resp
ondi
ng n
umbe
r of b
eans
in a
n eg
g ca
rton
with
eac
h se
ction
labe
led
1-5.
Ex. M
ove
bead
s on
an a
bacu
s as a
noth
er st
uden
t cou
nts o
ne to
five
.Ex
. Giv
en a
n eg
g ca
rton
, pla
ce fi
ve sti
cker
s in
each
secti
on.
Leve
l II A
A S
tude
nts
will
:EE
K.CC
.4. D
emon
stra
te o
ne o
bjec
t’s c
orre
spon
denc
e w
ith o
ne o
bjec
t.Ex
. Use
s one
-to-o
ne c
orre
spon
denc
e w
hen
coun
ting
up to
thre
e co
mm
on o
bjec
ts in
cl
assr
oom
(cra
yons
, blo
cks,
butt
ons)
.Ex
. Giv
en b
owls,
pla
ce th
ree
balls
in e
ach.
Ex. M
atch
obj
ects
by
pairi
ng e
ach
obje
ct w
ith o
ne a
nd o
nly
one
othe
r num
ber.
Ex. G
iven
“one
” le
tter i
n ea
ch st
uden
t’s m
ailb
ox to
go
hom
e.
Leve
l I A
A S
tude
nts
will
:EE
K.CC
.4. W
ith g
uida
nce
and
supp
ort,
coun
t one
obj
ect.
Ex. P
lace
“one
” le
tter i
n ea
ch st
uden
t’s m
ailb
ox to
go
hom
e.Ex
. Put
one
obj
ect i
n ea
ch se
ction
of a
n eg
g ca
rton
.Ex
. Ind
icat
e “o
ne”
obje
ct w
hen
aske
d, “
Whe
re is
one
<na
me
of fa
mili
ar o
bjec
t>?”
Ex. G
ive
one
penc
il to
eac
h cl
assm
ate.
12 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Es
senti
al E
lem
ents
Inst
ructi
onal
Ach
ieve
men
t Lev
el D
escr
ipto
r
K.CC
.5. C
ount
to a
nsw
er “
how
m
any?
” qu
estio
ns a
bout
as
man
y as
20
thin
gs a
rran
ged
in
a lin
e, a
rect
angu
lar a
rray
, or a
ci
rcle
, or a
s man
y as
10
thin
gs in
a
scatt
ered
con
figur
ation
; giv
en
a nu
mbe
r fro
m 1
–20,
cou
nt o
ut
that
man
y ob
ject
s.
EEK.
CC.5
. Cou
nt o
ut u
p to
thre
e ob
ject
s fro
m a
larg
er se
t, pa
iring
ea
ch o
bjec
t with
one
and
onl
y on
e nu
mbe
r nam
e to
tell
how
m
any.
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
CC.5
. Cou
nts fi
ve o
bjec
ts o
ut o
f a g
roup
of m
ore
than
five
obj
ects
.Co
unts
a g
iven
set o
f five
obj
ects
, pai
ring
each
obj
ect w
ith o
ne a
nd o
nly
one
num
ber
nam
e an
d w
hen
aske
d, “
how
man
y”, s
ays fi
ve w
ithou
t rec
ounti
ng.
Ex. G
iven
a b
ox o
f cra
yons
, sel
ect fi
ve c
rayo
ns a
s req
uest
ed b
y te
ache
r.Ex
. Giv
en a
set o
f five
obj
ects
, cou
nt o
ut th
ree
obje
cts.
Ex. F
rom
an
arra
y of
five
obj
ects
, cou
nt e
ach
obje
ct in
the
grou
p on
ly o
ne ti
me
and
tell
how
man
y w
as in
the
grou
p w
ithou
t rec
ounti
ng th
e ob
ject
s.Ex
. Cou
nt fi
ve c
hild
ren
out o
f all
the
child
ren
only
one
tim
e an
d te
ll ho
w m
any
with
out
reco
untin
g.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
CC.5
. Cou
nt o
ut u
p to
thre
e ob
ject
s fro
m a
larg
er se
t, pa
iring
eac
h ob
ject
with
one
an
d on
ly o
ne n
umbe
r nam
e to
tell
how
man
y.Ex
. Giv
en a
n ar
ray
of o
bjec
ts, c
ount
out
thre
e of
the
obje
cts,
cou
nting
eac
h ob
ject
onl
y on
ce a
nd te
ll ho
w m
any.
Ex. G
iven
a b
ox o
f cra
yons
, sel
ect t
hree
cra
yons
as r
eque
sted
by
teac
her.
Ex. C
ount
out
thre
e co
untin
g be
ars f
rom
a g
roup
of fi
ve.
Ex. P
ass o
ut th
ree
page
s to
each
stud
ent f
rom
a st
ack
of p
aper
, cou
nting
one
, tw
o, th
ree
each
tim
e, a
nd te
ll ho
w m
any
they
gav
e to
the
stud
ents
.
Leve
l II A
A S
tude
nts
will
:EE
K.CC
.5. C
ount
s eith
er o
ne o
r tw
o ob
ject
s out
of a
gro
up o
f five
obj
ects
.Ex
. Giv
en a
box
of c
rayo
ns, s
elec
t eith
er o
ne o
r tw
o cr
ayon
s as r
eque
sted
by
teac
her.
Ex. C
ount
out
two
coun
ting
bear
s fro
m a
gro
up o
f five
.
Leve
l I A
A S
tude
nts
will
:EE
K.CC
.5. I
denti
fy o
ne o
bjec
t out
of a
gro
up o
f obj
ects
.Ex
. Ide
ntify
bet
wee
n a
set w
ith o
ne o
r tw
o ap
ples
whe
n as
ked,
“sho
w m
e on
e ap
ple”
and
m
ake
a ch
oice
.Ex
. Go
to th
e pr
ize b
ox a
nd p
ick
one
obje
ct.
Math | Kindergarten-5 Grade 13
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Es
senti
al E
lem
ents
Inst
ructi
onal
Ach
ieve
men
t Lev
el D
escr
ipto
r
Com
pare
num
bers
.
K.CC
.6. I
denti
fy w
heth
er th
e nu
mbe
r of o
bjec
ts in
one
gro
up
is gr
eate
r tha
n, le
ss th
an, o
r eq
ual t
o th
e nu
mbe
r of o
bjec
ts
in a
noth
er g
roup
, e.g
., by
us
ing
mat
chin
g an
d co
untin
g st
rate
gies
.
EEK.
CC.6
. Ide
ntify
whe
ther
the
num
ber o
f obj
ects
in o
ne g
roup
is
mor
e or
less
than
(whe
n th
e qu
antiti
es a
re c
lear
ly d
iffer
ent)
or
equ
al to
the
num
ber o
f ob
ject
s in
anot
her g
roup
.
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
CC.6
. Ide
ntify
whe
ther
the
num
ber o
f obj
ects
in o
ne g
roup
is m
ore
or le
ss th
an o
r eq
ual t
o th
e nu
mbe
r of o
bjec
ts in
ano
ther
gro
up.
Ex. I
denti
fy w
hich
gro
up h
as m
ore
from
two
grou
ps c
reat
ed b
y th
e te
ache
r (e.
g., T
he te
ache
r cr
eate
s tw
o gr
oups
of m
anip
ulati
ve o
bjec
ts w
hose
tota
l qua
ntity
is w
ithin
thre
e. G
iven
two
grou
ps
of b
lock
s, fo
r exa
mpl
e, o
ne g
roup
has
seve
n bl
ocks
and
the
othe
r has
four
, the
stud
ent i
s abl
e to
id
entif
y w
hich
gro
up h
as m
ore
bloc
ks.
The
teac
her a
sks w
hich
gro
up h
as m
ore
and
the
stud
ent
iden
tifies
it.
Ex. G
iven
two
grou
ps o
f blo
cks,
one
gro
up h
as e
ight
blo
cks a
nd o
ther
has
five
, ide
ntify
whi
ch g
roup
ha
s les
s blo
cks.
Ex. G
iven
five
pap
ers t
o pa
ss o
ut to
a g
roup
of e
ight
stud
ents
, ind
icat
e th
at th
ere
are
MO
RE st
uden
ts
than
pap
ers b
y co
untin
g th
e pe
ople
and
then
cou
nting
the
pape
rs.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
CC.6
. Ide
ntify
whe
ther
the
num
ber o
f obj
ects
in o
ne g
roup
is m
ore
or le
ss (w
hen
the
quan
tities
are
cle
arly
diff
eren
t) o
r equ
al to
the
num
ber o
f obj
ects
in a
noth
er g
roup
.Ex
. Giv
en a
cho
ice
of tw
o bo
xes o
f blo
cks,
one
box
with
nin
e bl
ocks
and
one
box
with
four
blo
cks,
id
entif
y w
hich
box
has
mor
e bl
ocks
.Ex
. Giv
en a
cho
ice
of tw
o bo
xes o
f blo
cks,
one
box
with
eig
ht b
lock
s and
one
box
with
four
blo
cks,
id
entif
y w
hich
box
has
few
er b
lock
s.
Leve
l II A
A S
tude
nts
will
:EE
K.CC
.6. G
iven
two
grou
ps o
f dra
mati
cally
diff
eren
t qua
ntitie
s of o
bjec
ts, i
denti
fy w
hich
gr
oup
has m
ore.
Ex. W
hen
two
grou
ps o
f obj
ects
are
cou
nted
out
to th
e st
uden
t, id
entif
y w
hich
has
mor
e ob
ject
s th
an a
noth
er g
roup
(e.g
., us
ing
mat
chin
g an
d co
untin
g st
rate
gies
).Ex
. Giv
en tw
o bo
wls
of sn
acks
with
a la
rge
diffe
renc
e in
qua
ntity
, ide
ntify
whi
ch h
as m
ore.
Ex. G
iven
a c
hoic
e of
two
boxe
s of b
lock
s with
a d
iffer
ence
in q
uanti
ty o
f at l
east
twic
e th
e ot
her,
iden
tify
whi
ch h
as m
ore.
Leve
l I A
A S
tude
nts
will
:EE
K.CC
.6. E
xplo
re g
roup
s tha
t hav
e m
ore
and
less
.Ex
. Usin
g sa
nd/w
ater
/bal
l tab
les w
ith d
rasti
cally
diff
eren
t qua
ntitie
s of m
ater
ials,
exp
lore
the
quan
tity
whi
le th
e te
ache
r is t
alki
ng a
bout
the
lang
uage
of m
ore.
Ex. P
lace
silly
ban
ds/b
angl
es/b
ells
with
dra
stica
lly d
iffer
ent q
uanti
ties o
n th
e ar
ms o
r leg
s of t
he
stud
ents
and
exp
lore
the
quan
tity
of m
ore
whi
le th
e te
ache
r use
s the
lang
uage
of m
ore.
Ex. G
iven
two
grou
ps o
f butt
ons w
ith v
ery
diffe
rent
am
ount
s, id
entif
y th
e gr
oup
that
has
“m
ore”
by
poin
ting
to p
ictu
re sy
mbo
ls of
mor
e/le
ss, b
ig/s
mal
l.KK
.CC.
7. C
ompa
re tw
o nu
mbe
rs
betw
een
1 an
d 10
pre
sent
ed a
s w
ritten
num
eral
s.
EEK.
CC.7
. N/A
14 Common Core Essential Elements
Kin
der
gar
ten
Mat
hem
atic
s St
and
ard
s: O
per
atio
ns
and
Alg
ebra
ic T
hin
kin
g
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
addi
tion
as
putti
ng
toge
ther
and
add
ing
to, a
nd
unde
rsta
nd s
ubtr
acti
on a
s ta
king
apa
rt a
nd ta
king
from
.
K.O
A.1
. Rep
rese
nt a
dditi
on a
nd
subt
racti
on w
ith o
bjec
ts, fi
nger
s,
men
tal i
mag
es, d
raw
ings
1 , so
unds
(e.g
., cl
aps)
, acti
ng o
ut
situa
tions
, ver
bal e
xpla
natio
ns,
expr
essio
ns, o
r equ
ation
s.
EEK.
OA
.1. R
epre
sent
add
ition
as
“putti
ng to
geth
er”
or su
btra
ction
as
“ta
king
from
” in
eve
ryda
y ac
tiviti
es.
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
OA
.1. R
epre
sent
add
ition
as “
putti
ng to
geth
er”
and
subt
racti
on a
s “ta
king
from
” w
ith
quan
tities
to 1
0.Ex
. Com
bine
two
sets
of o
bjec
ts, p
ictu
res,
or t
hing
s to
mak
e on
e se
t of 1
0 th
roug
h th
e us
e of
as
sistiv
e te
chno
logy
or A
AC d
evic
e.Ex
. Tak
e aw
ay o
ne se
t of o
bjec
ts fr
om 1
0 an
d de
term
ine
how
man
y re
mai
n.Ex
. Usin
g a
simpl
e st
ory
cont
ext a
nd o
bjec
ts, t
he st
uden
t put
s tog
ethe
r and
take
s fro
m a
s ap
prop
riate
by
dire
ctly
mod
elin
g th
e pr
oble
m w
ith o
bjec
ts, a
ction
s, o
r sym
bols.
Ex. F
ollo
w d
irecti
ons t
o ga
ther
eno
ugh
mat
eria
ls fo
r eve
ryon
e an
d th
en p
asse
s the
m o
ut to
eac
h st
uden
t.Ex
. Put
a c
ounti
ng b
ear w
ith a
gro
up to
add
or t
ake
away
a c
ounti
ng b
ear t
o su
btra
ct.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
OA
.1. R
epre
sent
add
ition
as “
putti
ng to
geth
er”
or su
btra
ction
as “
taki
ng fr
om”
in
ever
yday
acti
vitie
s.Ex
. Ide
ntify
the
tota
l num
ber o
f cra
yons
whe
n on
e st
uden
t has
thre
e cr
ayon
s and
ano
ther
stud
ent
has t
wo,
and
they
put
thei
r cra
yons
toge
ther
to sh
are.
Des
crib
e th
e ac
tion
as p
ut to
geth
er.
Ex. A
dd to
a g
roup
of c
rayo
ns w
hen
told
to a
dd to
gro
up.
Ex. T
ake
away
from
a g
roup
of c
rayo
ns w
hen
told
to ta
ke a
way
from
the
grou
p.Ex
. Giv
en fi
ve sti
cker
s, g
ive
anot
her s
tude
nt o
ne o
f the
five
stick
ers,
and
des
crib
es th
e ac
tion
as ta
ke
away
.Ex
. Joi
n lin
king
cub
es to
show
acti
on/p
roce
ss o
f putti
ng to
geth
er o
r add
ition
.Ex
. Bre
ak a
part
link
ing
cube
s/sn
ap b
lock
s/br
istle
blo
cks/
pop-
bead
s to
show
acti
on/p
roce
ss o
f tak
ing
from
or s
ubtr
actio
n.
Leve
l II A
A S
tude
nts
will
:EE
K.O
A.1
. Fol
low
dire
ction
s to
“put
toge
ther
” by
add
ing
one
or “
take
from
” by
taki
ng o
ne.
Ex. G
iven
a b
owl o
f cou
nting
bea
rs, a
dd a
cou
nting
bea
r to
the
bow
l. T
he te
ache
r cal
ls th
e ac
tion
“putti
ng to
geth
er”
or a
dditi
on.
Ex. T
ake
one
whe
n th
e te
ache
r is p
assin
g ou
t sup
plie
s and
dire
cts t
he st
uden
ts to
take
one
. Th
e te
ache
r cal
ls th
e ac
tion
“tak
ing
away
” or
subt
racti
on.
Ex. P
lace
pop
sicle
stick
s int
o a
circ
le a
nd u
se la
ngua
ge to
des
crib
e ad
ditio
n or
“pu
tting
toge
ther
”.Ex
. Usin
g cu
bes,
cre
ate
tow
ers b
y ad
ding
or t
akin
g aw
ay o
ne c
ube
at a
tim
e.Ex
. Rem
ove
pops
icle
stick
s fro
m a
circ
le a
nd u
se la
ngua
ge to
des
crib
e su
btra
ction
or “
taki
ng fr
om”.
Leve
l I A
A S
tude
nts
will
:EE
K.O
A.1
. “Pu
t tog
ethe
r” o
r “ta
ke fr
om”
with
teac
her.
Ex. T
he te
ache
r and
stud
ent t
oget
her a
dd a
blo
ck to
a st
ack
whi
le te
ache
r say
s, “
put t
oget
her.”
Ex. T
he te
ache
r and
stud
ent t
oget
her t
ake
a bl
ock
from
a st
ack
whi
le th
e te
ache
r say
s, “
take
aw
ay.”
Math | Kindergarten-5 Grade 15
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
K.O
A.2
. Sol
ve a
dditi
on a
nd
subt
racti
on w
ord
prob
lem
s, a
nd
add
and
subt
ract
with
in 1
0, e
.g.,
by u
sing
obje
cts o
r dra
win
gs to
re
pres
ent t
he p
robl
em.
EEK.
OA
.2. N
/A
K.O
A.3
. Dec
ompo
se n
umbe
rs
less
than
or e
qual
to 1
0 in
to
pairs
in m
ore
than
one
way
by
usin
g ob
ject
s or d
raw
ings
, and
re
cord
eac
h de
com
positi
on b
y a
draw
ing
or e
quati
on (e
.g.,
5 =
2 +
3 an
d 5
= 4
+ 1)
.
EEK.
OA
.3. N
/A
K.O
A.4
. For
any
num
ber f
rom
1
to 9
, find
the
num
ber t
hat m
akes
10
whe
n ad
ded
to th
e gi
ven
num
ber,
e.g.
, by
usin
g ob
ject
s or
draw
ings
, and
reco
rd th
e an
swer
w
ith a
dra
win
g or
equ
ation
.
EEK.
OA
.4. N
/A
K.O
A.5
. Flu
ently
add
and
su
btra
ct w
ithin
5.
EEK.
OA
.5. N
/A
16 Common Core Essential Elements
Kin
der
gar
ten
Mat
hem
atic
s St
and
ard
s: N
um
ber
an
d O
per
atio
ns
in B
ase
Ten
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Wor
k w
ith
num
bers
11-
19 to
ga
in fo
unda
tion
s fo
r pl
ace
valu
e.
K.N
BT.1
. Com
pose
and
de
com
pose
num
bers
from
11
to 1
9 in
to te
n on
es a
nd
som
e fu
rthe
r one
s, e
.g.,
by
usin
g ob
ject
s or d
raw
ings
, and
re
cord
eac
h co
mpo
sition
or
deco
mpo
sition
by
a dr
awin
g or
eq
uatio
n (s
uch
as 1
8 =
10 +
8);
unde
rsta
nd th
at th
ese
num
bers
ar
e co
mpo
sed
of te
n on
es a
nd
one,
two,
thre
e, fo
ur, fi
ve, s
ix,
seve
n, e
ight
, or n
ine
ones
.
EEK.
NBT
.1. N
/A (S
ee E
EK.N
BT.1
.4
and
EEK.
NBT
.1.6
)
Math | Kindergarten-5 Grade 17
Kin
der
gar
ten
Mat
hem
atic
s St
and
ard
s: M
easu
rem
ent
and
Dat
a
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Des
crib
e an
d co
mpa
re
mea
sura
ble
attri
bute
s.
K.M
D.1
. Des
crib
e m
easu
rabl
e att
ribut
es o
f obj
ects
, suc
h as
le
ngth
or w
eigh
t. D
escr
ibe
seve
ral m
easu
rabl
e att
ribut
es o
f a
singl
e ob
ject
.
K.M
D.2
. Dire
ctly
com
pare
two
obje
cts w
ith a
mea
sura
ble
attrib
ute
in c
omm
on, t
o se
e w
hich
obj
ect h
as “
mor
e of
”/“l
ess
of”
the
attrib
ute,
and
des
crib
e th
e di
ffere
nce.
For
exa
mpl
e,
dire
ctly
com
pare
the
heig
hts
of
two
child
ren
and
desc
ribe
one
child
as
talle
r/sh
orte
r.
Clas
sify
obj
ects
and
cou
nt t
he
num
ber
of o
bjec
ts in
eac
h ca
tego
ry.
K.M
D.3
. Cla
ssify
obj
ects
into
gi
ven
cate
gorie
s; c
ount
the
num
bers
of o
bjec
ts in
eac
h ca
tego
ry a
nd so
rt th
e ca
tego
ries
by c
ount
.2
EEK.
MD
.1-3
. Cla
ssify
obj
ects
ac
cord
ing
to a
ttrib
utes
(big
/sm
all,
heav
y/lig
ht).
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
MD
.1-3
. Ord
er o
bjec
ts a
ccor
ding
to a
ttrib
utes
(big
/sm
alle
r/sm
alle
st, h
eavy
/ligh
ter/
light
est)
.Ex
. Giv
en tw
o ba
ckpa
cks o
f diff
eren
t wei
ght,
desc
ribe
or d
emon
stra
te w
hich
one
is h
eavi
er.
Ex. G
iven
two
cube
s of d
iffer
ent s
izes,
des
crib
e or
dem
onst
rate
whi
ch c
ube
is bi
gger
and
whi
ch c
ube
is sm
alle
r.Ex
. Com
pare
hei
ghts
of t
wo
clas
smat
es to
a st
anda
rd su
ch a
s a m
eter
stick
.Ex
. Com
pare
spor
ts b
alls
(bas
ebal
l, ba
sket
ball,
tenn
is ba
ll, e
tc.)
usin
g va
rious
leng
ths o
f yar
n.Ex
. Giv
en b
lock
s of v
aryi
ng si
zes,
iden
tify
whi
ch a
re h
eavi
er/li
ghte
r and
smal
ler/
bigg
er.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
MD
.1-3
. Cla
ssify
obj
ects
acc
ordi
ng to
att
ribut
es (b
ig/s
mal
l, he
avy/
light
).Ex
. Giv
en a
big
boo
k an
d a
smal
l boo
k, d
escr
ibe
or d
emon
stra
te w
hich
one
is b
igge
r and
whi
ch o
ne
is sm
alle
r.Ex
. Giv
en th
e sh
oe o
f a st
uden
t and
the
teac
her,
iden
tify
whi
ch o
ne is
big
ger a
nd w
hich
one
is
smal
ler.
Ex. S
ort h
eavy
and
ligh
t obj
ects
acc
ordi
ng to
wei
ght.
Ex. G
iven
the
hand
of a
stud
ent i
n th
e cl
ass a
nd th
e ha
nd o
f the
teac
her,
iden
tify
whi
ch o
ne is
big
ger
and
whi
ch o
ne is
smal
ler.
Ex. G
iven
two
obje
cts o
f var
ying
wei
ght,
desc
ribe
or d
emon
stra
te w
hich
is h
eavy
/ligh
t or l
arge
/sm
all.
Leve
l II A
A S
tude
nts
will
:EE
K.M
D.1
-3. U
sing
a m
odel
or a
tem
plat
e, so
rt o
bjec
ts b
y on
e att
ribut
e (b
ig/s
mal
l or
heav
y/lig
ht).
Ex. S
ort c
ounti
ng b
ears
by
size
usin
g a
mod
el o
r tem
plat
e.Ex
. Giv
en tw
o ob
ject
s, w
here
one
is a
t lea
st tw
ice
the
size
of th
e ot
her,
iden
tify
whi
ch o
ne is
big
ger
and
whi
ch o
ne is
smal
ler w
ith d
escr
iptiv
e pr
ompt
s fro
m th
e te
ache
r.Ex
. Ide
ntify
big
ger b
all w
hen
show
n a
beac
h ba
ll an
d a
tenn
is ba
ll, a
nd li
sten
ing
to th
e te
ache
r use
vo
ice
infle
ction
s and
kin
esth
etic
moti
ons t
o ex
agge
rate
big
ger a
nd sm
alle
r.Ex
. Ide
ntify
the
bigg
er b
all w
hen
show
n a
golf
ball
and
beac
h ba
ll an
d lis
teni
ng to
the
teac
her u
sing
voic
e in
flecti
ons a
nd m
otion
s to
exag
gera
te.
Ex. S
ort o
bjec
ts in
the
clas
sroo
m in
to g
roup
s of h
eavy
and
ligh
t (e.
g., b
owlin
g ba
ll, b
each
bal
l, an
d a
rock
).Ex
. Giv
en tw
o pi
ctur
es o
f rea
l-life
obj
ects
, sel
ect t
he b
igge
r one
.
Leve
l I A
A S
tude
nts
will
:EE
K.M
D.1
-3. M
atch
obj
ects
by
attrib
ute
big
and
smal
l.Ex
. Tou
ch a
larg
e ob
ject
(suc
h as
a p
umpk
in) a
s tea
cher
des
crib
es it
as b
ig w
hen
com
pare
d to
a
smal
ler p
umpk
in to
y.Ex
. Ind
icat
e sm
all p
umpk
in a
s tea
cher
des
crib
es it
as s
mal
l whe
n co
mpa
red
with
a la
rge
pum
pkin
.Ex
. Ind
icat
e if
they
wan
t the
big
bal
l or t
he sm
all b
all.
18 Common Core Essential Elements
Kin
der
gar
ten
Mat
hem
atic
s St
and
ard
s: G
eom
etry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Iden
tify
and
des
crib
e sh
apes
(s
quar
es, c
ircl
es, t
rian
gles
, re
ctan
gles
, hex
agon
s, c
ubes
, co
nes,
cyl
inde
rs, a
nd s
pher
es).
K.G
.1. D
escr
ibe
obje
cts i
n th
e en
viro
nmen
t usin
g na
mes
of
shap
es, a
nd d
escr
ibe
the
rela
tive
positi
ons o
f the
se o
bjec
ts u
sing
term
s suc
h as
abo
ve, b
elow
, be
side
, in
fron
t of,
behi
nd, a
nd
next
to.
EEK.
G.1
. Ide
ntify
wor
ds o
f pr
oxim
ity to
des
crib
e th
e re
lativ
e po
sition
.
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
G.1
. Use
wor
ds re
ferr
ing
to fr
ames
of r
efer
ence
or d
emon
stra
te re
lativ
e po
sition
.Ex
. Giv
en m
anip
ulati
ves,
follo
w d
irecti
ons t
o pl
ace
them
in p
rope
r pos
ition
(put
the
dog
behi
nd th
e bo
y).
Ex. W
hen
look
ing
at b
irds o
utsid
e th
e w
indo
w, te
ll w
here
the
bird
is (e
.g.,
in th
e tr
ee, o
r on
the
wire
).Ex
. Giv
en a
pic
ture
, ind
icat
e th
e ob
ject
that
is in
the
nam
ed p
ositi
on (p
oint
to th
e pe
rson
stan
ding
in
fron
t of t
he w
indo
w).
Ex. L
ooki
ng a
t a p
ictu
re in
a b
ook,
use
the
corr
ect w
ord
to d
escr
ibe
the
positi
on o
f ite
ms i
n th
e pi
ctur
es.
Ex. P
lay
“Sim
on S
ays”
usin
g po
sition
al w
ords
.Ex
. “Is
the
ball
next
to y
ou, i
n fr
ont o
f you
, or b
ehin
d yo
u?”
Ex. G
iven
a se
t of b
uild
ing
bloc
ks, s
tack
them
to d
emon
stra
te b
esid
e an
d be
twee
n.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
G.1
. Ide
ntify
wor
ds o
f pro
xim
ity to
des
crib
e th
e re
lativ
e po
sition
.Ex
. Giv
en m
anip
ulati
ves,
follo
w d
irecti
on to
pla
ce th
em in
pro
per p
ositi
on (o
ne b
lock
“on
top”
of
anot
her)
.Ex
. Giv
en a
pic
ture
, ind
icat
e th
e ob
ject
that
is in
the
nam
ed p
ositi
on (p
oint
to th
e pe
rson
stan
ding
be
twee
n th
e tr
ees)
.Ex
. Ind
icat
e w
here
ano
ther
teac
her i
s rel
ative
to th
eir p
ositi
on w
hen
wal
king
side
-by-
side
(e.g
., “A
m I
wal
king
nex
t to
you
or b
esid
e yo
u? B
esid
e m
e?”)
.Ex
. Ind
icat
e th
e re
lativ
e po
sition
of a
des
k (e
.g.,
besid
e).
Ex. G
iven
man
ipul
ative
s, fo
llow
dire
ction
to p
lace
them
in p
rope
r pos
ition
(put
the
dog
unde
r the
ta
ble)
.
Leve
l II A
A S
tude
nts
will
:EE
K.G
.1. R
espo
nd to
spati
al w
ords
that
des
crib
e re
lativ
e po
sition
of a
n ob
ject
usin
g po
sition
term
s (e.
g., o
n, in
, off)
.Ex
. Giv
en a
pic
ture
, ind
icat
e th
e ob
ject
that
is in
the
nam
ed p
ositi
on (e
.g.,
poin
t to
the
pers
on
stan
ding
on
the
ladd
er).
Ex. P
lay
hide
-and
-see
k w
ith a
n ob
ject
and
tell
the
teac
her w
here
to h
ide
it (o
n or
in so
met
hing
).
Anot
her p
erso
n co
mes
in th
e ro
om to
find
the
obje
ct.
The
stud
ents
tell
them
whe
re th
e ob
ject
is
loca
ted
(on
or in
som
ethi
ng).
Ex. A
fter l
isten
ing
to a
stor
y, su
ch a
s Hop
on
Pop,
indi
cate
ans
wer
s to
positi
onal
que
stion
s (e.
g., “
Is
the
ball
in th
e bo
x or
out
side
of th
e bo
x?”)
.Ex
. Fol
low
teac
her d
irecti
ons w
hen
clea
ning
up
from
an
activ
ity b
y pu
tting
item
s aw
ay, s
uch
as p
ut
your
cra
yons
“in
” yo
ur p
enci
l box
.Ex
. Ind
icat
e ch
oice
whe
n th
e te
ache
r ask
s the
stud
ent a
serie
s of q
uesti
ons,
such
as “
do y
ou w
ant
your
hat
‘on’
you
r hea
d or
‘in’
you
r bac
kpac
k?”
whi
le p
repa
ring
to g
o ho
me.
Leve
l I A
A S
tude
nts
will
:EE
K.G
.1. R
epea
t pos
ition
al w
ords
dur
ing
an a
ctivi
ty o
r les
son
in w
hich
the
teac
her
dem
onst
rate
s the
rela
tive
positi
on o
f an
obje
ct.
Ex. R
epea
t or i
ndic
ate
the
positi
onal
wor
d th
e te
ache
r use
s as (
s)he
mov
es th
e st
uden
t to
phys
ical
ly
dem
onst
rate
pos
ition
term
s (on
, in)
.Ex
. Rep
eat “
in”
as th
e te
ache
r put
s on
a st
uden
t’s sh
oes a
nd d
escr
ibes
the
actio
n as
putti
ng th
e st
uden
ts’ f
eet i
n th
e sh
oe.
Math | Kindergarten-5 Grade 19
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
K.G
.2. C
orre
ctly
nam
e sh
apes
re
gard
less
of t
heir
orie
ntati
ons
or o
vera
ll siz
e.
K.G
.3. I
denti
fy sh
apes
as t
wo-
dim
ensio
nal (
lyin
g in
a p
lane
, “fl
at”;
or t
hree
-dim
ensio
nal,
“sol
id”)
.
EEK.
G.2
-3. M
atch
two-
dim
ensio
nal s
hape
s (ci
rcle
, sq
uare
, tria
ngle
).
Leve
l IV
AA
Stu
dent
s w
ill:
EEK.
G.2
-3. M
atch
two-
dim
ensio
nal s
hape
s tha
t var
y in
size
(circ
le, s
quar
e, tr
iang
le).
Ex. G
iven
an
asso
rtm
ent o
f sha
pes t
hat v
ary
in si
ze, m
atch
the
shap
es a
ccor
ding
to sh
ape
and
size.
Ex. U
sing
com
pute
r soft
war
e, se
lect
a tr
iang
le a
nd m
atch
it to
a ta
rget
tria
ngle
that
is a
di
ffere
nt si
ze.
Ex. G
iven
a c
ircle
, go
on a
“Ci
rcle
Hun
t” to
find
oth
er e
xam
ples
of c
ircle
s aro
und
the
scho
ol.
Leve
l III
AA
Stu
dent
s w
ill:
EEK.
G.2
-3. M
atch
two-
dim
ensio
nal s
hape
s (ci
rcle
, squ
are,
tria
ngle
).Ex
. Giv
en a
col
lecti
on o
f pai
rs o
f ide
ntica
lly si
zed
shap
es, m
atch
the
shap
es.
Ex. M
atch
shap
es in
an
inte
racti
ve w
hite
boar
d ac
tivity
.Ex
. Giv
en fo
ur p
oker
chi
ps a
nd fo
ur b
lock
s, m
atch
the
obje
cts b
ased
on
shap
e.
Leve
l II A
A S
tude
nts
will
:EE
K.G
.2-3
. Mat
ch a
shap
e to
its d
uplic
ate.
Ex. G
iven
one
shap
e an
d sh
own
two
shap
es, s
elec
t the
mat
chin
g sh
ape
from
the
two
choi
ces t
o on
e of
her
s/hi
s.Ex
. Mat
ch a
col
ored
con
stru
ction
pap
er c
ircle
to a
n ou
tline
on
pape
r.Ex
. Com
plet
e a
shap
e-so
rting
box
.
Leve
l I A
A S
tude
nts
will
:EE
K.G
.2-3
. Rep
eat a
mod
el to
mat
ch sh
apes
.Ex
. Mat
ch sh
aped
obj
ects
with
teac
her m
odel
. Re
peat
afte
r obs
ervi
ng a
teac
her-d
irect
ed
mat
chin
g ac
tivity
routi
ne in
volv
ing
shap
es.
Ex. M
atch
shap
ed o
bjec
ts w
ith te
ache
r pro
mpt
s. R
epea
t afte
r obs
ervi
ng th
e te
ache
r m
atch
the
corr
ect s
hape
d ob
ject
to th
e sa
me
obje
ct.
Ex. R
epea
t afte
r obs
ervi
ng th
e te
ache
r use
pic
ture
s cut
from
mag
azin
es th
at sh
ow c
ircle
s an
d sq
uare
s. T
each
er h
olds
up
a pi
ctur
e an
d as
ks w
hat s
hape
it is
, the
n pl
aces
it o
n a
larg
e ci
rcle
or s
quar
e m
at.
20 Common Core Essential Elements
CO
MM
ON
CO
RE
ESS
EN
TIA
L E
LEM
EN
TS
AN
D A
CH
IEV
EM
EN
T
DE
SCR
IPT
OR
S FO
R F
IRST
-GR
AD
EFi
rst
Gra
de
Mat
hem
atic
s St
and
ard
s: O
per
atio
ns
and
Alg
ebra
ic T
hin
kin
g
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
sol
ve p
robl
ems
invo
lvin
g ad
diti
on a
nd
subt
racti
on.
1.O
A.1
. Use
add
ition
and
su
btra
ction
with
in 2
0 to
solv
e w
ord
prob
lem
s inv
olvi
ng
situa
tions
of a
ddin
g to
, tak
ing
from
, putti
ng to
geth
er, t
akin
g ap
art,
and
com
parin
g, w
ith
unkn
owns
in a
ll po
sition
s, e
.g.,
by u
sing
obje
cts,
dra
win
gs, a
nd
equa
tions
with
a sy
mbo
l for
the
unkn
own
num
ber t
o re
pres
ent
the
prob
lem
.
EE1.
OA
.1.a
. Use
lang
uage
to
desc
ribe
putti
ng to
geth
er a
nd
taki
ng a
part
, asp
ects
of a
dditi
on
and
subt
racti
on.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
OA
.1.a
. Use
wor
ds li
ke ta
ke a
way
, sub
trac
t, gi
ve, a
dd, m
ore,
and
sam
e qu
antit
y, w
hen
putti
ng to
geth
er a
nd ta
king
apa
rt.
Ex. W
hen
gath
erin
g an
d di
strib
uting
cla
ssro
om su
pplie
s, a
ppro
pria
tely
use
wor
ds li
ke
“mor
e” a
nd “
take
aw
ay”
(han
ding
out
pap
er, p
enci
ls, o
r oth
er to
ols u
sed
in a
less
on).
Ex. W
hen
pick
ing
team
s for
P.E.
, use
the
lang
uage
of “
I nee
d on
e m
ore
stud
ent”
or “
I nee
d to
take
aw
ay o
ne m
ore
from
my
team
.”Ex
. Req
uest
“one
mor
e” o
r “ta
ke a
way
” on
e or
mor
e w
hen
the
teac
her h
as se
t up
an
activ
ity w
here
ther
e is
an u
neve
n nu
mbe
r of s
uppl
ies.
Ex. D
urin
g an
acti
vity
, use
“add
,” “m
ore,
” “l
ess,”
etc
. to
indi
cate
whe
n a
diffe
rent
am
ount
is
need
ed.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
OA
.1.a
. Use
lang
uage
to d
escr
ibe
putti
ng to
geth
er a
nd ta
king
apa
rt, a
spec
ts o
f ad
ditio
n an
d su
btra
ction
.Ex
. Afte
r the
teac
her s
how
s six
blo
cks a
nd re
mov
es tw
o, la
bel t
he a
ction
as “
take
aw
ay”
or
info
rmal
lang
uage
with
the
sam
e m
eani
ng.
Ex. A
ppro
pria
tely
use
“m
ore”
and
“giv
e” to
exp
ress
des
ire fo
r mor
e sn
acks
or b
lock
s.Ex
. Use
one
-to-o
ne c
orre
spon
denc
e to
line
up
two
sets
of o
bjec
ts a
nd a
sk w
hich
gro
up
has m
ore/
less
.Ex
. Dur
ing
prac
tice
of a
ddin
g __
mor
e to
a n
umer
al, s
how
cor
rect
flas
hcar
d w
hen
aske
d, “
I ha
ve tw
o; w
ho h
as tw
o m
ore
(four
)?”
Leve
l II A
A S
tude
nts
will
:EE
1.O
A.1
.a. P
ut to
geth
er o
r tak
e aw
ay.
Ex. T
ake
away
one
cra
yon
from
the
box.
Ex. P
ut to
geth
er re
d bl
ocks
and
gre
en b
lock
s whe
n as
ked.
Ex. G
ive
coin
s to
purc
hase
an
item
or t
ake
chan
ge a
t end
of p
urch
ase.
Ex. G
ive
the
teac
her t
wo
bloc
ks a
nd th
en tw
o m
ore
bloc
ks.
Leve
l I A
A S
tude
nts
will
:EE
1.O
A.1
.a. F
ollo
w d
irecti
ons t
o pu
t tog
ethe
r or t
ake
away
an
obje
ct w
ith a
ver
bal
prom
pt.
Ex. I
n a
clas
sroo
m ro
utine
and
whe
n pr
esen
ted
with
a c
ompo
nent
nee
ded
for t
he ro
utine
, gi
ve c
ompo
nent
(s) w
hen
aske
d to
put
toge
ther
for t
he a
ctivi
ty.
Ex. T
ake
a pa
per o
r obj
ect f
rom
pee
r whe
n pa
ssed
out
.Ex
. Offe
r pap
er o
r obj
ect t
o pe
er to
put
toge
ther
with
gro
up’s
wor
k w
hen
colle
cted
at t
he
end
of th
e le
sson
.
Math | Kindergarten-5 Grade 21
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
OA
.1.b
. Rec
ogni
ze tw
o gr
oups
that
hav
e th
e sa
me
or
equa
l qua
ntity
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
OA
.1.b
. Cre
ate
two
grou
ps th
at h
ave
the
sam
e or
equ
al q
uanti
ty.
Ex. F
ill tw
o bo
ok b
ags w
ith fi
ve b
ooks
eac
h.Ex
. Put
an
equa
l num
ber o
f cha
irs a
t tw
o ta
bles
.Ex
. Cou
nt o
ut a
nd p
ass b
ooks
/mat
eria
l in
grou
ps o
f tw
o ite
ms t
o ea
ch st
uden
t at
begi
nnin
g of
less
on.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
OA
.1.b
. Rec
ogni
ze tw
o gr
oups
that
hav
e th
e sa
me
or e
qual
qua
ntity
.Ex
. Whe
n pr
esen
ted
with
two
grou
ps o
f ite
ms,
indi
cate
if th
ey h
ave
the
sam
e qu
antit
y.
“Are
they
equ
al?”
Ex. D
urin
g an
art
acti
vity
, rec
ogni
ze th
at e
very
one
has a
n eq
ual a
mou
nt o
f sup
plie
s (e
very
one
has t
wo
goog
ly e
yes,
one
shee
t of p
aper
, and
one
glu
e sti
ck.)
Ex. W
hile
pla
ying
a g
ame
with
dic
e, re
cogn
ize w
hen
the
sam
e qu
antit
y is
rolle
d on
eac
h di
e.Ex
. Giv
en th
ree
grou
ps o
f obj
ects
arr
ange
d on
the
tabl
e, tw
o w
ith th
e sa
me
num
ber o
f ob
ject
s, o
ne w
ith a
diff
eren
t num
ber o
f obj
ects
, ide
ntify
whi
ch tw
o se
ts o
f obj
ects
are
the
sam
e/eq
ual.
Leve
l II A
A S
tude
nts
will
:EE
1.O
A.1
.b. A
dd o
ne m
ore
to a
gro
up to
mak
e it
the
sam
e or
equ
al to
the
othe
r.Ex
. At t
he re
ques
t of t
he te
ache
r, ad
d on
e m
ore
obje
ct to
mak
e th
e gr
oups
equ
al a
fter t
he
teac
her m
akes
two
grou
ps o
f obj
ects
, one
gro
up h
avin
g tw
o ob
ject
s and
one
gro
up o
nly
one
obje
ct.
Ex. A
dd o
ne m
ore
chai
r at t
he re
ques
t of t
he te
ache
r whe
n th
ere
are
two
stud
ents
and
on
e ch
air.
Ex. U
se 1
0 fr
ames
to a
dd b
eans
to a
qua
ntity
to m
ake
one
mor
e in
ord
er to
mat
ch th
e te
ache
r mod
el.
Ex. A
dd o
ne m
ore
stud
ent t
o a
grou
p to
pla
y a
gam
e or
com
plet
e a
coop
erati
ve g
roup
with
te
ache
r pro
mpt
s.
Leve
l I A
A S
tude
nts
will
:EE
1.O
A.1
.b. R
eplic
ate
a gr
oup
of o
bjec
ts.
Ex. G
iven
two
bloc
ks a
nd sh
own
a m
odel
of t
wo
bloc
ks to
geth
er, d
uplic
ate
the
mod
el.
Ex. G
iven
the
outli
ne o
f tw
o ci
rcle
s, p
lace
two
disk
s on
the
circ
les t
o du
plic
ate
the
mod
el.
22 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
1.O
A.2
. Sol
ve w
ord
prob
lem
s th
at c
all f
or a
dditi
on o
f thr
ee
who
le n
umbe
rs w
hose
sum
is
less
than
or e
qual
to 2
0, e
.g.,
by u
sing
obje
cts,
dra
win
gs, a
nd
equa
tions
with
a sy
mbo
l for
the
unkn
own
num
ber t
o re
pres
ent
the
prob
lem
.
EE1.
OA
.2. U
se “
putti
ng
toge
ther
” to
solv
e pr
oble
ms w
ith
two
sets
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
OA
.2. U
se “
putti
ng to
geth
er”
to so
lve
prob
lem
s usin
g th
ree
sets
.Ex
. Giv
en a
sim
ple
stor
y th
at p
rese
nts a
pro
blem
invo
lvin
g th
ree
sets
, put
the
sets
to
geth
er to
mak
e on
e (e
.g.,
John
wen
t to
a pa
rty
and
brou
ght o
ne g
ift, K
aren
wen
t to
the
part
y an
d br
ough
t tw
o gi
fts, T
om w
ent t
o th
e pa
rty
and
brou
ght o
ne g
ift; h
ow m
any
gifts
di
d th
ey h
ave
alto
geth
er?)
.Ex
. Put
toge
ther
obj
ects
to so
lve
a pr
oble
m (e
.g.,
Sara
h pu
t tw
o ap
ples
in th
e ba
sket
, Ja
vier
put
thre
e ap
ples
in th
e ba
sket
, Sas
ha p
ut o
ne a
pple
in th
e ba
sket
; how
man
y ap
ples
ar
e in
the
bask
et?)
.Ex
. Dra
w o
bjec
ts n
ext t
o a
verti
cal a
dditi
on p
robl
em to
solv
e.Ex
. Util
ize a
pic
toria
l mat
h pr
ogra
m o
n th
e co
mpu
ter t
o so
lve
for t
hree
qua
ntity
add
ition
pr
oble
ms.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
OA
.2. U
se “
putti
ng to
geth
er”
to so
lve
prob
lem
s with
two
sets
.Ex
. Tak
e att
enda
nce
for a
gro
up o
f five
or f
ewer
stud
ents
. De
term
ine
num
ber o
f boy
s an
d nu
mbe
r of g
irls.
Put
toge
ther
num
ber o
f boy
s and
girl
s to
dete
rmin
e ho
w m
any
clas
smat
es to
tal.
Ex. U
sing
nam
e ca
rds,
det
erm
ine
for a
gro
up o
f five
or f
ewer
stud
ents
the
num
ber o
f ch
ildre
n w
ho w
ant t
o bu
y lu
nch
from
the
cafe
teria
, and
the
num
ber o
f chi
ldre
n w
ho
brou
ght a
sack
lunc
h. P
ut to
geth
er th
e nu
mbe
r of s
tude
nts e
ating
lunc
h.Ex
. Lin
e up
for s
peci
al c
lass
on
num
bers
on
clas
sroo
m fl
oor a
nd te
ll ho
w m
any
stud
ents
ar
e in
line
.Ex
. Use
cou
nting
stick
s to
solv
e a
prob
lem
.
Leve
l II A
A S
tude
nts
will
:EE
I.OA
.2. U
se “
putti
ng to
geth
er”
to so
lve
a pr
oble
m w
ith o
ne se
t and
add
ing
one
mor
e.Ex
. Giv
en a
set o
f cou
nting
bea
rs (f
ewer
than
five
), pu
t tog
ethe
r one
mor
e to
mak
e th
e ne
xt n
umbe
r.Ex
. Whe
n cl
eani
ng u
p th
e ac
tivity
cen
ter,
“put
toge
ther
” th
e to
ys, t
o m
ake
the
next
nu
mbe
r (e.
g., “
I hav
e tw
o bl
ocks
. Ca
n yo
u pu
t the
m to
geth
er w
ith o
ne m
ore
to m
ake
thre
e?”)
.Ex
. Use
dry
era
se b
oard
to so
lve
a pr
oble
m b
y ad
ding
one
mor
e.
Leve
l I A
A S
tude
nts
will
:EE
1.O
A.2
. Put
in a
n ite
m fr
om a
gro
up, u
sing
tech
nolo
gy o
r obj
ects
.Ex
. Dro
p on
e m
ore
bean
bag
into
a b
ucke
t with
a v
erba
l pro
mpt
.Ex
. Dro
p on
e pi
ng-p
ong
ball
into
a P
ringl
es c
an w
ith h
ole
cut i
nto
lid.
Ex. F
ollo
w d
irecti
ons t
o ad
d on
e co
untin
g bl
ock
to a
gro
up.
Math | Kindergarten-5 Grade 23
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
and
appl
y pr
oper
ties
of o
pera
tion
s an
d th
e re
lati
onsh
ip b
etw
een
addi
tion
an
d su
btra
ction
.
1.O
A.3
. App
ly p
rope
rties
of
oper
ation
s as s
trat
egie
s to
add
and
subt
ract
.3 Exa
mpl
es: I
f 8 +
3
= 11
is k
now
n, th
en 3
+ 8
= 1
1 is
als
o kn
own.
(Co
mm
utati
ve
prop
erty
of a
dditi
on.)
To
add
2 +
6 +
4, th
e se
cond
two
num
bers
can
be
adde
d to
mak
e a
10, s
o 2
+ 6
+ 4
= 2
+ 10
=
12.
(Ass
ocia
tive
prop
erty
of
addi
tion.
)
EE1.
OA
.3. N
/A
1.O
A.4
. Und
erst
and
subt
racti
on
as a
n un
know
n-ad
dend
pro
blem
. Fo
r exa
mpl
e, s
ubtr
act 1
0 –
8 by
fin
ding
the
num
ber t
hat m
akes
10
whe
n ad
ded
to 8
. A
dd a
nd
subt
ract
with
in 2
0.
EE1.
OA
.4. N
/A (S
ee E
ENBT
.1.4
an
d EE
NBT
.1.6
)
24 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Add
and
sub
trac
t wit
hin
20.
1.O
A.5
. Rel
ate
coun
ting
to
addi
tion
and
subt
racti
on (e
.g.,
by
coun
ting
on 2
to a
dd 2
).
EE1.
OA
.5.a
. Use
man
ipul
ative
s or
visu
al re
pres
enta
tions
to
indi
cate
the
num
ber t
hat r
esul
ts
whe
n ad
ding
one
mor
e.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
OA
.5.a
. Ind
icat
e th
e nu
mer
al th
at re
sults
whe
n ad
ding
one
mor
e to
the
num
bers
.Ex
. With
nin
e be
ads o
n th
e st
ring,
indi
cate
“10
” aft
er a
ddin
g on
e m
ore.
Ex. A
fter t
akin
g att
enda
nce,
indi
cate
how
man
y st
uden
ts a
re p
rese
nt w
hen
addi
ng o
ne
mor
e st
uden
t.Ex
. Sta
nd o
n la
rge
floor
num
ber l
ine,
det
erm
ine
how
man
y, an
d th
en a
dd o
ne m
ore
to
dete
rmin
e su
m.
Ex. U
se ta
ble
num
ber l
ine
to li
ne u
p co
untin
g sti
cks,
then
add
one
mor
e to
eac
h.Ex
. Whe
n te
achi
ng ti
me
to th
e ho
ur, t
each
er sa
ys it
is 2
:00,
(and
poi
nts t
o cl
ock)
wha
t tim
e w
ill it
be
in o
ne h
our?
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
OA
.5.a
. Use
man
ipul
ative
s or v
isual
repr
esen
tatio
ns to
indi
cate
the
num
ber t
hat
resu
lts w
hen
addi
ng o
ne m
ore.
Ex. T
here
are
four
cra
cker
s on
the
tabl
e. “
If I a
dd o
ne m
ore,
how
man
y w
ill I
have
?”
Answ
er is
five
.Ex
. If t
hree
chi
ldre
n ar
e sitti
ng a
t the
tabl
e w
ith fo
ur c
hairs
, ind
icat
e “f
our”
whe
n as
ked,
“H
ow m
any
will
we
have
whe
n Li
nda
arriv
es?”
Ex. U
sing
toke
ns a
s pos
itive
rein
forc
emen
t, te
ache
r poi
nts o
ut th
at th
e st
uden
t has
five
to
kens
, the
n ad
ds o
ne m
ore
and
asks
how
man
y.
Leve
l II A
A S
tude
nts
will
:EE
1.O
A.5
.a. I
ndic
ate
the
num
bers
that
resu
lt w
hen
addi
ng o
ne m
ore
to th
e nu
mbe
rs fr
om
one
to fi
ve.
Ex. A
dd o
ne m
ore
to a
set o
f fou
r obj
ects
.Ex
. Whe
n pr
esen
ted
with
four
bea
ds o
n a
strin
g, a
dd o
ne m
ore.
Ex. W
hile
follo
win
g st
eps t
o pl
ay a
gam
e, a
dd o
ne m
ore
card
to a
set o
f car
ds.
Leve
l I A
A S
tude
nts
will
:EE
1.O
A.5
.a. D
o or
giv
e on
e m
ore.
Ex. W
hen
aske
d, h
and
or g
ive
the
teac
her o
ne m
ore
bloc
k.Ex
. Whe
n as
ked,
cla
p on
e m
ore
time.
Ex. U
se a
Big
Mac
switc
h to
requ
est o
ne m
ore
song
, tur
n, o
r ite
m w
ith te
ache
r pro
mpt
.Ex
. In
adap
tive
P.E.
, per
form
one
mor
e ex
erci
se, b
all t
hrow
, etc
. upo
n re
ques
t.Ex
. Loo
k at
a b
lock
whe
n as
ked
to g
ive
one
mor
e.
Math | Kindergarten-5 Grade 25
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
OA
.5.b
. App
ly k
now
ledg
e of
“o
ne le
ss”
to su
btra
ct o
ne fr
om
the
num
bers
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
OA
.5.b
. Ind
icat
e th
e nu
mer
al th
at is
one
less
.Ex
. With
14
bead
s on
the
strin
g, in
dica
te “
13”
after
subt
racti
ng o
ne.
Ex. S
how
n 10
bea
ds o
n a
strin
g, a
nd a
sked
, “W
hat i
s one
less
?” in
dica
te “
nine
.”Ex
. Afte
r tak
ing
atten
danc
e, in
dica
te h
ow m
any
stud
ents
are
pre
sent
afte
r one
stud
ent
goes
hom
e.Ex
. Giv
en a
ver
tical
num
ber s
ente
nce,
dra
w o
bjec
ts to
mat
ch fi
rst n
umbe
r and
then
cro
ss
out t
he c
orre
spon
ding
am
ount
of t
he se
cond
num
ber t
o ar
rive
at d
iffer
ence
.Ex
. Poi
nt to
the
num
ber l
eft w
hen
10 st
uden
ts a
re st
andi
ng in
a li
ne a
nd o
ne si
ts d
own.
Ex. L
isten
to th
e te
ache
r rea
d 10
Litt
le M
onke
ys Ju
mpi
ng o
n th
e Be
d an
d te
ll ho
w m
any
are
left
at e
ach
page
.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
OA
.5.b
. App
ly k
now
ledg
e of
“one
less
” to
subt
ract
one
from
the
num
bers
.Ex
. Ide
ntify
the
num
ber r
emai
ning
whe
n on
e ob
ject
is ta
ken
away
from
a g
roup
of s
ix
obje
cts a
rran
ged
on th
e ta
ble.
Ex. G
iven
five
task
s to
com
plet
e, te
ll ho
w m
any
task
s are
left
to c
ompl
ete
befo
re lu
nch
as
the
teac
her c
heck
s eac
h off
the
list.
Ex. T
ell h
ow m
any
chai
rs a
re le
ft ea
ch ti
me
whe
n pl
ayin
g m
usic
al c
hairs
as t
he te
ache
r ta
kes a
way
one
cha
ir ea
ch ti
me.
Ex. U
sing
a co
mpu
ter w
ith to
uch
scre
en a
nd m
ath
softw
are
to c
lick
and
drag
obj
ects
one
at
a ti
me
away
from
tota
l, de
term
ine
how
man
y ar
e le
ft ea
ch ti
me
an o
bjec
t is d
ragg
ed
away
from
the
tota
l set
.
Leve
l II A
A S
tude
nts
will
:EE
1.O
A.5
.b. I
ndic
ate
how
man
y ar
e le
ft w
hen
one
is ta
ken
away
from
two
to fo
ur o
bjec
ts.
Ex. W
ith fo
ur c
ounti
ng c
ubes
, tak
e aw
ay o
ne to
leav
e th
ree
coun
ting
cube
s.Ex
. Whe
n pr
esen
ted
with
four
bea
ds o
n a
strin
g, ta
ke a
way
one
and
indi
cate
how
man
y ar
e le
ft.Ex
. Giv
en fo
ur q
uart
ers,
spen
d on
e at
the
scho
ol st
ore
and
then
tell
the
teac
her h
ow m
any
quar
ters
are
left
in b
ank.
Ex. U
sing
mat
eria
ls pr
esen
ted
at a
tabl
e, e
ach
stud
ent t
akes
one
as t
he g
roup
cou
nts
back
war
ds.
Leve
l I A
A S
tude
nts
will
:EE
1.O
A.5
.b. R
emov
e or
take
one
aw
ay.
Ex. E
rase
one
mar
k fr
om a
gro
up o
f tw
o on
a d
ry e
rase
boa
rd.
Ex. T
ake
away
one
cou
nting
bea
r fro
m a
gro
up o
f thr
ee.
Ex. T
ake
one
bloc
k fr
om a
gro
up o
f tw
o.
26 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
1.O
A.6
. Add
and
subt
ract
with
in
20, d
emon
stra
ting
fluen
cy
for a
dditi
on a
nd su
btra
ction
w
ithin
10.
Use
stra
tegi
es su
ch
as c
ounti
ng o
n; m
akin
g te
n (e
.g.,
8 +
6 =
8 +
2 +
4 =
10 +
4
= 14
); de
com
posin
g a
num
ber
lead
ing
to a
ten
(e.g
., 13
– 4
=
13 –
3 –
1 =
10
– 1
= 9)
; usin
g th
e re
latio
nshi
p be
twee
n ad
ditio
n an
d su
btra
ction
(e.g
., kn
owin
g th
at 8
+ 4
= 1
2, o
ne k
now
s 12
– 8
= 4)
; and
cre
ating
equ
ival
ent
but e
asie
r or k
now
n su
ms (
e.g.
, ad
ding
6 +
7 b
y cr
eatin
g th
e kn
own
equi
vale
nt 6
+ 6
+ 1
= 1
2 +
1 =
13).
EE1.
OA
.6. N
/A
Wor
k w
ith
addi
tion
and
su
btra
ction
equ
ation
s.
1.O
A.7
. Und
erst
and
the
mea
ning
of
the
equa
l sig
n, a
nd d
eter
min
e if
equa
tions
invo
lvin
g ad
ditio
n an
d su
btra
ction
are
true
or
false
. Fo
r exa
mpl
e, w
hich
of t
he
follo
win
g eq
uatio
ns a
re tr
ue a
nd
whi
ch a
re fa
lse?
6 =
6, 7
= 8
– 1
, 5
+ 2
= 2
+ 5,
4 +
1 =
5 +
2.
EE1.
OA
.7. N
/A (S
ee E
E1.O
A.1.
b)
1.O
A.8
. Det
erm
ine
the
unkn
own
who
le n
umbe
r in
an a
dditi
on
or su
btra
ction
equ
ation
re
latin
g th
ree
who
le n
umbe
rs.
For e
xam
ple,
det
erm
ine
the
unkn
own
num
ber t
hat m
akes
th
e eq
uatio
n tr
ue in
eac
h of
the
equa
tions
8 +
? =
11,
5 =
_ –
3, 6
+
6 =
_.
EE1.
OA
.8. N
/A
Math | Kindergarten-5 Grade 27
Firs
t G
rad
e M
ath
emat
ics
Stan
dar
ds:
Nu
mb
er a
nd
Op
erat
ion
s in
Bas
e T
en
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Exte
nd th
e co
unti
ng s
eque
nce.
1.N
BT.1
. Cou
nt to
120
, sta
rting
at
any
num
ber l
ess t
han
120.
In
this
rang
e, re
ad a
nd w
rite
num
eral
s and
repr
esen
t a
num
ber o
f obj
ects
with
a w
ritten
nu
mer
al.
EE1.
NBT
.1.a
. Cou
nt b
y on
es.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.1.a
. Cou
nt fr
om 1
- 30
with
mea
ning
; car
dina
lity.
Ex. P
artic
ipat
e in
a c
lass
room
cha
nt to
cou
nt n
umbe
rs 1
– 3
0.Ex
. Rec
ite th
e co
unt s
eque
nce
1 –
30.
Ex. S
ing
num
bers
to 3
0.
Leve
l III
AA
Stu
dent
s w
ill:
EE1N
BT.1
.a. C
ount
by
ones
.Ex
. Par
ticip
ate
in a
cla
ssro
om c
hant
to c
ount
num
bers
1 –
20.
Ex. R
ecite
the
coun
t seq
uenc
e 1
– 20
.Ex
. Sin
g nu
mbe
rs to
20.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.1
.a. C
ount
to 1
0.Ex
. Par
ticip
ate
in a
cla
ssro
om c
hant
1 -1
0.Ex
. Rec
ite n
umbe
rs 1
-10.
Ex. S
ing
num
bers
1-1
0.
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.1
.a. C
ount
to tw
o.Ex
. Sin
g nu
mbe
rs u
p to
two
with
teac
her.
Ex. C
ount
alo
ng u
sing
a vo
ice
outp
ut c
omm
unic
ative
dev
ice
that
will
cou
nt in
ord
er (1
-2)
upon
eac
h ac
tivati
on.
Ex. A
ctiva
te a
pre
-pro
gram
med
sequ
ence
d co
mm
unic
ation
dev
ice
repe
ated
ly to
reci
te th
e nu
mbe
rs o
ne a
nd tw
o.
28 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
NBT
.1.b
. Cou
nt a
s man
y as
10
obj
ects
and
repr
esen
t the
qu
antit
y w
ith th
e co
rres
pond
ing
num
eral
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.1.b
. Cou
nt u
p to
20
obje
cts a
nd re
pres
ent t
he q
uanti
ty w
ith a
num
eral
.Ex
. Cou
nt a
num
ber o
f dot
s on
a ca
rd a
nd w
rite
or se
lect
the
corr
espo
ndin
g nu
mer
al.
Ex. C
ount
the
num
ber o
f nam
es o
n th
e att
enda
nce
char
t and
writ
e th
e co
rres
pond
ing
num
ber u
p to
20.
Ex. C
ount
up
num
ber o
f pen
nies
/tok
ens i
n ba
nk a
t end
of d
ay a
nd re
cord
on
bala
nce
shee
t.Ex
. Usin
g tw
o 10
fram
es, c
ount
out
disk
s in
a ba
g an
d re
cord
resu
lt to
cla
ssro
om g
raph
.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
NBT
.1.b
. Cou
nt a
s man
y as
10
obje
cts a
nd re
pres
ent t
he q
uanti
ty w
ith th
e co
rres
pond
ing
num
eral
.Ex
. Tea
cher
will
show
the
stud
ent n
umer
al n
ine
and
ask
them
to g
ive
them
that
man
y bl
ocks
.Ex
. Whe
n sh
own
the
num
ber fi
ve, c
ount
five
cra
yons
.Ex
. Mat
ch a
num
eral
car
d to
a g
roup
of o
bjec
ts.
Ex. W
rite
or d
raw
the
num
eral
that
cor
resp
onds
with
the
num
ber o
f cou
nting
stick
s.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.1
.b. C
ount
as m
any
as fi
ve o
bjec
ts a
nd/o
r rep
rese
nt th
e qu
antit
y w
ith th
e ap
prop
riate
num
eral
.Ex
. Tap
obj
ects
whi
le c
ounti
ng.
Ex. D
urin
g te
ache
r-led
cou
nting
/cla
ppin
g ro
utine
, cla
p on
ce fo
r eac
h nu
mbe
r the
teac
her
reci
tes.
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.1
.b. C
ount
up
to tw
o ob
ject
s.Ex
. Use
tapp
ing,
switc
hing
, blin
king
, cla
ppin
g, c
hanti
ng to
cou
nt tw
o ob
ject
s.Ex
. Han
d ite
ms t
o pe
er o
ne a
t a ti
me,
whi
le p
eer c
ount
s.Ex
. Use
eye
gaz
e w
ith la
rge
num
ber l
ine
to lo
ok a
t eac
h nu
mbe
r as t
each
er c
ount
s.
Math | Kindergarten-5 Grade 29
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
plac
e va
lue.
1.N
BT.2
. Und
erst
and
that
the
two
digi
ts o
f a tw
o-di
git n
umbe
r re
pres
ent a
mou
nts o
f ten
s and
on
es.
Und
erst
and
the
follo
win
g as
spec
ial c
ases
:
10 c
an b
e th
ough
t of a
s a
bund
le o
f ten
one
s — c
alle
d a
“ten
.”
The
num
bers
from
11
to 1
9 ar
e co
mpo
sed
of a
ten
and
one,
two,
thre
e, fo
ur, fi
ve, s
ix,
seve
n, e
ight
, or n
ine
ones
.
The
num
bers
10,
20,
30
, 40,
50,
60,
70,
80,
90
refe
r to
one
, tw
o, th
ree,
four
, five
, six
, se
ven,
eig
ht, o
r nin
e te
ns (a
nd 0
on
es).
EE1.
NBT
.2. C
reat
e se
ts o
f 10.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.2. C
reat
e m
ultip
le se
ts o
f ten
with
an
odd
num
ber o
f obj
ects
(rem
aind
ers)
.Ex
. Giv
en a
bow
l of 2
7 co
untin
g be
ars a
nd b
aggi
es, p
ut 1
0 at
a ti
me
in e
ach
bagg
ie a
nd
leav
e th
e le
ftove
rs in
the
bow
l.Ex
. Giv
en a
box
of 3
2 pa
perc
lips a
nd e
nvel
opes
, put
10
at a
tim
e in
eac
h en
velo
pe.
Ex. U
se a
10
com
part
men
t egg
car
ton
to c
ount
out
10
penn
ies t
o ex
chan
ge fo
r a d
ime.
Pu
t rem
aind
ers b
ack
in b
ank.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
NBT
.2. C
reat
e se
ts o
f 10.
Ex. G
iven
20
cray
ons,
div
ide
them
into
two
sets
of 1
0.Ex
. Giv
en 3
0 pl
ayin
g ca
rds,
pas
s out
10
card
s to
thre
e pl
ayer
s.Ex
. Dur
ing
cale
ndar
, stu
dent
s cou
nt o
ut 1
0 st
raw
s to
repr
esen
t 10
days
in sc
hool
and
bu
ndle
s the
m a
nd m
oves
the
bund
le to
the
tens
pla
ce p
ocke
t.Ex
. Fiv
e st
uden
ts w
ork
coop
erati
vely
to c
ount
out
10
penn
ies e
ach,
com
bine
and
roll
for
the
bank
.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.2
. Cre
ate
one
set o
f 10
to m
atch
ano
ther
set o
f 10.
Ex. C
reat
e on
e se
t of 1
0 us
ing
a jig
, mod
el, o
r tem
plat
e to
mat
ch a
noth
er se
t of 1
0.Ex
. Giv
en a
set o
f 10
obje
cts a
rran
ged
in a
row,
mak
e an
othe
r row
of 1
0 ob
ject
s.Ex
. Giv
en a
hul
a ho
op, g
roup
a se
t of 1
0 be
anba
gs in
it.
Ex. C
ount
out
eno
ugh
toy
rings
for e
ach
of 1
0 fin
gers
and
put
them
on
and
chec
k fo
r ac
cura
cy.
Ex. M
ake
a “b
ean
stick
” by
cou
nting
out
10
bean
s and
glu
ing
them
on
a po
psic
le sti
ck to
m
atch
a m
odel
.Ex
. Acc
ess a
switc
h th
at sa
ys “s
top”
or “
that
’s it”
whe
n w
atch
ing
or li
sten
ing
to a
noth
er
indi
vidu
al a
rran
ge se
ts o
r gro
ups o
f 10.
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.2
. Ide
ntify
a se
t of fi
ve.
Ex. S
elec
t a se
t of fi
ve o
bjec
ts fr
om a
cho
ice
of tw
o or
mor
e se
ts.
Ex. C
hoos
e fr
om a
set o
f mar
kers
and
a se
t of c
rayo
ns.
(Exp
osur
e to
voc
abul
ary:
set)
Ex. C
hoos
e fr
om tw
o se
ts o
f pic
ture
s the
one
that
mat
ches
the
mod
el se
t of fi
ve.
30 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
1.N
BT.3
. Com
pare
two
two-
digi
t num
bers
bas
ed o
n m
eani
ngs o
f the
tens
and
one
s di
gits
, rec
ordi
ng th
e re
sults
of
com
paris
ons w
ith th
e sy
mbo
ls >,
=,
and
<.
EE1.
NBT
.3. C
ompa
re tw
o gr
oups
of
10
or fe
wer
item
s whe
n th
e qu
antit
y of
item
s in
each
gro
up
is sim
ilar.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.3. C
hoos
e th
e la
rger
/sm
alle
r set
of i
tem
s tha
t are
<10
, >10
whe
n th
e se
ts d
iffer
by
thre
e or
few
er.
Ex. G
iven
two
stac
ks o
f boo
ks, i
denti
fy w
hich
set h
as <
10, >
10.
Ex. G
iven
two
penc
il bo
xes,
iden
tify
whi
ch p
enci
l box
con
tain
s <10
, >10
pen
cils.
Ex. G
iven
two
stac
ks o
f cup
s, id
entif
y w
hich
set h
as <
10, >
10.
Ex. G
iven
two
clas
s lin
es o
f stu
dent
s, id
entif
y w
hich
set h
as <
10, >
10.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
NBT
.3. C
ompa
re tw
o gr
oups
of 1
0 or
few
er it
ems w
hen
the
quan
tity
of it
ems i
n ea
ch
grou
p is
simila
r.Ex
. Giv
en tw
o pe
ncil
boxe
s, o
ne w
ith fi
ve a
nd o
ne w
ith 1
0 pe
ncils
, ide
ntify
whi
ch p
enci
l bo
x co
ntai
ns th
e sm
alle
r set
of i
tem
s.Ex
. Giv
en o
ne se
t of c
ubes
with
1-4
cub
es, a
nd a
seco
nd se
t of c
ubes
with
6-1
0, id
entif
y th
e se
t with
less
than
five
.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.3
. Cho
ose
the
mat
chin
g se
t of i
tem
s.Ex
. Giv
en th
ree
penc
il bo
xes,
iden
tify
whi
ch tw
o pe
ncil
boxe
s con
tain
the
sam
e nu
mbe
r of
item
s.Ex
. Giv
en th
ree
brac
elet
s, m
atch
a se
cond
set o
f thr
ee b
race
lets
from
two
choi
ces.
Ex. G
iven
one
set o
f cou
nting
cub
es w
ith 1
-4 c
ubes
, and
a se
cond
set o
f cou
nting
cub
es
with
6-9
cub
es, i
denti
fy th
e la
rger
set.
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.3
. Mat
ch se
ts o
f one
, tw
o, o
r thr
ee o
bjec
ts .s
how
ing
the
sam
e nu
mbe
r of o
bjec
ts.
Ex. G
iven
thre
e se
ts o
f obj
ects
of o
ne o
r tw
o ob
ject
s, m
atch
the
two
show
ing
the
sam
e nu
mbe
r.
Math | Kindergarten-5 Grade 31
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
pla
ce v
alue
und
erst
andi
ng
and
prop
erti
es o
f ope
rati
ons
to
add
and
subt
ract
.
1.N
BT.4
. Add
with
in 1
00,
incl
udin
g ad
ding
a tw
o-di
git
num
ber a
nd a
one
-dig
it nu
mbe
r, an
d ad
ding
a tw
o-di
git n
umbe
r an
d a
mul
tiple
of 1
0, u
sing
conc
rete
mod
els o
r dra
win
gs
and
stra
tegi
es b
ased
on
plac
e va
lue,
pro
perti
es o
f ope
ratio
ns,
and/
or th
e re
latio
nshi
p be
twee
n ad
ditio
n an
d su
btra
ction
; rel
ate
the
stra
tegy
to a
writt
en m
etho
d an
d ex
plai
n th
e re
ason
ing
used
. U
nder
stan
d th
at in
add
ing
two-
digi
t num
bers
, one
add
s ten
s an
d te
ns, o
nes a
nd o
nes;
and
so
meti
mes
it is
nec
essa
ry to
co
mpo
se a
ten.
EE1.
NBT
.4. C
ompo
se n
umbe
rs
less
than
or e
qual
to fi
ve in
mor
e th
an o
ne w
ay.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.4. C
ompo
se n
umbe
rs le
ss th
an o
r equ
al to
10
in m
ore
than
one
way
.Ex
. Giv
en a
bow
l of p
enni
es, a
nd m
ake
sets
of 1
0 w
ith d
iffer
ent n
umbe
rs o
f pen
nies
.Ex
. Giv
en la
nyar
ds o
r str
ing
and
two
colo
rs o
f bea
ds, c
reat
e br
acel
ets w
ith v
aryi
ng c
ombi
natio
ns
of 1
0 co
lore
d be
ads.
(O
ne b
race
let w
ith 1
0 bl
ue b
eads
, one
bra
cele
t with
five
blu
e be
ads,
five
red
bead
s, e
tc.).
Ex. U
sing
a tr
iang
le g
raph
ic o
rgan
izer,
plac
e ra
ndom
am
ount
s of m
anip
ulati
ves i
n tw
o ba
se a
ngle
s an
d m
ove/
com
bine
them
at t
he to
p an
d co
unt h
ow m
any.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
NBT
.4. C
ompo
se n
umbe
rs le
ss th
an o
r equ
al to
five
in m
ore
than
one
way
.Ex
. Giv
en a
set o
f red
cou
nting
cub
es a
nd a
set o
f gre
en c
ounti
ng c
ubes
, cre
ate
a se
t of o
nly
red,
a
set o
f onl
y gr
een,
and
a se
t of m
ixed
red
and
gree
n to
talin
g fiv
e in
eac
h ca
se.
Ex. G
iven
a fi
ve-p
iece
inse
t puz
zle a
nd tw
o tr
ays,
take
out
and
sort
the
puzz
le p
iece
s int
o th
e tr
ays i
n m
ore
than
one
way
.Ex
. Pla
ce c
olor
ed m
acar
oni p
iece
s on
each
num
ber o
n a
num
ber l
ine
up to
five
in a
ny c
ombi
natio
n,
then
strin
g.Ex
. Sha
ke tw
o siz
es o
f mar
kers
or p
aint
ed b
eans
in a
cup
and
spill
. As
k st
uden
ts to
cou
nt e
ach
colo
r an
d th
en c
ount
all
toge
ther
.Ex
. Dra
w c
ircle
s and
squa
res t
o m
ake
five
in a
ny c
ombi
natio
n.Ex
. Use
a m
uffin
pan
with
five
wel
ls to
pla
ce o
ne c
olor
ed b
lock
in e
ach
wel
l, th
en c
ount
to fi
nd to
tal.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.4
. Ide
ntify
(sub
itize
) set
s of o
ne to
thre
e ob
ject
s.Ex
. Giv
en a
set o
f tw
o sti
cker
s and
a se
t of t
hree
stick
ers o
n a
page
, find
the
set o
f thr
ee sti
cker
s w
hen
aske
d fo
r thr
ee.
Ex. G
iven
a d
omin
o w
ith o
ne d
ot a
nd a
dom
ino
with
thre
e do
ts, l
ocat
e th
e do
min
o w
ith o
ne d
ot
whe
n as
ked
for o
ne.
Ex. G
iven
sets
of o
ne to
thre
e ob
ject
s, in
dica
te th
e se
t with
thre
e ob
ject
s whe
n as
ked
for t
hree
. If
the
stud
ent c
ount
s, te
ache
r ask
s aga
in fo
r thr
ee a
nd re
info
rce,
“Th
is is
thre
e.”
Ex. T
each
er h
olds
up
1-3
finge
rs a
nd a
sks h
ow m
any.
If s
tude
nt c
ount
s, te
ache
r ask
s aga
in fo
r fina
l nu
mbe
r and
rein
forc
e, “
This
is th
ree.
”
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.4
. Rep
eat t
he n
umbe
r of o
bjec
ts in
sets
of 1
-3 o
bjec
ts.
Ex. W
atch
as t
he te
ache
r use
s one
scar
f, sa
ying
, “I h
ave
one
scar
f. H
ow m
any?
”Ex
. Atte
nd to
a fi
nger
-pla
y of
“Th
ree
Litt
le M
onke
ys”
told
with
fing
er-p
uppe
ts a
nd re
peat
s how
man
y m
onke
ys.
Ex. R
epea
t whe
n te
ache
r say
s how
man
y ey
es, n
ose,
ear
s, m
outh
, etc
. he/
she
has.
Ex. P
oint
to o
r ind
icat
e ite
ms o
f clo
thin
g as
teac
her c
ount
s how
man
y (e
.g.,
“I h
ave
two
shoe
s. H
ow
man
y sh
oes?
” “
I hav
e on
e ha
t. H
ow m
any
hats
?” “
I hav
e tw
o m
itten
s. H
ow m
any
mitt
ens?
” “
I ha
ve o
ne c
oat.
How
man
y co
ats?
”).
1.N
BT.5
. Giv
en a
two-
digi
t nu
mbe
r, m
enta
lly fi
nd 1
0 m
ore
or 1
0 le
ss th
an th
e nu
mbe
r, w
ithou
t hav
ing
to c
ount
; exp
lain
th
e re
ason
ing
used
.
EE1.
NBT
.5. N
/A (S
ee E
E1.O
A.5.
a an
d EE
1.O
A.5.
b)
32 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
1.N
BT.6
. Sub
trac
t mul
tiple
s of
10
in th
e ra
nge
10-9
0 fr
om
mul
tiple
s of 1
0 in
the
rang
e 10
-90
(pos
itive
or z
ero
diffe
renc
es),
usin
g co
ncre
te m
odel
s or
draw
ings
and
stra
tegi
es b
ased
on
pla
ce v
alue
, pro
perti
es
of o
pera
tions
, and
/or t
he
rela
tions
hip
betw
een
addi
tion
and
subt
racti
on; r
elat
e th
e st
rate
gy to
a w
ritten
met
hod
and
expl
ain
the
reas
onin
g us
ed.
EE1.
NBT
.6. D
ecom
pose
num
bers
le
ss th
an o
r equ
al to
five
in m
ore
than
one
way
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
NBT
.6. D
ecom
pose
num
bers
less
than
or e
qual
to 1
0 in
mor
e th
an o
ne w
ay.
Ex. G
iven
10
or fe
wer
bea
n ba
gs a
nd tw
o ba
sket
s, to
ss b
ean
bags
into
bas
kets
cre
ating
diff
eren
t set
s ea
ch ti
me
usin
g a
dry
eras
e bo
ard.
Ex. G
iven
10
or fe
wer
cou
nting
blo
cks,
arr
ange
them
into
two
diffe
rent
gro
up c
ombi
natio
ns.
Ex. G
iven
a tr
iang
le g
raph
ic o
rgan
izer w
ith u
p to
10
man
ipul
ative
s in
the
tip, s
epar
ate
the
tota
l int
o tw
o (a
ny si
ze) g
roup
s in
the
base
ang
les.
Ex. A
sk st
uden
ts h
ow m
any
way
s the
y ca
n cr
eate
10
cent
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
NBT
.6. D
ecom
pose
num
bers
less
than
or e
qual
to fi
ve in
mor
e th
an o
ne w
ay.
Ex. G
iven
five
boo
ks, d
ivid
e th
em in
to tw
o gr
oups
in m
ore
than
one
way
.Ex
. Giv
en fi
ve m
atch
box
cars
and
two
card
boar
d “g
arag
es,”
“par
k” th
e ca
rs in
the
gara
ges i
n va
ryin
g w
ays.
(Fi
rst ti
me,
stud
ent m
ay p
ut tw
o ca
rs in
one
gar
age
and
thre
e ca
rs in
the
othe
r gar
age,
and
te
ache
r ask
s, “
Can
you
do it
a d
iffer
ent w
ay th
is tim
e?”
and
stud
ent c
ontin
ues t
o di
strib
ute
the
cars
in
var
ying
way
s.)
Ex. G
iven
five
cou
nting
blo
cks,
div
ide
them
into
two
grou
ps in
mor
e th
an o
ne w
ay.
Ex. U
se te
ache
r-mad
e di
ce to
roll
com
bina
tions
tota
ling
up to
five
.Ex
. Pla
y a
finge
r gam
e w
here
two
stud
ents
put
up
rand
om n
umbe
r of fi
nger
s on
one
hand
eac
h to
cr
eate
five
. If
they
do,
the
stud
ents
’ tea
m e
arns
a p
oint
.Ex
. Use
a d
ry e
rase
boa
rd to
dec
ompo
se n
umbe
rs le
ss th
an fi
ve in
mor
e th
an o
ne w
ay.
Leve
l II A
A S
tude
nts
will
:EE
1.N
BT.6
. Dec
ompo
se n
umbe
rs le
ss th
an o
r equ
al to
five
in o
ne w
ay.
Ex. G
iven
a h
andf
ul o
f blo
cks (
up to
five
), se
para
te in
to tw
o pi
les i
n an
y or
der.
Cou
nt a
nd la
bel e
ach
pile
with
teac
her a
ssist
ance
.Ex
. Sor
t up
to fi
ve it
ems i
nto
two
grou
ps.
Ex. G
iven
a g
roup
of fi
ve to
kens
com
pose
d of
two
diffe
rent
col
ors,
cou
nt o
ut to
tal,
sort
with
teac
her
by c
olor
and
cou
nt e
ach
grou
p.
Leve
l I A
A S
tude
nts
will
:EE
1.N
BT.6
. Ide
ntify
two
sets
of t
he sa
me
obje
ct (l
ess t
han
five)
as t
hey
are
bein
g de
com
pose
d.Ex
. Ask
ed to
find
the
sam
e ite
m a
s sho
wn
som
ewhe
re e
lse in
the
room
, brin
g tw
o of
the
sam
e ite
ms
toge
ther
to m
ake
a bi
gger
set.
Ex. R
epea
t as t
he te
ache
r dec
ompo
ses t
wo
obje
cts i
nto
two
grou
ps (e
.g.,
Teac
her h
as tw
o ba
lls,
rolls
one
to th
e st
uden
ts.
Teac
her s
ays,
“Yo
u ha
ve o
ne b
all,
I hav
e on
e ba
ll. H
ow m
any
balls
do
you
have
?” S
tude
nt ro
lls it
bac
k at
pro
mpt
. Te
ache
r say
s, “
Now
, I h
ave
two
balls
. “ H
ow m
any
balls
do
I ha
ve?”
Rep
eat w
ith v
ario
us c
ombi
natio
ns.).
Ex. R
epea
t as t
he te
ache
r dec
ompo
ses t
wo
coun
ting
bear
s on
the
tabl
e in
a p
ile (e
.g.,
Teac
her s
ays,
“H
ere
are
two
bear
s. H
ow m
any
bear
s are
ther
e? T
ake
one.
Now
ther
e is
one
bear
on
the
tabl
e.
How
man
y be
ars a
re o
n th
e ta
ble
now
?”).
Ex. R
epea
t as t
he te
ache
r dec
ompo
ses t
wo
book
s (e.
g., T
each
er c
ount
s alo
ud th
e nu
mbe
r of b
ooks
as
they
are
han
ded
to e
ach
stud
ent.
Teac
her s
ays,
“Th
ere
are
two
book
s. H
ow m
any
book
s are
th
ere?
Her
e is
one
for y
ou.
How
man
y bo
oks d
o yo
u ha
ve?
Her
e is
one
for y
ou.
How
man
y bo
oks
do y
ou h
ave?
”).
Math | Kindergarten-5 Grade 33
Firs
t G
rad
e M
ath
emat
ics
Stan
dar
ds:
Mea
sure
men
t an
d D
ata
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Mea
sure
leng
ths
indi
rect
ly a
nd
by it
erati
ng le
ngth
uni
ts.
1.M
D.1
. Ord
er th
ree
obje
cts b
y le
ngth
; com
pare
the
leng
ths o
f tw
o ob
ject
s ind
irect
ly b
y us
ing
a th
ird o
bjec
t.
1.M
D.2
. Exp
ress
the
leng
th o
f an
obj
ect a
s a w
hole
num
ber o
f le
ngth
uni
ts, b
y la
ying
mul
tiple
co
pies
of a
shor
ter o
bjec
t (t
he le
ngth
uni
t) e
nd to
end
; un
ders
tand
that
the
leng
th
mea
sure
men
t of a
n ob
ject
is
the
num
ber o
f sam
e-siz
e le
ngth
uni
ts th
at sp
an it
with
no
gap
s or o
verla
ps.
Lim
it to
co
ntex
ts w
here
the
obje
ct b
eing
m
easu
red
is s
pann
ed b
y a
who
le
num
ber o
f len
gth
units
with
no
gaps
or o
verla
ps.
EE1.
MD
.1-2
. Use
app
ropr
iate
vo
cabu
lary
to d
escr
ibe
the
leng
th o
f an
obje
ct u
sing
the
lang
uage
of l
onge
r/sh
orte
r, ta
ller/
shor
ter.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.1-2
. Mea
sure
and
com
pare
two
simila
r obj
ects
alig
ned
at th
e sa
me
star
ting
poin
t, an
d de
scrib
e w
hich
is lo
nger
/sho
rter
, tal
ler/
shor
ter.
Ex. I
ndic
ate
who
is ta
ller a
nd w
ho is
shor
ter w
hen
two
stud
ents
stan
d sid
e-by
-sid
e.Ex
. Mea
sure
the
heig
ht o
f the
ir de
sks a
nd th
e he
ight
of t
he te
ache
r’s d
esk
with
inte
rlock
ing
cube
s an
d th
en la
y th
em d
own
horiz
onta
lly si
de-b
y-sid
e on
a ta
ble
to c
ompa
re.
Ex. U
se fo
otpr
ints
to m
easu
re o
ff le
ngth
of c
lass
room
ver
sus h
all a
nd st
ate
whi
ch is
long
er/ s
hort
er.
Ex. U
se a
strin
g to
mea
sure
two
obje
cts a
nd te
ll w
hich
is lo
nger
.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.1-2
. Use
app
ropr
iate
voc
abul
ary
to d
escr
ibe
the
leng
th o
f an
obje
ct u
sing
the
lang
uage
of l
onge
r/sh
orte
r, ta
ller/
shor
ter.
Ex. G
iven
two
piec
es o
f str
ing
plac
ed si
de-b
y-sid
e, u
se “
long
er”
and
“sho
rter
” to
des
crib
e th
eir
rela
tive
leng
ths (
e.g.
, “Lo
ok a
t the
se tw
o ob
ject
s and
tell
me
abou
t the
ir le
ngth
.”).
Ex. G
iven
two
penc
ils la
id si
de-b
y-sid
e, u
se “
long
er/s
hort
er”
to d
escr
ibe
each
one
.Ex
. Giv
en tw
o di
ffere
nt k
inds
of o
bjec
ts, t
hat a
re si
mila
r in
all a
ttrib
utes
exc
ept f
or le
ngth
(e.g
. pen
cil
to m
arke
r), b
ut o
ne is
sign
ifica
ntly
long
er th
an th
e ot
her,
tell
whi
ch is
long
er.
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.1
-2. W
ith g
uida
nce
and
supp
ort,
sele
ct fr
om tw
o ev
eryd
ay o
bjec
ts b
ased
on
the
stat
ed a
ttrib
ute
(long
/sho
rt, t
all/s
hort
).Ex
. Usin
g a
mod
el, s
elec
t the
one
that
is sh
orte
r fro
m tw
o op
tions
(e.g
., us
ing
two
sets
of p
ictu
res
the
teac
her s
ays “
Here
are
two
boys
. Th
is on
e is
shor
ter.”
“He
re a
re tw
o do
gs.
Show
me
the
shor
ter o
ne.”)
.Ex
. Poi
nt to
or i
ndic
ate
in a
pic
ture
show
ing
two
stor
y ch
arac
ters
stan
ding
side
-by-
side
the
one
that
is
talle
r (e.
g., “
In th
e st
ory,
Bob
is ta
ller t
han
Joe.
Lo
ok a
t the
pic
ture
. W
hich
one
is ta
ller?
”).
Ex. U
sing
a m
odel
of a
bar
gra
ph, s
elec
t the
bar
that
is ta
ller o
n a
seco
nd g
raph
(e.g
., us
ing
two
bar
grap
hs, t
he te
ache
r say
s “He
re is
the
talle
r bar
on
this
grap
h.”
Sho
w a
seco
nd b
ar g
raph
of d
aily
te
mpe
ratu
res a
nd sa
y, “W
hich
bar
is ta
ller.”
).Ex
. Afte
r bei
ng sh
own
one
boot
and
one
shoe
, ide
ntify
the
“tal
lest
.”
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.1
-2. E
xplo
re ta
ll/sh
ort o
bjec
ts.
Ex. F
ocus
on
the
shor
t and
tall
obje
cts w
hen
the
teac
her i
s pre
senti
ng a
stor
y ab
out l
ong
and
shor
t.Ex
. Exp
lore
soft
bloc
ks (o
ne ta
ll, o
ne sh
ort)
on
thei
r whe
elch
air t
ray,
whi
le te
ache
r say
s and
de
mon
stra
tes,
“Re
ach
up h
igh
to to
uch
the
tall
bloc
k, n
ow to
uch
the
shor
t blo
ck.”
Ex. W
hen
pres
ente
d w
ith a
mod
el, u
se c
lay
to m
ake
a “l
ong
snak
e an
d a
shor
t sna
ke”
and
com
pare
th
em.
Ex. F
irst s
it an
d th
en st
and
to e
xplo
re sh
ort a
nd ta
ll (e
.g.,
Stan
d up
; Now
you
are
tall.
Sit
dow
n; N
ow
you
are
shor
t.)
34 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Tell
and
wri
te ti
me.
1.M
D.3
. Tel
l and
writ
e tim
e in
hou
rs a
nd h
alf-h
ours
usin
g an
alog
and
dig
ital c
lock
s.
EE1.
MD
.3.a
. Dem
onst
rate
an
unde
rsta
ndin
g of
the
term
s “t
omor
row,
yes
terd
ay, a
nd
toda
y.”
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.3.a
. Use
the
wor
ds “
toda
y, to
mor
row,
and
yes
terd
ay”
to re
fer t
o pe
rson
al
activ
ities
and
eve
nts.
Ex. U
sing
lunc
h m
enu,
ans
wer
que
stion
s suc
h as
, “W
hat d
id y
ou h
ave
for l
unch
ye
ster
day?
”, “W
hat d
id y
ou e
at to
day?
”, an
d “W
hat w
ill y
ou h
ave
tom
orro
w?”
Ex. U
se c
lass
room
cal
enda
r to
find
toda
y’s a
ctivi
ties,
afte
r bei
ng sh
own
yest
erda
y’s.
Ex. C
ompl
ete
a gr
aphi
c or
gani
zer b
y pl
acin
g in
dex
card
with
day
of t
he w
eek
writt
en o
n it
and
plac
e it
in th
e co
rrec
t col
umn
unde
r “Ye
ster
day,”
“To
day,”
or “
Tom
orro
w”.
Ex. F
ind
“Tod
ay”
in m
onth
ly p
lann
er w
hen
give
n da
te b
y te
ache
r and
poi
nts t
o it.
Mov
e fin
ger b
ackw
ard
and
forw
ard
to fi
nd “
Yest
erda
y” a
nd “
Tom
orro
w.”
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.3.a
. Dem
onst
rate
und
erst
andi
ng o
f the
term
s “to
mor
row,
yes
terd
ay, a
nd to
day.”
Ex. I
ndic
ate
yest
erda
y, to
day,
or to
mor
row
whe
n te
ache
r ask
s abo
ut a
favo
rite
activ
ity a
nd
whe
n it
happ
ened
or w
ill h
appe
n.Ex
. Giv
en a
cla
ssro
om c
alen
dar,
find
a pi
ctur
e of
an
activ
ity th
at fi
ts w
ith “
Wha
t hap
pens
to
mor
row
?”Ex
. Giv
en a
cal
enda
r, fin
d “T
oday
” an
d pl
ace
a sti
cker
on
it.Ex
. Fin
d “T
omor
row
’s” lu
nch
choi
ce o
n ca
fete
ria m
onth
ly m
enu.
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.3
.a. I
ndic
ate
unde
rsta
ndin
g of
the
term
“to
day.”
Ex. W
hen
show
n tw
o pi
ctur
e ca
rds o
r mat
h cu
e ca
rds o
f dai
ly a
ctivi
ties,
sele
ct th
e ev
ent
that
hap
pens
toda
y.Ex
. Dur
ing
cale
ndar
acti
vity
, ans
wer
the
ques
tion,
“Sh
ow m
e to
day
on th
e ca
lend
ar.
Wha
t is
the
wea
ther
like
toda
y?”
Ex. I
ndic
ate
“Tod
ay”
by p
ointi
ng to
the
corr
ect d
ay o
f the
wee
k, d
raw
ing
a lin
e fr
om it
to
the
corr
ect d
ay o
f the
wee
k, o
r circ
ling
the
day
from
a fi
eld
of th
ree
optio
ns.
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.3
.a. I
denti
fy a
n ac
tivity
that
will
take
pla
ce “
toda
y.”Ex
. Ind
icat
e a
pref
eren
ce w
hen
aske
d an
d sh
own
the
play
item
s, “
Yest
erda
y yo
u pl
ayed
w
ith th
e bl
ocks
. Do
you
wan
t to
play
with
the
bloc
ks o
r the
bal
ls to
day?
”Ex
. Atte
nd to
cla
ss d
iscus
sion
durin
g ca
lend
ar a
nd th
en c
hoos
e pi
ctur
ed a
ctivi
ties f
or
toda
y on
car
ds to
pla
ce o
n th
eir v
isual
sche
dule
.
Math | Kindergarten-5 Grade 35
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
MD
.3.b
. Nam
e a
day
of
the
wee
k fo
r tom
orro
w a
nd
yest
erda
y.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.3.b
. Usin
g a
cale
ndar
, rec
all t
he se
ven
days
of t
he w
eek
and
iden
tify
the
appr
opria
te d
ay fo
r tom
orro
w a
nd y
este
rday
.Ex
. If t
oday
is M
onda
y, w
hat d
ay is
tom
orro
w?
Ex. I
f yes
terd
ay w
as F
riday
, wha
t day
is to
day?
Ex. F
ill in
the
blan
ks to
com
plet
e se
nten
ces w
ith in
dex
card
s with
the
nam
es o
f the
da
ys o
n th
em (i
.e.,
Yest
erda
y w
as _
____
___,
toda
y is
____
____
, and
tom
orro
w w
ill b
e __
____
_.).
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.3.b
. Nam
e a
day
of th
e w
eek
for t
omor
row
and
yes
terd
ay.
Ex. U
se a
cal
enda
r to
dete
rmin
e th
e da
y be
fore
and
the
day
after
toda
y.Ex
. Giv
en to
day,
iden
tify
wha
t tom
orro
w is
?Ex
. If t
oday
is T
uesd
ay, w
hat i
s tom
orro
w?
Ex. I
f tod
ay is
Mon
day,
wha
t was
yes
terd
ay?
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.3
.b. N
ame
a da
y of
the
wee
k.Ex
. Nam
es th
e da
ys o
f the
wee
k, b
ut n
ot in
ord
er.
Ex. W
hen
aske
d, id
entif
y to
day.
Ex. S
ing
a “D
ays o
f the
Wee
k” so
ng.
Ex. A
nsw
er q
uesti
ons b
y na
min
g th
e da
y of
the
wee
k, “
Wha
t day
do
you
go to
chu
rch?
” or
“W
hat d
ay d
o w
e co
ok?”
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.3
.b. I
denti
fy a
n ac
tivity
that
is h
appe
ning
toda
y.Ex
. Ind
icat
e on
e ac
tivity
on
a pi
ctur
e sc
hedu
le w
hen
aske
d, “
Wha
t are
we
doin
g to
day?
”Ex
. Ind
icat
e th
at to
day
is a
scho
ol d
ay.
Ex. D
urin
g ar
t cla
ss, i
denti
fy a
pai
nt b
rush
as t
he to
ol n
eede
d fo
r tod
ay’s
activ
ity w
hen
pres
ente
d w
ith a
cho
ice
of p
aint
brus
h an
d a
sock
.Ex
. Loo
k at
visu
al sc
hedu
le a
nd u
sing
pict
ure
sym
bol,
indi
cate
the
mus
ic sy
mbo
l to
repr
esen
t the
cur
rent
acti
vity
.
36 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
MD
.3.c
. Ide
ntify
acti
vitie
s th
at c
ome
next
, bef
ore,
and
aft
er.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.3.c
. Cor
rect
ly se
quen
ce th
e ac
tiviti
es g
iven
the
dire
ction
to id
entif
y w
hat c
omes
ne
xt, b
efor
e, a
nd a
fter i
n th
e da
y’s o
r wee
k’s s
ched
ule.
Ex. I
denti
fy w
hat i
s the
firs
t acti
vity
of t
he d
ay, a
nd th
en id
entif
y w
hat c
omes
afte
r tha
t.Ex
. Giv
en a
n ac
tivity
such
as g
oing
out
to re
cess
, cor
rect
ly se
quen
ce th
ree
pict
ure
card
s fro
m th
e da
ily sc
hedu
le il
lust
ratin
g ge
tting
read
y to
go
outs
ide.
Ex. S
eque
nce
3-4
even
ts in
a st
ory
with
pic
ture
cue
s.Ex
. Rep
eat a
thre
e-st
ep d
irecti
on a
nd th
en c
arry
it o
ut (i
.e.,
Firs
t, I _
__, n
ext,
I ___
, and
last
, I _
__.)
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.3.c
. Ide
ntify
acti
vitie
s tha
t com
e ne
xt, b
efor
e, a
nd a
fter.
Ex. G
iven
a p
erso
nal s
ched
ule,
ans
wer
que
stion
s suc
h as
, “W
hat d
o w
e ne
ed to
do
next
?”Ex
. Giv
en d
igita
l cam
era
pict
ures
of a
chi
ld e
ngag
ed in
the
day’
s acti
vitie
s, a
nsw
er q
uesti
ons s
uch
as, “
Wha
t did
you
do
befo
re lu
nch
toda
y? W
hat d
id y
ou d
o ne
xt?
Wha
t did
you
do
after
you
afte
r th
at?”
Ex. U
se a
cal
enda
r to
iden
tify
next
, bef
ore,
and
afte
r.Ex
. Seq
uenc
e a
set o
f pic
ture
s dep
ictin
g a
shoe
tyin
g or
jack
et zi
ppin
g ro
utine
.Ex
. At t
he e
nd o
f the
day
, tea
cher
ask
s stu
dent
s to
sequ
ence
the
day’
s eve
nts t
o in
clud
e in
the
pare
nt c
omm
unic
ator
.Ex
. Use
a v
isual
sche
dule
or s
eque
nce
card
s to
com
plet
e an
acti
vity
that
offe
r firs
t, se
cond
, and
third
st
eps.
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.3
.c. I
ndic
ate
activ
ities
that
com
e ne
xt.
Ex. G
iven
a d
aily
sche
dule
listi
ng th
e da
y’s a
ctivi
ties,
ans
wer
the
ques
tion,
“W
e ju
st fi
nish
ed lu
nch.
W
hat h
appe
ns n
ext?
”Ex
. Whe
n pa
rtici
patin
g in
a tr
ansiti
on ro
utine
(mov
ing
from
one
acti
vity
to a
new
acti
vity
), in
dica
te
the
next
acti
vity
.Ex
. Tel
l the
nex
t ste
p in
a fa
mili
ar a
ctivi
ty (e
.g.,
Teac
her c
omm
unic
ates
cla
ssro
om ro
utine
s co
nsist
ently
and
then
ask
s stu
dent
s que
stion
s to
rein
forc
e th
e le
arni
ng b
y as
king
, “W
hat s
tep
com
es
next
to tu
rn in
wor
k?”)
.Ex
. Use
the
clas
sroo
m sc
hedu
le to
indi
cate
wha
t hap
pens
nex
t (e.
g., A
fter ti
mer
ring
s to
end
an
activ
ity, t
he te
ache
r ask
s stu
dent
s, “
Wha
t hap
pens
nex
t?”
and
refe
rs to
the
clas
sroo
m sc
hedu
le.).
Ex. G
iven
a p
atter
n w
ith tw
o re
petiti
ons,
iden
tify
the
“nex
t” o
bjec
t in
the
patte
rn se
quen
ce.
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.3
.c. R
ecog
nize
the
next
acti
vity
.Ex
. Usin
g a
pict
ure
sche
dule
, ide
ntify
the
next
acti
vity
by
indi
catin
g th
e ne
xt p
ictu
re.
Ex. U
sing
a Fi
rst/
Then
gra
phic
with
self-
stick
ing
non-
adhe
sive
pict
ures
, rem
ove
the
Firs
t pic
ture
w
hen
the
task
is d
one.
Ex. W
hen
show
n a
thre
e-pa
rt il
lust
ratio
n of
an
activ
ity w
ith a
bef
ore-
durin
g-aft
er se
quen
ce, i
ndic
ate
whi
ch o
f the
acti
ons c
omes
nex
t.Ex
. Giv
en a
pic
ture
sche
dule
, cho
ose
the
next
acti
vity
pic
ture
to in
dica
te w
hat i
s nex
t.Ex
. Pul
l the
self-
stick
ing
non-
adhe
sive
pict
ure
off th
e sc
hedu
le a
t the
end
of t
he a
ctivi
ty a
nd p
oint
to
the
next
acti
vity
pic
ture
d.
Math | Kindergarten-5 Grade 37
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE1.
MD
.3.d
. Dem
onst
rate
an
unde
rsta
ndin
g th
at te
lling
tim
e is
the
sam
e ev
ery
day.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.3.d
. Dem
onst
rate
an
unde
rsta
ndin
g of
telli
ng ti
me
with
a c
lock
or w
atch
rela
ted
to re
al-li
fe c
onte
xt.
Ex. I
ndic
ate
from
a se
t of t
ools
(e.g
., ru
ler,
mea
surin
g cu
p, w
atch
) wha
t you
will
use
to
know
whe
n it
is tim
e fo
r lun
ch.
Ex. M
atch
noo
n on
an
anal
og c
lock
to lu
nch.
Ex. C
hoos
e pi
ctur
es o
f diff
eren
t sty
le c
lock
s and
wat
ches
and
put
into
a c
ateg
ory,
reje
cting
di
stra
cter
pic
ture
s.Ex
. Mat
ch a
pic
ture
of a
clo
ck to
a c
lock
and
tell
wha
t a c
lock
is u
sed
for.
Ex. M
atch
the
curr
ent ti
me
on a
clo
ck w
ith th
e ap
prop
riate
acti
vity
from
a p
ictu
re
sche
dule
.Ex
. Poi
nt to
var
ious
acti
vitie
s and
thei
r cor
resp
ondi
ng ti
mes
on
cloc
ks th
at h
ave
been
po
sted
with
cor
resp
ondi
ng a
ctivi
ties o
n th
e cl
assr
oom
bul
letin
boa
rd.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.3.d
. Dem
onst
rate
an
unde
rsta
ndin
g th
at te
lling
tim
e is
the
sam
e ev
ery
day.
Ex. S
how
the
sche
dule
for t
oday
and
tom
orro
w si
de-b
y-sid
e. W
hen
teac
her i
ndic
ates
we
wen
t to
lunc
h at
noo
n to
day,
indi
cate
we
will
go
to lu
nch
at n
oon
tom
orro
w.
Ex. T
each
er a
nnou
nces
the
time
to g
o ho
me
ever
y da
y. T
hen,
the
teac
her a
nnou
nces
the
time
and
asks
, “W
hat h
appe
ns e
very
day
at t
his ti
me?
”
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.3
.d. D
emon
stra
te a
n un
ders
tand
ing
of th
e us
e of
a c
lock
(tim
e).
Ex. I
ndic
ate
the
use
of a
clo
ck w
hen
aske
d w
hat t
ool i
s nee
ded
to te
ll tim
e.Ex
. Ind
icat
e a
cloc
k w
hen
aske
d w
hat t
ool i
s nee
ded
to h
elp
you
awak
e fr
om a
nig
ht’s
sleep
.Ex
. Loo
k at
the
cloc
k, re
peat
the
time
after
the
teac
her,
and
follo
w th
e te
ache
r dire
ction
s w
hen
the
teac
her m
odel
s, u
sing
“Thi
nk a
loud
s,” b
y an
noun
cing
var
ious
tim
es th
roug
hout
th
e da
y.Ex
. Afte
r list
enin
g to
stor
ies a
bout
tim
e, a
nsw
er q
uesti
ons t
o de
mon
stra
te a
n un
ders
tand
ing
of ti
me.
Ex. U
se o
bjec
ts fo
r tra
nsiti
onin
g to
pre
dict
tim
e of
day
(spo
on re
pres
ents
lunc
h, b
ackp
ack
repr
esen
ts h
ome,
boo
k re
pres
ents
read
ing/
lang
uage
)
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.3
.d. R
ecog
nize
repr
esen
tatio
ns o
f diff
eren
t par
ts o
f the
day
; mor
ning
, noo
n, a
nd
nigh
t.Ex
. Poi
nt to
a p
ictu
re o
f a b
ed w
hen
prom
pted
.Ex
. Poi
nt to
a p
ictu
re o
f a su
nrise
whe
n pr
ompt
ed.
Ex. P
oint
to a
clo
ck w
hen
prom
pted
.Ex
. Poi
nts t
o fo
od p
ictu
res t
o in
dica
te m
eal ti
mes
.
38 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
inte
rpre
t dat
a.
1.M
D.4
. Org
anize
, rep
rese
nt,
and
inte
rpre
t dat
a w
ith u
p to
thre
e ca
tego
ries;
ask
and
an
swer
que
stion
s abo
ut th
e to
tal n
umbe
r of d
ata
poin
ts, h
ow
man
y in
eac
h ca
tego
ry, a
nd h
ow
man
y m
ore
or le
ss a
re in
one
ca
tego
ry th
an in
ano
ther
.
EE1.
MD
.4. G
iven
a c
ount
of t
he
tota
l num
ber o
f dat
a po
ints
in
two
cate
gorie
s, d
eter
min
e w
heth
er th
ere
are
mor
e or
less
in
eac
h ca
tego
ry.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
MD
.4. C
olle
ct a
nd c
ount
dat
a in
to a
t lea
st tw
o ca
tego
ries t
o an
swer
que
stion
s abo
ut
the
tota
l num
ber o
f dat
a po
ints
and
whe
ther
ther
e ar
e m
ore
or le
ss in
one
cat
egor
y th
an
in a
noth
er.
Ex. C
olle
ct d
ata
from
a c
lass
vot
e an
d ca
tego
rize
it to
det
erm
ine
the
cate
gory
with
the
mos
t vot
es (e
.g.,
the
clas
s tak
es a
vot
e, c
ount
s the
vot
e, a
nd d
ecid
es w
hich
cho
ice
won
).Ex
. Col
lect
dat
a ab
out c
lass
cho
ices
and
cat
egor
ize th
e co
unt t
o de
term
ine
whi
ch is
the
favo
rite
(e.g
., ho
t lun
ch c
hoic
es, m
ilk c
hoic
es, a
ny a
ctivi
ty w
here
you
are
cou
nting
and
ta
llyin
g in
two
or m
ore
choi
ces)
.Ex
. Atte
nd to
a b
ar g
raph
of d
aily
tem
pera
ture
s in
win
ter a
nd d
eter
min
e if
ther
e w
ere
mor
e da
ys o
f ind
oor o
r out
door
rece
ss.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
MD
.4. G
iven
a c
ount
of t
he to
tal n
umbe
r of d
ata
poin
ts in
two
cate
gorie
s, d
eter
min
e w
heth
er th
ere
are
mor
e or
less
in e
ach
cate
gory
.Ex
. Giv
en a
gra
phic
al d
ispla
y of
dat
a (lu
nch
coun
t) o
f the
num
ber o
f dat
a po
ints
in e
ach
cate
gory
, det
erm
ine
whe
ther
ther
e ar
e m
ore
or le
ss in
eac
h ca
tego
ry (e
.g.,
did
mor
e st
uden
ts b
uy c
hees
e sa
ndw
ich)
.Ex
. Giv
en a
pic
togr
aph
of th
e nu
mbe
r of b
oys a
nd g
irls i
n cl
ass,
cho
ose
the
grou
p w
ith
mor
e.Ex
. Sta
nd n
ext t
o on
e of
two
book
s for
cla
ss to
vot
e on
wha
t boo
k to
read
dur
ing
stor
y tim
e. A
fter t
each
er c
ount
s eac
h gr
oup,
det
erm
ine
whi
ch b
ook
won
.
Leve
l II A
A S
tude
nts
will
:EE
1.M
D.4
. Put
obj
ects
and
cho
ices
into
cat
egor
ies.
Ex. G
iven
a p
ictu
re o
f the
type
of d
rink
(e.g
., ch
ocol
ate
milk
, pla
in m
ilk, j
uice
), pl
ace
thei
r ch
oice
on
a lu
nch
char
t to
repr
esen
t the
num
ber w
ho w
ants
eac
h ty
pe o
f drin
k. T
he
teac
her c
ount
s the
num
ber o
f eac
h dr
ink
choi
ce o
n th
e ch
art.
Ex. T
ape
a pa
per d
oll t
o att
enda
nce
char
t to
repr
esen
t one
self
(e.g
., Ea
ch g
irl h
as a
pap
er
doll
repr
esen
ting
“girl
” an
d ea
ch b
oy h
as o
ne re
pres
entin
g “b
oy.”
Afte
r stu
dent
s tap
e th
eir d
olls
to th
e att
enda
nce
char
t, th
e te
ache
r cou
nts t
he n
umbe
r of b
oys a
nd th
e nu
mbe
r of g
irls o
n th
e ch
art.)
.Ex
. Usin
g a
dry
eras
e bo
ard,
ent
er a
tally
into
the
appr
opria
te c
olum
n pr
ovid
ed b
y th
e te
ache
r (e.
g., p
refe
rred
acti
vity
of s
tory
read
ing
vers
us b
lock
cou
nting
, etc
.).Ex
. Dro
p on
e m
arbl
e in
to a
“ye
s” o
r “no
” ca
n to
ans
wer
a q
uesti
on.
The
teac
her c
ount
s th
e nu
mbe
r of m
arbl
es a
nd th
e co
rrec
t ans
wer
is re
veal
ed.
Ex. U
se a
cla
ssro
om c
licke
r sys
tem
to re
spon
d to
que
stion
s, o
ne v
ote/
resp
onse
per
pe
rson
.
Leve
l I A
A S
tude
nts
will
:EE
1.M
D.4
. Par
ticip
ate
in d
ata
colle
ction
by
votin
g or
oth
erw
ise c
hoos
ing.
Ex. I
ndic
ate
penc
il or
cra
yon
whe
n as
ked,
“Do
you
like
pen
cils
or c
rayo
ns b
etter
?”Ex
. Ind
icat
e pr
efer
ence
(vot
e) w
hen
aske
d, “
Who
wan
ts to
pla
y ou
tsid
e?”
Math | Kindergarten-5 Grade 39
Firs
t G
rad
e M
ath
emat
ics
Stan
dar
ds:
Geo
met
ry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Reas
on w
ith
shap
es a
nd th
eir
attri
bute
s.
1.G
.1. D
isting
uish
bet
wee
n de
finin
g att
ribut
es (e
.g.,
tria
n-gl
es a
re c
lose
d an
d th
ree-
sided
) ve
rsus
non
-defi
ning
att
ribut
es
(e.g
., co
lor,
orie
ntati
on, o
vera
ll siz
e); b
uild
and
dra
w sh
apes
to
poss
ess d
efini
ng a
ttrib
utes
.
1.G
.2. C
ompo
se tw
o-di
men
sion-
al sh
apes
(rec
tang
les,
squa
res,
tr
apez
oids
, tria
ngle
s, h
alf-c
ircle
s,
and
quar
ter-c
ircle
s) o
r thr
ee-d
i-m
ensio
nal s
hape
s (cu
bes,
righ
t re
ctan
gula
r pris
ms,
righ
t circ
ular
co
nes,
and
righ
t circ
ular
cyl
-in
ders
) to
crea
te a
com
posit
e sh
ape,
and
com
pose
new
shap
es
from
the
com
posit
e sh
ape.
4
EE1.
G.1
. Ide
ntify
com
mon
tw
o-di
men
siona
l sha
pes:
squa
re,
circ
le, t
riang
le, a
nd re
ctan
gle.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
G.1
-2. I
denti
fy a
ttrib
utes
of c
omm
on tw
o-di
men
siona
l sha
pes:
squa
re, c
ircle
, tria
ngle
, an
d re
ctan
gle.
Ex. G
iven
shap
es o
f diff
eren
t size
s, a
nd o
rient
ation
s, so
rt b
y sh
ape
attrib
ute.
Ex. G
iven
a tr
iang
le a
nd a
sked
, “Ho
w m
any
sides
doe
s a tr
iang
le h
ave?
” In
dica
te th
ree.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
G.1
-2. I
denti
fy c
omm
on tw
o-di
men
siona
l sha
pes:
squa
re, c
ircle
, tria
ngle
, and
rect
an-
gle.
Ex. G
iven
an
arra
y of
shap
es, i
denti
fy th
e sh
ape
whe
n as
ked.
Ex. G
iven
a p
ictu
re, i
denti
fy c
omm
on sh
apes
with
in th
e pi
ctur
e.Ex
. Giv
en a
car
d w
ith a
shap
e on
it, a
nsw
er, a
nd “
Is th
is a
squa
re?”
Leve
l II A
A S
tude
nts
will
:EE
1.G
.1-2
. Mat
ch sh
ape
to sh
ape
Ex. M
atch
a tw
o-di
men
siona
l sha
pe to
a tw
o-di
men
siona
l sha
pe in
thei
r env
ironm
ent.
Ex. G
iven
a sh
ape
puzz
le, c
ompl
ete
the
puzz
le.
Leve
l I A
A S
tude
nts
will
:EE
1.G
.1-2
. Rec
ogni
ze a
shap
e.Ex
. Giv
en a
circ
le a
nd a
sked
“Sh
ow m
e ci
rcle
,” po
int t
o th
e ci
rcle
.Ex
. Giv
en a
car
d w
ith a
shap
e, p
oint
to th
e sh
ape.
40 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
1.G
.3. P
artiti
on c
ircle
s and
rect
-an
gles
into
two
and
four
equ
al
shar
es, d
escr
ibe
the
shar
es u
sing
the
wor
ds h
alve
s, fo
urth
s, a
nd
quar
ters
, and
use
the
phra
ses
half
of, f
ourt
h of
, and
qua
rter
of.
De
scrib
e th
e w
hole
as t
wo
of, o
r fo
ur o
f the
shar
es.
Und
erst
and
for t
hese
exa
mpl
es th
at d
ecom
-po
sing
into
mor
e eq
ual s
hare
s cr
eate
s sm
alle
r sha
res.
EE1.
G.3
. Put
toge
ther
two
piec
es
to m
ake
a sh
ape
that
rela
tes t
o th
e w
hole
(i.e
., tw
o se
mic
ircle
s to
mak
e a
circ
le, t
wo
squa
res t
o m
ake
a re
ctan
gle)
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE1.
G.3
. Dem
onst
rate
par
t and
who
le te
rmin
olog
y un
ders
tand
ing.
Ex. G
iven
an
arra
y of
hal
f sha
pes s
uch
as ta
ngra
ms,
sele
ct tw
o an
d pu
t the
m to
geth
er to
m
ake
a ci
rcle
, squ
are,
or t
riang
le.
Ex. O
n an
inte
racti
ve w
hite
boar
d, m
ove
two
squa
res t
oget
her t
o fo
rm a
rect
angl
e an
d th
em ta
ke th
em a
part
aga
in.
Leve
l III
AA
Stu
dent
s w
ill:
EE1.
G.3
. Put
toge
ther
two
piec
es to
mak
e a
shap
e th
at re
late
s to
the
who
le (i
.e.,
two
sem
icirc
les t
o m
ake
a ci
rcle
, tw
o sq
uare
s to
mak
e a
rect
angl
e).
Ex. P
ut to
geth
er tw
o pa
rts o
f a c
ircle
to c
reat
e a
who
le c
ircle
.Ex
. Put
two
squa
res t
oget
her t
o fo
rm a
rect
angl
e.Ex
. Giv
en h
alf o
f an
inde
x ca
rd w
ith a
par
tial s
hape
or p
ictu
re, fi
nd a
pee
r who
has
the
oth-
er h
alf t
o m
ake
a co
mpl
ete
shap
e or
pic
ture
.
Leve
l II A
A S
tude
nts
will
:EE
1.G
.3. P
ut to
geth
er tw
o pi
eces
.Ex
. Usin
g an
inse
t puz
zle a
s a m
odel
, put
toge
ther
a w
hole
circ
le fr
om h
alf-c
ircle
puz
zle
part
s.Ex
. Giv
en a
tem
plat
e, p
ut to
geth
er tw
o pi
eces
to fo
rm a
who
le.
Ex. U
sing
plas
tic e
ggs,
pra
ctice
bre
akin
g ap
art i
nto
two
equa
l par
ts, a
nd p
ut to
geth
er to
m
ake
a w
hole
.
Leve
l I A
A S
tude
nts
will
:EE
1.G
.3. G
iven
an
inse
t puz
zle o
r tec
hnol
ogy
equi
vale
nt, i
nser
t a sh
ape.
Ex. U
sing
a on
e-sh
ape
puzz
le, i
nser
t miss
ing
piec
e.Ex
. Whi
le u
sing
shap
e-ba
sed
char
t, st
uden
t ins
erts
shap
e in
to o
pen
slot.
Ex. M
atch
a p
aper
cut
-out
shap
e to
an
outli
ne o
n pi
ctur
e an
d gl
ue.
Ex. U
se a
touc
h w
indo
w to
clic
k an
d dr
ag a
shap
e fr
om sh
ape
bank
to in
sert
into
out
line
in
pict
ure.
Math | Kindergarten-5 Grade 41
CO
MM
ON
CO
RE
ESS
EN
TIA
L E
LEM
EN
TS
AN
D A
CH
IEV
EM
EN
T
DE
SCR
IPT
OR
S FO
R S
EC
ON
D G
RA
DE
Seco
nd
Gra
de
Mat
hem
atic
s St
and
ard
s: O
per
atio
ns
and
Alg
ebra
ic T
hin
kin
g
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
sol
ve p
robl
ems
invo
lvin
g ad
diti
on a
nd
subt
racti
on.
2.O
A.1
. Use
add
ition
and
su
btra
ction
with
in 1
00 to
so
lve
one-
and
two-
step
wor
d pr
oble
ms i
nvol
ving
situ
ation
s of
addi
ng to
, tak
ing
from
, putti
ng
toge
ther
, tak
ing
apar
t, an
d co
mpa
ring,
with
unk
now
ns in
all
positi
ons,
e.g
., by
usin
g dr
awin
gs
and
equa
tions
with
a sy
mbo
l fo
r the
unk
now
n nu
mbe
r to
repr
esen
t the
pro
blem
.
EE2.
OA
.1. A
dd a
nd su
btra
ct to
so
lve
real
wor
ld o
ne-s
tep
stor
y pr
oble
ms f
rom
0-2
0 w
hen
the
resu
lt is
unkn
own.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
OA
.1. A
dd a
nd su
btra
ct to
solv
e re
al w
orld
one
-ste
p st
ory
prob
lem
s fro
m 0
-20
whe
n an
y nu
mbe
r in
the
prob
lem
is u
nkno
wn
(res
ult,
star
t, ch
ange
, diff
eren
ce).
Ex. D
urin
g ad
aptiv
e P.
E., t
here
are
five
stud
ents
and
thre
e ba
lls.
Dete
rmin
e ho
w m
any
mor
e ba
lls a
re n
eede
d so
eve
ry st
uden
t will
hav
e a
ball,
repr
esen
ting
the
unkn
own
with
a
blan
k (e
.g.,
thre
e ba
lls +
__
balls
is e
qual
to fi
ve b
alls)
.Ex
. Giv
en a
real
-wor
ld st
ory
invo
lvin
g ad
ditio
n or
subt
racti
on, r
epre
sent
the
prob
lem
usin
g nu
mbe
rs a
nd th
e +
or -
sym
bol,
and
solv
e th
e pr
oble
m, w
ith th
e un
know
n as
any
num
ber.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
OA
.1. A
dd a
nd su
btra
ct to
solv
e re
al w
orld
one
-ste
p st
ory
prob
lem
s fro
m 0
-20
whe
n th
e re
sult
is un
know
n.Ex
. Giv
en c
oncr
ete
obje
cts,
repr
esen
t and
solv
e a
stor
y pr
oble
m w
ith a
dditi
on o
r su
btra
ction
with
the
unkn
own
as th
e re
sult.
Ex. G
iven
con
cret
e ob
ject
s, so
lve
a sim
ple
one-
step
stor
y pr
oble
m u
sing
subt
racti
on.
Leve
l II A
A S
tude
nts
will
:EE
2.O
A.1
. Giv
en th
e eq
uatio
n, a
dd to
solv
e re
al w
orld
one
-ste
p st
ory
prob
lem
s fro
m 0
-10.
Ex. U
sing
a dr
y er
ase
boar
d w
ith p
ictu
res i
n pl
ace
of n
umbe
rs, s
olve
a re
al w
orld
add
ition
pr
oble
m (e
.g.,
add
the
num
ber o
f girl
s and
boy
s to
dete
rmin
e th
e nu
mbe
r of p
enci
ls ne
eded
).Ex
. Giv
en a
felt
boar
d st
ory
prob
lem
abo
ut Jo
hnny
App
lese
ed, p
oint
to th
e nu
mbe
r or
pict
ure
show
ing
the
tota
l app
les t
hat h
e pl
ante
d in
one
day
plu
s ano
ther
day
.
Leve
l I A
A S
tude
nts
will
:EE
2.O
A.1
. Ide
ntify
the
obje
ct(s
) tha
t app
ear i
n th
e re
al w
orld
one
-ste
p st
ory
prob
lem
.Ex
. Giv
en a
stor
y pr
oble
m a
nd c
oncr
ete
repr
esen
tatio
ns o
f the
obj
ects
poi
nt to
the
corr
ect
obje
ct(s
).Ex
. Giv
en a
felt
boar
d st
ory
prob
lem
abo
ut Jo
hnny
App
lese
ed a
nd a
sked
wha
t you
are
ad
ding
, ind
icat
e ap
ples
.A
dd a
nd s
ubtr
act w
ithi
n 20
.
2.O
A.2
. Flu
ently
add
and
su
btra
ct w
ithin
20
usin
g m
enta
l st
rate
gies
.5 By
end
of G
rade
2,
know
from
mem
ory
all s
ums o
f tw
o on
e-di
git n
umbe
rs.
EE2.
OA
.2. N
/A (S
ee E
E2.N
BT.7
)
42 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Wor
k w
ith
equa
l gro
ups
of
obje
cts
to g
ain
foun
dati
ons
for
mul
tipl
icati
on.
2.O
A.3
. Det
erm
ine
whe
ther
a
grou
p of
obj
ects
(up
to 2
0)
has a
n od
d or
eve
n nu
mbe
r of
mem
bers
, e.g
., by
pai
ring
obje
cts
or c
ounti
ng th
em b
y 2s
; writ
e an
equ
ation
to e
xpre
ss a
n ev
en
num
ber a
s a su
m o
f tw
o eq
ual
adde
nds.
EE2.
OA
.3. E
qual
ly d
istrib
ute
even
num
bers
of o
bjec
ts
betw
een
two
grou
ps.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
OA
.3. D
eter
min
e th
at a
qua
ntity
of o
bjec
ts is
eve
n or
odd
by
sepa
ratin
g th
em in
to
two
grou
ps.
Ex. G
iven
a X
qua
ntity
of o
bjec
ts, d
istrib
ute
them
into
two
grou
ps.
Indi
cate
that
if th
ere
are
lefto
vers
, the
qua
ntity
is o
dd a
nd if
the
quan
tity
divi
des e
venl
y, th
e nu
mbe
r is e
ven.
Ex. G
iven
two
plas
tic ri
ngs a
nd n
ine
cube
s dist
ribut
e th
e cu
bes e
venl
y in
to th
e rin
gs a
nd
dete
rmin
e if
ther
e ar
e an
y le
ftove
rs.
Indi
cate
if th
e nu
mbe
r of c
ubes
was
eve
n or
odd
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
OA
.3. E
qual
ly d
istrib
ute
even
num
bers
of o
bjec
ts b
etw
een
two
grou
ps.
Ex. D
istrib
ute
eigh
t obj
ects
equ
ally
bet
wee
n tw
o bo
xes a
nd c
ount
the
tota
l num
ber o
f ob
ject
s in
each
box
.Ex
. Div
ide
10 c
rayo
ns in
to tw
o eq
ual c
olle
ction
can
s.
Leve
l II A
A S
tude
nts
will
:EE
2.O
A.3
. Sep
arat
e ob
ject
s int
o tw
o gr
oups
.Ex
. Giv
en a
n as
sort
men
t of o
bjec
ts, d
ivid
e in
to tw
o gr
oups
and
indi
cate
how
man
y in
eac
h gr
oup.
Ex. G
iven
cou
nting
cub
es in
two
sizes
, sor
t the
m in
to tw
o pi
les.
Leve
l I A
A S
tude
nts
will
:EE
2.O
A.3
. Mak
e tw
o gr
oups
of t
wo.
Ex. G
iven
a g
roup
of f
our o
bjec
ts, t
wo
each
of t
wo
unlik
e ob
ject
s (e.
g., a
bal
l and
a b
ox),
sepa
rate
them
into
two
grou
ps o
f tw
o w
ith li
ke o
bjec
ts in
eac
h gr
oup.
Ex. G
iven
two
unlik
e ob
ject
s (e.
g., a
cub
e an
d a
pyra
mid
), se
para
te th
em.
Then
, whe
n sh
own
two
obje
cts t
hat m
atch
the
prev
ious
ly p
rese
nted
obj
ects
, pla
ce th
em w
ith th
e m
atch
ing
obje
ct to
mak
e a
grou
p (t
wo
cube
s, tw
o py
ram
ids)
.Ex
. Gro
up o
bjec
ts in
to li
ke se
ts.
Math | Kindergarten-5 Grade 43
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.O
A.4
. Use
add
ition
to fi
nd th
e to
tal n
umbe
r of o
bjec
ts a
rran
ged
in re
ctan
gula
r arr
ays w
ith u
p to
5
row
s and
up
to 5
col
umns
; writ
e an
equ
ation
to e
xpre
ss th
e to
tal
as a
sum
of e
qual
add
ends
.
EE2.
OA
.4. U
se a
dditi
on to
find
th
e to
tal n
umbe
r of o
bjec
ts
arra
nged
with
in e
qual
gro
ups u
p to
a to
tal o
f 10.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
OA
.4. U
se a
dditi
on to
find
the
tota
l num
ber o
f obj
ects
arr
ange
d w
ithin
equ
al g
roup
s be
yond
10.
Ex. U
sing
pape
r pla
tes,
put
equ
al a
mou
nt o
f obj
ects
on
each
pla
te (1
-6),
com
bine
and
so
lve
for t
otal
num
ber o
f obj
ects
.Ex
. Giv
en a
poc
ket c
hart
, arr
ange
12
red
card
s int
o se
ts o
f equ
al g
roup
s and
tell
if th
ere
is an
othe
r way
the
card
s cou
ld b
e pu
t int
o eq
ual g
roup
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
OA
.4. U
se a
dditi
on to
find
the
tota
l num
ber o
f obj
ects
arr
ange
d w
ithin
equ
al g
roup
s up
to a
tota
l of 1
0.Ex
. Add
two
equa
l gro
ups o
f cou
nting
bea
rs to
get
a to
tal.
Ex. G
iven
four
larg
e bl
ocks
and
four
smal
l blo
cks,
mat
ch th
em in
to li
ke g
roup
s and
indi
cate
ho
w m
any
obje
cts t
here
are
in a
ll.
Leve
l II A
A S
tude
nts
will
:EE
2.O
A.4
. Rec
ogni
ze th
at tw
o gr
oups
are
mad
e up
of e
qual
qua
ntitie
s up
to a
tota
l of l
ess
than
10.
Ex. G
iven
thre
e se
ts o
f obj
ects
, find
the
sets
that
con
tain
equ
al a
mou
nts i
n ea
ch a
nd st
ate
the
num
ber.
Ex. G
iven
bag
s of o
bjec
ts, t
wo
of w
hich
hav
e tw
o ob
ject
s and
one
of w
hich
hav
e on
e ob
ject
, find
the
bags
that
con
tain
an
equa
l num
ber o
f obj
ects
.
Leve
l I A
A S
tude
nts
will
:EE
2.O
A.4
. Diff
eren
tiate
sam
e/di
ffere
nt w
hen
pres
ente
d w
ith tw
o ob
ject
s.Ex
. Giv
en tw
o ob
ject
s (ba
ll an
d cu
p), i
ndic
ate
if th
ey a
re th
e sa
me
or d
iffer
ent.
Ex. G
iven
a v
arie
ty o
f ite
ms,
mat
ch tw
o lik
e ite
ms.
44 Common Core Essential Elements
Seco
nd
Gra
de
Mat
hem
atic
s: N
um
ber
an
d O
per
atio
ns
in B
ase
Ten
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
plac
e va
lue.
2.N
BT.1
. Und
erst
and
that
the
thre
e di
gits
of a
thre
e-di
git
num
ber r
epre
sent
am
ount
s of
hund
reds
, ten
s, a
nd o
nes;
e.g
., 70
6 eq
uals
7 hu
ndre
ds, 0
tens
, an
d 6
ones
. U
nder
stan
d th
e fo
llow
ing
as sp
ecia
l cas
es:
10
0 ca
n be
thou
ght o
f as
a b
undl
e of
ten
tens
— c
alle
d a
“hun
dred
.”
The
num
bers
100
, 200
, 30
0, 4
00, 5
00, 6
00, 7
00, 8
00,
900
refe
r to
one,
two,
thre
e,
four
, five
, six
, sev
en, e
ight
, or
nine
hun
dred
s (an
d 0
tens
and
0
ones
).
EE2.
NBT
.1. R
epre
sent
num
bers
th
roug
h 30
with
sets
of t
ens a
nd
ones
with
obj
ects
in c
olum
ns o
r ar
rays
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.1. P
ut n
umbe
rs th
roug
h 30
into
sets
of t
ens a
nd o
nes w
ith n
umbe
rs.
Ex. G
iven
a p
ictu
re o
f 24
obje
cts,
indi
cate
/circ
le tw
o gr
oups
of 1
0 an
d fo
ur o
nes.
Tel
l how
m
any
tens
ther
e ar
e an
d ho
w m
any
ones
ther
e ar
e.Ex
. Giv
en a
pla
ce v
alue
cha
rt a
nd th
e pr
ompt
, “Sh
ow m
e ‘2
0,’”
indi
cate
that
the
“2”
goes
in
the
tens
col
umn
and
the
“0”
goes
in th
e on
es p
lace
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.1. R
epre
sent
num
bers
thro
ugh
30 w
ith se
ts o
f ten
s and
one
s with
obj
ects
in
colu
mns
or a
rray
s.Ex
. Giv
en a
ver
tical
poc
ket c
hart
(3 c
olum
ns o
f 10
each
), in
sert
col
ored
inde
x ca
rds t
o fil
l in
the
colu
mn(
s) to
indi
cate
the
num
ber o
f ten
s and
one
s.Ex
. Whe
n he
arin
g a
stor
y th
at in
volv
es g
roup
s of 1
0, c
olle
ct g
roup
s of 1
0, a
nd g
athe
r th
em, w
ith re
mai
nder
one
s not
incl
uded
.Ex
. Giv
en p
opsic
le sti
cks l
ess t
han
or e
qual
to 3
0, m
ake
grou
ps o
f ten
s and
one
s.Ex
. Giv
en a
n in
tera
ctive
whi
tebo
ard,
cre
ate
grou
ps o
f ten
s and
one
s by
pulli
ng o
ver i
tem
s in
to a
col
lecti
on a
rea.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.1
. Ind
icat
e th
at 1
0 on
es e
qual
s one
10
and
zero
one
s (ba
se 1
0).
Ex. G
iven
10
obje
cts (
i.e.,
10 p
aper
clip
s, 1
0 di
scs)
, pla
ce th
em o
n a
stra
ight
-line
grid
.Ex
. Giv
en a
mod
el o
r a te
mpl
ate,
cre
ate
one
set o
f 10.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.1
. Dem
onst
rate
s one
-to-o
ne c
orre
spon
denc
e.Ex
. Giv
en fi
ve o
bjec
ts a
nd fi
ve b
oxes
, pla
ce o
ne o
bjec
t in
each
box
.Ex
. Put
a n
ote
into
eve
ry st
uden
t’s c
ubby
.
Math | Kindergarten-5 Grade 45
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.N
BT.2
. Cou
nt w
ithin
100
0;
skip
-cou
nt b
y 5s
, 10s
, and
100
s.EE
2.N
BT.2
.a. C
ount
from
1
to 3
0 (c
ount
with
mea
ning
; ca
rdin
ality
).
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.2.a
. Cou
nt b
eyon
d 30
(cou
nt w
ith m
eani
ng; c
ardi
nalit
y).
Ex. C
ount
obj
ects
bey
ond
30.
Ex. C
ount
tally
mar
ks b
eyon
d 30
.Ex
. Dur
ing
cale
ndar
tim
e, c
ount
up
to 3
1 da
ys o
n th
e ca
lend
ar.
Ex. C
ount
the
stud
ents
in li
ne fo
r lun
ch.
Ex. R
ecog
nize
err
ors i
n ot
hers
’ cou
nting
from
1 to
30.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.2.a
. Cou
nt fr
om 1
to 3
0 (c
ount
with
mea
ning
; car
dina
lity)
.Ex
. Cou
nt 3
0 us
ing
coun
ting
cube
s.Ex
. Cou
nt th
e nu
mbe
r of d
ays (
with
in 3
0) u
ntil a
fiel
d tr
ip.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.2
.a. C
ount
num
bers
1 to
20,
skip
ping
num
bers
or r
epea
ting.
Ex. C
ount
1-5
.Ex
. Cou
nt 1
-10.
Ex. C
ount
1-2
0.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.2
.a. R
epea
t num
bers
1 to
30.
Ex. D
urin
g ca
lend
ar ti
me,
repe
at th
e da
te.
Ex. W
hen
swin
ging
on
the
play
grou
nd, i
mita
te th
e te
ache
r cal
ling
out t
he sw
ings
bac
k an
d fo
rth.
Ex. C
ount
with
the
teac
her f
rom
1 to
30.
46 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE2.
NBT
.2.b
. Nam
e th
e ne
xt
num
ber i
n a
sequ
ence
bet
wee
n 1
and
10.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.2.b
. Cou
nt fo
rwar
d be
ginn
ing
from
a g
iven
num
ber w
ithin
the
know
n se
quen
ce 2
to
10
(inst
ead
of h
avin
g to
beg
in a
t one
).Ex
. Dur
ing
cale
ndar
tim
e, st
art o
n th
e da
y’s d
ate
and
coun
t for
war
d up
to 1
0.Ex
. Usin
g a
num
ber p
ath,
star
t on
a gi
ven
num
ber a
nd c
ount
forw
ard
up to
10.
Ex. G
iven
a n
umbe
r, co
unt f
orw
ard
to 1
0.Ex
. Giv
en tw
o se
ts a
nd to
ld th
e qu
antit
y in
the
first
set,
conti
nue
coun
ting
on th
e ne
xt se
t to
find
the
tota
l num
ber o
f the
two
sets
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.2.b
. Nam
e th
e ne
xt n
umbe
r in
a se
quen
ce b
etw
een
1 an
d 10
.Ex
. Giv
en a
sequ
ence
of n
umbe
rs, r
espo
nds w
ith th
e ne
xt n
umbe
r in
the
sequ
ence
(e.g
., 5,
6, 7
, nam
e 8)
.Ex
. Whi
le p
layi
ng th
e ga
me,
“Sa
y th
e ne
xt n
umbe
r,” c
orre
ctly
iden
tify
the
next
num
ber
betw
een
1 an
d 10
.Ex
. Whe
n co
untin
g off
, say
the
next
num
ber i
n co
rrec
t seq
uenc
e w
hen
calle
d on
.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.2
.b. I
ndic
ate
the
high
er n
umbe
r in
a pr
ogre
ssio
n of
num
bers
(with
or w
ithou
t ga
ps).
Ex. G
iven
a n
umbe
r seq
uenc
e (e
.g.,
give
n 1,
2, 3
, 4, r
espo
nd w
ith a
ny h
ighe
r num
ber)
.Ex
. Giv
en a
num
ber,
pick
a h
ighe
r num
ber.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.2
.b. C
omm
unic
ate
a nu
mbe
r.Ex
. Whe
n nu
mbe
ring
off in
to g
roup
s, re
spon
d w
ith a
ny n
umbe
r whe
n it’
s his
or h
er tu
rn.
Ex. W
hen
taki
ng lu
nch
coun
ts, i
ndic
ate
his o
r her
par
t of t
he g
roup
with
a n
umbe
r.
Math | Kindergarten-5 Grade 47
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.N
BT.3
. Rea
d an
d w
rite
num
bers
to 1
000
usin
g ba
se-te
n nu
mer
als,
num
ber n
ames
, and
ex
pand
ed fo
rm.
EE2.
NBT
.3. I
denti
fy n
umbe
r sy
mbo
ls 1
to 3
0.Le
vel I
V A
A S
tude
nts
will
:EE
2.N
BT.3
. Exp
ress
num
ber s
ymbo
ls be
yond
30.
Ex. A
sked
to p
rodu
ce a
num
ber,
corr
ectly
pro
duce
the
num
ber.
Ex. G
iven
a c
alen
dar a
nd a
sked
to id
entif
y a
date
, cor
rect
ly id
entif
y th
e da
te.
Ex. G
iven
a n
umbe
rs c
hart
and
ask
ed to
iden
tify
a nu
mbe
r, co
rrec
tly id
entif
y th
e nu
mbe
r.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.3. I
denti
fy n
umbe
r sym
bols
1 to
30.
Ex. P
lay
a ga
me
that
requ
ires n
umbe
r sym
bol r
ecog
nitio
n fr
om 1
to 3
0 (e
.g.,
BIN
GO).
Ex. W
hile
pla
ying
the
gam
e “I
Spy
” w
ith n
umbe
rs a
roun
d th
e ro
om, i
denti
fy th
e nu
mbe
r ca
lled.
Ex. I
denti
fy n
umbe
r sym
bols
whe
n th
ey a
re a
rran
ged
on th
e de
sk in
fron
t of t
hem
.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.3
. Ide
ntify
num
ber s
ymbo
ls 1-
10.
Ex. G
iven
num
ber c
ards
from
1-1
0, w
in th
e ca
rd b
y id
entif
ying
the
num
ber o
n th
e ca
rd.
Ex. G
iven
a n
umbe
r pat
h fr
om 1
-10,
iden
tify
the
prom
pted
num
ber.
Ex. G
iven
num
bere
d pa
per fi
sh o
n fis
hing
pol
es, i
denti
fy th
e nu
mbe
r on
the
fish.
Ex. G
iven
num
ber s
ymbo
ls w
ritten
on
the
boar
d, id
entif
y nu
mbe
r sym
bols
from
1 to
10.
Ex. U
se n
umbe
rs 1
to 1
0 to
repr
esen
t qua
ntitie
s.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.3
.a. D
iffer
entia
te b
etw
een
num
bers
and
lette
rs.
Ex. W
hen
pres
ente
d w
ith a
lette
r and
a n
umbe
r, pi
ck o
ut th
e nu
mbe
r.
48 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.N
BT.4
. Com
pare
two,
thre
e-di
git n
umbe
rs b
ased
on
mea
ning
s of t
he h
undr
eds,
tens
, an
d on
es d
igits
, usin
g >,
=, a
nd <
sy
mbo
ls to
reco
rd th
e re
sults
of
com
paris
ons.
EE2.
NBT
.4. C
ompa
re se
ts o
f ob
ject
s and
num
bers
usin
g ap
prop
riate
voc
abul
ary
(mor
e,
less
, equ
al).
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.4. C
ompa
re se
ts o
f obj
ects
and
num
bers
usin
g ap
prop
riate
voc
abul
ary
as e
qual
or
mor
e or
less
whe
n tw
o or
few
er u
nits
apa
rt.
Ex. W
hen
give
n tw
o se
ts o
f obj
ects
, a b
ox w
ith 1
0 an
d a
box
of n
ine
iden
tify
that
the
box
with
10
has o
ne m
ore
and
asso
ciat
e th
e nu
mer
al.
Ex. W
hen
give
n tw
o re
war
d st
rips w
ith sti
cker
s tw
o or
less
uni
ts a
part
, det
erm
ine
whi
ch
strip
has
mor
e re
war
d sti
cker
s on
it.Ex
. Giv
en tw
o gr
oups
of t
hree
red
coun
ters
, det
erm
ine
that
they
are
equ
al.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.4. C
ompa
re se
ts o
f obj
ects
and
num
bers
usin
g ap
prop
riate
voc
abul
ary
(mor
e,
less
, equ
al).
Ex. G
iven
a fo
ur a
nd a
six,
det
erm
ine
that
six
is m
ore
than
four
.Ex
. Giv
en tw
o gr
oups
of t
hree
red
coun
ters
, det
erm
ine
that
they
are
equ
al.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.4
. Det
erm
ine
equa
lity
of se
ts o
f obj
ects
usin
g ap
prop
riate
voc
abul
ary
(equ
al).
Ex. G
iven
sets
of t
wo
bear
s and
two
appl
es, b
e ab
le to
indi
cate
that
the
sets
are
equ
al.
Ex. G
iven
two
sets
, tw
o of
whi
ch a
re e
qual
, be
able
to in
dica
te th
e se
ts th
at a
re e
qual
.Ex
. Joh
n ha
s thr
ee b
ears
and
Sus
ie h
as tw
o be
ars.
Joh
n ha
s one
mor
e be
ar th
an S
usie
.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.4
. Mat
ch g
roup
s of o
bjec
ts.
Ex. G
iven
two
sets
of o
bjec
ts m
atch
like
gro
ups.
Ex. G
iven
a se
t of t
wo
obje
cts,
ass
embl
es tw
o ob
ject
s in
a gr
oup
to m
atch
the
give
n se
t.Ex
. Whe
n pr
esen
ted
with
thre
e gr
oups
of o
bjec
ts (e
.g.,
two
grou
ps o
f one
cub
e an
d a
grou
p of
two
cube
s), m
atch
the
two
with
the
sam
e nu
mbe
r of o
bjec
ts in
it.
Math | Kindergarten-5 Grade 49
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
pla
ce v
alue
und
erst
andi
ng
and
prop
erti
es o
f ope
rati
ons
to
add
and
subt
ract
.
2.N
BT.5
. Flu
ently
add
and
su
btra
ct w
ithin
100
usin
g st
rate
gies
bas
ed o
n pl
ace
valu
e,
prop
ertie
s of o
pera
tions
, and
/or
the
rela
tions
hip
betw
een
addi
tion
and
subt
racti
on.
EE2.
NBT
.5.a
. Ide
ntify
the
mea
ning
of t
he “
+” si
gn (i
.e.,
com
bine
, plu
s, a
dd),
and
the
“=”
sign
(equ
al).
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.5.a
. Ide
ntify
the
mea
ning
of t
he “
+” si
gn (i
.e.,
com
bine
, plu
s, a
dd),
the
“=”
sign
(equ
al),
and
the
“-”
sign
(min
us, t
ake
away
, les
s).
Ex. G
iven
thre
e gr
oups
of o
bjec
ts re
pres
entin
g a
subt
racti
on e
quati
on, i
denti
fy th
e co
rrec
t sig
n to
use
.Ex
. Giv
en a
subt
racti
on e
quati
on, p
lace
the
min
us si
gn a
nd th
e eq
ual s
ign
in th
e co
rrec
t pl
aces
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.5.a
. Ide
ntify
the
mea
ning
of t
he “
+” si
gn (i
.e.,
com
bine
, plu
s, a
dd),
and
the
“=”
sign
(equ
al).
Ex. G
iven
an
equa
tion,
poi
nt to
the
plus
or e
qual
sign
in a
n eq
uatio
n.Ex
. Giv
en th
ree
grou
ps o
f obj
ects
(tw
o ad
dend
s and
the
sum
), id
entif
y th
e “+
” sig
n.
Leve
l II S
tude
nts
will
:EE
2.N
BT.5
.a. R
ecog
nize
the
“+”
and
“=”
signs
.Ex
. Whe
n sh
own
a gr
oup
of sy
mbo
ls, p
oint
to/id
entif
y th
e pl
us/e
qual
sign
whe
n pr
ompt
ed
by th
e te
ache
r.Ex
. Whe
n sh
own
the
plus
/equ
al si
gns t
aped
on
the
floor
, ind
icat
e th
e sig
n w
hen
prom
pted
by
the
teac
her.
Ex. W
hen
show
n th
e pl
us/e
qual
sign
s dra
wn
on th
e bo
ard,
indi
cate
the
sign
whe
n pr
ompt
ed b
y th
e te
ache
r.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.5
.a. M
atch
the
“+”
and
“=”
signs
.Ex
. Whe
n gi
ven
a cu
e, m
atch
the
plus
sign
(e.g
., Th
e te
ache
r sho
ws a
“+”
sign
and
an
“=”
then
poi
nts t
o th
e “+
” sig
n. T
he te
ache
r say
s, “
This
is a
plus
sign
. Pi
ck th
e on
e th
at is
the
sam
e.”)
.Ex
. Whe
n gi
ven
a cu
e, m
atch
the
equa
l sig
n (e
.g.,
The
teac
her s
how
s a “
+” si
gn a
nd a
n “=
” th
en p
oint
s to
the
“=”
sign.
The
teac
her s
ays,
“Th
is is
an e
qual
sign
. Pi
ck th
e on
e th
at is
th
e sa
me.
”).
Ex. W
hen
give
n tw
o ca
rds w
ith p
lus/
equa
l sig
ns a
nd o
ne d
istra
cter
, mat
ch th
e ap
prop
riate
sig
n.
50 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE2.
NBT
.5.b
. Usin
g co
ncre
te
exam
ples
, com
pose
and
de
com
pose
num
bers
up
to 1
0 in
m
ore
than
one
way
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.5.b
. Usin
g nu
mbe
rs o
r rep
rese
ntati
ons,
com
pose
and
dec
ompo
se n
umbe
rs u
p to
10
in m
ore
than
one
way
.Ex
. Giv
en p
ictu
res o
f sev
en g
rizzly
bea
rs, i
denti
fy o
ne g
roup
of t
hree
and
one
gro
up o
f fo
ur a
s dec
ompo
sing
seve
n, a
nd o
ne g
roup
of t
wo
and
one
grou
p of
five
as d
ecom
posin
g se
ven.
Ex. W
hen
show
n th
e nu
mbe
r five
, ind
icat
e th
at it
is m
ade
up o
f one
and
four
, or t
wo
and
thre
e.Ex
. Sho
wn
grou
ps o
f dot
s, re
cogn
ize th
e qu
antit
y au
tom
atica
lly.
Ex. G
iven
a tr
iang
le g
raph
ic o
rgan
izer,
with
the
num
ber 1
0 in
the
tip, p
lace
num
bers
in th
e ba
se a
ngle
s to
show
the
deco
mpo
sition
of 1
0.Ex
. Sho
wn
grou
ps o
f dot
s for
an
amou
nt u
p to
10,
reco
gnize
with
out c
ounti
ng th
e qu
antit
y it
repr
esen
ts a
nd id
entif
y th
e nu
mer
al.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.5.b
. Usin
g co
ncre
te e
xam
ples
, com
pose
and
dec
ompo
se n
umbe
rs u
p to
10
in
mor
e th
an o
ne w
ay.
Ex. G
iven
eig
ht b
ears
in a
row,
pla
ce a
stra
w a
nd m
ake
a gr
oup
of fo
ur a
nd a
gro
up o
f fou
r to
show
it m
akes
eig
ht.
Ex. G
iven
two
grou
ps o
f bea
rs to
talin
g 10
bea
rs, p
ut th
em to
geth
er to
cre
ate
one
grou
p.Ex
. Div
ide
(dec
ompo
se) 1
0 co
untin
g be
ars i
nto
two
grou
ps (e
.g.,
eigh
t and
two,
five
and
fiv
e, fo
ur a
nd si
x, e
tc.)
in a
t lea
st tw
o w
ays;
then
show
with
blo
cks t
hat t
he to
tal o
f the
tw
o gr
oups
is 1
0 (c
ompo
sed)
.Ex
. Sho
wn
grou
ps o
f dot
s for
an
amou
nt u
p to
10,
reco
gnize
with
out c
ounti
ng th
e qu
antit
y it
repr
esen
ts.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.5
.b. U
sing
conc
rete
exa
mpl
es, c
ompo
se a
nd d
ecom
pose
num
bers
up
to fi
ve in
at
leas
t one
way
.Ex
. Giv
en fo
ur c
ount
ers i
n a
row,
pla
ce a
stra
w a
nd m
ake
a gr
oup
of tw
o an
d a
grou
p of
th
ree
and
show
it m
akes
five
.Ex
. Giv
en a
gro
up o
f five
cou
nter
s tha
t has
bee
n di
vide
d (d
ecom
pose
d) in
to tw
o gr
oups
of
four
and
one
, sho
w w
ith b
lock
s tha
t the
tota
l of t
he tw
o gr
oups
is fi
ve (c
ompo
sed)
.Ex
. Sho
wn
grou
ps o
f dot
s for
an
amou
nt u
p to
five
, rec
ogni
ze w
ithou
t cou
nting
the
quan
tity
it re
pres
ents
and
iden
tify
the
num
eral
.
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.5
.b. R
ecog
nize
that
gro
ups o
f obj
ects
can
be
put t
oget
her o
r tak
en a
part
.Ex
. Giv
en a
gro
up o
f fou
r cou
nting
bea
rs o
n a
circ
le m
at, s
epar
ate
them
into
two
grou
ps.
Ex. G
iven
two
sepa
rate
gro
ups o
f cou
nter
s (on
e an
d th
ree)
, put
them
toge
ther
to m
ake
one
grou
p of
four
.Ex
. Sho
wn
four
obj
ects
and
one
take
n aw
ay, c
ount
s the
one
take
n aw
ay to
find
how
man
y w
ere
take
n.
Math | Kindergarten-5 Grade 51
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.N
BT.6
. Add
up
to fo
ur tw
o-di
git
num
bers
usin
g st
rate
gies
bas
ed
on p
lace
val
ue a
nd p
rope
rties
of
oper
ation
s.
2.N
BT.7
. Add
and
subt
ract
with
in
1000
, usin
g co
ncre
te m
odel
s or
draw
ings
and
stra
tegi
es b
ased
on
pla
ce v
alue
, pro
perti
es
of o
pera
tions
, and
/or t
he
rela
tions
hip
betw
een
addi
tion
and
subt
racti
on; r
elat
e th
e st
rate
gy to
a w
ritten
met
hod.
U
nder
stan
d th
at in
add
ing
or
subt
racti
ng th
ree-
digi
t num
bers
, on
e ad
ds o
r sub
trac
ts h
undr
eds
and
hund
reds
, ten
s and
tens
, on
es a
nd o
nes;
and
som
etim
es
it is
nece
ssar
y to
com
pose
or
deco
mpo
se te
ns o
r hun
dred
s.
EE2.
NBT
.6-7
. Use
obj
ects
, re
pres
enta
tions
, and
num
bers
(0
-20)
to a
dd a
nd su
btra
ct.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
NBT
.6-7
. Use
obj
ects
, rep
rese
ntati
ons,
and
num
bers
bey
ond
20 to
add
and
subt
ract
.Ex
. Giv
en th
e lu
nch
card
s for
the
clas
s and
two
abse
nt st
uden
ts, s
ubtr
act t
wo
to g
et th
e lu
nch
coun
t for
the
day.
Ex. U
sing
pict
ures
of o
bjec
ts, t
ally
mar
ks, o
r num
ber c
ards
with
num
bers
to 2
0, c
ompl
ete
an a
dditi
on o
r sub
trac
tion
equa
tion.
Ex. G
iven
12
coun
ting
cube
s, c
ount
eig
ht m
ore
begi
nnin
g fr
om tw
elve
(e.g
., 12
, 13,
14,
15,
. .
. 20
).
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
NBT
.6-7
. Use
obj
ects
, rep
rese
ntati
ons,
and
num
bers
(0-2
0) to
add
and
subt
ract
.Ex
. Add
two
sets
of o
bjec
ts to
sum
up
to 2
0.Ex
. Giv
en a
set o
f obj
ects
up
to 2
0, ta
ke a
way
a g
iven
num
ber a
nd in
dica
te h
ow m
any
are
left.
Ex. U
se o
bjec
ts to
add
by
coun
ting
(e.g
., “I
hav
e th
ree
appl
es a
nd I
get 1
0 m
ore.
How
m
any
do I
have
?” S
tude
nt c
ount
s out
thre
e ob
ject
s and
then
cou
nts 1
0 m
ore
to fi
nd th
e to
tal.)
.
Leve
l II A
A S
tude
nts
will
:EE
2.N
BT.6
-7. U
se o
bjec
ts, r
epre
sent
ation
s, a
nd n
umbe
rs (0
-10)
to a
dd.
Ex. G
iven
a n
umbe
r pat
h, m
ove
ahea
d tw
o an
d in
dica
te th
e ne
w p
ositi
on.
Ex. G
iven
two
milk
s for
five
stud
ents
, det
erm
ine
that
thre
e m
ore
are
need
ed fo
r eac
h st
uden
t to
have
one
.Ex
. Giv
en th
ree
coun
ting
cube
s, d
eter
min
e ho
w m
any
mor
e ar
e ne
eded
to m
ake
six.
Ex. U
se o
bjec
ts to
add
by
coun
ting
(e.g
. “I h
ave
thre
e ap
ples
and
I ge
t tw
o m
ore.
How
m
any
do I
have
?” S
tude
nt c
ount
s out
thre
e ob
ject
s and
then
cou
nts t
wo
mor
e to
find
the
tota
l.).
Leve
l I A
A S
tude
nts
will
:EE
2.N
BT.6
-7. C
ount
obj
ects
1-1
0.Ex
. Giv
en th
ree
coun
ting
cube
s, c
ount
one
, tw
o, th
ree.
Ex. C
ount
the
num
ber o
f mar
ks o
n a
tally
boa
rd.
2.N
BT.8
. Men
tally
add
10
or 1
00
to a
giv
en n
umbe
r 100
–900
, and
m
enta
lly su
btra
ct 1
0 or
100
from
a
give
n nu
mbe
r 100
–900
.
2.N
BT.9
. Exp
lain
why
add
ition
an
d su
btra
ction
stra
tegi
es
wor
k, u
sing
plac
e va
lue
and
the
prop
ertie
s of o
pera
tions
.6
EE2.
NBT
.8-9
. N/A
52 Common Core Essential Elements
Seco
nd
Gra
de
Mat
hem
atic
s: M
easu
rem
ent
and
Dat
a
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Mea
sure
and
esti
mat
e le
ngth
s in
sta
ndar
d un
its.
2.M
D.1
. Mea
sure
the
leng
th o
f an
obj
ect b
y se
lecti
ng a
nd u
sing
appr
opria
te to
ols s
uch
as ru
lers
, ya
rdsti
cks,
met
er sti
cks,
and
m
easu
ring
tape
s.
2.M
D.2
. Mea
sure
the
leng
th o
f an
obj
ect t
wic
e, u
sing
leng
th
units
of d
iffer
ent l
engt
hs fo
r the
tw
o m
easu
rem
ents
; des
crib
e ho
w th
e tw
o m
easu
rem
ents
re
late
to th
e siz
e of
the
unit
chos
en.
EE2.
MD
.1. M
easu
re th
e le
ngth
of
obj
ects
usin
g no
n-st
anda
rd
units
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
MD
.1. M
easu
re le
ngth
of o
bjec
ts u
sing
stan
dard
tool
s, su
ch a
s rul
ers,
yar
dstic
ks, a
nd
met
er sti
cks,
by
repe
ating
the
use
of th
e m
easu
rem
ent t
ool/u
nit.
Ex. G
iven
a ro
w o
f thr
ee ti
le sq
uare
s on
the
floor
, mea
sure
the
leng
th o
f the
tile
s by
repe
ating
a ru
ler e
nd to
end
.Ex
. Giv
en a
hal
lway
from
the
clas
sroo
m to
the
bath
room
acr
oss t
he h
all,
mea
sure
the
dist
ance
with
a y
ards
tick
by re
peati
ng th
e ya
rdsti
ck fr
om e
nd to
end
.Ex
. Mea
sure
the
top
of th
e de
sk w
ith a
rule
r by
repe
ating
the
rule
r fro
m e
nd to
end
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.1. M
easu
re th
e le
ngth
of o
bjec
ts u
sing
non-
stan
dard
uni
ts.
Ex. M
easu
re th
e le
ngth
of a
giv
en d
istan
ce u
sing
a gi
ven
non-
stan
dard
mea
surin
g de
vice
.Ex
. Cou
nt th
e til
es o
n th
e flo
or to
see
how
man
y it
is fr
om th
e do
or o
f the
cla
ssro
om to
th
e dr
inki
ng fo
unta
in.
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.1
. Beg
in to
mea
sure
from
an
end
poin
t usin
g a
non-
stan
dard
tool
.Ex
. Pla
ce th
e m
easu
rem
ent t
ool (
pape
rclip
, blo
ck),
on th
e le
ft ed
ge.
Ex. G
iven
an
“All
Abou
t Me”
stor
y an
d bo
dy o
utlin
e, in
dica
te th
at h
e or
she
need
s to
star
t at
the
feet
or h
ead
and
mea
sure
to th
e ot
her e
nd to
mea
sure
hei
ght.
Ex. G
iven
thre
e pi
ctur
es w
ith a
n X
at th
e lo
wer
left,
upp
er ri
ght,
and
mid
dle,
indi
cate
that
th
e pi
ctur
e w
ith th
e X
at th
e lo
wer
left
illus
trat
es th
e co
rrec
t pla
ce to
star
t mea
surin
g.Ex
. Lay
nin
e cu
bes e
nd-t
o-en
d ne
xt to
a b
ook
to se
e ho
w lo
ng th
e bo
ok is
.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.1
. Mat
ch o
bjec
ts o
f lik
e le
ngth
.Ex
. Giv
en th
ree
diffe
rent
obj
ects
- on
e sh
orte
r and
two
of th
e sa
me
simila
r len
gth,
mat
ch
the
two
simila
r len
gth
obje
cts.
Ex. G
iven
thre
e pi
eces
of p
aper
of d
iffer
ent l
engt
h - t
wo
shor
t, on
e lo
ng, m
atch
the
two
simila
r len
gth
obje
cts.
Math | Kindergarten-5 Grade 53
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.M
D.3
. Esti
mat
e le
ngth
s us
ing
units
of i
nche
s, fe
et,
centi
met
ers,
and
met
ers.
2.M
D.4
. Mea
sure
to d
eter
min
e ho
w m
uch
long
er o
ne o
bjec
t is
than
ano
ther
, exp
ress
ing
the
leng
th d
iffer
ence
in te
rms o
f a
stan
dard
leng
th u
nit.
EE2.
MD
.3-4
. Ord
er b
y le
ngth
us
ing
non-
stan
dard
uni
ts.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
MD
.3-4
. Use
non
-sta
ndar
d un
its to
mea
sure
leng
th o
f obj
ects
(i.e
., pa
perc
lips,
blo
cks)
.Ex
. Det
erm
ine
how
man
y fo
otst
eps i
t tak
es to
cro
ss th
e cl
assr
oom
.Ex
. Det
erm
ine
how
man
y ha
ndpr
ints
it w
ill ta
ke to
mea
sure
the
leng
th (a
cros
s) a
des
ktop
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.3-4
. Ord
er b
y le
ngth
usin
g no
n-st
anda
rd u
nits
.Ex
. Giv
en th
ree
non-
stan
dard
uni
ts o
f mea
sure
men
t, su
ch a
s a p
aper
clip
, ind
ex c
ard,
and
co
nstr
uctio
n pa
per,
orde
r the
m b
y le
ngth
, sho
rtes
t to
long
est.
Ex. G
iven
a c
lass
room
of s
tude
nts,
ord
er th
em fr
om sh
orte
st to
talle
st (b
rick
wal
ls he
lp).
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.3
-4. C
ompa
re tw
o no
n-st
anda
rd u
nits
of l
engt
h an
d de
term
ine
whi
ch is
shor
ter
and
whi
ch is
long
er.
Ex. G
iven
two
piec
es o
f str
ing
of d
iffer
ing
leng
ths,
det
erm
ine
whi
ch is
shor
ter.
Ex. G
iven
a p
aper
clip
and
an
inde
x ca
rd, d
eter
min
e w
hich
is sh
orte
r.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.3
-4. C
ompa
re a
n ite
m to
a m
odel
that
is sh
orte
r or l
onge
r.Ex
. Com
pare
a fu
ll-le
ngth
pen
cil t
o a
golf
penc
il, id
entif
y th
at th
e go
lf pe
ncil
is sh
orte
r.Ex
. Com
pare
a y
ards
tick
to a
rule
r, id
entif
y th
at th
e ya
rdsti
ck is
long
er.
54 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Rela
te a
dditi
on a
nd s
ubtr
acti
on
to le
ngth
.
2.M
D.5
. Use
add
ition
and
su
btra
ction
with
in 1
00 to
solv
e w
ord
prob
lem
s inv
olvi
ng le
ngth
s th
at a
re g
iven
in th
e sa
me
units
, e.g
., by
usin
g dr
awin
gs
(suc
h as
dra
win
gs o
f rul
ers)
and
eq
uatio
ns w
ith a
sym
bol f
or th
e un
know
n nu
mbe
r to
repr
esen
t th
e pr
oble
m.
EE2.
MD
.5. I
ncre
ase
or d
ecre
ase
leng
th b
y ad
ding
or s
ubtr
actin
g un
it(s)
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
MD
.5. I
ncre
ase
or d
ecre
ase
leng
th b
y ad
ding
or s
ubtr
actin
g m
ultip
le u
nits
.Ex
. Giv
en a
pap
er c
hain
, inc
reas
e th
e le
ngth
by
addi
ng tw
o lin
ks.
Ex. G
iven
a c
hain
of 1
0 po
p-be
ads,
dec
reas
e th
e le
ngth
by
rem
ovin
g fo
ur b
eads
.Ex
. Giv
en a
row
of c
ounti
ng c
ubes
, inc
reas
e th
e le
ngth
by
addi
ng th
ree
cube
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.5. I
ncre
ase
or d
ecre
ase
leng
th b
y ad
ding
or s
ubtr
actin
g un
it(s)
.Ex
. Giv
en a
strin
g of
thre
e po
p-be
ads,
add
one
to m
ake
it lo
nger
(a le
ngth
of f
our p
op-
bead
s).
Ex. G
iven
a g
roup
of t
hree
cou
nting
cub
es, a
dd o
ne to
mak
e it
long
er -
a gr
oup
of fo
ur.
Ex. G
iven
a p
aper
cha
in re
pres
entin
g th
e nu
mbe
r of d
ays i
n th
e m
onth
, tea
r off
a lin
k at
th
e en
d of
eac
h da
y to
mak
e it
shor
ter (
poss
ibly
cou
ntdo
wn
to a
n an
ticip
ated
eve
nt).
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.5
. Inc
reas
e le
ngth
by
addi
ng a
sing
le u
nit.
Ex. G
iven
a p
aper
cha
in re
pres
entin
g th
e fir
st 2
0 da
ys o
f sch
ool,
add
anot
her l
ink
for o
ne
mor
e da
y.Ex
. Giv
en c
ounti
ng c
ubes
, inc
reas
e th
e le
ngth
by
addi
ng o
ne m
ore
to th
e st
ack.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.5
. Com
pare
two
obje
cts a
nd d
eter
min
e w
hich
is lo
nger
.Ex
. Giv
en a
pie
ce o
f str
ing
12 in
ches
long
and
a p
iece
of s
trin
g tw
o in
ches
long
, det
erm
ine
whi
ch is
long
er.
Ex. G
iven
a sh
ort s
trip
of p
aper
and
a lo
ng st
rip o
f pap
er, d
eter
min
e w
hich
is lo
nger
.
Math | Kindergarten-5 Grade 55
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.M
D.6
. Rep
rese
nt w
hole
nu
mbe
rs a
s len
gths
from
0
on a
num
ber l
ine
diag
ram
w
ith e
qual
ly sp
aced
poi
nts
corr
espo
ndin
g to
the
num
bers
0,
1, 2
, . .
. , a
nd re
pres
ent w
hole
-nu
mbe
r sum
s and
diff
eren
ces
with
in 1
00 o
n a
num
ber l
ine
diag
ram
.
EE2.
MD
.6. U
se a
num
ber l
ine
to
add
one
mor
e un
it of
leng
th.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
MD
.6. U
se a
num
ber l
ine
to a
dd m
ore
than
one
uni
t of l
engt
h.Ex
. Giv
en a
num
ber l
ine
with
1-fo
ot u
nits
mar
ked,
add
up
to fi
ve fe
et a
nd te
ll th
e to
tal.
Ex. G
iven
a n
umbe
r lin
e w
ith 1
-foot
uni
ts m
arke
d on
the
floor
and
a st
artin
g po
int,
add
feet
to re
ach
a sp
ecifi
ed p
oint
.Ex
. Tel
l the
tota
l len
gth
whe
n ad
ding
feet
from
a g
iven
poi
nt o
n th
e nu
mbe
r lin
e.Ex
. Tel
l the
dist
ance
bet
wee
n tw
o nu
mbe
rs o
n th
e nu
mbe
r lin
e.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.6. U
se a
num
ber l
ine
to a
dd o
ne m
ore
unit
of le
ngth
.Ex
. Giv
en th
e nu
mbe
r thr
ee o
n a
num
ber l
ine
show
ing
leng
th u
nits
mar
ked,
and
ask
ed to
ad
d on
e m
ore,
show
the
num
ber f
our.
Ex. G
iven
the
num
ber t
wo
on a
num
ber p
ath
mar
ked
by fo
ot u
nits
and
ask
ed to
add
one
m
ore,
show
/mov
e to
the
num
ber t
hree
feet
.Ex
. Giv
en a
num
ber l
ine
and
a st
artin
g po
int o
n th
e flo
or, a
dd o
ne m
ore.
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.6
. Cou
nt fo
rwar
d on
a n
umbe
r lin
e to
10
show
ing
units
of l
engt
h.Ex
. Cou
nt fo
rwar
d, ta
king
step
s fro
m o
ne fo
ot to
10
feet
with
one
-to-
one
corr
espo
nden
ce
with
or w
ithou
t tea
cher
mod
elin
g.Ex
. Giv
en a
num
ber p
ath
and
a st
artin
g po
int,
coun
t for
war
d to
10
on th
e nu
mbe
r lin
e.Ex
. Giv
en a
num
ber p
ath
and
10 c
ubes
, pla
ce a
cub
e on
eac
h nu
mbe
r as i
t is c
ount
ed.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.6
. Ind
icat
e on
e m
ore
num
ber o
n a
num
ber l
ine
and
trac
k le
ft to
righ
t.Ex
. Ind
icat
e on
e m
ore
on a
num
ber l
ine
by tr
acki
ng to
the
right
.Ex
. Giv
en a
num
ber l
ine
star
t on
the
left
and
mov
e to
the
right
.
56 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Wor
k w
ith
tim
e an
d m
oney
.
2.M
D.7
. Tel
l and
writ
e tim
e fr
om
anal
og a
nd d
igita
l clo
cks t
o th
e ne
ares
t five
min
utes
, usin
g a.
m.
and
p.m
.
EE2.
MD
.7. I
ndic
ate
the
digi
t tha
t te
lls th
e ho
ur o
n a
digi
tal c
lock
.Le
vel I
V A
A S
tude
nts
will
:EE
2.M
D.7
. Tel
l tim
e to
the
hour
on
a di
gita
l and
ana
log
cloc
k.Ex
. Whe
n sh
own
two
digi
tal c
lock
s and
ask
ed to
indi
cate
the
one
that
show
s “5:
00,”
indi
cate
the
corr
ect c
lock
.Ex
. Whe
n sh
own
an a
nalo
g an
d a
digi
tal c
lock
and
a ti
me
chec
k sh
eet a
nd p
rom
pt,
indi
cate
the
new
hou
r on
the
digi
tal c
lock
(e.g
., 5:
00, 1
2:00
).
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.7. I
ndic
ate
the
digi
t tha
t tel
ls th
e ho
ur o
n a
digi
tal c
lock
.Ex
. Giv
en a
dig
ital c
lock
, ind
icat
e th
e nu
mbe
r(s)
in th
e ho
ur p
ositi
on.
Ex. G
iven
car
ds sh
owin
g di
gita
l clo
cks -
with
one
clo
ck h
avin
g th
e ho
ur c
ircle
d an
d on
e cl
ock
with
the
min
utes
circ
led,
indi
cate
the
cloc
k w
ith th
e ho
ur c
ircle
d.Ex
. Usin
g a
pict
ure
sche
dule
, mat
ch th
e ho
ur o
f one
acti
vity
to th
e co
rrec
t pic
ture
of a
di
gita
l clo
ck.
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.7
. Ind
icat
e th
e re
latio
nshi
p be
twee
n a
cloc
k an
d th
eir d
aily
sche
dule
.Ex
. Giv
en th
eir s
ched
ules
and
two
cloc
ks w
ith a
spec
ific
activ
ity h
ighl
ight
ed, m
atch
the
time
on th
eir s
ched
ule
to th
e tim
e on
the
digi
tal c
lock
.Ex
. Sel
ect a
clo
ck sh
owin
g no
on w
hen
give
n tw
o cl
ocks
, one
set a
t 6:3
0 an
d on
e se
t at
noon
, whe
n as
ked,
“W
hen
do w
e go
to lu
nch?
”
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.7
. Ind
icat
e th
at a
clo
ck is
use
d to
tell
time.
Ex. G
iven
a c
lock
and
a sh
oe, a
nd a
sked
, “W
hich
tells
tim
e?”
indi
cate
that
the
cloc
k te
lls
time.
Ex. G
iven
two
kind
s of d
igita
l clo
cks a
nd a
dist
ract
er, m
atch
the
two
cloc
ks a
s tim
e-te
lling
to
ols.
Math | Kindergarten-5 Grade 57
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.M
D.8
. Sol
ve w
ord
prob
lem
s in
volv
ing
dolla
r bill
s, q
uart
ers,
di
mes
, nic
kels,
and
pen
nies
, us
ing
$ an
d ¢
sym
bols
appr
opria
tely.
Exa
mpl
e: If
you
ha
ve 2
dim
es a
nd 3
pen
nies
, ho
w m
any
cent
s do
you
have
?
EE2.
MD
.8. R
ecog
nize
that
mon
ey
has v
alue
.Le
vel I
V A
A S
tude
nts
will
:EE
2.M
D.8
. Rec
ogni
ze th
at m
oney
is u
sed
in e
xcha
nge
for g
oods
.Ex
. Giv
en a
cla
ssro
om st
ore,
pur
chas
es g
oods
with
mon
ey.
Ex. G
iven
a sc
hool
caf
eter
ia, p
urch
ase
good
s with
a p
rede
term
ined
am
ount
of m
oney
.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.8. R
ecog
nize
that
mon
ey h
as v
alue
.Ex
. Giv
en b
lock
s and
qua
rter
s and
ask
ed, “
If yo
u w
ant t
o bu
y a
juic
e, w
hich
wou
ld y
ou
use?
”, in
dica
te q
uart
ers.
Ex. G
iven
a sc
hool
book
fair
and
aske
d, “
If yo
u w
ant t
o bu
y a
book
at t
he b
ook
fair,
whi
ch
wou
ld y
ou n
eed,
a d
olla
r or a
n ap
ple?
”, in
dica
te d
olla
r.
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.8
. Sor
t mon
ey fr
om o
ther
obj
ects
.Ex
. Giv
en th
ree
obje
cts,
sele
ct th
e co
in.
Ex. G
iven
thre
e ob
ject
s, se
lect
the
dolla
r.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.8
. Und
erst
and
that
goo
ds (i
tem
s) h
ave
valu
e.Ex
. Giv
en a
gro
up o
f goo
ds (i
tem
s), s
elec
t a p
refe
rred
item
.Ex
. Giv
en a
rew
ard
box,
mak
es a
des
ired
sele
ction
.
58 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
inte
rpre
t dat
a.
2.M
D.9
. Gen
erat
e m
easu
rem
ent
data
by
mea
surin
g le
ngth
s of
seve
ral o
bjec
ts to
the
near
est
who
le u
nit,
or b
y m
akin
g re
peat
ed m
easu
rem
ents
of
the
sam
e ob
ject
. Sh
ow th
e m
easu
rem
ents
by
mak
ing
a lin
e pl
ot, w
here
the
horiz
onta
l sca
le
is m
arke
d off
in w
hole
-num
ber
units
.
2.M
D.1
0. D
raw
a p
ictu
re g
raph
an
d a
bar g
raph
(with
sing
le-u
nit
scal
e) to
repr
esen
t a d
ata
set
with
up
to fo
ur c
ateg
orie
s. S
olve
sim
ple
put-t
oget
her,
take
-apa
rt,
and
com
pare
pro
blem
s usin
g in
form
ation
pre
sent
ed in
a b
ar
grap
h.
EE2.
MD
.9-1
0. C
reat
e pi
ctur
e gr
aphs
from
col
lect
ed
mea
sure
men
t dat
a.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
MD
.9-1
0. O
rgan
ize, r
epre
sent
, and
inte
rpre
t len
gth/
heig
ht d
ata
usin
g co
ncre
te
obje
cts t
o cr
eate
pic
ture
gra
phs.
Ex. M
ake
a de
cisio
n ba
sed
on th
e m
easu
rem
ent d
ata
and
info
rmati
on fr
om g
raph
.Ex
. Com
pare
dat
a. T
each
er d
raw
s hei
ght m
ark
on w
all a
t 3.5
feet
. Ho
w m
any
peop
le a
re
talle
r tha
n th
e m
ark?
How
man
y pe
ople
are
shor
ter t
han
the
mar
k?Ex
. Col
lect
, gra
ph, a
nd in
terp
ret d
ata
abou
t cla
ss h
ot a
nd c
old
lunc
h pr
efer
ence
s.Ex
. Whe
n en
terin
g th
e cl
assr
oom
, pla
ce a
n ic
on in
the
appr
opria
te b
ar o
n th
e gr
aph
(e.g
., in
/not
in, b
uy lu
nch/
bag
lunc
h) a
nd a
nsw
er q
uesti
ons b
ased
on
that
gra
ph.
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
MD
.9-1
0. C
reat
e pi
ctur
e gr
aphs
from
col
lect
ed m
easu
rem
ent d
ata.
Ex. P
lace
pic
ture
car
d on
the
grap
h in
a ro
w fo
r one
of t
wo
poss
ible
cho
ices
(e.g
., lik
es
pean
ut b
utter
and
jelly
, lik
es m
acar
oni a
nd c
hees
e).
Ex. G
iven
pic
ture
s of l
unch
cho
ices
, pla
ce se
lecti
on o
n a
grap
h w
ith p
ictu
res f
rom
oth
er
stud
ents
mak
ing
the
sam
e se
lecti
on to
form
a p
ictu
re g
raph
.
Leve
l II A
A S
tude
nts
will
:EE
2.M
D.9
-10.
Cre
ate
pict
ure
grap
hs fr
om c
olle
cted
mea
sure
men
t dat
a us
ing
mod
el.
Ex. G
iven
a m
odel
, cre
ate
a pi
ctur
e gr
aph
usin
g co
lore
d di
sks o
r pap
er sq
uare
s.Ex
. Giv
en a
mod
el, c
reat
e a
pict
ure
grap
h us
ing
diffe
rent
shap
es so
rted
into
gro
ups.
Leve
l I A
A S
tude
nts
will
:EE
2.M
D.9
-10.
Con
trib
ute
to d
ata
colle
ction
.Ex
. Sel
ect a
pic
ture
that
repr
esen
ts p
erso
nal c
hoic
e fr
om o
ption
s pre
sent
ed d
urin
g da
ta
colle
ction
.Ex
. Sor
t ite
ms i
nto
two
grou
ps.
Math | Kindergarten-5 Grade 59
Seco
nd
Gra
de
Mat
hem
atic
s St
and
ard
s: G
eom
etry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Reas
on w
ith
shap
es a
nd t
heir
att
ribu
tes.
2.G
.1. R
ecog
nize
and
dra
w
shap
es h
avin
g sp
ecifi
ed
attrib
utes
, suc
h as
a g
iven
nu
mbe
r of a
ngle
s or a
gi
ven
num
ber o
f equ
al
face
s.7 I
denti
fy tr
iang
les,
qu
adril
ater
als,
pen
tago
ns,
hexa
gons
, and
cub
es.
EE2.
G.1
. Des
crib
e att
ribut
es
of tw
o-di
men
siona
l sha
pes.
Leve
l IV
AA
Stu
dent
s w
ill:
EE2.
G.1
. Des
crib
e m
athe
mati
cal a
ttrib
utes
of t
wo-
and
thre
e-di
men
siona
l sha
pes.
Ex. P
lay
a ga
me
with
a p
artn
er w
here
one
stud
ent d
escr
ibes
att
ribut
es o
f a sh
ape
from
a sh
ape
card
, and
the
othe
r stu
dent
mus
t sel
ect f
rom
a se
t of f
our s
hape
ca
rds w
hich
one
fits
the
desc
riptio
n.Ex
. Afte
r the
teac
her p
lace
s tw
o- a
nd th
ree-
dim
ensio
nal s
hape
s int
o a
bag,
feel
on
e of
the
shap
es a
nd d
escr
ibe
it w
ithou
t loo
king
.Ex
. Des
crib
e th
e nu
mbe
r of s
ides
for b
asic
shap
es (e
.g.,
thre
e –
tria
ngle
, fou
r –
squa
re).
Leve
l III
AA
Stu
dent
s w
ill:
EE2.
G.1
. Des
crib
e att
ribut
es o
f tw
o-di
men
siona
l sha
pes.
Ex. G
iven
an
arra
y of
col
ors a
nd si
zes,
sele
ct a
ttrib
utes
that
des
crib
e th
e se
lect
ed
shap
e.Ex
. Pro
vide
d w
ith a
gro
up o
f tw
o-di
men
siona
l sha
pes,
des
crib
e co
mm
on
attrib
utes
.Ex
. Giv
en a
gro
up o
f obj
ects
, sor
t the
m b
y an
y att
ribut
e; th
en id
entif
y w
hat
attrib
ute
was
use
d to
sort
(i.e
., siz
e, sh
ape,
col
or).
Ex. P
lay
“I S
py”
and
find
item
s in
the
envi
ronm
ent w
ith o
ne c
omm
on a
ttrib
ute
(i.e.
, all
circ
les,
all
red
item
s, a
ll th
ings
smal
ler t
han
my
nose
).
Leve
l II A
A S
tude
nts
will
:EE
2.G
.1. S
ort b
y on
e att
ribut
e (s
hape
).Ex
. Pul
l out
the
all o
f the
circ
les f
rom
a b
owl o
f circ
les a
nd sq
uare
s.Ex
. Put
all
the
tria
ngle
s int
o a
bow
l fro
m a
pile
of t
riang
les a
nd re
ctan
gles
.Ex
. Sta
ck d
ishes
by
shap
e aft
er c
lean
ing
(bow
ls, c
ups,
spoo
ns, e
tc.).
Ex. P
ut a
way
blo
cks s
orte
d by
shap
e.
Leve
l I A
A S
tude
nts
will
:EE
2.G
.1. E
xplo
re sh
apes
with
diff
eren
t att
ribut
es.
Ex. C
olor
all
the
squa
res b
lue
and
all t
he c
ircle
s red
with
teac
her p
rom
pt (e
.g.,
“Her
e is
a ci
rcle
; col
or it
red.
”).
Ex. U
sing
sand
/wat
er ta
ble,
loca
te th
e sh
apes
hid
den
in v
ario
us m
ater
ials.
Ex. P
lay
a ga
me
calle
d “S
ame
or D
iffer
ent”
whe
re th
e te
ache
r hol
ds u
p tw
o ob
ject
s and
ask
stud
ents
if th
e ob
ject
s are
exa
ctly
the
sam
e or
diff
eren
t.Ex
. Ide
ntify
thin
gs th
at a
re si
mila
r (e.
g., y
ello
w, sq
uare
, big
, litt
le, s
oft, h
ard)
.
60 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
2.G
.2. P
artiti
on a
rect
angl
e in
to ro
ws a
nd c
olum
ns o
f sa
me-
size
squa
res a
nd c
ount
to
find
the
tota
l num
ber o
f th
em.
EE2.
G.2
. N/A
2.G
.3. P
artiti
on c
ircle
s and
re
ctan
gles
into
two,
thre
e, o
r fo
ur e
qual
shar
es, d
escr
ibe
the
shar
es u
sing
the
wor
ds
halv
es, t
hird
s, h
alf o
f, a
third
of,
etc.
, and
des
crib
e th
e w
hole
as t
wo
halv
es,
thre
e th
irds,
four
four
ths.
Re
cogn
ize th
at e
qual
shar
es
of id
entic
al w
hole
s nee
d no
t ha
ve th
e sa
me
shap
e.
EE2.
G.3
. N/A
Math | Kindergarten-5 Grade 61
CO
MM
ON
CO
RE
ESS
EN
TIA
L E
LEM
EN
TS
AN
D A
CH
IEV
EM
EN
T
DE
SCR
IPT
OR
S FO
R T
HIR
D G
RA
DE
Th
ird
Gra
de
Mat
hem
atic
s St
and
ard
s: O
per
atio
ns
and
Alg
ebra
ic T
hin
kin
g
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
sol
ve p
robl
ems
invo
lvin
g m
ulti
plic
ation
and
di
visi
on.
3.O
A.1
. Int
erpr
et p
rodu
cts o
f w
hole
num
bers
, e.g
., in
terp
ret
5 ×
7 as
the
tota
l num
ber o
f ob
ject
s in
5 gr
oups
of 7
obj
ects
ea
ch.
For e
xam
ple,
des
crib
e a
cont
ext i
n w
hich
a to
tal n
umbe
r of
obj
ects
can
be
expr
esse
d as
5
× 7.
3.O
A.2
. Int
erpr
et w
hole
-num
ber
quoti
ents
of w
hole
num
bers
, e.
g., i
nter
pret
56
÷ 8
as th
e nu
mbe
r of o
bjec
ts in
eac
h sh
are
whe
n 56
obj
ects
are
par
tition
ed
equa
lly in
to 8
shar
es, o
r as a
nu
mbe
r of s
hare
s whe
n 56
ob
ject
s are
par
tition
ed in
to
equa
l sha
res o
f 8 o
bjec
ts e
ach.
Fo
r exa
mpl
e, d
escr
ibe
a co
ntex
t in
whi
ch a
num
ber o
f sha
res
or a
num
ber o
f gro
ups
can
be
expr
esse
d as
56
÷ 8.
EE3.
OA
.1-2
. Use
repe
ated
ad
ditio
n an
d eq
ual g
roup
s to
find
the
tota
l num
ber o
f obj
ects
to
find
the
sum
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
OA
.1-2
. Use
repe
ated
add
ition
to fi
nd th
e to
tal n
umbe
r of o
bjec
ts a
rran
ged
in a
sq
uare
or r
ecta
ngul
ar a
rray
.Ex
. Usin
g til
es in
a te
mpl
ate,
iden
tify
the
tota
l num
ber o
f tile
s by
addi
ng th
e til
es in
the
tem
plat
e.
11
1
11
1
11
13
+ 3
+ 3
= 9
Ex. F
ill sp
ace
of sq
uare
s and
rect
angl
es w
ith 1
-inch
tile
s, a
dd ti
les i
n ro
ws o
r col
umns
to
dete
rmin
e to
tal n
umbe
r of ti
les i
t tak
es to
fill
the
shap
e (s
quar
e/re
ctan
gle)
.Ex
. Use
an
abac
us to
find
the
tota
l.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
OA
.1-2
. Use
repe
ated
add
ition
and
equ
al g
roup
s to
find
the
tota
l num
ber o
f obj
ects
to
find
the
sum
.Ex
. Tw
o bi
rds +
two
Bird
s + tw
o bi
rds =
six
bird
s.Ex
. Giv
en a
repe
ated
add
ition
num
ber s
ente
nce,
use
a n
umbe
r lin
e to
find
the
sum
.
Leve
l II A
A S
tude
nts
will
:EE
3.O
A.1
-2. U
se a
dditi
on to
find
the
tota
l num
ber o
f obj
ects
.Ex
. Thr
ee a
pple
s + fo
ur a
pple
s = si
x ap
ples
.Ex
. Add
to fi
nd th
e to
tal n
umbe
r of s
tars
.
Ex. S
kip
coun
t by
twos
to te
ll ho
w m
any.
Leve
l I A
A S
tude
nts
will
:EE
3.O
A.1
-2. I
denti
fy w
hich
gro
up h
as m
ore
or le
ss w
hen
obje
cts a
re a
dded
or t
aken
aw
ay.
Ex. W
hen
an o
bjec
t is a
dded
to a
gro
up o
f thr
ee, “
Is th
is m
ore?
” an
d “I
s thi
s les
s?”
Ex. W
hen
an o
bjec
t is t
aken
from
a g
roup
of t
hree
, “Is
this
mor
e?”
and
“Is t
his l
ess?
”
62 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.O
A.3
. Use
mul
tiplic
ation
and
di
visio
n w
ithin
100
to so
lve
wor
d pr
oble
ms i
n sit
uatio
ns
invo
lvin
g eq
ual g
roup
s, a
rray
s,
and
mea
sure
men
t qua
ntitie
s,
e.g.
, by
usin
g dr
awin
gs a
nd
equa
tions
with
a sy
mbo
l for
the
unkn
own
num
ber t
o re
pres
ent
the
prob
lem
.
EE3.
OA
.3. S
ee E
E3.O
A.1.
fo
r rep
eate
d ad
ditio
n,
a fo
unda
tiona
l ski
ll fo
r m
ultip
licati
on a
nd d
ivisi
on.
(M
ultip
licati
on b
egin
s in
grad
e 4
and
divi
sion
begi
ns in
gra
de 5
).
Math | Kindergarten-5 Grade 63
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.O
A.4
. Det
erm
ine
the
unkn
own
who
le n
umbe
r in
a m
ultip
licati
on
or d
ivisi
on e
quati
on re
latin
g th
ree
who
le n
umbe
rs.
For
exam
ple,
det
erm
ine
the
unkn
own
num
ber t
hat m
akes
th
e eq
uatio
n tr
ue in
eac
h of
the
equa
tions
8 ×
? =
48,
5 =
_ ÷
3,
6 ×
6 =
?
EE3.
OA
.4. S
olve
add
ition
and
su
btra
ction
pro
blem
s whe
n re
sult
is un
know
n w
ith n
umbe
r 0-
30.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
OA
.4. S
olve
add
ition
and
subt
racti
on p
robl
ems w
hen
any
num
ber i
n th
e pr
oble
m is
un
know
n (r
esul
t, st
art,
chan
ge, d
iffer
ence
) with
num
bers
to 5
0.Ex
. Usin
g ba
se-1
0 pi
eces
, add
and
subt
ract
two-
digi
t num
bers
to fi
nd th
e su
m a
nd th
e di
ffere
nce.
Ex. U
se p
ictu
res o
f num
bers
to a
dd a
nd su
btra
ct tw
o-di
git n
umbe
rs to
find
the
sum
and
th
e di
ffere
nce.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
OA
.4. S
olve
add
ition
and
subt
racti
on p
robl
ems w
hen
resu
lt is
unkn
own
with
num
ber
0-30
.Ex
. Usin
g ba
se-1
0 pi
eces
or c
ount
ers,
add
and
subt
ract
.Ex
. Use
a 1
00s c
hart
to fi
nd th
e su
m o
r diff
eren
ce o
f giv
en p
robl
ems.
Ex. U
se c
ount
on
stra
tegi
es to
add
(e.g
., W
hen
aske
d w
hat i
s 5 +
2, t
he st
uden
t say
s 5 .
. . 6
. .
. 7)
.
Leve
l II A
A S
tude
nts
will
:EE
3.O
A.4
. Sol
ve a
dditi
on a
nd su
btra
ction
pro
blem
s with
num
bers
0-1
0.Ex
. Use
cou
nter
s to
add
and
subt
ract
.Ex
. Use
num
ber l
ines
to a
dd o
r sub
trac
t.
Ex. M
atch
the
sym
bol t
o m
ore
or le
ss th
an.
Ex. A
dd o
ne to
a n
umbe
r by
indi
catin
g th
e ne
xt n
umbe
r whe
n as
ked
(e.g
., w
hen
the
teac
her s
ays 3
, 4, 5
, the
stud
ent s
ays 6
).
Leve
l I A
A S
tude
nts
will
:EE
3.O
A.4
. Ide
ntify
num
bers
1 to
9.
Ex .G
iven
a se
t of fi
ve, m
atch
it to
the
num
ber.
Ex .G
iven
a se
t of t
hree
, ide
ntify
the
num
ber o
f obj
ects
on
num
ber l
ines
.
64 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
prop
erti
es
of m
ulti
plic
ation
and
the
rela
tion
ship
bet
wee
n m
ulti
plic
ation
and
div
isio
n.
3.O
A.5
. App
ly p
rope
rties
of
oper
ation
s as s
trat
egie
s to
mul
tiply
and
div
ide.
8 Exa
mpl
es:
If 6
× 4
= 24
is k
now
n, th
en
4 ×
6 =
24 is
als
o kn
own.
(C
omm
utati
ve p
rope
rty
of
mul
tiplic
ation
.) 3
× 5
× 2
can
be
foun
d by
3 ×
5 =
15,
then
15
× 2
= 30
, or b
y 5
× 2
= 10
, the
n 3
× 10
= 3
0. (
Ass
ocia
tive
prop
erty
of
mul
tiplic
ation
.) K
now
ing
that
8
× 5
= 40
and
8 ×
2 =
16,
one
ca
n fin
d 8
× 7
as 8
× (5
+ 2
) =
(8 ×
5) +
(8 ×
2) =
40
+ 16
= 5
6.
(Dis
trib
utive
pro
pert
y.)
EE3.
OA
.5. N
/A (M
ultip
licati
on
begi
ns a
t gra
de 4
).
3.O
A.6
. Und
erst
and
divi
sion
as
an u
nkno
wn-
fact
or p
robl
em.
For
exam
ple,
find
32
÷ 8
by fi
ndin
g th
e nu
mbe
r tha
t mak
es 3
2 w
hen
mul
tiplie
d by
8.
EE3.
OA
.6. N
/A (D
ivisi
on b
egin
s at
gra
de 5
).
Mul
tipl
y an
d di
vide
wit
hin
100.
3.O
A.7
. Flu
ently
mul
tiply
an
d di
vide
with
in 1
00,
usin
g st
rate
gies
such
as
the
rela
tions
hip
betw
een
mul
tiplic
ation
and
div
ision
(e.g
., kn
owin
g th
at 8
× 5
= 4
0, o
ne
know
s 40
÷ 5
= 8)
or p
rope
rties
of
ope
ratio
ns.
By th
e en
d of
Gr
ade
3, k
now
from
mem
ory
all p
rodu
cts o
f tw
o on
e-di
git
num
bers
.
EE3.
OA
.7. N
/A (M
ultip
licati
on
begi
ns g
rade
4 a
nd d
ivisi
on
begi
ns in
gra
de 5
).
Math | Kindergarten-5 Grade 65
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Solv
e pr
oble
ms
invo
lvin
g th
e fo
ur o
pera
tion
s, a
nd id
enti
fy
and
expl
ain
patt
erns
in
arit
hmeti
c.
3.O
A.8
. Sol
ve tw
o-st
ep w
ord
prob
lem
s usin
g th
e fo
ur
oper
ation
s. R
epre
sent
thes
e pr
oble
ms u
sing
equa
tions
w
ith a
lette
r sta
ndin
g fo
r the
un
know
n qu
antit
y. A
sses
s the
re
ason
able
ness
of a
nsw
ers
usin
g m
enta
l com
puta
tion
and
estim
ation
stra
tegi
es in
clud
ing
roun
ding
.9
EE3.
OA
.8. A
dd to
solv
e re
al
wor
ld o
ne-s
tep
stor
y pr
oble
ms
from
0-3
0.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
OA
.8. A
dd to
solv
e re
al w
orld
one
-ste
p st
ory
prob
lem
s with
sum
s up
to 5
0 us
ing
vario
us p
robl
em-s
olvi
ng m
odel
s.Ex
. Sol
ve b
y ad
ding
(e.g
. “Th
ere
are
25 b
irds i
n a
tree
and
10
mor
e jo
ined
them
. Ho
w
man
y bi
rds a
re in
a tr
ee?”
).Ex
. Sol
ve b
y ad
ding
(e.g
., “I
hav
e 15
snac
ks o
n th
e ca
rt a
nd 2
5 sn
acks
in th
e cu
pboa
rd,
how
man
y sn
acks
do
I hav
e al
l tog
ethe
r?)
Ex. S
olve
by
addi
ng (e
.g.,
“Add
the
penc
ils in
two
boxe
s and
tell
how
man
y pe
ncils
we
have
.”)
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
OA
.8. A
dd to
solv
e re
al w
orld
one
-ste
p st
ory
prob
lem
s fro
m 0
-30.
Rep
rese
nt th
e pr
oble
m in
pic
ture
s or w
ith o
bjec
ts.
Ex. S
olve
by
addi
ng (e
.g.,
“Her
e ar
e 10
pen
cils.
We
need
10
mor
e fo
r eac
h pe
rson
to g
et a
pe
ncil.
How
man
y w
ill w
e ne
ed in
all?
”)Ex
. Sol
ve b
y ad
ding
(e.g
., “C
onni
e ha
d fiv
e m
arbl
es.
Juan
gav
e he
r eig
ht m
ore
mar
bles
. Ho
w m
any
mar
bles
doe
s Con
nie
have
all
toge
ther
?”)
Ex. S
olve
by
addi
ng (e
.g.,
“Add
the
cray
ons i
n th
ese
two
boxe
s and
show
me
how
man
y w
e ha
ve in
all.
”)
Leve
l II A
A S
tude
nts
will
:EE
3.O
A.8
. Add
to so
lve
wor
d pr
oble
ms i
denti
fied
thro
ugh
sym
bol r
epre
sent
ation
.Ex
. Com
plet
e w
ord
prob
lem
s tha
t hav
e pi
ctur
es ra
ther
than
wor
ds.
Ex. S
olve
by
addi
ng (e
.g.,
“The
re a
re th
ree
duck
s in
the
pond
, tw
o m
ore
join
ed.
How
m
any
duck
s are
in th
e po
nd?”
[pic
ture
repr
esen
tatio
n])
Leve
l I A
A S
tude
nts
will
:EE
3.O
A.8
. Ide
ntify
the
obje
ct(s
) tha
t app
ear i
n a
real
wor
ld o
ne-s
tep
stor
y pr
oble
m.
Ex. G
iven
a si
mpl
e w
ord
prob
lem
and
ask
ed “
Wha
t is t
he p
robl
em a
bout
?” p
oint
to a
n ob
ject
from
a c
hoic
e of
two
that
repr
esen
ts w
hat t
he p
robl
em w
as a
bout
(e.g
., bo
x, to
y).
Ex. I
ndic
ate
whi
ch o
bjec
t a w
ord
prob
lem
is a
bout
from
an
arra
y of
two
choi
ces.
66 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.O
A.9
. Ide
ntify
arit
hmeti
c pa
ttern
s (in
clud
ing
patte
rns
in th
e ad
ditio
n ta
ble
or
mul
tiplic
ation
tabl
e), a
nd
expl
ain
them
usin
g pr
oper
ties
of o
pera
tions
. Fo
r exa
mpl
e,
obse
rve
that
4 ti
mes
a n
umbe
r is
alw
ays
even
, and
exp
lain
w
hy 4
tim
es a
num
ber c
an b
e de
com
pose
d in
to tw
o eq
ual
adde
nds.
EE3.
OA
.9. I
denti
fy a
rithm
etic
patte
rns.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
OA
.9. C
ompl
ete
a co
mpl
ex a
rithm
etic
patte
rn.
Ex. C
ompl
ete
the
patte
rn u
sing
mor
e th
an tw
o nu
mbe
rs (i
.e.,
A, B
, C, A
, B, C
).Ex
. Usin
g a
100s
num
ber c
hart
, com
plet
e th
e pa
ttern
iden
tified
.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
OA
.9. I
denti
fy a
rithm
etic
patte
rns.
Ex. W
hen
prov
ided
arit
hmeti
c pa
ttern
s on
a 10
0s c
hart
, ide
ntify
the
next
num
ber i
n th
e pa
ttern
.Ex
. Whe
n gi
ven
two
num
ber s
tam
ps, s
tam
p an
arit
hmeti
c pa
ttern
.
Leve
l II A
A S
tude
nts
will
:EE
3.O
A.9
. Ide
ntify
a p
atter
n.Ex
. Mak
e pa
ttern
jum
ps o
n a
num
ber l
ine.
Ex. S
ing
song
s and
iden
tify
the
patte
rn in
the
song
.
Leve
l I A
A S
tude
nts
will
:EE
3.O
A.9
. Fol
low
patt
erns
.Ex
. Sin
g “H
ead,
Sho
ulde
rs, K
nees
, and
Toes
” an
d m
imic
the
patte
rn.
Ex. U
sing
tacti
le o
bjec
ts (f
ur, s
and,
sand
, fur
) in
a pa
ttern
, rep
eat t
he p
atter
n.Ex
. Usin
g m
anip
ulati
ves,
mim
ic th
e te
ache
r to
crea
te a
patt
ern.
Math | Kindergarten-5 Grade 67
Th
ird
Gra
de
Mat
hem
atic
s St
and
ard
s: N
um
ber
an
d O
per
atio
ns
in B
ase
Ten
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
pla
ce v
alue
und
erst
andi
ng
and
prop
erti
es o
f ope
rati
ons
to
perf
orm
mul
ti-d
igit
ari
thm
etic.
10
3.N
BT.1
. Use
pla
ce v
alue
un
ders
tand
ing
to ro
und
who
le
num
bers
to th
e ne
ares
t 10
or
100.
EE3.
NBT
.1. I
denti
fy th
e tw
o 10
s a
num
ber c
omes
in b
etw
een
on a
nu
mbe
r lin
e (n
umbe
rs 0
-30)
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
NBT
.1. I
denti
fy th
e tw
o 10
s a n
umbe
r com
es in
bet
wee
n an
d te
ll w
hich
is c
lose
st
(num
bers
0-5
0).
Ex. U
se a
col
or b
eade
d nu
mbe
r lin
e to
iden
tify
the
num
ber a
nd ro
und
to th
e cl
oses
t 10.
Ex. G
iven
a n
umbe
r lin
e se
para
ted
into
tens
(0-1
0, 1
0-20
, etc
.), st
and
on a
num
ber a
nd
iden
tify
the
10 th
at is
clo
ser.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
NBT
.1. I
denti
fy th
e tw
o 10
s a n
umbe
r com
es in
bet
wee
n on
a n
umbe
r lin
e (n
umbe
rs
0-30
).Ex
. Use
a c
olor
bea
ded
num
ber l
ine
to id
entif
y th
e tw
o 10
s a n
umbe
r fal
ls be
twee
n.Ex
. Giv
en th
e nu
mbe
r 14,
they
wou
ld id
entif
y 10
and
20.
Leve
l II A
A S
tude
nts
will
:EE
3.N
BT.1
. Ide
ntify
tens
on
a nu
mbe
r lin
e.Ex
. Giv
en a
num
ber l
ine,
circ
le th
e te
ns.
Ex. S
tand
on
a nu
mbe
r cha
rt o
n 10
, 20,
30,
etc
.
Leve
l I A
A S
tude
nts
will
:EE
3.N
BT.1
. Ide
ntify
a n
umbe
r.Ex
. Poi
nt to
any
num
ber f
rom
one
to th
ree
on a
num
ber l
ine.
Ex. P
artic
ipat
e in
a c
ake
wal
k. W
hen
the
mus
ic st
ops,
look
to se
e if
they
are
on
the
num
ber t
hat i
s cal
led
out.
Ex. I
denti
fy a
num
ber w
hen
poin
t to
or p
rese
nted
on
a ca
rd.
Ex. G
iven
a n
umbe
r fro
m o
ne to
thre
e, p
oint
to th
e nu
mbe
r sym
bol.
68 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.N
BT.2
. Flu
ently
add
and
su
btra
ct w
ithin
100
0 us
ing
stra
tegi
es a
nd a
lgor
ithm
s bas
ed
on p
lace
val
ue, p
rope
rties
of
ope
ratio
ns, a
nd/o
r the
re
latio
nshi
p be
twee
n ad
ditio
n an
d su
btra
ction
.
EE3.
NBT
.2. I
denti
fy p
lace
val
ue
to te
ns.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
NBT
.2. I
denti
fy p
lace
val
ue to
50.
Ex. B
uild
num
bers
with
pla
ce v
alue
pie
ces.
Ex. I
denti
fy th
e nu
mbe
r in
the
ones
and
tens
pla
ce v
alue
(i.e
., th
e pr
ice
of a
n ite
m).
Ex. W
rite
the
num
ber i
n ex
pand
ed fo
rm –
43
= 40
+ 3
.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
NBT
.2. I
denti
fy p
lace
val
ue to
tens
.Ex
. Whe
n gi
ven
two-
digi
t num
ber c
ards
, ide
ntify
the
num
ber i
n th
e te
ns p
lace
val
ue.
Ex. W
hen
give
n a
grou
p of
10
fram
e m
odel
s, a
rran
ge a
nd c
ount
the
valu
e of
the
num
ber.
I saw
thre
e gr
oups
of 1
0 an
d fiv
e ex
tras
, so
thre
e gr
oups
of 1
0 =
30 a
nd 5
mor
e m
akes
35.
Leve
l II A
A S
tude
nts
will
:EE
3.N
BT.2
. Cou
nt to
10
usin
g on
e-to
-one
cor
resp
onde
nce.
Ex. G
iven
a b
ag o
f Ski
ttle
s, p
ull 1
0 Sk
ittle
s out
of t
he b
ag.
Ex. S
elec
t a d
omin
o an
d te
ll w
hat n
umbe
r the
dot
s rep
rese
nt.
Ex. S
how
n a
set o
f 10
obje
cts,
cre
ate
a du
plic
ate
colle
ction
.Ex
. Giv
en a
con
tain
er o
f pen
nies
, cou
nt o
ut 1
0 fr
om th
e co
ntai
ner.
Leve
l I A
A S
tude
nts
will
:EE
3.N
BT.2
. Ide
ntify
mor
e or
less
.Ex
. Giv
en tw
o co
llecti
ons o
f obj
ects
(gro
up o
f 10,
gro
up o
f 20)
, ind
icat
e, “
Whi
ch h
as
mor
e?”
Ex. G
iven
mat
h m
anip
ulati
ves r
epre
senti
ng a
sing
le u
nit a
nd m
ultip
le u
nits
, poi
nt to
the
mul
tiple
uni
t rep
rese
ntati
on w
hen
aske
d “w
hich
is m
ore?
”
Math | Kindergarten-5 Grade 69
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.N
BT.3
. Mul
tiply
one
-dig
it w
hole
num
bers
by
mul
tiple
s of
10 in
the
rang
e 10
-90
(e.g
., 9
× 80
, 5 ×
60)
usin
g st
rate
gies
bas
ed
on p
lace
val
ue a
nd p
rope
rties
of
oper
ation
s.
EE3.
NBT
.3. C
ount
by
tens
usin
g m
oney
.Le
vel I
V A
A S
tude
nts
will
:EE
3.N
BT.3
. Com
pare
the
valu
e of
mon
ey b
ased
on
plac
e va
lue.
Ex. U
se m
oney
(dim
es a
nd p
enni
es) t
o re
pres
ent p
lace
val
ue.
Ex. G
iven
15
penn
ies,
cre
ate
a on
e gr
oup
of 1
0 an
d a
grou
p of
five
one
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
NBT
.3. C
ount
by
tens
usin
g m
oney
.Ex
. Giv
en th
ree
dim
es, c
ount
by
10 to
det
erm
ine
tota
l.Ex
. Giv
en fi
ve d
imes
, cou
nt b
y 10
to d
eter
min
e to
tal.
Leve
l II A
A S
tude
nts
will
:EE
3.N
BT.3
. Ide
ntify
who
le n
umbe
rs to
10.
Ex. G
iven
sets
of 1
0 pe
nnie
s, p
air w
ith n
umbe
rs.
Ex. G
iven
sets
of 1
0 pe
nnie
s, p
air w
ith d
imes
.
Leve
l I A
A S
tude
nts
will
:EE
3.N
BT.3
. Cou
nt p
enni
es to
10.
70 Common Core Essential Elements
Th
ird
Gra
de
Mat
hem
atic
s St
and
ard
s: N
um
ber
an
d O
per
atio
ns-
-Fra
ctio
ns1
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Dev
elop
und
erst
andi
ng o
f fr
acti
ons
as n
umbe
rs.
3.N
F.1.
Und
erst
and
a fr
actio
n 1/
b as
the
quan
tity
form
ed b
y 1
part
whe
n a
who
le is
par
tition
ed
into
b e
qual
par
ts; u
nder
stan
d a
frac
tion
a/b
as th
e qu
antit
y fo
rmed
by
a pa
rts o
f size
1/b
.
3.N
F.2.
Und
erst
and
a fr
actio
n as
a
num
ber o
n th
e nu
mbe
r lin
e;
repr
esen
t fra
ction
s on
a nu
mbe
r lin
e di
agra
m.
Re
pres
ent a
frac
tion
1/b
on a
num
ber l
ine
diag
ram
by
defin
ing
the
inte
rval
from
0 to
1 a
s the
who
le
and
parti
tioni
ng it
into
b e
qual
par
ts.
Reco
gnize
that
eac
h pa
rt h
as si
ze 1
/b a
nd
that
the
endp
oint
of t
he p
art b
ased
at 0
lo
cate
s the
num
ber 1
/b o
n th
e nu
mbe
r lin
e.
Repr
esen
t a fr
actio
n a/
b on
a
num
ber l
ine
diag
ram
by
mar
king
off
a le
ngth
s 1/b
from
0.
Reco
gnize
that
the
resu
lting
inte
rval
has
size
a/b
and
that
its
endp
oint
loca
tes t
he n
umbe
r a/b
on
the
num
ber l
ine.
EE3.
NF.
1-3.
Diff
eren
tiate
a
frac
tiona
l par
t fro
m a
who
le.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
NF.
1-3.
Iden
tify
halv
es o
r fou
rths
as r
elat
ed to
the
who
le.
Ex. I
denti
fy p
ictu
res o
r obj
ects
that
are
split
into
four
ths.
Ex. F
old
a sq
uare
pie
ce o
f pap
er in
to fo
ur e
qual
par
ts a
nd id
entif
y it
as fo
ur p
arts
of a
w
hole
.Ex
. Com
plet
e a
pict
ure
of h
alf a
n ob
ject
with
the
othe
r hal
f to
mak
e th
e w
hole
.Ex
. Giv
en a
set o
f pic
ture
s, c
olor
a h
alf o
f eac
h w
hole
.Ex
. Sho
wn
four
hal
ves,
ass
embl
e th
em in
to tw
o w
hole
s and
stat
e th
e nu
mbe
r of w
hole
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
NF.
1-3.
Diff
eren
tiate
a fr
actio
nal p
art f
rom
a w
hole
.Ex
. Sor
t pic
ture
s of w
hole
obj
ects
and
par
ts in
to th
e ap
prop
riate
cat
egor
y.Ex
. Use
a v
arie
ty o
f rea
l-wor
ld o
bjec
ts (p
izza,
segm
ente
d ch
ocol
ate
bar,
etc.
) to
dem
onst
rate
that
eac
h pi
ece
repr
esen
ts a
par
t of t
he w
hole
.Ex
. Sho
wn
four
hal
ves,
ass
embl
e th
em in
to tw
o w
hole
s.
Leve
l II A
A S
tude
nts
will
:EE
3.N
F.1-
3. R
ecog
nize
that
frac
tions
are
par
t of a
who
le.
Ex. U
sing
a se
lf-sti
ckin
g no
n-ad
hesiv
e sh
ape,
take
apa
rt a
nd p
ut to
geth
er fr
actio
nal p
arts
of
a w
hole
.Ex
. Util
ize w
oode
n sh
apes
, sep
arat
e in
to h
alve
s and
put
bac
k to
geth
er in
to w
hole
.Le
vel I
AA
Stu
dent
s w
ill:
EE3.
NF.
1-3.
Iden
tify
a w
hole
.Ex
. Giv
en a
par
t of a
nd th
e w
hole
real
-wor
ld o
bjec
t (pi
zza,
segm
ente
d ch
ocol
ate
bar,
segm
ente
d to
y pi
e, e
tc.),
poi
nt to
the
who
le.
Ex. G
iven
a p
uzzle
with
miss
ing
piec
es a
nd a
puz
zle w
ith c
ompl
ete
piec
es, i
denti
fy th
e w
hole
.
1 G
rade
3 e
xpec
tatio
ns in
this
dom
ain
are
limite
d to
frac
tions
with
den
omin
ator
s 2, 3
, 4, 6
, 8.
Math | Kindergarten-5 Grade 71
3.N
F.3.
Exp
lain
equ
ival
ence
of
frac
tions
in sp
ecia
l cas
es, a
nd
com
pare
frac
tions
by
reas
onin
g ab
out t
heir
size.
U
nder
stan
d tw
o fr
actio
ns a
s eq
uiva
lent
(equ
al) i
f the
y ar
e th
e sa
me
size,
or t
he sa
me
poin
t on
a nu
mbe
r lin
e.
Reco
gnize
and
gen
erat
e sim
ple
equi
vale
nt fr
actio
ns, (
e.g.
, 1/2
=
2/4,
4/6
= 2
/3).
Exp
lain
why
the
frac
tions
are
equ
ival
ent,
e.g.
, by
usin
g a
visu
al fr
actio
n m
odel
.
Expr
ess w
hole
num
bers
as
frac
tions
, and
reco
gnize
frac
tions
th
at a
re e
quiv
alen
t to
who
le n
umbe
rs.
Exam
ples
: Exp
ress
3 in
the
form
3 =
3/1
; re
cogn
ize
that
6/1
= 6
; loc
ate
4/4
and
1 at
the
sam
e po
int o
f a n
umbe
r lin
e di
agra
m.
Co
mpa
re tw
o fr
actio
ns
with
the
sam
e nu
mer
ator
or t
he sa
me
deno
min
ator
by
reas
onin
g ab
out t
heir
size.
Rec
ogni
ze th
at c
ompa
rison
s are
va
lid o
nly
whe
n th
e tw
o fr
actio
ns re
fer
to th
e sa
me
who
le.
Reco
rd th
e re
sults
of
com
paris
ons w
ith th
e sy
mbo
ls >,
=,
or <
, and
justi
fy th
e co
nclu
sions
, e.g
., by
us
ing
a vi
sual
frac
tion
mod
el.
72 Common Core Essential Elements
Th
ird
Gra
de
Mat
hem
atic
s St
and
ard
s: M
easu
rem
ent
and
Dat
a
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Solv
e pr
oble
ms
invo
lvin
g m
easu
rem
ent
and
esti
mati
on
of in
terv
als
of ti
me,
liqu
id
volu
mes
, and
mas
ses
of o
bjec
ts.
3.M
D.1
. Tel
l and
writ
e tim
e to
th
e ne
ares
t min
ute
and
mea
sure
tim
e in
terv
als i
n m
inut
es.
Solv
e w
ord
prob
lem
s inv
olvi
ng
addi
tion
and
subt
racti
on o
f tim
e in
terv
als i
n m
inut
es, e
.g.,
by
repr
esen
ting
the
prob
lem
on
a nu
mbe
r lin
e di
agra
m.
EE3.
MD
.1. T
ell ti
me
to th
e ho
ur
on a
dig
ital c
lock
.Le
vel I
V A
A S
tude
nts
will
:EE
3.M
D.1
. Tel
l tim
e to
the
half
hour
usin
g a
digi
tal c
lock
.Ex
. Loo
k at
a d
igita
l clo
ck a
nd re
ad th
e tim
e.Ex
. Whe
n lo
okin
g at
a sc
hedu
le, i
denti
fy th
e ho
ur.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
MD
.1. T
ell ti
me
to th
e ho
ur o
n a
digi
tal c
lock
.Ex
. Giv
en a
tim
e w
ritten
to th
e ho
ur, w
rite
the
digi
tal ti
me.
Ex. I
denti
fy th
e tim
e of
a d
igita
l clo
ck th
at is
set t
o th
e ho
ur.
Ex. G
iven
a ti
me
on a
dig
ital c
lock
, say
the
time
to th
e ho
ur.
Leve
l II A
A S
tude
nts
will
:EE
3.M
D.1
. Ide
ntify
whi
ch is
the
hour
on
a di
gita
l clo
ck.
Ex. R
elat
e th
e ho
ur w
ith th
e tim
e on
thei
r dai
ly sc
hedu
le.
Ex. G
iven
car
ds sh
owin
g di
gita
l clo
cks -
with
one
clo
ck h
avin
g th
e ho
ur c
ircle
d an
d on
e cl
ock
with
the
min
utes
circ
led,
indi
cate
the
cloc
k w
ith th
e ho
ur c
ircle
d.
Leve
l I A
A S
tude
nts
will
:EE
3.M
D.1
. Diff
eren
tiate
a d
igita
l clo
ck fr
om o
ther
mea
sure
men
t too
ls as
a to
ol fo
r tel
ling
time.
Ex. G
iven
a d
igita
l clo
ck a
nd a
mea
surin
g cu
p, id
entif
y th
e cl
ock
for t
ellin
g tim
e.Ex
. Ask
ed, “
How
do
we
know
whe
n it
is tim
e to
go
to lu
nch?
” in
dica
te a
clo
ck.
Math | Kindergarten-5 Grade 73
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.M
D.2
. Mea
sure
and
esti
mat
e liq
uid
volu
mes
and
mas
ses o
f ob
ject
s usin
g st
anda
rd u
nits
of
gra
ms (
g), k
ilogr
ams (
kg),
and
liter
s (l).
11 A
dd, s
ubtr
act,
mul
tiply,
or d
ivid
e to
solv
e on
e-st
ep w
ord
prob
lem
s inv
olvi
ng
mas
ses o
r vol
umes
that
are
gi
ven
in th
e sa
me
units
, e.g
., by
us
ing
draw
ings
(suc
h as
a b
eake
r w
ith a
mea
sure
men
t sca
le) t
o re
pres
ent t
he p
robl
em.12
EE3.
MD
.2. I
denti
fy st
anda
rd
units
of m
easu
re fo
r mas
s and
liq
uid.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
MD
.2. M
easu
re li
quid
vol
umes
and
mas
ses o
f obj
ects
usin
g st
anda
rd u
nits
of g
ram
s (g
), ki
logr
ams (
kg),
and
liter
s (l).
Ex. M
easu
re o
ut it
ems i
n a
reci
pe.
Ex. C
ompa
re th
e m
ass o
f tw
o ite
ms u
sing
a tw
o-pa
n ba
lanc
e (b
alan
ce sc
ale)
.Ex
. Giv
en a
stan
dard
uni
t sca
le, w
eigh
10
gram
s of s
and.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
MD
.2. I
denti
fy st
anda
rd u
nits
of m
easu
re fo
r mas
s and
liqu
id.
Ex. S
ort t
he fo
llow
ing
real
-wor
ld it
ems a
s bei
ng m
easu
red
by g
ram
s or l
iters
whe
n sh
own
the
mea
sure
men
t too
ls (a
pple
mea
sure
d in
gra
ms a
nd ju
ice
in li
ters
).Ex
. Whe
n sh
own
pict
ures
of t
he to
ol, i
denti
fy w
hat w
ould
be
mea
sure
d gr
ams o
r lite
rs.
Leve
l II A
A S
tude
nts
will
:EE
3.M
D.2
. Sel
ect t
he a
ppro
pria
te to
ol to
mea
sure
a so
lid o
r a li
quid
.Ex
. Whe
n pr
ovid
ed tw
o pi
ctur
es, o
ne sh
owin
g a
rule
r and
one
show
ing
a sc
ale,
iden
tify
whi
ch to
ol m
easu
res m
ass.
Ex. W
hen
prov
ided
two
tool
s, a
mea
surin
g cu
p an
d a
scal
e, id
entif
y w
hich
tool
mea
sure
s liq
uid.
Ex. S
elec
t fro
m a
var
iety
of t
ools
the
appr
opria
te to
ol to
mea
sure
eith
er m
ass o
r vol
ume.
Ex. G
iven
a ro
ck a
nd a
gla
ss o
f wat
er, i
denti
fy w
hich
wou
ld b
e m
easu
red
usin
g a
mea
surin
g cu
p.
Leve
l I A
A S
tude
nts
will
:EE
3.M
D.2
. Det
erm
ine
if an
obj
ect i
s a so
lid a
nd a
liqu
id.
Ex. P
lace
obj
ects
from
the
room
into
the
appr
opria
te m
easu
rem
ent c
ateg
ory
(sol
id o
r liq
uid)
.Ex
. Giv
en a
rock
and
a g
lass
of w
ater
, ide
ntify
whi
ch is
solid
.
74 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
inte
rpre
t dat
a.
3.M
D.3
. Dra
w a
scal
ed p
ictu
re
grap
h an
d a
scal
ed b
ar g
raph
to
repr
esen
t a d
ata
set w
ith se
vera
l ca
tego
ries.
Sol
ve o
ne- a
nd
two-
step
“ho
w m
any
mor
e” a
nd
“how
man
y le
ss”
prob
lem
s usin
g in
form
ation
pre
sent
ed in
scal
ed
bar g
raph
s. F
or e
xam
ple,
dra
w a
ba
r gra
ph in
whi
ch e
ach
squa
re
in th
e ba
r gra
ph m
ight
repr
esen
t 5
pets
.
EE3.
MD
.3. U
se p
ictu
re o
r bar
gr
aph
data
to a
nsw
er q
uesti
ons
abou
t dat
a.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
MD
.3. I
nter
pret
dat
a to
ans
wer
que
stion
s.Ex
. Ide
ntify
how
they
kno
w th
ere
wer
e no
rain
y da
ys th
at w
eek
base
d on
the
char
t.Ex
. Sta
te tw
o fa
cts a
bout
the
data
on
a gr
aph.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
MD
.3. U
se p
ictu
re o
r bar
gra
ph d
ata
to a
nsw
er q
uesti
ons a
bout
dat
a.Ex
. Ide
ntify
from
a p
ictu
re o
r bar
gra
ph h
ow m
any
stud
ents
in th
e cl
ass w
ere
iden
tified
as
wea
ring
blue
shirt
s.Ex
. Sta
te h
ow m
any
days
wer
e su
nny
as c
hart
ed o
n a
wea
ther
cha
rt.
Leve
l II A
A S
tude
nts
will
:EE
3.M
D.3
. Org
anize
dat
a.Ex
. Tak
e da
ta c
olle
cted
from
the
lunc
h ch
oice
s and
pla
ce d
ata
into
app
ropr
iate
cat
egor
ies.
Ex. P
lace
dat
a on
a c
hart
to re
pres
ent t
he d
ata
colle
cted
.
Leve
l I A
A S
tude
nts
will
:EE
3.M
D.3
. Col
lect
dat
a.Ex
. Usin
g tw
o po
ster
s, o
ne fo
r the
stud
ents
with
bro
wn
hair,
and
one
for t
he st
uden
ts w
ith
“yel
low
” ha
ir, p
lace
thei
r pic
ture
on
the
post
er b
oard
that
indi
cate
s wha
t col
or h
air t
hey
have
.Ex
. Use
a d
aily
surv
ey to
col
lect
dat
a on
diff
eren
t int
eres
t.
Math | Kindergarten-5 Grade 75
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.M
D.4
. Gen
erat
e m
easu
rem
ent
data
by
mea
surin
g le
ngth
s usin
g ru
lers
mar
ked
with
hal
ves a
nd
four
ths o
f an
inch
. Sh
ow th
e da
ta b
y m
akin
g a
line
plot
, whe
re
the
horiz
onta
l sca
le is
mar
ked
off in
app
ropr
iate
uni
ts—
who
le
num
bers
, hal
ves,
or q
uart
ers.
EE3.
MD
.4. M
easu
re le
ngth
of
obje
cts u
sing
stan
dard
tool
s,
such
as r
uler
s, y
ards
ticks
, and
m
eter
stick
s.
Leve
l IV
AA
Stu
dent
s w
ill:
EE3.
MD
.4. M
easu
re le
ngth
of o
bjec
ts u
sing
stan
dard
tool
s, su
ch a
s rul
ers,
yar
dstic
ks, a
nd
met
er sti
cks,
by
repe
ating
the
use
of th
e m
easu
rem
ent t
ool/u
nit.
Ex. G
iven
a ro
w o
f thr
ee ti
le sq
uare
s on
the
floor
, mea
sure
the
leng
th o
f the
tile
s by
repe
ating
a ru
ler e
nd to
end
.Ex
. Giv
en a
hal
lway
from
the
clas
sroo
m to
the
bath
room
acr
oss t
he h
all,
mea
sure
the
dist
ance
with
a y
ards
tick
by re
peati
ng th
e ya
rdsti
ck fr
om e
nd to
end
.Ex
. Giv
e on
e ru
ler l
engt
h of
yar
n to
eac
h cl
assm
ate
for a
pro
ject
.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
MD
.4. M
easu
re le
ngth
of o
bjec
ts u
sing
stan
dard
tool
s, su
ch a
s rul
ers,
yar
dstic
ks, a
nd
met
er sti
cks.
Ex. G
iven
an
obje
ct a
nd a
mea
surin
g to
ol, u
se th
e to
ol to
mar
k th
e le
ngth
of t
he o
bjec
t.Ex
. Giv
en a
rule
r and
snow
fall,
mar
k th
e de
pth
of th
e sn
ow w
ith a
rule
r.Ex
. Giv
en a
yar
dstic
k, m
easu
re d
iffer
ent l
engt
hs o
r wid
ths o
f the
room
and
reco
rd th
e m
easu
rem
ent.
Leve
l II A
A S
tude
nts
will
:EE
3.M
D.4
. Mea
sure
leng
th w
ith n
on-s
tand
ard
units
of m
easu
rem
ent.
Ex. I
denti
fy th
e le
ngth
of i
tem
s in
the
clas
sroo
m u
sing
a ya
rdsti
ck e
nd-to
-end
and
reco
rd
as n
umbe
r of y
ards
ticks
.Ex
. Whe
n pr
ovid
ed tw
o no
n-st
anda
rd m
easu
ring
units
, ide
ntify
whi
ch o
ne is
mos
t ap
prop
riate
for w
hat i
s to
be m
easu
red
(pen
cil o
r lon
g sti
ck to
mea
sure
the
leng
th o
f the
cl
assr
oom
).
Leve
l I A
A S
tude
nts
will
:EE
3.M
D.4
. Pla
ce a
stan
dard
mea
surin
g to
ol w
here
one
wou
ld b
egin
to m
easu
re th
e le
ngth
of
an
obje
ct.
Ex. G
iven
a st
ring,
pla
ce th
e ru
ler a
t the
end
of t
he st
ring
whe
re o
ne w
ould
beg
in a
m
easu
re.
Ex. S
how
n a
pict
ure
of a
boy
stan
ding
aga
inst
a h
eigh
t mea
sure
, and
ask
ed w
here
you
w
ould
look
to fi
nd th
e bo
y’s h
eigh
t, in
dica
te th
e to
p of
the
boy’
s hea
d.Ex
. Giv
en a
boo
kshe
lf an
d a
rule
r, pl
ace
the
rule
r on
the
low
er le
ft co
rner
of t
he b
ooks
helf
fron
t. (A
nyth
ing
with
a d
efini
te lo
wer
left
edge
that
will
not
allo
w th
e st
uden
t to
go
beyo
nd it
will
wor
k.)
76 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Geo
met
ric
mea
sure
men
t:
unde
rsta
nd c
once
pts
of a
rea
and
rela
te a
rea
to m
ulti
plic
ation
an
d to
add
ition
.
3.M
D.5
. Rec
ogni
ze a
rea
as a
n att
ribut
e of
pla
ne fi
gure
s and
un
ders
tand
con
cept
s of a
rea
mea
sure
men
t.
A sq
uare
with
side
leng
th o
f 1
unit,
cal
led
“a u
nit s
quar
e,”
is sa
id to
ha
ve “o
ne sq
uare
uni
t” o
f are
a, a
nd c
an
be u
sed
to m
easu
re a
rea.
A
plan
e fig
ure,
whi
ch c
an b
e co
vere
d w
ithou
t gap
s or o
verla
ps b
y n
unit
squa
res,
is sa
id to
hav
e an
are
a of
n
squa
re u
nits
.
3.M
D.6
. Mea
sure
are
as b
y co
untin
g un
it sq
uare
s (sq
uare
cm
, squ
are
m, s
quar
e in
, squ
are
ft, a
nd im
prov
ised
units
).
3.M
D.7
. Rel
ate
area
to th
e op
erati
ons o
f mul
tiplic
ation
and
ad
ditio
n.
Find
the
area
of a
rect
angl
e w
ith
who
le-n
umbe
r sid
e le
ngth
s by
tilin
g it,
an
d sh
ow th
at th
e ar
ea is
the
sam
e as
w
ould
be
foun
d by
mul
tiply
ing
the
side
leng
ths.
M
ultip
ly si
de le
ngth
s to
find
area
s of
rect
angl
es w
ith w
hole
-num
ber s
ide
leng
ths i
n th
e co
ntex
t of s
olvi
ng re
al
wor
ld a
nd m
athe
mati
cal p
robl
ems,
an
d re
pres
ent w
hole
-num
ber p
rodu
cts
as re
ctan
gula
r are
as in
mat
hem
atica
l re
ason
ing.
U
se ti
ling
to sh
ow in
a
conc
rete
cas
e th
at th
e ar
ea o
f a re
ctan
gle
with
who
le-n
umbe
r sid
e le
ngth
s a a
nd
b +
c is
the
sum
of a
× b
and
a ×
c.
Use
ar
ea m
odel
s to
repr
esen
t the
dist
ributi
ve
prop
erty
in m
athe
mati
cal r
easo
ning
.
Reco
gnize
are
a as
add
itive
. Fi
nd a
reas
of r
ectil
inea
r figu
res b
y de
com
posin
g th
em in
to n
on-o
verla
ppin
g re
ctan
gles
and
add
ing
the
area
s of t
he
non-
over
lapp
ing
part
s, a
pply
ing
this
tech
niqu
e to
solv
e re
al w
orld
pro
blem
s.
EE3.
MD
.5-7
. N/A
(Are
a be
gins
at
grad
e 6)
.
Math | Kindergarten-5 Grade 77
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Geo
met
ric
mea
sure
men
t:
reco
gniz
e pe
rim
eter
as
an
attri
bute
of p
lane
figu
res
and
disti
ngui
sh b
etw
een
linea
r an
d ar
ea m
easu
res.
3.M
D.8
. Sol
ve re
al w
orld
an
d m
athe
mati
cal p
robl
ems
invo
lvin
g pe
rimet
ers o
f pol
ygon
s,
incl
udin
g fin
ding
the
perim
eter
gi
ven
the
side
leng
ths,
find
ing
an u
nkno
wn
side
leng
th, a
nd
exhi
bitin
g re
ctan
gles
with
the
sam
e pe
rimet
er a
nd d
iffer
ent
area
s or w
ith th
e sa
me
area
and
di
ffere
nt p
erim
eter
s.
EE3.
MD
.8. N
/A (P
erim
eter
be
gins
at g
rade
7).
78 Common Core Essential Elements
Th
ird
Gra
de
Mat
hem
atic
s St
and
ard
s: G
eom
etry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Reas
on w
ith
shap
es a
nd th
eir
attri
bute
s.
3.G
.1. U
nder
stan
d th
at sh
apes
in
diff
eren
t cat
egor
ies (
e.g.
, rh
ombu
ses,
rect
angl
es, a
nd
othe
rs) m
ay sh
are
attrib
utes
(e
.g.,
havi
ng fo
ur si
des)
, and
th
at th
e sh
ared
att
ribut
es c
an
defin
e a
larg
er c
ateg
ory
(e.g
., qu
adril
ater
als)
. Re
cogn
ize
rhom
buse
s, re
ctan
gles
, an
d sq
uare
s as e
xam
ples
of
qua
drila
tera
ls, a
nd d
raw
ex
ampl
es o
f qua
drila
tera
ls th
at
do n
ot b
elon
g to
any
of t
hese
su
bcat
egor
ies.
EE3.
G.1
. Rec
ogni
ze th
at sh
apes
in
diff
eren
t cat
egor
ies c
an sh
are
attrib
utes
.
Leve
l IV
AA
Stu
dent
s w
ill:
DD
3.G
.1. I
denti
fy th
e sh
ared
att
ribut
es o
f sha
pes i
n di
ffere
nt c
ateg
orie
s.Ex
. Giv
en a
Ven
n di
agra
m, s
ort a
ttrib
utes
of s
hape
s (i.e
., st
raig
ht e
dges
, cur
ved
edge
s,
both
).Ex
. Tra
ce th
e sh
ared
att
ribut
es o
f tw
o di
ffere
nt sh
apes
.
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
G.1
. Rec
ogni
ze th
at sh
apes
in d
iffer
ent c
ateg
orie
s can
shar
e att
ribut
es.
Ex. S
how
n di
ffere
nt sh
apes
ans
wer
s, “
Wha
t is t
he sa
me?
”Ex
. Pla
ce in
the
appr
opria
te c
ateg
ory
shap
es w
ith c
omm
on a
ttrib
utes
.
Leve
l II A
A S
tude
nts
will
:EE
3.G
.1. S
ort s
hape
s by
attrib
utes
.Ex
. Giv
en a
sorti
ng m
ap, s
ort s
hape
s by
give
n att
ribut
es.
Ex. G
iven
a so
rting
map
, sor
t diff
eren
t size
sam
e sh
apes
into
the
sam
e ca
tego
ry (e
.g.,
larg
e an
d sm
all t
riang
le w
ould
go
in th
e sa
me
cate
gory
).
Leve
l I A
A S
tude
nts
will
:EE
3.G
.1. M
atch
shap
es (e
.g.,
squa
res,
rect
angl
es, c
ircle
s, tr
iang
les)
.Ex
. Mat
ch sh
apes
to th
e sh
ape
of o
bjec
ts w
ithin
the
clas
sroo
m.
Ex. M
atch
shap
es th
at a
re th
e sa
me.
Math | Kindergarten-5 Grade 79
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
3.G
.2. P
artiti
on sh
apes
into
pa
rts w
ith e
qual
are
as.
Expr
ess
the
area
of e
ach
part
as a
uni
t fr
actio
n of
the
who
le.
For
exam
ple,
par
tition
a s
hape
into
4
part
s w
ith e
qual
are
a, a
nd
desc
ribe
the
area
of e
ach
part
as
1/4
of th
e ar
ea o
f the
sha
pe.
EE3.
G.2
. Rec
ogni
ze th
at sh
apes
ca
n be
par
tition
ed in
to e
qual
ar
eas.
Leve
l IV
AA
Stu
dent
s w
ill:
3.G
.2. G
iven
shap
es w
ith m
ultip
le li
nes o
f sym
met
ry, w
ill b
e ab
le to
iden
tify
equa
l are
as.
Ex. C
ompl
ete
simpl
e ta
ngra
m p
uzzle
s with
tang
ram
pie
ces.
Ex. I
denti
fy e
qual
are
as o
n co
mpl
ex sh
apes
(i.e
., st
ars,
rect
angl
e cu
t on
the
diag
onal
)
Leve
l III
AA
Stu
dent
s w
ill:
EE3.
G.2
. Rec
ogni
ze th
at sh
apes
can
be
parti
tione
d in
to e
qual
are
as.
Ex. G
iven
a sh
ape,
cut
the
shap
e in
to e
qual
are
as.
Ex. C
ut a
pizz
a in
to e
qual
are
as to
han
d ou
t to
stud
ents
in th
e cl
ass.
Leve
l II A
A S
tude
nts
will
:EE
3.G
.2. C
reat
e sh
apes
.Ex
. Wor
k a
patte
rn b
lock
puz
zle th
at re
sults
in a
shap
e.Ex
. Giv
en th
ree
smal
l rec
tang
les,
rear
rang
e th
em in
to a
larg
er re
ctan
gle.
Leve
l I A
A S
tude
nts
will
:EE
3.G
.2. M
atch
shap
es.
Ex. M
atch
a p
ictu
re o
f a sh
ape,
to a
shap
e in
the
clas
sroo
m.
Ex. M
atch
two
shap
es fr
om a
n ar
ray
of th
ree
in w
hich
one
is d
iffer
ent.
80 Common Core Essential Elements
CO
MM
ON
CO
RE
ESS
EN
TIA
L E
LEM
EN
TS
AN
D A
CH
IEV
EM
EN
T
DE
SCR
IPT
OR
S FO
R F
OU
RT
H G
RA
DE
Fou
rth
Gra
de
Mat
hem
atic
s St
and
ard
s: O
per
atio
ns
and
Alg
ebra
ic T
hin
kin
g
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
the
four
ope
rati
ons
wit
h w
hole
num
bers
to s
olve
pr
oble
ms.
4.O
A.1
. Int
erpr
et a
mul
tiplic
ation
eq
uatio
n as
a c
ompa
rison
, e.
g., i
nter
pret
35
= 5
× 7
as a
st
atem
ent t
hat 3
5 is
5 tim
es
as m
any
as 7
and
7 ti
mes
as
man
y as
5.
Repr
esen
t ver
bal
stat
emen
ts o
f mul
tiplic
ative
co
mpa
rison
s as m
ultip
licati
on
equa
tions
.
4.O
A.2
. Mul
tiply
or d
ivid
e to
so
lve
wor
d pr
oble
ms i
nvol
ving
m
ultip
licati
ve c
ompa
rison
, e.
g., b
y us
ing
draw
ings
and
eq
uatio
ns w
ith a
sym
bol f
or th
e un
know
n nu
mbe
r to
repr
esen
t th
e pr
oble
m, d
isting
uish
ing
mul
tiplic
ative
com
paris
on fr
om
addi
tive
com
paris
on.
EE4.
OA
.1-2
. Dem
onst
rate
the
conn
ectio
n be
twee
n re
peat
ed
addi
tion
and
mul
tiplic
ation
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
OA
.1-2
. App
ly re
peat
ed a
dditi
on to
solv
e a
mul
tiplic
ation
pro
blem
repr
esen
ted
with
nu
mbe
rs.
Ex. P
rese
nted
with
a m
ultip
licati
on p
robl
em su
ch a
s 3 x
6, u
se e
gg c
arto
ns a
nd c
oncr
ete
obje
cts t
o cr
eate
arr
ays (
e.g.
, sor
t thr
ee o
bjec
ts in
to si
x eg
g slo
ts o
r six
obj
ects
into
thre
e slo
ts).
Ex. W
hen
pres
ente
d w
ith tw
o ch
oice
s of a
rray
s on
the
smar
t boa
rd a
nd a
mul
tiplic
ation
pr
oble
m, i
denti
fy (i
.e.,
eye
gaze
) the
cor
rect
arr
ay.
Ex. U
se sk
ip c
ounti
ng o
n a
num
ber l
ine
to so
lve
mul
tiplic
ation
pro
blem
s (e.
g., m
ove
two
digi
ts fi
ve ti
mes
for t
he p
robl
em 2
x 5
).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
OA
.1-2
. Dem
onst
rate
the
conn
ectio
n be
twee
n re
peat
ed a
dditi
on a
nd m
ultip
licati
on.
Ex. S
kip
coun
t by
two,
five
, and
10
to so
lve
mul
tiplic
ation
pro
blem
s.Ex
. Usin
g th
ree
grou
ps o
f tw
o ob
ject
s, c
omm
unic
ate
that
2 +
2 +
2 is
equ
al to
3 x
2.
Ex. U
sing
plas
tic e
ggs a
nd a
n eg
g ca
rton
to h
old
the
eggs
in p
lace
, pla
ce a
n ob
ject
in e
ach
egg
to il
lust
rate
6 +
6 =
12
or 6
x 2
= 1
2.Ex
. Rep
rese
nt th
e ch
airs
in a
cla
ss w
ith th
ree
row
s of f
our c
hairs
in e
ach
(e.g
., id
entif
y 4
+ 4
+ 4)
.
Leve
l II A
A S
tude
nts
will
:EE
4.O
A.1
-2. D
emon
stra
te re
peat
ed a
dditi
on to
sum
s of 1
0.Ex
. Ski
p co
unt b
y tw
o an
d fiv
e to
10.
Ex. A
dd 1
+ 1
+ 1
.Ex
. Add
2 +
2 +
2.
Ex. A
dd 3
+ 3
+ 3
.Ex
. Add
2 +
2 +
2 +
2 +
2 to
equ
al 1
0.Ex
. Pre
sent
ed w
ith a
pic
ture
of t
wo
chai
rs in
a ro
w a
nd g
iven
four
pic
ture
s of i
ndiv
idua
l ch
airs
, arr
ange
the
addi
tiona
l fou
r cha
irs in
to e
qual
row
s and
cou
nt a
ll of
the
chai
rs.
Leve
l I A
A S
tude
nts
will
:EE
4.O
A.1
-2. M
ake
a se
t of 1
0 an
d co
unt t
o 10
.Ex
. Usin
g fin
gers
cou
nt to
10.
Ex. U
sing
a 10
fram
e, p
lace
a c
ube
in e
ach
squa
re.
Ex. U
se a
switc
h to
cou
nt to
10.
Ex. C
ount
like
obj
ects
to m
ake
a se
t of 1
0.
Math | Kindergarten-5 Grade 81
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.O
A.3
. Sol
ve m
ultis
tep
wor
d pr
oble
ms p
osed
with
who
le
num
bers
and
hav
ing
who
le-
num
ber a
nsw
ers u
sing
the
four
op
erati
ons,
incl
udin
g pr
oble
ms
in w
hich
rem
aind
ers m
ust b
e in
terp
rete
d. R
epre
sent
thes
e pr
oble
ms u
sing
equa
tions
w
ith a
lette
r sta
ndin
g fo
r the
un
know
n qu
antit
y. A
sses
s the
re
ason
able
ness
of a
nsw
ers
usin
g m
enta
l com
puta
tion
and
estim
ation
stra
tegi
es in
clud
ing
roun
ding
.
EE4.
OA
.3. S
olve
one
-ste
p w
ord
prob
lem
s usin
g ad
ditio
n or
su
btra
ction
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
OA
.3. S
olve
two-
step
pro
blem
s usin
g ad
ditio
n or
subt
racti
on w
hen
a nu
mbe
r in
the
prob
lem
is u
nkno
wn
(res
ult,
star
t, ch
ange
, diff
eren
ce).
Ex. U
se a
num
ber l
ine
to so
lve
two-
step
pro
blem
s.Ex
. Use
a h
undr
eds c
hart
to so
lve
a tw
o-st
ep p
robl
em.
Ex. S
olve
a tw
o-st
ep w
ord
prob
lem
invo
lvin
g ad
ditio
n (e
.g.,
“If A
my
has 1
0 sh
eets
of p
aper
an
d yo
u ha
ve 1
0 m
ore
shee
ts th
an A
my,
how
man
y sh
eets
do
you
have
? [a
dditi
on –
co
mpa
re to
tal u
nkno
wn]
).Ex
. Sol
ve a
two-
step
wor
d pr
oble
m in
volv
ing
subt
racti
ons (
e.g.
, “Sa
ndi h
as 1
0 ca
ts a
nd
20 d
ogs –
doe
s she
hav
e m
ore
cats
or d
ogs?
How
man
y m
ore?
” [s
ubtr
actio
n - c
ompa
re
diffe
renc
e un
know
n]).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
OA
.3. S
olve
one
-ste
p pr
oble
ms u
sing
addi
tion
or su
btra
ction
.Ex
. Use
man
ipul
ative
s to
add
or su
btra
ct tw
o gr
oups
.Ex
. Use
man
ipul
ative
s on
a nu
mbe
r lin
e to
solv
e ad
ditio
n or
subt
racti
on p
robl
ems.
Ex. S
olve
one
-ste
p w
ord
prob
lem
invo
lvin
g ad
ditio
n (e
.g.,
“If S
am g
ave
away
10
appl
es a
nd
has fi
ve a
pple
s left
how
man
y di
d he
star
t with
?” [a
dditi
on –
star
t unk
now
n]).
Ex. S
olve
one
-ste
p w
ord
prob
lem
invo
lvin
g su
btra
ction
s (e.
g., “
If Ju
ne h
ad 5
0 do
llars
and
sp
ent t
en, h
ow m
uch
does
she
have
left?
” [s
ubtr
actio
n –
clas
sic ta
ke a
way
]).Ex
. Sol
ve o
ne-s
tep
wor
d pr
oble
m in
volv
ing
addi
tion
(e.g
., “I
f Jes
sie h
ad 2
0 ca
kes a
nd
boug
ht fi
ve m
ore,
how
man
y do
es h
e ha
ve n
ow?”
[add
ition
join
-par
t/pa
rt –
who
le]).
Ex. S
olve
one
-ste
p w
ord
prob
lem
invo
lvin
g su
btra
ction
s (e.
g., “
If Sa
ndy
wan
ted
to c
olle
ct
35 c
ards
and
she
alre
ady
has 1
5, h
ow m
any
mor
e do
es sh
e ne
ed?”
[sub
trac
tion
defic
it m
issin
g am
ount
]).
Leve
l II A
A S
tude
nts
will
:EE
4.O
A.3
. Sol
ve o
ne-s
tep
addi
tion
or su
btra
ction
pro
blem
s whe
n th
ere
is an
unk
now
n (r
esul
t, st
art,
chan
ge, d
iffer
ence
) up
to 1
0.Ex
. Giv
en a
gro
up o
f five
item
s, d
eter
min
e ho
w m
any
mor
e ar
e ne
ed to
mak
e 10
.Ex
. Giv
en a
gro
up o
f eig
ht it
ems,
det
erm
ine
how
man
y to
take
aw
ay to
mak
e fiv
e.
Leve
l I A
A S
tude
nts
will
:EE
4.O
A.3
. Add
up
to fi
ve.
Ex. G
iven
a g
roup
of t
wo,
add
obj
ects
to a
tota
l of fi
ve.
Ex. G
iven
a g
roup
of t
hree
, add
obj
ects
to a
tota
l of fi
ve.
82 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Gai
n fa
mili
arit
y w
ith
fact
ors
and
mul
tipl
es.
4.O
A.4
. Fin
d al
l fac
tor p
airs
for
a w
hole
num
ber i
n th
e ra
nge
1–10
0. R
ecog
nize
that
a w
hole
nu
mbe
r is a
mul
tiple
of e
ach
of
its fa
ctor
s. D
eter
min
e w
heth
er a
gi
ven
who
le n
umbe
r in
the
rang
e 1–
100
is a
mul
tiple
of a
giv
en
one-
digi
t num
ber.
Det
erm
ine
whe
ther
a g
iven
who
le n
umbe
r in
the
rang
e 1–
100
is pr
ime
or
com
posit
e.
EE4.
OA
.4. S
how
one
way
to
arriv
e at
pro
duct
.Le
vel I
V A
A S
tude
nts
will
:EE
4.O
A.4
. Sho
w m
ultip
le w
ays t
o ar
rive
at th
e sa
me
prod
uct.
Ex. G
iven
a p
rodu
ct, u
se m
anip
ulati
ves t
o cr
eate
gro
ups t
hat r
epre
sent
the
prod
uct.
Ex. G
iven
a n
umbe
r (pr
oduc
t) o
f the
day
, mat
ch th
eir f
acto
r car
ds to
ano
ther
stud
ent’s
fa
ctor
car
d to
equ
al th
e pr
oduc
t.Ex
. Giv
en a
n eq
uatio
n on
a d
ry e
rase
boa
rd (e
.g.,
2 x
4 =
8), m
ake
equa
l gro
ups t
o sh
ow
poss
ible
fact
ors f
or e
ight
(e.g
., on
e gr
oup
of e
ight
, tw
o gr
oups
of f
our,
four
gro
ups o
f tw
o).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
OA
.4. S
how
one
way
to a
rriv
e at
a p
rodu
ct.
Ex. U
sing
a gr
oup
of m
anip
ulati
ves,
sepa
rate
into
equ
al g
roup
s.Ex
. Pro
vide
d w
ith c
ount
ers,
pie
ces o
f str
ing,
or y
arn
and
a w
ork
map
, mak
e eq
ual s
ets t
o ar
rive
at th
e pr
oduc
t.Ex
. Giv
en e
ight
obj
ects
that
repr
esen
t the
pro
duct
, mak
e eq
ual s
ets t
o re
pres
ent t
he
fact
ors (
e.g.
, 2 +
2 +
2 +
2) a
nd c
ount
to a
rriv
e at
the
prod
uct (
e.g.
, 8).
Leve
l II A
A S
tude
nts
will
:EE
4.O
A.4
. Mak
e eq
ual s
ets a
nd c
ount
to d
eter
min
e th
e pr
oduc
t.Ex
. Usin
g tw
o sp
inne
rs, s
pin
first
spin
ner t
o de
term
ine
the
num
ber o
f gro
ups a
nd th
e se
cond
spin
ner t
o de
term
ine
how
man
y in
eac
h gr
oup.
Sup
ply
the
num
bers
from
the
spin
ners
as f
acto
rs in
the
mul
tiplic
ation
equ
ation
(e.g
., __
x _
_ =
___)
.
Leve
l I A
A S
tude
nts
will
:EE
4.O
A.4
. Rep
licat
e on
e w
ay to
arr
ive
at a
pro
duct
.Ex
. Cop
y a
teac
her-c
reat
ed m
odel
usin
g m
anip
ulati
ves.
Ex. G
iven
a se
t, re
plic
ate
the
equa
l set
.
Math | Kindergarten-5 Grade 83
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Gen
erat
e an
d an
alyz
e pa
tter
ns.
4.O
A.5
. Gen
erat
e a
num
ber o
r sh
ape
patte
rn th
at fo
llow
s a
give
n ru
le.
Iden
tify
appa
rent
fe
atur
es o
f the
patt
ern
that
w
ere
not e
xplic
it in
the
rule
its
elf.
For
exa
mpl
e, g
iven
the
rule
“Add
3”
and
the
star
ting
num
ber 1
, gen
erat
e te
rms
in
the
resu
lting
seq
uenc
e an
d ob
serv
e th
at th
e te
rms
appe
ar to
al
tern
ate
betw
een
odd
and
even
nu
mbe
rs.
Expl
ain
info
rmal
ly w
hy
the
num
bers
will
con
tinue
to
alte
rnat
e in
this
way
.
EE4.
OA
.5. U
se re
peati
ng
patte
rns t
o m
ake
pred
ictio
ns.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
OA
.5. C
reat
e a
patte
rn b
ased
on
a gi
ven
rule
and
thei
r pre
dicti
on o
f wha
t com
es n
ext.
Ex. G
iven
an
AABC
AABC
rule
, cre
ate
a pa
ttern
bas
ed o
n th
e ru
le.
Ex. G
iven
a d
ie w
ith p
lus t
wo,
or p
lus t
hree
, rol
ls th
e di
e an
d cr
eate
s a n
umbe
r patt
ern
base
d on
the
outc
ome.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
OA
.5. U
se re
peati
ng p
atter
ns to
mak
e pr
edic
tions
.Ex
. Usin
g a
num
ber l
ine,
pre
dict
wha
t the
nex
t num
ber w
ill b
e w
hen
you
appl
y th
e ru
le
“add
2.”
Ex. U
sing
a sh
ape
patte
rn (e
.g.,
squa
res,
circ
les,
tria
ngle
s) p
redi
ct w
hat w
ill c
ome
next
in
the
serie
s of t
hree
shap
es.
Ex. G
iven
a si
mpl
e AB
CABC
patt
ern,
indi
cate
, “W
hat c
omes
nex
t?”
Leve
l II A
A S
tude
nts
will
:EE
4.O
A.5
. Rep
licat
e a
patte
rn.
Ex. U
sing
woo
den
bead
s, c
opy
a pa
ttern
.Ex
. Rhy
thm
ic o
r tac
tile
patte
rns.
Leve
l I A
A S
tude
nts
will
:EE
4.O
A.5
. Diff
eren
tiate
bet
wee
n a
patte
rn a
nd a
non
-patt
ern.
Ex. A
pile
of b
lock
s vs.
an
ABAB
patt
ern
of b
lock
s.Ex
. Pla
y lis
teni
ng g
ame
to d
eter
min
e rh
ythm
ic p
atter
ns v
ersu
s non
-patt
erns
.
84 Common Core Essential Elements
Fou
rth
Gra
de
Mat
hem
atic
s St
and
ard
s: N
um
ber
s an
d O
per
atio
ns
in B
ase
Ten
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Gen
eral
ize
plac
e va
lue
unde
rsta
ndin
g fo
r m
ulti
-dig
it
who
le n
umbe
rs.
4.N
BT.1
. Rec
ogni
ze th
at in
a
mul
ti-di
git w
hole
num
ber,
a di
git i
n on
e pl
ace
repr
esen
ts te
n tim
es w
hat i
t rep
rese
nts i
n th
e pl
ace
to it
s rig
ht.
For e
xam
ple,
re
cogn
ize
that
700
÷ 7
0 =
10 b
y ap
plyi
ng c
once
pts
of p
lace
val
ue
and
divi
sion
.
EE4.
NBT
.1. C
ompa
re n
umbe
rs
to e
ach
othe
r bas
ed o
n pl
ace
valu
e gr
oups
by
com
posin
g an
d de
com
posin
g to
50.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
NBT
.1. C
ompa
re n
umbe
rs to
eac
h ot
her b
ased
on
plac
e va
lue
grou
ps b
y co
mpo
sing
and
deco
mpo
sing
grea
ter t
han
50.
Ex. G
iven
a n
umbe
r ove
r 50,
use
pla
ce v
alue
blo
cks t
o in
dica
te th
e va
lue
of e
ach
digi
t.Ex
. Usin
g po
psic
le sti
cks w
ith b
eans
glu
ed to
it in
gro
ups o
f 10
and
loos
e be
ans,
illu
stra
te a
m
ulti-
digi
t num
ber.
Ex. S
how
a n
umbe
r on
the
num
ber l
ine
and
answ
er th
e nu
mbe
r of t
ens a
nd o
nes i
n th
e gi
ven
num
ber.
Ex. D
ecom
pose
num
bers
to 5
0 in
mul
tiple
way
s (e.
g., 3
6 is
thre
e 10
s and
six
ones
, or t
wo
10s a
nd 1
6 on
es, o
r 36
ones
).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NBT
.1. C
ompa
re n
umbe
rs to
eac
h ot
her b
ased
on
plac
e va
lue
grou
ps b
y co
mpo
sing
and
deco
mpo
sing
to 5
0.Ex
. Giv
en a
two
digi
t num
ber u
p to
50,
use
pla
ce v
alue
blo
cks t
o in
dica
te th
e te
ns v
alue
an
d th
e on
es v
alue
.Ex
. Use
mon
ey (d
imes
and
pen
nies
) to
repr
esen
t pla
ce v
alue
.Ex
. Dec
ompo
se n
umbe
rs to
50
(e.g
., 15
is o
ne 1
0 an
d fiv
e on
es, 2
2 is
two
10s a
nd tw
o on
es, 3
6 is
thre
e 10
s and
six
ones
, 41
is fo
ur 1
0s a
nd a
one
, 57
is fiv
e 10
s and
seve
n on
es).
Ex. D
ecom
pose
num
bers
in o
ne w
ay (e
.g. 3
6 is
thre
e se
ts o
f 10
and
six o
nes)
.
Leve
l II A
A S
tude
nts
will
:EE
4.N
BT.1
. Com
pose
and
dec
ompo
se w
hole
num
bers
to 2
0.Ex
. Giv
en 1
5 pe
nnie
s, c
reat
e a
grou
p of
one
10
and
a gr
oup
of fi
ve o
nes.
Ex. U
se a
num
ber b
alan
ce to
det
erm
ine
wha
t tw
o nu
mbe
rs a
re n
eede
d to
equ
al th
e nu
mbe
r on
the
othe
r sid
e.
Leve
l I A
A S
tude
nts
will
:EE
4.N
BT.1
. Ide
ntify
who
le n
umbe
rs to
10.
Ex. G
iven
sets
, pai
r with
num
bers
.Ex
. Giv
en n
umbe
rs, m
atch
to se
ts.
Math | Kindergarten-5 Grade 85
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.N
BT.2
. Rea
d an
d w
rite
mul
ti-di
git w
hole
num
bers
usin
g ba
se-
ten
num
eral
s, n
umbe
r nam
es,
and
expa
nded
form
. Co
mpa
re
two
mul
ti-di
git n
umbe
rs b
ased
on
mea
ning
s of t
he d
igits
in
each
pla
ce, u
sing
>, =
, and
<
sym
bols
to re
cord
the
resu
lts o
f co
mpa
rison
s.
EE4.
NBT
.2. C
ompa
re w
hole
nu
mbe
rs (<
, >, =
).Le
vel I
V A
A S
tude
nts
will
:EE
4.N
BT.2
. Com
pare
who
le n
umbe
rs u
sing
sym
bols
(<, >
, =).
Ex. U
tilize
a n
umbe
r lin
e to
com
pare
two
num
bers
gre
ater
than
50
and
plac
e a
card
with
th
e co
rrec
t sym
bol o
n th
e lin
e to
show
the
rela
tions
hip
(<, >
).Ex
. Dur
ing
P.E.
, com
pare
scor
es o
f a g
ame
to d
eter
min
e th
e w
inne
r. U
se th
e sy
mbo
l to
show
the
rela
tions
hip
betw
een
the
scor
es.
Ex. S
tate
or m
atch
mea
ning
of >
, <, a
nd =
as g
reat
er th
an, l
ess t
han,
or e
qual
to.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NBT
.2. C
ompa
re w
hole
num
bers
(<, >
, =).
Ex. G
iven
two
grou
ps o
f blo
cks,
clo
se o
r equ
al in
val
ue, d
eter
min
e w
hich
is g
reat
er, l
ess,
or
equa
l.Ex
. Usin
g a
floor
num
ber l
ine,
two
stud
ents
stan
d on
two
diffe
rent
num
bers
and
de
term
ine
whi
ch is
gre
ater
or l
ess t
han.
Leve
l II A
A S
tude
nts
will
:EE
4.N
BT.2
. Com
pare
who
le n
umbe
rs (<
, >, =
) fro
m 0
-20.
Ex. G
iven
two
grou
ps o
f obj
ects
, sev
en b
lock
s and
10
bloc
ks, d
eter
min
e w
hich
is g
reat
er o
r w
hich
is le
ss.
Ex. P
lay
a fis
h ga
me:
One
fish
and
two
pond
s, e
ach
with
a c
erta
in n
umbe
r of b
ugs,
turn
fis
h to
war
ds th
e po
nd w
ith th
e m
ost b
ugs.
Leve
l I A
A S
tude
nts
will
:EE
4.N
BT.2
. Com
pare
who
le n
umbe
rs (<
, >) f
rom
0-1
0.Ex
. Use
a 1
0 fr
ame
with
two
tacti
le d
ots a
nd a
10
fram
e w
ith 1
0 ta
ctile
dot
s, d
eter
min
e w
hich
is m
ore
or le
ss.
Ex. G
iven
two
sets
of o
bjec
ts, d
eter
min
e w
hich
is m
ore.
86 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.N
BT.3
. Use
pla
ce v
alue
un
ders
tand
ing
to ro
und
mul
ti-di
git w
hole
num
bers
to a
ny
plac
e.
EE4.
NBT
.3. R
ound
one
- and
two-
digi
t who
le n
umbe
rs fr
om 0
—50
to
the
near
est 1
0.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
NBT
.3. R
ound
one
- and
two-
digi
t num
bers
, gre
ater
than
50,
to th
e ne
ares
t 10.
Ex. R
oll t
he d
ice
to c
ount
up
the
roun
ding
tape
and
stat
e th
e ne
ares
t 10.
Ex. U
sing
a hu
ndre
ds c
hart
and
a g
iven
num
ber b
etw
een
50-1
00, r
ound
to th
e ne
ares
t te
ns p
lace
.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NBT
.3. R
ound
sing
le o
ne- a
nd tw
o-di
git w
hole
num
bers
from
0-5
0 to
the
near
est 1
0.Ex
. Pos
ter b
oard
s, d
istrib
uted
aro
und
the
room
, lab
eled
by
tens
up
to 5
0, b
e gi
ven
a nu
mbe
r, an
d as
ked
to g
o to
the
near
est 1
0.Ex
. Usin
g pe
nnie
s ear
ned,
exc
hang
e fo
r dim
es.
Leve
l II A
A S
tude
nts
will
:EE
4.N
BT.3
. Rou
nd si
ngle
one
-dig
it nu
mbe
rs to
the
near
est 1
0.Ex
. Usin
g pa
per p
late
s lab
eled
zero
and
10,
giv
en a
car
d w
ith a
num
ber z
ero
to 1
0, p
lace
it
on th
e co
rrec
t pla
te.
Ex. U
se a
num
ber l
ine
to ro
und
to th
e ne
ares
t 10.
Leve
l I A
A S
tude
nts
will
:EE
4.N
BT.3
. Ide
ntify
num
bers
that
are
mor
e or
less
than
five
on
a nu
mbe
r lin
e.Ex
. Pla
ce th
eir fi
nger
s on
five
on a
num
ber l
ine
and
coun
t to
find
a nu
mbe
r gre
ater
than
fiv
e.Ex
. Sho
wn
five
on a
num
ber l
ine,
iden
tify
a nu
mbe
r tha
t is l
ess t
han
five.
Math | Kindergarten-5 Grade 87
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
pla
ce v
alue
und
erst
andi
ng
and
prop
erti
es o
f ope
rati
ons
to
perf
orm
mul
ti-d
igit
ari
thm
etic.
4.N
BT.4
. Flu
ently
add
and
su
btra
ct m
ulti-
digi
t who
le
num
bers
usin
g th
e st
anda
rd
algo
rithm
.
EE4.
NBT
4. A
dd a
nd su
btra
ct
doub
le-d
igit
who
le n
umbe
rs.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
NBT
.4. A
dd a
nd su
btra
ct m
ulti-
digi
t who
le n
umbe
rs.
Ex. G
iven
bas
e te
n pi
eces
, mak
e ex
chan
ges t
o so
lve
mul
ti-di
git a
dditi
on a
nd su
btra
ction
pr
oble
ms.
Ex. U
se a
cal
cula
tor a
nd sh
ow h
ow th
e pr
oble
m is
solv
ed.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NBT
.4. A
dd a
nd su
btra
ct d
oubl
e-di
git w
hole
num
bers
.Ex
. Use
a so
rting
box
div
ided
into
two
secti
ons w
ith m
anip
ulati
ves t
o ad
d, su
btra
ct, a
nd
regr
oup
to so
lve
addi
tion
and
subt
racti
on p
robl
ems.
Ex. U
se b
reak
-apa
rt n
umbe
rs (e
.g.,
20 +
30
= 50
, 3 +
5 =
8, 4
0 +
8 =
48).
Ex. U
se a
num
ber l
ine
to d
emon
stra
te a
dditi
on b
y te
ns.
Leve
l II A
A S
tude
nts
will
:EE
4.N
BT.4
. Sol
ve a
dditi
on w
ith n
umbe
rs 2
0-50
and
subt
racti
on p
robl
ems w
ith n
umbe
rs
0-20
.Ex
. Use
cou
nter
s to
add
and
subt
ract
.Ex
. Use
num
ber l
ines
to a
dd o
r sub
trac
t.Ex
. Pro
duce
add
ends
to 1
0 flu
ently
.Ex
. The
teac
her o
rally
stat
es 1
4 –
1 =
13 a
nd u
se m
agne
tic sy
mbo
ls to
disp
lay
the
prob
lem
.
Leve
l I A
A S
tude
nts
will
:EE
4.N
BT.4
. Sol
ve si
ngle
dig
it ad
ditio
n pr
oble
ms t
o ad
d on
e to
ano
ther
num
ber.
Ex .U
se c
ount
ers t
o ad
d on
e to
ano
ther
num
ber.
Ex .U
se n
umbe
r lin
es to
add
one
to a
noth
er n
umbe
r.
88 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.N
BT.5
. Mul
tiply
a w
hole
nu
mbe
r of u
p to
four
dig
its b
y a
one-
digi
t who
le n
umbe
r, an
d m
ultip
ly tw
o tw
o-di
git n
umbe
rs,
usin
g st
rate
gies
bas
ed o
n pl
ace
valu
e an
d th
e pr
oper
ties
of o
pera
tions
. Ill
ustr
ate
and
expl
ain
the
calc
ulati
on b
y us
ing
equa
tions
, rec
tang
ular
arr
ays,
an
d/or
are
a m
odel
s.
EE4.
NBT
5. N
/A (S
ee E
E. 4
.OA.
1.)
4.N
BT.6
. Fin
d w
hole
-num
ber
quoti
ents
and
rem
aind
ers
with
up
to fo
ur-d
igit
divi
dend
s an
d on
e-di
git d
iviso
rs, u
sing
stra
tegi
es b
ased
on
plac
e va
lue,
th
e pr
oper
ties o
f ope
ratio
ns,
and/
or th
e re
latio
nshi
p be
twee
n m
ultip
licati
on a
nd d
ivisi
on.
Illus
trat
e an
d ex
plai
n th
e ca
lcul
ation
by
usin
g eq
uatio
ns,
rect
angu
lar a
rray
s, a
nd/o
r are
a m
odel
s.
EE4.
NBT
6. N
/A
Math | Kindergarten-5 Grade 89
Fou
rth
Gra
de
Mat
hem
atic
s St
and
ard
s: N
um
ber
an
d O
per
atio
ns-
-Fra
ctio
ns2
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Exte
nd u
nder
stan
ding
of
frac
tion
equ
ival
ence
and
or
deri
ng.
4.N
F.1.
Exp
lain
why
a fr
actio
n a/
b is
equi
vale
nt to
a fr
actio
n (n
× a
)/(n
× b
) by
usin
g vi
sual
fr
actio
n m
odel
s, w
ith a
ttenti
on
to h
ow th
e nu
mbe
r and
size
of
the
part
s diff
er e
ven
thou
gh th
e tw
o fr
actio
ns th
emse
lves
are
th
e sa
me
size.
Use
this
prin
cipl
e to
reco
gnize
and
gen
erat
e eq
uiva
lent
frac
tions
.
4.N
F.2.
Com
pare
two
frac
tions
w
ith d
iffer
ent n
umer
ator
s and
di
ffere
nt d
enom
inat
ors,
e.g
., by
cr
eatin
g co
mm
on d
enom
inat
ors
or n
umer
ator
s, o
r by
com
parin
g to
a b
ench
mar
k fr
actio
n su
ch a
s 1/
2. R
ecog
nize
that
com
paris
ons
are
valid
onl
y w
hen
the
two
frac
tions
refe
r to
the
sam
e w
hole
. Re
cord
the
resu
lts o
f co
mpa
rison
s with
sym
bols
>, =
, or
<, a
nd ju
stify
the
conc
lusio
ns,
e.g.
, by
usin
g a
visu
al fr
actio
n m
odel
.
EE4.
NF.
1-2.
Und
erst
and
2/4
= 1/
2.Le
vel I
V A
A S
tude
nts
will
:EE
4.N
F.1-
2. U
nder
stan
d tw
o fr
actio
ns h
avin
g un
like
deno
min
ator
s are
equ
ival
ent i
f the
y re
pres
ent t
he sa
me
size
porti
on o
f a w
hole
.Ex
. Giv
en tw
o sq
uare
s of p
aper
, one
scor
ed fo
r 1/2
s and
one
scor
ed fo
r 1/8
s, fo
ld th
e ea
ch
pape
r as s
core
d, th
en u
nfol
d th
e pa
per s
core
d fo
r 1/3
s and
com
pare
to th
e on
e fo
lded
in
to 1
/2 to
find
the
sam
e siz
e po
rtion
(e.g
., 4/
8 =
1/2)
.
Ex. U
se ta
ngra
ms.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NF.
1-2.
Und
erst
and
2/4
= 1/
2.Ex
. Giv
en tw
o re
ctan
gles
, cut
one
rect
angl
e in
to h
alf a
nd a
seco
nd in
to fo
urth
s and
co
mpa
re th
e re
ctan
gles
to d
eter
min
e ho
w m
any
four
ths e
qual
a h
alf.
Ex. W
orki
ng w
ith tw
o re
ctan
gles
of t
he sa
me
size,
fold
one
rect
angl
e in
hal
f and
the
othe
r in
four
ths a
nd c
ompa
re to
find
how
man
y fo
urth
s equ
al h
alf.
Ex. U
sing
a pi
ctur
e of
two
circ
les,
cut
one
in h
alf a
nd th
e ot
her i
n fo
urth
s and
com
pare
th
em to
find
how
man
y fo
urth
s equ
al h
alf.
Leve
l II A
A S
tude
nts
will
:EE
4.N
F.1-
2. U
nder
stan
d 4/
4 or
2/2
= 1
.Ex
. Com
plet
e tw
o- a
nd fo
ur-p
iece
puz
zles.
Ex. F
ile fo
lder
gam
e w
ith se
lf-sti
ckin
g no
n-ad
hesiv
e pi
eces
that
mak
e a
who
le.
Leve
l I A
A S
tude
nts
will
:EE
4.N
F.1-
2. U
nder
stan
d th
at tw
o ha
lves
is e
quiv
alen
t to
one
who
le.
Ex. W
oode
n sh
apes
are
sepa
rate
d in
to h
alve
s and
put
bac
k to
geth
er in
to a
who
le.
Ex. P
lasti
c eg
gs a
re b
roke
n in
to h
alve
s and
put
bac
k to
who
le.
2 G
rade
4 e
xpec
tatio
ns in
this
dom
ain
are
limite
d to
frac
tions
with
den
omin
ator
s 2, 3
, 4, 5
, 6, 8
, 10,
12,
100
.
90 Common Core Essential Elements
Build
frac
tion
s fr
om u
nit
frac
tion
s by
app
lyin
g an
d ex
tend
ing
prev
ious
un
ders
tand
ings
of o
pera
tion
s on
w
hole
num
bers
.
4.N
F.3.
Und
erst
and
a fr
actio
n a/
b w
ith a
> 1
as a
sum
of
frac
tions
1/b
.
Und
erst
and
addi
tion
and
subt
racti
on o
f fra
ction
s as
join
ing
and
sepa
ratin
g pa
rts
refe
rrin
g to
the
sam
e w
hole
.
Deco
mpo
se a
frac
tion
into
a su
m o
f fra
ction
s with
th
e sa
me
deno
min
ator
in m
ore
than
one
way
, rec
ordi
ng e
ach
deco
mpo
sition
by
an e
quati
on.
Justi
fy d
ecom
positi
ons,
e.g
., by
us
ing
a vi
sual
frac
tion
mod
el.
Exam
ples
: 3/8
= 1
/8 +
1/8
+ 1
/8
; 3/8
= 1
/8 +
2/8
; 2
1/8
= 1
+ 1
+ 1/
8 =
8/8
+ 8/
8 +
1/8.
Ad
d an
d su
btra
ct m
ixed
nu
mbe
rs w
ith li
ke d
enom
inat
ors,
e.
g., b
y re
plac
ing
each
mix
ed
num
ber w
ith a
n eq
uiva
lent
fr
actio
n, a
nd/o
r by
usin
g pr
oper
ties o
f ope
ratio
ns a
nd th
e re
latio
nshi
p be
twee
n ad
ditio
n an
d su
btra
ction
.
Solv
e w
ord
prob
lem
s in
volv
ing
addi
tion
and
subt
racti
on o
f fra
ction
s ref
errin
g to
the
sam
e w
hole
and
hav
ing
like
deno
min
ator
s, e
.g.,
by
usin
g vi
sual
frac
tion
mod
els
and
equa
tions
to re
pres
ent t
he
prob
lem
.
EE4.
NF.
3. D
iffer
entia
te b
etw
een
who
le, h
alf,
and
four
th.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
NF.
3. D
iffer
entia
te fr
actio
nal p
arts
less
than
1/4
.Ex
. With
frac
tion
bars
labe
led
1/2,
com
pare
the
1/2
to fr
actio
n ba
rs le
ss th
an.
Ex. U
sing
squa
res,
fold
it in
1/2
, 1/4
, 1/8
, . .
.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
NF.
3. D
iffer
entia
te b
etw
een
who
le, h
alf,
and
four
th.
Ex. U
se fr
actio
n st
rips a
nd fr
actio
n til
es to
iden
tify
who
le a
nd h
alf,
and
whi
ch is
mor
e.Ex
. Usin
g sq
uare
s of p
aper
, fol
d it
in 1
/2 a
nd 1
/4 a
nd id
entif
y th
e pa
rts.
Leve
l II A
A S
tude
nts
will
:EE
4.N
F.3.
Diff
eren
tiate
bet
wee
n w
hole
and
hal
f.Ex
. Giv
en a
who
le sa
ndw
ich
vers
us a
hal
f san
dwic
h cu
t hor
izont
ally,
ver
tical
ly, a
nd
diag
onal
ly se
lect
the
who
le o
r hal
f upo
n re
ques
t.Ex
. Sho
w th
e ha
lfway
poi
nt o
n a
num
ber l
ine.
Ex. W
ith p
ictu
res c
ut in
to h
alve
s and
pic
ture
s not
cut
, sor
t the
pic
ture
s int
o ha
lves
and
w
hole
s.
Leve
l I A
A S
tude
nts
will
:EE
4.N
F.3.
Rec
ogni
ze th
at fr
actio
ns a
re p
art o
f a w
hole
.Ex
. Usin
g a
self-
stick
ing
non-
adhe
sive
shap
e, ta
ke a
part
and
put
toge
ther
frac
tiona
l par
ts
of a
who
le.
Ex. U
tilize
woo
den
shap
es, s
epar
ate
into
hal
ves a
nd p
ut b
ack
toge
ther
into
who
le.
Ex. S
how
n pi
ctur
es o
f the
who
le c
lass
and
par
t of t
he c
lass
, sel
ect t
he p
ictu
re th
at sh
ows
part
of t
he c
lass
upo
n re
ques
t.
Math | Kindergarten-5 Grade 91
4.N
F.4.
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
mul
tiplic
ation
to m
ultip
ly a
fr
actio
n by
a w
hole
num
ber.
U
nder
stan
d a
frac
tion
a/b
as a
mul
tiple
of 1
/b.
For
exam
ple,
use
a v
isua
l fra
ction
m
odel
to re
pres
ent 5
/4 a
s th
e pr
oduc
t 5 ×
(1/4
), re
cord
ing
the
conc
lusi
on b
y th
e eq
uatio
n 5/
4 =
5 ×
(1/4
).
Und
erst
and
a m
ultip
le
of a
/b a
s a m
ultip
le o
f 1/b
, an
d us
e th
is un
ders
tand
ing
to
mul
tiply
a fr
actio
n by
a w
hole
nu
mbe
r. F
or e
xam
ple,
use
a
visu
al fr
actio
n m
odel
to e
xpre
ss
3 ×
(2/5
) as
6 ×
(1/5
), re
cogn
izin
g th
is p
rodu
ct a
s 6/
5. (
In g
ener
al,
n ×
(a/b
) = (n
× a
)/b.
).
Solv
e w
ord
prob
lem
s in
volv
ing
mul
tiplic
ation
of a
fr
actio
n by
a w
hole
num
ber,
e.g.
, by
usin
g vi
sual
frac
tion
mod
els
and
equa
tions
to re
pres
ent t
he
prob
lem
. Fo
r exa
mpl
e, if
eac
h pe
rson
at a
par
ty w
ill e
at 3
/8 o
f a
poun
d of
roas
t bee
f, an
d th
ere
will
be
5 pe
ople
at t
he p
arty
, ho
w m
any
poun
ds o
f roa
st b
eef
will
be
need
ed?
Bet
wee
n w
hat
two
who
le n
umbe
rs d
oes
your
an
swer
lie?
EE4.
NF.
4. N
/A (S
ee E
E. 4
.OA.
1-2.
)
92 Common Core Essential Elements
Und
erst
and
deci
mal
not
ation
fo
r fr
acti
ons,
and
com
pare
de
cim
al fr
acti
ons.
4.N
F.5.
Exp
ress
a fr
actio
n w
ith
deno
min
ator
10
as a
n eq
uiva
lent
fr
actio
n w
ith d
enom
inat
or 1
00,
and
use
this
tech
niqu
e to
add
tw
o fr
actio
ns w
ith re
spec
tive
deno
min
ator
s 10
and
100.
13
For e
xam
ple,
exp
ress
3/1
0 as
30
/100
, and
add
3/1
0 +
4/10
0 =
34/1
00.
4.N
F.6.
Use
dec
imal
not
ation
fo
r fra
ction
s with
den
omin
ator
s 10
or 1
00.
For e
xam
ple,
rew
rite
0.62
as
62/1
00; d
escr
ibe
a le
ngth
as
0.6
2 m
eter
s; lo
cate
0.6
2 on
a
num
ber l
ine
diag
ram
.
4.N
F.7.
Com
pare
two
deci
mal
s to
hun
dred
ths b
y re
ason
ing
abou
t the
ir siz
e. R
ecog
nize
th
at c
ompa
rison
s are
val
id o
nly
whe
n th
e tw
o de
cim
als r
efer
to
the
sam
e w
hole
. Re
cord
the
resu
lts o
f com
paris
ons w
ith th
e sy
mbo
ls >,
=, o
r <, a
nd ju
stify
th
e co
nclu
sions
, e.g
., by
usin
g a
visu
al m
odel
.
EE4.
NF.
5. N
/A (D
ecim
als b
egin
at
grad
e 7)
.
Math | Kindergarten-5 Grade 93
Fou
rth
Gra
de
Mat
hem
atic
s St
and
ard
s: M
easu
rem
ent
and
Dat
a
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Solv
e pr
oble
ms
invo
lvin
g m
easu
rem
ent
and
conv
ersi
on
of m
easu
rem
ents
from
a la
rger
un
it to
a s
mal
ler
unit
.
4.M
D.1
. Kno
w re
lativ
e siz
es
of m
easu
rem
ent u
nits
with
in
one
syst
em o
f uni
ts in
clud
ing
km, m
, cm
; kg,
g; l
b, o
z.; l
, ml;
hr, m
in, s
ec.
With
in a
sing
le
syst
em o
f mea
sure
men
t, ex
pres
s m
easu
rem
ents
in a
larg
er u
nit i
n te
rms o
f a sm
alle
r uni
t. R
ecor
d m
easu
rem
ent e
quiv
alen
ts
in a
two-
colu
mn
tabl
e. F
or
exam
ple,
kno
w th
at 1
ft. i
s 12
tim
es a
s lo
ng a
s 1
in.
Expr
ess
the
leng
th o
f a 4
ft. s
nake
as
48
in.
Gen
erat
e a
conv
ersi
on ta
ble
for f
eet a
nd in
ches
listi
ng th
e nu
mbe
r pai
rs (1
, 12)
, (2,
24)
, (3,
36
), . .
.
EE4.
MD
.1. I
denti
fy th
e sm
alle
r m
easu
rem
ent u
nits
that
di
vide
a la
rger
uni
t with
in a
m
easu
rem
ent s
yste
m.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.1. S
olve
pro
blem
s by
dem
onst
ratin
g w
hole
uni
ts c
an b
e br
oken
into
smal
ler u
nits
.Ex
. Use
a o
ne-c
up m
easu
re to
pou
r wat
er in
to a
pin
t jar
to d
eter
min
e ho
w m
any
plan
ts
coul
d be
wat
ered
if e
ach
plan
t nee
ds o
ne c
up o
f wat
er.
Ex. P
our s
oil f
rom
a 1
/2-c
up m
easu
ring
cup
into
a p
int t
o se
e ho
w m
any
star
ter p
ots c
ould
be
fille
d w
ith a
pin
t of s
oil.
Ex. D
eter
min
e w
hich
is b
etter
for m
easu
ring
a de
skto
p, a
rule
r or a
yar
dstic
k. M
easu
re
the
tabl
et, m
ark
the
leng
th o
n th
e ru
ler,
and
com
pare
it to
the
yard
stick
.Ex
. Pou
r tab
lesp
oons
of w
ater
into
a 1
/2 c
up a
tabl
espo
on a
t a ti
me
and
dete
rmin
e ho
w
man
y on
e-ta
bles
poon
por
tions
ther
e ar
e in
a c
up.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.1. I
denti
fy th
e sm
alle
r mea
sure
men
t uni
ts th
at d
ivid
e a
larg
er u
nit w
ithin
a
mea
sure
men
t sys
tem
.Ex
. Ide
ntify
how
man
y in
ches
are
the
smal
ler u
nits
on
a ru
ler.
Ex. I
denti
fy h
ow m
any
feet
are
the
smal
ler u
nits
on
a ya
rdsti
ck.
Ex. I
denti
fy h
ow m
any
cups
are
the
smal
ler u
nits
on
a pi
nt m
easu
ring
cup.
Ex. G
iven
seve
ral m
easu
rem
ent t
ools,
mat
ch th
ree
rule
rs to
one
-yar
d sti
ck.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.1
. Ide
ntify
stan
dard
uni
ts o
f mea
sure
men
ts.
Ex. U
se d
iffer
ent m
easu
rem
ent t
ools
to m
easu
re sa
nd in
a tr
ay.
Ex. U
se th
e in
ch w
orm
s on
a fo
ot ru
ler o
r yar
d sti
ck to
mak
e th
e co
nnec
tion
that
whi
le
they
bot
h m
easu
re, o
ne u
nit i
s sm
alle
r tha
n th
e ot
her.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.1
. Use
mea
sure
men
t too
ls.Ex
. Com
pare
the
leng
th o
f a ru
ler t
o th
e le
ngth
of a
boo
k.Ex
. Use
a b
alan
ce sc
ale
to c
ompa
re d
iffer
ent s
ets o
f obj
ects
to d
eter
min
e w
hich
obj
ects
ar
e <,
>, o
r =.
94 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.M
D.2
. Use
the
four
ope
ratio
ns
to so
lve
wor
d pr
oble
ms i
nvol
ving
di
stan
ces,
inte
rval
s of ti
me,
liq
uid
volu
mes
, mas
ses o
f ob
ject
s, a
nd m
oney
, inc
ludi
ng
prob
lem
s inv
olvi
ng si
mpl
e fr
actio
ns o
r dec
imal
s, a
nd
prob
lem
s tha
t req
uire
exp
ress
ing
mea
sure
men
ts g
iven
in a
larg
er
unit
in te
rms o
f a sm
alle
r un
it. R
epre
sent
mea
sure
men
t qu
antiti
es u
sing
diag
ram
s suc
h as
num
ber l
ine
diag
ram
s tha
t fe
atur
e a
mea
sure
men
t sca
le.
EE4.
MD
.2.a
. Tel
l tim
e to
the
half
hour
usin
g a
digi
tal o
r to
the
hour
usin
g an
ana
log
cloc
k.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.2.a
. Tel
l tim
e to
the
quar
ter h
our u
sing
a di
gita
l or a
nalo
g cl
ock.
Ex. I
ndic
ate
time
to th
e qu
arte
r hou
r on
a di
gita
l clo
ck.
Ex. P
lace
clo
ck h
ands
to sh
ow th
e qu
arte
r hou
r.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.2.a
. Tel
l tim
e to
the
half
hour
usin
g a
digi
tal c
lock
or t
o th
e ho
ur u
sing
an a
nalo
g cl
ock.
Ex. I
denti
fy w
hich
clo
ck sh
ows a
stat
ed ti
me
on a
dig
ital c
lock
(i.e
., 2:
30).
Ex. M
ove
hand
s on
a cl
ock
to sh
ow a
stat
ed h
alf h
our.
Ex. S
ay th
e ho
ur o
n an
ana
log
cloc
k.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.2
.a. R
elat
e tim
e to
the
hour
to a
ctivi
ties.
Ex. L
ook
at c
lock
- 2:
00 is
tim
e to
go
hom
e.Ex
. Ide
ntify
acti
vity
on
sche
dule
by
mat
chin
g th
e ho
ur o
n th
e sc
hedu
le to
the
hour
on
the
cloc
k.Ex
. Poi
nt to
hou
r for
nex
t acti
vity
on
pers
onal
sche
dule
.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.2
.a. D
iffer
entia
te a
dig
ital a
nd a
nalo
g cl
ock
from
oth
er m
easu
rem
ent t
ools
as a
to
ol fo
r tel
ling
time.
Ex. G
iven
a d
igita
l or a
nalo
g cl
ock
and
a ru
ler,
iden
tify
the
cloc
k fo
r tel
ling
time.
Ex. A
sked
“Ho
w d
o w
e kn
ow w
hen
it is
time
to g
o to
lunc
h?”,
indi
cate
a c
lock
.
Math | Kindergarten-5 Grade 95
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE4.
MD
.2.b
. Sel
ect t
he
appr
opria
te m
easu
rem
ent t
ool
from
two
rela
ted
optio
ns to
so
lve
prob
lem
s.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.2.b
. Use
the
appr
opria
te m
easu
rem
ent t
ools
to so
lve
prob
lem
s.Ex
. Sel
ect a
nd u
se th
e ap
prop
riate
mea
surin
g to
ol to
mea
sure
diff
eren
t qua
ntitie
s for
as
signe
d ta
sks (
e.g.
, cup
for l
iqui
d an
d po
wde
r; sc
ale
for s
olid
s).
Ex. O
n a
field
trip
to th
e gr
ocer
y st
ore,
use
the
scal
e to
det
erm
ine
how
muc
h a
bag
of
appl
es w
eigh
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.2.b
. Sel
ect t
he a
ppro
pria
te m
easu
rem
ent t
ool f
rom
two
rela
ted
optio
ns to
solv
e pr
oble
ms.
Ex. D
urin
g a
scie
nce
expe
rimen
t, se
lect
the
best
tool
to u
se to
mea
sure
var
ious
in
gred
ient
s (e.
g., t
able
spoo
n or
cup
, rul
er o
r yar
dstic
k).
Ex. G
iven
a b
ook,
sele
ct th
e ap
prop
riate
mea
surin
g to
ol to
use
to m
easu
re it
s len
gth
(e.g
., ru
ler o
r yar
dstic
k).
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.2
.b. S
elec
t the
app
ropr
iate
mea
sure
men
t too
l fro
m tw
o un
rela
ted
optio
ns to
so
lve
prob
lem
s.Ex
. Giv
en o
ption
s of u
nrel
ated
mea
surin
g to
ols,
cho
ose
the
best
tool
for a
par
ticul
ar ta
sk
(e.g
., “W
hen
mak
ing
cook
ies,
whi
ch w
ould
you
use
to m
easu
re fl
our,
a cu
p or
rule
r?”)
.Ex
. In
a fie
ld tr
ip to
the
groc
ery
stor
e, sh
ow w
hich
mea
surin
g to
ol sh
ould
be
used
to w
eigh
a
bag
of a
pple
s. A
llow
stud
ents
to p
racti
ce b
y ch
oosin
g ot
her f
ruits
or v
eget
able
s to
wei
gh.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.2
.b. I
denti
fy m
easu
rem
ent t
ools.
Ex. S
ort n
on-s
tand
ard
and
stan
dard
mea
sure
men
t too
ls in
to tw
o di
ffere
nt g
roup
s.Ex
. Usin
g pi
ctur
es o
f sta
ndar
d an
d no
n-st
anda
rd to
ols,
iden
tify
whi
ch c
an b
e us
ed to
m
easu
re d
iffer
ent i
tem
s.
96 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE4.
MD
.2.c
. Use
stan
dard
m
easu
rem
ent t
o co
mpa
re
leng
ths o
f obj
ects
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.2.c
. Use
stan
dard
mea
sure
men
ts to
com
pare
leng
th o
f obj
ects
and
indi
cate
how
m
any
each
is b
y st
anda
rd m
easu
res.
Ex. G
iven
a p
enci
l and
boo
k, m
ark
the
leng
th o
f eac
h on
a ru
ler t
o te
ll w
hich
is lo
nger
and
ap
prox
imat
ely
how
man
y ea
ch is
by
inch
es.
Ex. G
iven
a ta
pe m
easu
re, m
ark
the
leng
th o
f a b
ookc
ase
and
the
teac
her’s
des
k on
the
tape
mea
sure
to sh
ow w
hich
is lo
nger
and
app
roxi
mat
ely
how
man
y ea
ch is
by
feet
.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.2.c
. Use
stan
dard
mea
sure
men
t to
com
pare
leng
ths o
f obj
ects
.Ex
. Giv
en a
pen
cil a
nd b
ook,
mar
k th
e le
ngth
of e
ach
on a
rule
r to
tell
whi
ch is
long
er.
Ex. G
iven
a ta
pe m
easu
re, m
ark
the
leng
th o
f a b
ookc
ase
and
the
teac
her’s
des
k on
the
tape
mea
sure
to sh
ow w
hich
is lo
nger
.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.2
.c. M
easu
re le
ngth
of o
bjec
ts u
sing
stan
dard
tool
s, su
ch a
s rul
ers,
yar
dstic
ks,
and
met
er sti
cks.
Ex. G
iven
an
obje
ct a
nd a
mea
surin
g to
ol, u
se th
e to
ol to
mar
k th
e le
ngth
of t
he o
bjec
t.Ex
. Giv
en a
rule
r and
sand
in a
buc
ket,
mar
k th
e de
pth
of th
e sa
nd o
n a
rule
r.Ex
. Giv
en a
yar
dstic
k, m
easu
re d
iffer
ent l
engt
hs o
r wid
ths o
f the
room
and
reco
rd th
e le
ngth
on
the
yard
stick
in n
umbe
r of y
ards
ticks
.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.2
.c. I
denti
fy it
ems a
s lon
g or
shor
t.Ex
. Giv
en tw
o di
ffere
nt it
ems,
one
muc
h lo
nger
than
the
first
, ind
icat
e lo
ng/s
hort
.Ex
. Afte
r tra
velin
g to
som
ewhe
re in
the
clas
sroo
m a
nd so
mew
here
out
side
of ro
om,
indi
cate
eac
h di
stan
ce a
s lon
g or
shor
t.
Math | Kindergarten-5 Grade 97
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE4.
MD
.2.d
. Ide
ntify
obj
ects
that
ha
ve v
olum
e.Le
vel I
V A
A S
tude
nts
will
:EE
4.M
D.2
.d. D
eter
min
e vo
lum
e of
a c
ube
by c
ounti
ng u
nits
of m
easu
re.
Ex. U
se c
ubes
to fi
ll a
box
(sm
all n
umbe
r, ho
w m
any)
and
cou
nt th
e nu
mbe
r of c
ubes
ne
eded
to fi
ll th
e bo
x.Ex
. Use
liqu
id to
fill
bow
l (ho
w m
uch,
one
cup
, etc
.).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.2.d
. Ide
ntify
obj
ects
that
hav
e vo
lum
e.Ex
. Giv
en a
gro
up o
f pic
ture
s (cu
p, ro
ck, f
ork)
, cho
ose
whi
ch o
ne c
an b
e fil
led.
Ex. I
denti
fy o
bjec
ts in
the
room
that
can
be
fille
d (c
up, fi
sh ta
nk, e
tc.).
Ex. G
iven
a sq
uare
and
a c
ube,
indi
cate
cub
e.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.2
.d. D
emon
stra
te so
lid o
r ful
l, em
pty
and
part
full.
Ex. G
iven
a p
iece
of p
aper
and
a c
ube,
indi
cate
, “W
hich
one
take
s up
mor
e sp
ace?
”Ex
. Fill
a c
up h
alf f
ull f
rom
the
wat
er fo
unta
in.
Ex. A
s the
teac
her i
s filli
ng a
cup
, say
stop
whe
n it
is ha
lf fu
ll.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.2
.d. I
denti
fy v
ocab
ular
y re
late
d to
vol
ume
(full,
em
pty)
.Ex
. Mat
ch p
ictu
re o
f uno
pene
d bo
ttle
of s
oda
to “
full.
”Ex
. Ide
ntify
an
“em
pty”
cup
.Ex
. Ind
icat
e w
hich
is fu
ll an
d/or
whi
ch is
em
pty
whe
n ho
ldin
g/fe
elin
g a
full
can
of so
da
and
an e
mpt
y ca
n of
soda
.
98 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE4.
MD
.2.e
. Ide
ntify
coi
ns
(pen
ny, n
icke
l, di
me,
qua
rter
) an
d th
eir v
alue
s.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.2.e
. Ide
ntify
rela
tive
valu
e of
diff
eren
t col
lecti
ons o
f coi
ns.
Ex. W
hen
aske
d w
hat i
s wor
th fi
ve c
ents
, cho
oses
a n
icke
l. W
hen
aske
d w
hat i
s wor
th 2
5 ce
nts,
cho
ose
a qu
arte
r.Ex
. Giv
en tw
o co
ins,
iden
tify
the
valu
e of
eac
h an
d in
dica
te w
hich
is m
ore.
Ex. G
iven
14
penn
ies a
nd tw
o di
mes
, ind
icat
e w
hich
set i
s wor
th m
ore.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.2.e
. Ide
ntify
coi
ns (p
enny
, nic
kel,
dim
e, q
uart
er) a
nd th
eir v
alue
s.Ex
. Giv
en tw
o co
ins,
cho
ose
corr
ect c
oin
by n
ame
and
valu
e.Ex
. Sho
wn
a co
in, n
ames
coi
n.Ex
. Sho
w re
lativ
e va
lues
of p
enny
, nic
kel,
dim
e, q
uart
er b
y ar
rang
ing
them
in o
rder
from
le
ast t
o m
ost.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.2
.e. M
atch
coi
ns th
at a
re a
like
(pen
ny, n
icke
l, di
me,
qua
rter
).Ex
. Giv
en a
gro
up o
f coi
ns, m
atch
coi
ns th
at a
re a
like.
Ex. G
iven
a p
ictu
re o
f a q
uart
er, c
hoos
e a
quar
ter f
rom
a g
roup
of c
oins
.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.2
.e. S
elec
t obj
ects
that
are
use
d fo
r mon
ey.
Ex. G
iven
thre
e pi
ctur
es (t
wo
non-
coin
s and
one
coi
n), i
denti
fy w
hich
one
is a
coi
n.Ex
. Giv
en tw
o ch
oice
s, id
entif
y w
hich
one
is a
coi
n.4.
MD
.3. A
pply
the
area
an
d pe
rimet
er fo
rmul
as fo
r re
ctan
gles
in re
al w
orld
and
m
athe
mati
cal p
robl
ems.
For
ex
ampl
e, fi
nd th
e w
idth
of a
re
ctan
gula
r roo
m g
iven
the
area
of
the
floor
ing
and
the
leng
th,
by v
iew
ing
the
area
form
ula
as a
m
ultip
licati
on e
quati
on w
ith a
n un
know
n fa
ctor
.
EE4.
MD
.3. N
/A (A
rea
begi
ns a
t 6t
h gr
ade
and
perim
eter
beg
ins
at 7
th g
rade
).
Math | Kindergarten-5 Grade 99
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
inte
rpre
t dat
a.
4.M
D.4
. Mak
e a
line
plot
to
disp
lay
a da
ta se
t of
mea
sure
men
ts in
frac
tions
of
a un
it (1
/2, 1
/4, 1
/8).
Sol
ve
prob
lem
s inv
olvi
ng a
dditi
on
and
subt
racti
on o
f fra
ction
s by
usin
g in
form
ation
pre
sent
ed in
lin
e pl
ots.
For
exa
mpl
e, fr
om a
lin
e pl
ot fi
nd a
nd in
terp
ret t
he
diffe
renc
e in
leng
th b
etw
een
the
long
est a
nd s
hort
est s
peci
men
s in
an
inse
ct c
olle
ction
.
EE4.
MD
.4.a
. Ins
ert d
ata
into
a
prec
onst
ruct
ed b
ar g
raph
te
mpl
ate.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.4.a
. Ins
ert d
ata
into
a g
raph
to re
pres
ent a
dat
a se
t with
a sc
ale
equa
l to
10 (0
to
10 b
y on
es).
Ex. U
sing
a ba
r gra
ph, e
nter
one
uni
t for
eac
h st
uden
t to
show
thei
r fav
orite
acti
vity
in th
e co
rrec
t cat
egor
y (lu
nch,
phy
sical
ther
apy,
mus
ic, P
.E.)
to d
eter
min
e m
ost p
opul
ar a
nd le
ast
popu
lar.
Ex. G
o to
the
lost
and
foun
d, c
ateg
orize
and
cou
nt ty
pes o
f ite
ms a
nd g
raph
them
to
dete
rmin
e m
ost a
nd le
ast.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.4.a
. Ins
ert d
ata
into
a p
reco
nstr
ucte
d ba
r gra
ph te
mpl
ate.
Ex. C
lean
out
des
ks, s
ort o
bjec
ts fo
und
into
reus
able
, rec
ycla
ble,
redu
cibl
e, o
r tak
e ho
me
item
s and
gra
ph re
sults
with
one
bar
for e
ach
– re
use,
recy
cle,
redu
ce, o
r tak
e ho
me.
Ex. G
iven
a p
reco
nstr
ucte
d ba
r gra
ph a
nd d
ata,
ent
er th
e da
ta o
n th
e ba
r gra
ph b
y sh
adin
g on
e un
it of
the
bar f
or e
ach
piec
e of
dat
a.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.4
.a. I
denti
fy a
n ap
prop
riate
scal
e fo
r the
dat
a se
t.Ex
. Ide
ntify
if it
is a
ppro
pria
te to
use
deg
rees
or o
unce
s on
a w
eath
er g
raph
.Ex
. Det
erm
ine
if it
is ap
prop
riate
to u
se in
ches
or p
ound
s on
a he
ight
gra
ph.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.4
.a. G
iven
a to
pic,
iden
tify
appr
opria
te d
ata
to c
olle
ct.
Ex. U
sing
a w
eath
er g
raph
, ide
ntify
app
ropr
iate
dat
a gi
ven
the
choi
ce b
etw
een
a pi
ctur
e of
the
sun
and
a pi
ctur
e of
a sh
oe.
Ex. G
iven
the
topi
c of
snac
ks, d
eter
min
e w
heth
er je
lly b
eans
or b
ooks
are
app
ropr
iate
for
the
grap
h.
100 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE4.
MD
.4.b
. Int
erpr
et d
ata
from
a
varie
ty o
f gra
phs t
o an
swer
qu
estio
ns.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
MD
.4.b
. Cre
ate
thei
r ow
n qu
estio
ns th
at c
an b
e an
swer
ed b
y th
e da
ta o
n a
pict
ure
and
bar g
raph
.Ex
. Cut
sim
ple
grap
hs fr
om n
ewsp
aper
s/m
agaz
ines
and
glu
e th
em o
nto
card
stoc
k, c
reat
e qu
estio
ns/a
nsw
ers b
ased
on
the
grap
h.Ex
. Cre
ate
thei
r ow
n qu
estio
ns/a
nsw
ers b
ased
on
the
info
rmati
on fr
om a
gra
ph sh
owin
g cl
ass p
refe
renc
es b
etw
een
two
diffe
rent
acti
vitie
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.4.b
. Int
erpr
et d
ata
from
a v
arie
ty o
f gra
phs t
o an
swer
que
stion
s.Ex
. Ans
wer
que
stion
s bas
ed o
n in
form
ation
pro
vide
d in
a p
ictu
re sc
hedu
le.
Ex. T
ell h
ow m
any
sunn
y da
ys th
ere
wer
e in
a m
onth
, bas
ed o
n a
wea
ther
gra
ph.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.4
.b. M
ake
obse
rvati
onal
stat
emen
ts a
bout
dat
a in
a p
ictu
re a
nd b
ar g
raph
.Ex
. Tel
l you
wha
t the
y ob
serv
e on
a g
raph
of s
tude
nts’
eye
col
ors.
Ex. S
how
stud
ents
a g
raph
of t
he B
ig 1
2 fo
otba
ll te
ams a
nd a
sk th
em w
hat t
hey
thin
k it
is ab
out.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.4
.b. D
emon
stra
te a
war
enes
s tha
t sym
bols
may
be
used
to re
pres
ent o
bjec
ts a
nd
even
ts.
Ex. P
ictu
re o
f ice
cre
am re
pres
ents
a fa
vorit
e fla
vor.
Ex. P
ictu
re o
f sno
w re
pres
ents
a sn
owy
day.
Math | Kindergarten-5 Grade 101
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Geo
met
ric
mea
sure
men
t:
unde
rsta
nd c
once
pts
of a
ngle
an
d m
easu
re a
ngle
s.
4.M
D.5
. Rec
ogni
ze a
ngle
s as
geom
etric
shap
es th
at a
re
form
ed w
here
ver t
wo
rays
sh
are
a co
mm
on e
ndpo
int,
and
unde
rsta
nd c
once
pts o
f ang
le
mea
sure
men
t:
An a
ngle
is m
easu
red
with
refe
renc
e to
a c
ircle
with
its
cent
er a
t the
com
mon
end
poin
t of
the
rays
, by
cons
ider
ing
the
frac
tion
of th
e ci
rcul
ar a
rc
betw
een
the
poin
ts w
here
the
two
rays
inte
rsec
t the
circ
le.
An
angl
e th
at tu
rns t
hrou
gh 1
/360
of
a c
ircle
is c
alle
d a
“one
-deg
ree
angl
e,”
and
can
be u
sed
to
mea
sure
ang
les.
An
ang
le th
at tu
rns
thro
ugh
n on
e-de
gree
ang
les i
s sa
id to
hav
e an
ang
le m
easu
re o
f n
degr
ees.
EE4.
MD
.5. R
ecog
nize
ang
les i
n ge
omet
ric sh
apes
.Le
vel I
V A
A S
tude
nts
will
:EE
4.M
D.5
. Lab
el d
iffer
ent t
ypes
of a
ngle
s in
geom
etric
shap
es.
Ex. C
onst
ruct
geo
met
ric sh
apes
usin
g co
untin
g sti
cks.
The
n de
term
ine
whe
ther
ang
les a
re
right
ang
les o
r not
.Ex
. Giv
en a
squa
re, d
eter
min
e w
heth
er th
e an
gles
are
righ
t ang
les o
r not
and
stat
e a
squa
re h
as fo
ur a
ngle
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.5. R
ecog
nize
ang
les i
n ge
omet
ric sh
apes
.Ex
. Dra
w a
n ar
c to
iden
tify
the
angl
es a
fter t
each
er d
raw
s a g
eom
etric
shap
e on
a
whi
tebo
ard.
Ex. G
iven
pic
ture
s of d
iffer
ent g
eom
etric
shap
es a
nd a
ngle
s tha
t mat
ch th
e sh
apes
, ov
erla
y sh
apes
with
mat
chin
g an
gles
.
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.5
. Ide
ntify
an
angl
e.Ex
. Wip
e aw
ay th
e sh
ape
that
doe
s not
con
tain
an
angl
e w
hen
teac
her d
raw
s a sh
ape
with
an
ang
le a
nd a
circ
le.
Ex. I
denti
fy a
s man
y an
gles
as t
hey
can
see
or fe
el o
n th
e pl
aygr
ound
.Ex
. Giv
en a
n an
gle
tem
plat
e, h
old
it to
shap
es in
the
clas
sroo
m a
nd te
ll if
it m
atch
es.
Ex. G
iven
a se
t of f
our s
hape
s (on
e w
ith a
ngle
s and
thre
e w
ith n
o an
gles
), in
dica
te th
e sh
ape
with
ang
les.
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.5
. Ide
ntify
shap
es th
at c
onta
in a
ngle
s.Ex
. Giv
en a
squa
re a
nd a
circ
le, i
denti
fy th
e sq
uare
.Ex
. Fin
d an
obj
ect t
hat i
s sha
ped
like
a sq
uare
in th
e cl
assr
oom
.
102 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.M
D.6
. Mea
sure
ang
les i
n w
hole
-num
ber d
egre
es u
sing
a pr
otra
ctor
. Sk
etch
ang
les o
f sp
ecifi
ed m
easu
re.
EE4.
MD
.6. I
denti
fy a
ngle
s as
larg
er a
nd sm
alle
r.Le
vel I
V A
A S
tude
nts
will
:EE
4.M
D.6
. Con
stru
ct a
ngle
s of v
ario
us si
zes.
Ex. C
onst
ruct
righ
t and
acu
te a
ngle
s.Ex
. Rep
licat
e an
gles
from
geo
met
ric sh
apes
con
tain
ing
right
and
acu
te a
ngle
s.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
MD
.6. I
denti
fy a
ngle
s as l
arge
r and
smal
ler.
Ex. G
iven
an
angl
e sh
aded
to le
ss th
an 4
5⁰ a
nd o
ne sh
aded
to m
ore
than
120
⁰, in
dica
te
“Whi
ch is
larg
er?”
Ex. G
iven
two
frac
tion
puzz
les p
iece
s, o
ne c
onta
inin
g a
signi
fican
tly la
rger
ang
le th
an th
e ot
her,
indi
cate
“W
hich
is sm
alle
r?”
Leve
l II A
A S
tude
nts
will
:EE
4.M
D.6
. Diff
eren
tiate
ang
les i
n sh
apes
.Ex
. Giv
en a
n an
gle
and
a ci
rcle
, ind
icat
es “
Whi
ch is
an
angl
e?”
Ex. G
iven
a b
all a
nd a
cub
e, in
dica
te “
Whi
ch h
as a
n an
gle?
”
Leve
l I A
A S
tude
nts
will
:EE
4.M
D.6
. Rep
licat
e an
ang
le.
Ex. U
se p
opsic
le sti
cks t
o re
plic
ate
a gi
ven
angl
e.Ex
. Ben
d a
pipe
cle
aner
to re
plic
ate
a gi
ven
angl
e.4.
MD
.7. R
ecog
nize
ang
le
mea
sure
as a
dditi
ve.
Whe
n an
ang
le is
dec
ompo
sed
into
no
n-ov
erla
ppin
g pa
rts,
the
angl
e m
easu
re o
f the
who
le is
the
sum
of t
he a
ngle
mea
sure
s of
the
part
s. S
olve
add
ition
and
su
btra
ction
pro
blem
s to
find
unkn
own
angl
es o
n a
diag
ram
in
real
wor
ld a
nd m
athe
mati
cal
prob
lem
s, e
.g.,
by u
sing
an
equa
tion
with
a sy
mbo
l for
the
unkn
own
angl
e m
easu
re.
EE4.
MD
.7. N
/A (S
ee E
E4.M
D.5.
)
Math | Kindergarten-5 Grade 103
Fou
rth
Gra
de
Mat
hem
atic
s St
and
ard
s: G
eom
etry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Dra
w a
nd id
enti
fy li
nes
and
angl
es, a
nd c
lass
ify s
hape
s by
pr
oper
ties
of t
heir
line
s an
d an
gles
.
4.G
.1. D
raw
poi
nts,
line
s,
line
segm
ents
, ray
s, a
ngle
s (r
ight
, acu
te, o
btus
e), a
nd
perp
endi
cula
r and
par
alle
l lin
es.
Iden
tify
thes
e in
two-
dim
ensio
nal fi
gure
s.
EE4.
G.1
. Disti
ngui
sh b
etw
een
para
llel a
nd in
ters
ectin
g lin
es.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
G.1
. Cre
ate
a re
pres
enta
tion
of p
aral
lel a
nd in
ters
ectin
g lin
es.
Ex. U
sing
pops
icle
stick
s, c
reat
e pa
ralle
l and
inte
rsec
ting
lines
.Ex
. Pla
y “S
imon
Say
s” to
illu
stra
te p
aral
lel a
nd in
ters
ectin
g lin
es w
ith a
rm
mov
emen
ts (o
r eye
gaz
e a
pict
ure
of st
uden
ts m
akin
g th
e co
rrec
t mov
emen
ts).
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
G.1
. Disti
ngui
sh b
etw
een
para
llel a
nd in
ters
ectin
g lin
es.
Ex. U
sing
a ro
ad m
ap ru
g, tr
ace
over
the
para
llel l
ines
and
then
trac
e ov
er th
e in
ters
ectin
g lin
es.
Ex. U
sing
a m
ap o
f the
scho
ol o
n an
inte
racti
ve w
hite
boar
d, tr
ace
the
clas
sroo
ms
that
are
in a
par
alle
l lin
e an
d th
e ha
llway
s tha
t int
erse
ct.
Ex. F
ind
para
llel l
ines
in sh
apes
.
Leve
l II A
A S
tude
nts
will
:EE
4.G
.1. I
denti
fy a
n in
ters
ectin
g lin
e.Ex
. Use
side
wal
k ch
alk
to d
raw
an
inte
rsec
ting
line.
Ex. G
o on
an
envi
ronm
ent h
unt a
nd id
entif
y in
ters
ectin
g lin
es.
Ex. T
race
inte
rsec
ting
lines
(e.g
., ro
ads o
r hal
lway
s) o
n a
map
.
Leve
l I A
A S
tude
nts
will
:EE
4.G
.1. I
denti
fy a
line
.Ex
. Usin
g ya
rn, s
tret
ch a
nd g
lue
a lin
e on
pap
er.
Ex. D
raw
a li
ne w
hen
dire
cted
.Ex
. Wal
k on
a li
ne ta
ped
to th
e flo
or w
hen
dire
cted
.Ex
. Giv
en a
line
and
a c
ircle
, ind
icat
e w
hich
is th
e lin
e.
104 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.G
.2. C
lass
ify tw
o-di
men
siona
l figu
res b
ased
on
the
pres
ence
or a
bsen
ce
of p
aral
lel o
r per
pend
icul
ar
lines
, or t
he p
rese
nce
or
abse
nce
of a
ngle
s of a
sp
ecifi
ed si
ze.
Reco
gnize
righ
t tr
iang
les a
s a c
ateg
ory,
and
iden
tify
right
tria
ngle
s.
EE4.
G.2
. Disti
ngui
sh b
etw
een
diffe
rent
att
ribut
es o
f sha
pes
(line
s, c
urve
s, a
ngle
s).
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
G.2
. Cla
ssify
shap
es a
ccor
ding
to a
ttrib
utes
.Ex
. Afte
r rea
ding
“Th
e Bu
tton
Box,”
det
erm
ine
whi
ch a
ttrib
utes
can
be
used
to
sort
geo
met
ric b
utton
s (bu
ttons
can
also
be
felt
by v
isual
ly im
paire
d st
uden
ts o
r te
ache
r can
trac
e th
e sh
apes
into
the
palm
of a
han
d).
Ex. G
iven
seve
ral s
hape
s, c
lass
ify th
e sh
apes
acc
ordi
ng to
att
ribut
es su
ch a
s sha
pe
and
angl
es.
(Tea
cher
will
trac
e ge
omet
ric sh
ape
into
stud
ent’s
pal
m a
nd, a
fter
give
n ch
oice
s of s
hape
s, a
ctiva
te a
switc
h to
indi
cate
a c
ateg
ory
of a
ttrib
ute.
)
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
G.2
. Disti
ngui
sh b
etw
een
diffe
rent
att
ribut
es o
f sha
pes (
lines
, cur
ves,
ang
les)
.Ex
. Sor
t diff
eren
t typ
es o
f obj
ects
to sh
ow li
nes,
cur
ves,
and
ang
les.
Ex. F
ind
pict
ures
that
repr
esen
t lin
es, a
ngle
s, a
nd c
urve
s.Ex
. Dra
w a
pic
ture
and
iden
tify
the
lines
, ang
les,
and
cur
ves u
sed
in th
e pi
ctur
e.
Leve
l II A
A S
tude
nts
will
:EE
4.G
.2. I
denti
fy a
ttrib
utes
of g
eom
etric
shap
es.
Ex. U
se a
ttrib
ute
bloc
ks to
sort
shap
es.
Ex. A
ssig
ned
a sh
ape,
cut
out
mag
azin
e pi
ctur
es to
repr
esen
t the
ass
igne
d sh
ape.
Leve
l I A
A S
tude
nts
will
:EE
4.G
.2. I
denti
fy c
urve
s.Ex
. Ass
embl
e a
sele
ction
of c
urve
d ite
ms.
Ex. U
sing
a ro
ad m
ap, u
se to
y ca
rs to
find
cur
ves.
Ex. G
iven
a sq
uare
and
a c
ircle
, ind
icat
e w
hich
is c
urve
d/ro
und.
Math | Kindergarten-5 Grade 105
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
4.G
.3. R
ecog
nize
a li
ne
of sy
mm
etry
for a
two-
dim
ensio
nal fi
gure
as a
line
ac
ross
the
figur
e su
ch th
at
the
figur
e ca
n be
fold
ed
alon
g th
e lin
e in
to m
atch
ing
part
s. I
denti
fy li
ne-s
ymm
etric
fig
ures
and
dra
w li
nes o
f sy
mm
etry
.
EE4.
G.3
. Rec
ogni
ze a
line
of
sym
met
ry in
a si
mpl
e sh
ape.
Leve
l IV
AA
Stu
dent
s w
ill:
EE4.
G.3
. Loc
ate
the
line
of sy
mm
etry
in a
geo
met
ric sh
ape.
Ex. F
old
pape
r, in
a g
eom
etric
shap
e, a
nd h
ave
stud
ent t
race
the
fold
line
to
iden
tify
the
line
of sy
mm
etry
.Ex
. Usin
g m
agne
tic sh
apes
, mat
ch a
giv
en p
atter
n of
shap
es to
cre
ate
a sy
mm
etric
al d
esig
n.
Leve
l III
AA
Stu
dent
s w
ill:
EE4.
G.3
. Rec
ogni
ze a
line
of s
ymm
etry
in a
sim
ple
shap
e.Ex
. Pla
ce d
ots o
f pai
nt o
n a
coffe
e fil
ter a
nd fo
ld in
hal
f. P
lace
a p
ipe
clea
ner o
n th
e lin
e of
sym
met
ry.
Ex. U
se a
sym
met
ry m
irror
, mov
e it
arou
nd o
n sh
apes
unti
l the
stud
ents
see
that
bo
th si
des m
atch
.
Leve
l II A
A S
tude
nts
will
:EE
4.G
.3. R
ecog
nize
pol
ygon
s.Ex
. Giv
en a
“m
yste
ry b
ag”
with
a g
eom
etric
shap
e in
it, fi
nd th
ree
obje
cts,
from
ar
ound
the
scho
ol th
at m
atch
the
shap
e an
d br
ing
them
bac
k to
cla
ss.
Take
s tur
ns
show
ing
thei
r ite
ms a
nd h
ave
the
rest
of t
he st
uden
ts g
uess
wha
t the
“m
yste
ry
shap
e” is
.Ex
. Ide
ntify
pol
ygon
s in
pict
ures
/sha
pe.
Leve
l I A
A S
tude
nts
will
:EE
4.G
.3. R
ecog
nize
sim
ple
shap
es (s
quar
e, tr
iang
le, a
nd re
ctan
gle)
.Ex
. Ide
ntify
the
shap
es o
f env
ironm
enta
l sig
ns.
Ex. M
atch
the
nam
e to
a sh
ape
from
two
choi
ces.
106 Common Core Essential Elements
CO
MM
ON
CO
RE
ESS
EN
TIA
L E
LEM
EN
TS
AN
D A
CH
IEV
EM
EN
T
DE
SCR
IPT
OR
S FO
R F
IFT
H G
RA
DE
Fift
h G
rad
e M
ath
emat
ics
Stan
dar
ds:
Op
erat
ion
an
d A
lgeb
raic
Th
inki
ng
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Wri
te a
nd in
terp
ret
num
eric
al
expr
essi
ons.
5.O
A.1
. Use
par
enth
eses
, br
acke
ts, o
r bra
ces i
n nu
mer
ical
ex
pres
sions
, and
eva
luat
e ex
pres
sions
with
thes
e sy
mbo
ls.
5.O
A.2
. Writ
e sim
ple
expr
essio
ns
that
reco
rd c
alcu
latio
ns
with
num
bers
, and
inte
rpre
t nu
mer
ical
exp
ress
ions
with
out
eval
uatin
g th
em.
For e
xam
ple,
ex
pres
s th
e ca
lcul
ation
“ad
d 8
and
7, th
en m
ultip
ly b
y 2”
as
2 ×
(8 +
7).
Rec
ogni
ze th
at 3
×
(189
32 +
921
) is
thre
e tim
es a
s la
rge
as 1
8932
+ 9
21, w
ithou
t ha
ving
to c
alcu
late
the
indi
cate
d su
m o
r pro
duct
.
EE5.
OA
.1-2
. N/A
Math | Kindergarten-5 Grade 107
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Ana
lyze
patt
erns
and
re
lati
onsh
ips.
5.O
A.3
. Gen
erat
e tw
o nu
mer
ical
pa
ttern
s usin
g tw
o gi
ven
rule
s.
Iden
tify
appa
rent
rela
tions
hips
be
twee
n co
rres
pond
ing
term
s.
Form
ord
ered
pai
rs c
onsis
ting
of c
orre
spon
ding
term
s fro
m
the
two
patte
rns,
and
gra
ph th
e or
dere
d pa
irs o
n a
coor
dina
te
plan
e. F
or e
xam
ple,
giv
en th
e ru
le “A
dd 3
” an
d th
e st
artin
g nu
mbe
r 0, a
nd g
iven
the
rule
“A
dd 6
” an
d th
e st
artin
g nu
mbe
r 0,
gen
erat
e te
rms
in th
e re
sulti
ng
sequ
ence
s, a
nd o
bser
ve th
at
the
term
s in
one
seq
uenc
e ar
e tw
ice
the
corr
espo
ndin
g te
rms
in th
e ot
her s
eque
nce.
Exp
lain
in
form
ally
why
this
is s
o.
EE5.
OA
.3. I
denti
fy a
nd e
xten
d nu
mer
ical
patt
erns
.Le
vel I
V A
A S
tude
nts
will
:EE
5.O
A.3
. Whe
n gi
ven
a ru
le, g
ener
ate
the
patte
rn.
Ex. S
how
me
a pa
ttern
that
incr
ease
s by
two
and
star
ts a
t 0 (i
.e.,
0, 2
, 4, 6
, . .
. ).
Ex. S
how
me
a pa
ttern
that
incr
ease
s by
five
and
star
ts w
ith 0
(i.e
., 0,
5, 1
0, 1
5, .
. . ).
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
OA
.3. I
denti
fy a
nd e
xten
d nu
mer
ical
patt
erns
.Ex
. Ide
ntify
the
follo
win
g pa
ttern
as c
ounti
ng b
y tw
os a
nd e
xten
d th
e pa
ttern
: 2, 4
, 6, _
_,
__, _
_.Ex
. Ide
ntify
the
follo
win
g pa
ttern
as c
ounti
ng b
y te
ns a
nd e
xten
d th
e pa
ttern
: 23,
33,
43,
__
, __.
Leve
l II A
A S
tude
nts
will
:EE
5.O
A.3
. Ext
end
a pi
ctur
e pa
ttern
.Ex
. Giv
en re
d, re
d, b
lue,
red,
red,
___
____
__, i
denti
fy th
e m
issin
g co
lor.
Ex. S
quar
e, c
ircle
, tria
ngle
, squ
are,
___
____
, tria
ngle
. Id
entif
y th
e m
issin
g sh
ape.
Leve
l I A
A S
tude
nts
will
:EE
5.O
A.3
. Rep
eat a
patt
ern.
Ex. T
each
er c
laps
twic
e, st
uden
t cla
ps tw
ice.
Ex. A
ctiva
te a
switc
h or
indi
cate
whi
ch c
hoic
e sh
own
repe
ats t
he p
atter
n sh
own.
108 Common Core Essential Elements
Fift
h G
rad
e M
ath
emat
ics
Stan
dar
ds:
Nu
mb
er a
nd
Op
erat
ion
s in
Bas
e T
en
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Und
erst
and
the
plac
e va
lue
syst
em.
5.N
BT.1
. Rec
ogni
ze th
at in
a
mul
ti-di
git n
umbe
r, a
digi
t in
one
plac
e re
pres
ents
10
times
as
muc
h as
it re
pres
ents
in th
e pl
ace
to it
s rig
ht a
nd 1
/10
of
wha
t it r
epre
sent
s in
the
plac
e to
its
left.
EE5.
NBT
.1. C
ompa
re n
umbe
rs
to e
ach
othe
r bas
ed o
n pl
ace
valu
e gr
oups
by
com
posin
g an
d de
com
posin
g to
99.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NBT
.1. C
ompa
re n
umbe
rs b
y co
mpo
sing
and
deco
mpo
sing
in tw
o di
ffere
nt w
ays.
Ex. D
ecom
pose
num
bers
by
plac
e va
lue
and
com
pare
by
hund
reds
, ten
s, a
nd o
nes (
with
th
e un
ders
tand
ing
that
one
100
, tw
o 10
s, a
nd th
ree
ones
com
bine
d is
123
ones
).Ex
. Com
pose
num
bers
bas
ed o
n pl
ace
valu
e an
d co
mpa
re to
ano
ther
num
ber o
n th
e nu
mbe
r lin
e.Ex
. Com
pare
two
num
bers
with
diff
eren
t num
bers
in th
e te
ns p
lace
(e.g
., 20
com
pare
d to
60
on
the
num
ber l
ine
and
expl
ain
20 h
as tw
o 10
s or 2
0 on
es a
nd 6
0 is
mad
e of
six
10s o
r 60
one
s as i
t is w
ritten
.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.1. C
ompa
re n
umbe
rs to
eac
h ot
her b
ased
on
plac
e va
lue
grou
ps b
y co
mpo
sing
and
deco
mpo
sing
to 9
9.Ex
. Com
pare
two
num
bers
with
diff
eren
t num
bers
in th
e te
ns p
lace
(e.g
., 20
com
pare
d to
60
on
the
num
ber l
ine)
.Ex
. Dem
onst
rate
the
diffe
renc
e be
twee
n tw
o nu
mbe
rs u
sing
dim
es (e
.g.,
10 c
ompa
red
to
50).
Ex. D
ecom
pose
a n
umbe
r int
o te
ns a
nd o
nes,
giv
en tw
o di
ffere
nt n
umbe
rs (w
ith th
e un
ders
tand
ing
that
two
10s a
nd th
ree
ones
com
bine
d is
23 o
nes)
.Ex
. Com
pare
num
bers
on
a ta
ble
of o
nes a
nd te
ns, g
iven
two
diffe
rent
num
bers
.
Leve
l II A
A S
tude
nts
will
:EE
5.N
BT.1
. Com
pare
num
bers
to 2
0.Ex
. Usin
g a
num
ber l
ine
and
give
n tw
o nu
mbe
rs, i
ndic
ate
whe
re o
n th
e nu
mbe
r lin
e th
e nu
mbe
rs b
elon
g be
twee
n th
e 10
mar
kers
.Ex
. Giv
en tw
o nu
mbe
rs, i
ndic
ate
whi
ch o
ne is
gre
ater
, or l
ess,
or w
hich
com
es fi
rst o
r las
t.
Leve
l I A
A S
tude
nts
will
:EE
5.N
BT.1
. Com
pare
num
bers
0-1
0.Ex
. Giv
en tw
o nu
mbe
rs, i
ndic
ate
if nu
mbe
rs a
re sa
me
or d
iffer
ent.
Ex. F
ind
two
num
bers
that
are
the
sam
e/ o
r tw
o th
at a
re d
iffer
ent.
Math | Kindergarten-5 Grade 109
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
BT.2
. Exp
lain
patt
erns
in th
e nu
mbe
r of z
eros
of t
he p
rodu
ct
whe
n m
ultip
lyin
g a
num
ber
by p
ower
s of 1
0, a
nd e
xpla
in
patte
rns i
n th
e pl
acem
ent o
f the
de
cim
al p
oint
whe
n a
deci
mal
is
mul
tiplie
d or
div
ided
by
a po
wer
of 1
0. U
se w
hole
-num
ber
expo
nent
s to
deno
te p
ower
s of
10.
EE5.
NBT
.2. R
ecog
nize
patt
erns
in
the
num
ber o
f zer
os w
hen
mul
tiply
ing
a nu
mbe
r by
pow
ers
of 1
0.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NBT
.2. E
xten
d pa
ttern
s in
the
num
ber o
f zer
os w
hen
mul
tiply
ing
by th
e po
wer
s of 1
0 up
to 1
,000
, ord
er n
umbe
rs to
100
.Ex
. Pla
ce n
umbe
rs in
ord
er.
Ex. G
iven
a ra
nge
of n
umbe
rs (e
.g. 2
00-3
00-2
53),
arra
nge
in o
rder
.Ex
. Ind
icat
e (e
.g. h
ead
stick
, poi
nting
) cor
rect
ord
er u
p to
100
.Ex
. Giv
en 2
0 di
mes
, cou
nt fr
om 1
0 to
100
by
tens
and
indi
cate
that
it is
$2.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.2. R
ecog
nize
patt
erns
in th
e nu
mbe
r of z
eros
whe
n m
ultip
lyin
g a
num
ber b
y po
wer
s of 1
0.Ex
. Pre
sent
ed w
ith li
sts o
f num
ber s
ente
nces
(e.g
., 10
x 1
= 1
0, 1
0 x
2 =
20, 1
0 x
3 =
30),
iden
tify
the
patte
rn.
Ex. A
rran
ge n
umbe
rs in
ord
er w
hen
pres
ente
d w
ith te
ns p
lace
val
ue n
umbe
r car
ds o
ut o
f or
der.
Ex. P
rese
nted
num
bers
10,
20,
30,
40,
__,
indi
cate
the
next
cor
rect
num
ber i
n th
e se
quen
ce.
Ex. G
iven
10
dim
es, c
ount
from
10
to 1
00 b
y te
ns a
nd in
dica
te th
at is
$1.
Leve
l II A
A S
tude
nts
will
:EE
5.N
BT.2
. Ord
er m
ultip
les o
f ten
rang
ing
from
0-5
0 in
sequ
entia
l ord
er le
ast t
o gr
eate
st.
Ex. P
rese
nted
a ra
nge
of n
umbe
rs 0
-50,
indi
cate
whe
ther
they
are
in c
orre
ct o
rder
.Ex
. Pre
sent
ed a
rang
e of
num
bers
(e.g
., 30
-50)
, ind
icat
e if
num
bers
are
in c
orre
ct o
rder
.Ex
. Giv
en fi
ve d
imes
, cou
nt fr
om 1
0 to
50
by te
ns a
nd in
dica
te th
at is
50
cent
s.
Leve
l I A
A S
tude
nts
will
:EE
5.N
BT.2
. Ind
icat
e th
e se
quen
tial o
rder
of n
umbe
rs to
10.
Ex. I
ndic
ate
if nu
mbe
rs 1
-10
are
in c
orre
ct o
rder
whe
n pr
esen
ted
(in a
nd o
ut o
f ord
er).
Ex. I
ndic
ate
whe
re o
n nu
mbe
r lin
e ea
ch n
umbe
r bel
ongs
.Ex
. Giv
en 1
0 pe
nnie
s, c
ount
to 1
0.
110 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
BT.3
. Rea
d, w
rite,
and
co
mpa
re d
ecim
als t
o 10
00th
s.
Re
ad a
nd w
rite
deci
mal
s to
100
0ths
usin
g ba
se-te
n nu
mer
als,
num
ber n
ames
, and
ex
pand
ed fo
rm, e
.g.,
347.
392
= 3
× 10
0 +
4 ×
10 +
7 ×
1 +
3 ×
(1/1
0)
+ 9
× (1
/100
) + 2
× (1
/100
0).
Co
mpa
re tw
o de
cim
als
to 1
000t
hs b
ased
on
mea
ning
s of
the
digi
ts in
eac
h pl
ace,
usin
g >,
=, a
nd <
sym
bols
to re
cord
the
resu
lts o
f com
paris
ons.
EE5.
NBT
.3. R
ound
two-
digi
t w
hole
num
bers
to th
e ne
ares
t 10
from
0—
90.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NBT
.3. R
ound
thre
e-di
git w
hole
num
bers
to h
undr
eds p
lace
.Ex
. Cho
ose
card
with
cor
rect
ans
wer
on
it aft
er b
eing
pre
sent
ed a
thre
e-di
git n
umbe
r and
to
ld to
roun
d to
nea
rest
hun
dred
s pla
ce v
alue
.Ex
. Giv
en a
thre
e-di
git n
umbe
r, ge
nera
te (s
peak
s, ty
pes,
etc
.) th
e an
swer
for r
ound
ing
to
the
near
est h
undr
eds p
lace
val
ue.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.3. R
ound
two-
digi
t who
le n
umbe
rs to
the
near
est 1
0 fr
om 0
-90.
Ex. G
iven
a n
umbe
r bet
wee
n 1-
89 a
nd c
ards
with
the
answ
er o
n on
e, p
ick
corr
ect n
umbe
r w
hen
ask
to ro
und
to n
eare
st 1
0.Ex
. Usin
g a
num
ber l
ine,
roun
d to
nea
rest
10.
Leve
l II A
A S
tude
nts
will
:EE
5.N
BT.3
. Det
erm
ine
if a
singl
e-di
git n
umbe
r is c
lose
r to
zero
or 1
0.Ex
. Giv
en a
num
ber b
etw
een
one
and
nine
, ind
icat
e if
the
num
ber i
s clo
ser t
o ze
ro o
r 10.
Ex. U
sing
a nu
mbe
r lin
e, in
dica
te if
giv
en n
umbe
r is c
lose
r to
10 o
r zer
o.
Leve
l I A
A S
tude
nts
will
:EE
5.N
BT.3
. Ind
icat
e m
ore
or le
ss th
an fi
ve.
Ex. U
sing
a pe
gboa
rd w
ith p
egs p
lace
d in
the
hole
s div
ided
into
two
diffe
rent
sets
, ind
icat
e w
hich
has
mor
e or
less
.Ex
. Pre
sent
ed w
ith a
set o
f five
, and
ano
ther
set,
indi
cate
if se
cond
set i
s mor
e or
less
than
fiv
e.Ex
. Pre
sent
ed w
ith th
ree
penn
ies o
r five
pen
nies
, cho
ose
whi
ch is
mor
e.Ex
. Giv
en a
num
ber l
ine,
indi
cate
if tw
o or
four
is c
lose
r to
five.
Math | Kindergarten-5 Grade 111
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
BT.4
. Use
pla
ce v
alue
un
ders
tand
ing
to ro
und
deci
mal
s to
any
pla
ce.
EE5.
NBT
.4. R
ound
mon
ey to
a
near
est d
olla
r.Le
vel I
V A
A S
tude
nts
will
:EE
5.N
BT.4
. Rou
nd m
oney
to th
e ne
ares
t dim
e.Ex
. Rou
nd c
ents
to th
e ne
ares
t ten
th o
f a d
olla
r (e.
g., 0
.82
is cl
oser
to 0
.80)
.Ex
. Usin
g ad
verti
sem
ents
with
cos
ts o
f ite
ms,
iden
tify
how
man
y w
hole
dol
lars
it w
ould
ta
ke to
pur
chas
e th
e ite
m (e
.g.,
if an
item
cos
ts $
3.65
, is $
3.64
wou
ld it
take
$3.
60 o
r $3
.70
to p
ay fo
r it?
).
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.4. R
ound
mon
ey to
the
near
est d
olla
r.Ex
. Rou
nd c
oins
to th
e ne
ares
t dol
lar.
Ex. I
denti
fy h
ow m
any
who
le d
olla
rs it
wou
ld ta
ke to
pur
chas
e an
item
(e.g
., if
an it
em
cost
s thr
ee d
olla
rs a
nd th
ree
quar
ters
($3.
75),
it w
ould
take
$4,
not
$3
to p
ay fo
r it.
Ex. P
ick
an it
em fr
om a
n ad
and
tell
how
man
y do
llars
it w
ould
take
to b
uy th
e ite
m.
Leve
l II A
A S
tude
nts
will
:EE
5.N
B.4.
Rou
nd m
oney
to th
e ne
ares
t dim
e.Ex
. Giv
en 1
2 pe
nnie
s, in
dica
te w
heth
er o
ne d
ime
or tw
o is
clos
est.
Ex. U
sing
penn
ies e
arne
d, e
xcha
nge
for d
imes
.
Leve
l I A
A S
tude
nts
will
:EE
5.N
B.4.
Indi
cate
whi
ch m
oney
am
ount
is m
ore.
Ex. G
iven
thre
e pe
nnie
s or a
qua
rter
, ind
icat
e th
e qu
arte
r is m
ore.
Ex. O
ffere
d th
ree
penn
ies a
nd o
ne d
ime,
indi
cate
the
dim
e is
mor
e.Ex
. Offe
red
a di
me
and
a qu
arte
r, in
dica
te th
e qu
arte
r is m
ore.
112 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Perf
orm
ope
rati
ons
wit
h m
ulti
-di
git w
hole
num
bers
and
wit
h de
cim
als
to h
undr
edth
s.
5.N
BT.5
. Flu
ently
mul
tiply
mul
ti-di
git w
hole
num
bers
usin
g th
e st
anda
rd a
lgor
ithm
.
EE5.
NBT
.5. M
ultip
ly w
hole
nu
mbe
rs u
p to
5 x
5.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NBT
.5. I
denti
fy b
asic
mul
tiplic
ation
fact
s for
num
bers
gre
ater
than
five
.Ex
. Ide
ntify
36
as th
e an
swer
to 6
x 6
.Ex
. Whe
n sh
own
a fla
sh c
ard
with
7 x
3, i
denti
fy 2
1 as
the
answ
er.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.5. M
ultip
ly w
hole
num
bers
up
5 x
5.Ex
. Cho
ose
corr
ect a
nsw
er fo
r 3 x
3.
Ex. W
hen
aske
d w
hat 4
x 4
equ
als,
iden
tify
16 fr
om a
n ar
ray
of c
hoic
es.
Leve
l II A
A S
tude
nts
will
:EE
5.N
BT.5
. Use
repe
ated
add
ition
to sh
ow m
ultip
licati
on w
ith si
ngle
dig
its 1
-5.
Ex. A
dd 2
+ 2
+ 2
to ju
stify
2 x
3.
Ex. W
hen
give
n a
pict
ure
of a
gar
den
with
two
row
s of fi
ve c
arro
t pla
nts i
n ea
ch, i
denti
fy 5
+
5.
Leve
l I A
A S
tude
nts
will
:EE
5.N
BT.5
. Use
con
cret
e re
pres
enta
tions
to sh
ow n
umbe
rs 1
-5.
Ex. G
iven
pic
ture
s of fi
ve c
ars,
arr
ange
them
into
one
row
.Ex
. Cou
nt fo
ur c
hairs
in a
row
.
Math | Kindergarten-5 Grade 113
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
BT.6
. Fin
d w
hole
-num
ber
quoti
ents
of w
hole
num
bers
w
ith u
p to
four
-dig
it di
vide
nds
and
two-
digi
t div
isors
, usin
g st
rate
gies
bas
ed o
n pl
ace
valu
e,
the
prop
ertie
s of o
pera
tions
, an
d/or
the
rela
tions
hip
betw
een
mul
tiplic
ation
and
div
ision
. Ill
ustr
ate
and
expl
ain
the
calc
ulati
on b
y us
ing
equa
tions
, re
ctan
gula
r arr
ays,
and
/or a
rea
mod
els.
5.N
BT.7
. Add
, sub
trac
t, m
ultip
ly, a
nd d
ivid
e de
cim
als
to h
undr
edth
s, u
sing
conc
rete
m
odel
s or d
raw
ings
and
st
rate
gies
bas
ed o
n pl
ace
valu
e,
prop
ertie
s of o
pera
tions
, and
/or
the
rela
tions
hip
betw
een
addi
tion
and
subt
racti
on; r
elat
e th
e st
rate
gy to
a w
ritten
met
hod
and
expl
ain
the
reas
onin
g us
ed.
EE5.
NBT
.6-7
. Illu
stra
te th
e co
ncep
t of d
ivisi
on u
sing
fair
and
equa
l sha
res.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NBT
.6-7
. App
ly th
e co
ncep
t of f
air s
hare
and
equ
al sh
ares
to so
lve
a di
visio
n pr
oble
m.
Ex. D
ivid
e a
snac
k eq
ually
am
ong
clas
smat
es.
Ex. D
ivid
e a
squa
re p
iece
of p
aper
equ
ally
am
ong
clas
smat
es.
Ex. D
ivid
e th
emse
lves
into
equ
al te
ams.
Ex. D
ivid
e a
quan
tity
into
equ
al sh
ares
(e.g
., “I
f I fi
nd 2
0 do
llars
, how
cou
ld fi
ve p
eopl
e sh
are
this?
” 20
/5=4
(div
ision
stru
ctur
e pa
rtitiv
e/fa
ir sh
ares
).
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NBT
.6-7
. Illu
stra
te th
e co
ncep
t of d
ivisi
on u
sing
fair
and
equa
l sha
res.
Ex. F
old
pape
r in
equa
l sha
res.
Ex. G
iven
10
coun
ting
cube
s div
ided
am
ong
thre
e st
uden
ts, r
ecog
nize
whe
n st
uden
ts h
ave
the
sam
e nu
mbe
r (eq
ual s
hare
) and
whe
n st
uden
ts d
o no
t hav
e th
e sa
me
num
ber (
not
equa
l sha
re).
Leve
l II A
A S
tude
nts
will
:EE
5.N
BT.6
-7. C
onst
ruct
equ
al se
ts.
Ex. U
sing
sorti
ng tr
ay a
nd c
olor
ed b
lock
s to
cons
truc
t equ
al se
ts.
Ex. G
iven
16
penc
ils, s
hare
equ
ally
ont
o fo
ur st
uden
ts.
Ex. U
se a
n or
gani
zer t
o gr
oup
or p
artiti
on o
bjec
ts in
to tw
o or
mor
e se
ts.
Ex. C
reat
e a
mod
el o
f equ
al se
ts b
y co
untin
g th
e ob
ject
s in
each
set.
Leve
l I A
A S
tude
nts
will
:EE
5.N
BT.6
-7. R
eplic
ate
an e
qual
set f
rom
a m
odel
.Ex
. Cou
nt o
ut th
ree
obje
cts a
fter t
each
er c
ount
s out
thre
e ob
ject
s.Ex
. Giv
en a
set o
f thr
ee o
bjec
ts, fi
ndin
g a
mat
chin
g se
t.
114 Common Core Essential Elements
Fift
h G
rad
e M
ath
emat
ics
Stan
dar
ds:
Nu
mb
er a
nd
Op
erat
ion
s--F
ract
ion
s
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Use
equ
ival
ent
frac
tion
s as
a
stra
tegy
to a
dd a
nd s
ubtr
act
frac
tion
s.
5.N
F.1.
Add
and
subt
ract
fr
actio
ns w
ith u
nlik
e de
nom
inat
ors (
incl
udin
g m
ixed
nu
mbe
rs) b
y re
plac
ing
give
n fr
actio
ns w
ith e
quiv
alen
t fr
actio
ns in
such
a w
ay a
s to
prod
uce
an e
quiv
alen
t sum
or
diffe
renc
e of
frac
tions
with
like
de
nom
inat
ors.
For
exa
mpl
e, 2
/3
+ 5/
4 =
8/12
+ 1
5/12
= 2
3/12
. (In
gen
eral
, a/b
+ c
/d =
(ad
+ bc
)/bd
).
EE5.
NF.
1. D
iffer
entia
te b
etw
een
halv
es, f
ourt
hs, a
nd e
ight
hs.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NF.
1. D
iffer
entia
te fr
actio
nal p
arts
less
than
1/4
.Ex
. With
frac
tion
bars
labe
led
1/4,
com
pare
the
1/4
to fr
actio
n ba
rs to
thos
e le
ss th
an 1
/4
and
iden
tify
the
frac
tion
usin
g nu
mer
als.
Ex. U
sing
squa
res,
fold
it in
1/4
, and
then
1/8
, and
tell
whi
ch is
mor
e an
d w
hich
is le
ss.
Ex. D
ivid
e a
squa
re in
to 1
/4 a
nd th
en 1
/8 a
nd te
ll w
hich
is m
ore.
Ex. D
ivid
e a
circ
le in
to th
e co
rrec
t fra
ction
s whe
n sh
own
the
num
eric
al re
pres
enta
tion
of
1/2,
1/4
, or 1
/8.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NF.
1. D
iffer
entia
te b
etw
een
halv
es, f
ourt
hs, a
nd e
ight
hs.
Ex. W
ith p
ictu
res c
ut in
to h
alve
s, p
ictu
res c
ut in
to fo
urth
s, a
nd p
ictu
res c
ut in
eig
hths
, sor
t th
e pi
ctur
es.
Ex. U
sing
frac
tion
bars
, ide
ntify
the
bar t
hat i
s 1/2
, 1/4
, or 1
/8 o
f the
who
le u
sing
a te
mpl
ate.
Ex. G
iven
a p
artiti
oned
shap
e, sh
ade
it to
show
1/2
, 1/4
, or 1
/8 w
hen
aske
d.Ex
. Usin
g an
ana
log
cloc
k, sh
ade
the
cloc
k to
show
the
quar
ter h
our.
Leve
l II A
A S
tude
nts
will
:EE
5.N
F.1.
Diff
eren
tiate
bet
wee
n w
hole
and
a p
art.
Ex. G
iven
a w
hole
sand
wic
h, c
ut th
e sa
ndw
ich
in h
alf (
e.g.
, cut
hor
izont
ally,
ver
tical
ly, a
nd
diag
onal
ly),
indi
cate
whi
ch is
hal
f and
whi
ch is
who
le.
Ex. D
raw
a sq
uare
on
a dr
y er
ase
boar
d; th
en d
raw
a li
ne to
cut
the
squa
re in
hal
f.Ex
. Whe
n pl
ayin
g a
gam
e in
whi
ch th
e cl
ass i
s div
ided
into
two
team
s, in
dica
te th
at o
nly
half
the
clas
s is o
n ea
ch te
am.
Leve
l I A
A S
tude
nts
will
:EE
5.N
F.1.
Rec
ogni
ze th
at fr
actio
ns a
re p
art o
f a w
hole
.Ex
. Ass
embl
e a
simpl
e pu
zzle
to d
emon
stra
te p
iece
s of a
who
le.
Ex. U
sing
a se
lf-sti
ckin
g no
n-ad
hesiv
e sh
ape,
take
apa
rt a
nd p
ut to
geth
er fr
actio
nal p
arts
of
a w
hole
.
Math | Kindergarten-5 Grade 115
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
F.2.
Sol
ve w
ord
prob
lem
s in
volv
ing
addi
tion
and
subt
racti
on o
f fra
ction
s ref
errin
g to
the
sam
e w
hole
, inc
ludi
ng
case
s of u
nlik
e de
nom
inat
ors,
e.
g., b
y us
ing
visu
al fr
actio
n m
odel
s or e
quati
ons t
o re
pres
ent t
he p
robl
em.
Use
be
nchm
ark
frac
tions
and
nu
mbe
r sen
se o
f fra
ction
s to
estim
ate
men
tally
and
ass
ess t
he
reas
onab
lene
ss o
f ans
wer
s. F
or
exam
ple,
reco
gniz
e an
inco
rrec
t re
sult
2/5
+ 1/
2 =
3/7,
by
obse
rvin
g th
at 3
/7 <
1/2
.
EE5.
NF.
2. S
olve
two-
step
wor
d pr
oble
ms u
sing
addi
tion
and
subt
racti
on o
f who
le n
umbe
rs.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
NF.
2. S
olve
two-
step
wor
d pr
oble
ms u
sing
addi
tion
and
subt
racti
on o
f num
bers
afte
r sh
owin
g th
e pr
oble
m in
num
eral
s.Ex
. Sus
an h
as 3
5 co
mpa
ct d
isks.
She
bou
ght t
hree
mor
e an
d ga
ve fo
ur to
her
litt
le
brot
her,
Dyla
n. H
ow m
any
com
pact
disc
s doe
s Sus
an h
ave
now
? S
how
the
prob
lem
and
ex
plai
n w
hy th
e an
swer
is re
ason
able
.Ex
. Joh
nny
has a
bag
of 3
6 co
okie
s. H
e at
e fo
ur o
f the
m a
nd g
ave
two
to A
my.
How
man
y co
okie
s doe
s he
have
? S
how
the
prob
lem
and
exp
lain
why
ans
wer
is re
ason
able
.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
NF.
2. S
olve
two-
step
wor
d pr
oble
ms u
sing
addi
tion
and
subt
racti
on o
f who
le
num
bers
.Ex
. Bill
y ju
mpe
d ro
pe fo
r 10
min
utes
, pla
yed
bask
etba
ll fo
r 15
min
utes
, and
ran
for fi
ve
min
utes
. Ho
w m
any
min
utes
did
he
spen
d ex
erci
sing?
Ex. J
enny
has
30
text
mes
sage
s left
on
her c
ell p
hone
pla
n. S
he se
nt 1
0 m
essa
ges t
o Ga
ry
and
rece
ived
eig
ht m
essa
ges f
rom
her
mom
. Ho
w m
any
text
mes
sage
s are
left
on h
er
plan
?
Leve
l II A
A S
tude
nts
will
:EE
5.N
F.2.
Sol
ve o
ne-s
tep
prob
lem
s usin
g ad
ditio
n an
d su
btra
ction
.Ex
. Con
nie
had
five
mar
bles
. Ju
an g
ave
her e
ight
mor
e m
arbl
es.
How
man
y m
arbl
es d
oes
Conn
ie h
ave
all t
oget
her?
Ex. Y
ou h
ave
eigh
t pen
nies
. Gi
ve m
e tw
o pe
nnie
s. H
ow m
any
penn
ies d
o yo
u ha
ve n
ow?
Leve
l I A
A S
tude
nts
will
:EE
5.N
F.3.
Rec
ogni
ze w
ords
that
are
use
d fo
r add
ition
and
subt
racti
on.
Ex. U
sing
flash
car
ds, i
ndic
ate
whe
ther
the
wor
d is
used
for a
dditi
on o
r sub
trac
tion
(e.g
., m
ore,
incr
ease
d, le
ss, t
ake
away
, dec
reas
ed).
Ex. B
uild
a w
all o
f wor
ds u
sed
for a
dditi
on—
sum
, all
toge
ther
, add
, mor
e, in
crea
sed,
etc
.Ex
. Bui
ld a
wal
l of w
ords
use
d fo
r sub
trac
tion—
diffe
renc
e, d
ecre
ased
, tak
e aw
ay, l
ess,
sp
ent,
etc.
Ex. I
ndic
ate
the
conc
ept o
f mor
e (a
dditi
on) a
nd le
ss (s
ubtr
actio
n).
116 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
App
ly a
nd e
xten
d pr
evio
us
unde
rsta
ndin
gs o
f mul
tipl
icati
on
and
divi
sion
to m
ulti
ply
and
divi
de fr
acti
ons.
5.N
F.3.
Inte
rpre
t a fr
actio
n as
di
visio
n of
the
num
erat
or b
y th
e de
nom
inat
or (a
/b =
a ÷
b).
So
lve
wor
d pr
oble
ms i
nvol
ving
di
visio
n of
who
le n
umbe
rs
lead
ing
to a
nsw
ers i
n th
e fo
rm o
f fr
actio
ns o
r mix
ed n
umbe
rs, e
.g.,
by u
sing
visu
al fr
actio
n m
odel
s or
equ
ation
s to
repr
esen
t the
pr
oble
m.
For e
xam
ple,
inte
rpre
t 3/
4 as
the
resu
lt of
div
idin
g 3
by 4
, noti
ng th
at 3
/4 m
ultip
lied
by 4
equ
als
3, a
nd th
at w
hen
3 w
hole
s ar
e sh
ared
equ
ally
am
ong
4 pe
ople
eac
h pe
rson
has
a
shar
e of
siz
e 3/
4. I
f 9 p
eopl
e w
ant t
o sh
are
a 50
-pou
nd s
ack
of ri
ce e
qual
ly b
y w
eigh
t, h
ow
man
y po
unds
of r
ice
shou
ld
each
per
son
get?
Bet
wee
n w
hat
two
who
le n
umbe
rs d
oes
your
an
swer
lie?
EE5.
NF.
3. N
/A (S
ee E
E5.N
F.1)
Math | Kindergarten-5 Grade 117
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
F.4.
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
mul
tiplic
ation
to m
ultip
ly a
fr
actio
n or
who
le n
umbe
r by
a fr
actio
n.
Inte
rpre
t the
pro
duct
(a/b
) ×
q as
a p
arts
of a
par
tition
of q
into
b
equa
l par
ts; e
quiv
alen
tly, a
s the
resu
lt of
a
sequ
ence
of o
pera
tions
a ×
q ÷
b.
For
exam
ple,
use
a v
isua
l fra
ction
mod
el to
sh
ow (2
/3) ×
4 =
8/3
, and
cre
ate
a st
ory
cont
ext f
or th
is e
quati
on.
Do
the
sam
e w
ith (2
/3) ×
(4/5
) = 8
/15.
(In
gen
eral
, (a
/b) ×
(c/d
) = a
c/bd
.)
Find
the
area
of a
rect
angl
e w
ith fr
actio
nal s
ide
leng
ths b
y til
ing
it w
ith u
nit s
quar
es o
f the
app
ropr
iate
uni
t fr
actio
n sid
e le
ngth
s, a
nd sh
ow th
at th
e ar
ea is
the
sam
e as
wou
ld b
e fo
und
by
mul
tiply
ing
the
side
leng
ths.
Mul
tiply
fr
actio
nal s
ide
leng
ths t
o fin
d ar
eas
of re
ctan
gles
, and
repr
esen
t fra
ction
pr
oduc
ts a
s rec
tang
ular
are
as.
5.N
F.5.
Inte
rpre
t mul
tiplic
ation
as
scal
ing
(res
izing
), by
:
Com
parin
g th
e siz
e of
a
prod
uct t
o th
e siz
e of
one
fact
or o
n th
e ba
sis o
f the
size
of t
he o
ther
fact
or,
with
out p
erfo
rmin
g th
e in
dica
ted
mul
tiplic
ation
.
Expl
aini
ng w
hy m
ultip
lyin
g a
give
n nu
mbe
r by
a fr
actio
n gr
eate
r tha
n 1
resu
lts in
a p
rodu
ct g
reat
er th
an th
e gi
ven
num
ber (
reco
gnizi
ng m
ultip
licati
on
by w
hole
num
bers
gre
ater
than
1 a
s a
fam
iliar
cas
e); e
xpla
inin
g w
hy m
ultip
lyin
g a
give
n nu
mbe
r by
a fr
actio
n le
ss th
an
1 re
sults
in a
pro
duct
smal
ler t
han
the
give
n nu
mbe
r; an
d re
latin
g th
e pr
inci
ple
of fr
actio
n eq
uiva
lenc
e a/
b =
(n ×
a)/
(n ×
b)
to th
e eff
ect o
f mul
tiply
ing
a/b
by 1
.
EE5.
NF.
4-5.
N/A
118 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
5.N
F.6.
Sol
ve re
al w
orld
pr
oble
ms i
nvol
ving
mul
tiplic
ation
of
frac
tions
and
mix
ed n
umbe
rs,
e.g.
, by
usin
g vi
sual
frac
tion
mod
els o
r equ
ation
s to
repr
esen
t the
pro
blem
.
5.N
F.7.
App
ly a
nd e
xten
d pr
evio
us u
nder
stan
ding
s of
divi
sion
to d
ivid
e un
it fr
actio
ns
by w
hole
num
bers
and
who
le
num
bers
by
unit
frac
tions
.14
In
terp
ret d
ivisi
on o
f a u
nit
frac
tion
by a
non
-zer
o w
hole
num
ber,
and
com
pute
such
quo
tient
s. F
or
exam
ple,
cre
ate
a st
ory
cont
ext f
or (1
/3)
÷ 4,
and
use
a v
isua
l fra
ction
mod
el to
sh
ow th
e qu
otien
t. U
se th
e re
latio
nshi
p be
twee
n m
ultip
licati
on a
nd d
ivis
ion
to
expl
ain
that
(1/3
) ÷ 4
= 1
/12
beca
use
(1/1
2) ×
4 =
1/3
.
Inte
rpre
t div
ision
of a
who
le
num
ber b
y a
unit
frac
tion,
and
com
pute
su
ch q
uotie
nts.
For
exa
mpl
e, c
reat
e a
stor
y co
ntex
t for
4 ÷
(1/5
), an
d us
e a
visu
al fr
actio
n m
odel
to s
how
the
quoti
ent.
Use
the
rela
tions
hip
betw
een
mul
tiplic
ation
and
div
isio
n to
exp
lain
that
4
÷ (1
/5) =
20
beca
use
20 ×
(1/5
) = 4
.
Solv
e re
al w
orld
pro
blem
s in
volv
ing
divi
sion
of u
nit f
racti
ons b
y no
n-ze
ro w
hole
num
bers
and
div
ision
of
who
le n
umbe
rs b
y un
it fr
actio
ns,
e.g.
, by
usin
g vi
sual
frac
tion
mod
els a
nd
equa
tions
to re
pres
ent t
he p
robl
em.
For
exam
ple,
how
muc
h ch
ocol
ate
will
eac
h pe
rson
get
if 3
peo
ple
shar
e 1/
2 lb
of
choc
olat
e eq
ually
? H
ow m
any
1/3-
cup
serv
ings
are
in 2
cup
s of
rais
ins?
EE5.
NF.
6-7
. N/A
Math | Kindergarten-5 Grade 119
Fift
h G
rad
e M
ath
emat
ics
Stan
dar
ds:
Mea
sure
men
t an
d D
ata
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Conv
ert l
ike
mea
sure
men
t un
its
wit
hin
a gi
ven
mea
sure
men
t sy
stem
.
5.M
D.1
. Con
vert
am
ong
diffe
rent
-size
d st
anda
rd
mea
sure
men
t uni
ts w
ithin
a
give
n m
easu
rem
ent s
yste
m (e
.g.,
conv
ert 5
cm
to 0
.05
m),
and
use
thes
e co
nver
sions
in so
lvin
g m
ulti-
step
, rea
l wor
ld p
robl
ems.
EE5.
MD
.1.a
. Tel
l tim
e us
ing
an
anal
og o
r dig
ital c
lock
to th
e ha
lf or
qua
rter
hou
r.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
MD
.1.a
. Tel
l tim
e us
ing
a di
gita
l clo
ck to
the
min
ute
and
an a
nalo
g cl
ock
to th
e ne
ares
t five
min
utes
.Ex
. Tel
l tim
e to
the
min
ute
on a
dig
ital c
lock
.Ex
. Pla
ce h
and
on a
clo
ck w
ithin
five
min
utes
of t
he st
ated
tim
e.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
MD
.1.a
. Tel
l tim
e us
ing
an a
nalo
g or
dig
ital c
lock
to th
e ha
lf or
qua
rter
hou
r.Ex
. Ind
icat
e tim
e to
the
quar
ter h
our o
n a
digi
tal c
lock
.Ex
. Pla
ce c
lock
han
ds to
show
the
half
hour
on
an a
nalo
g cl
ock.
Leve
l II A
A S
tude
nts
will
:EE
5.M
D.1
.a. T
ell ti
me
to th
e ha
lf ho
ur u
sing
a di
gita
l clo
ck a
nd to
the
half
hour
usin
g an
an
alog
clo
ck.
Ex. I
denti
fy w
hich
clo
ck sh
ows a
stat
ed ti
me
on a
dig
ital c
lock
(3:3
0).
Ex. M
ove
hand
s on
a cl
ock
to sh
ow a
stat
ed h
our.
Leve
l I A
A S
tude
nts
will
:EE
5.M
D.1
.a. I
denti
fy m
orni
ng a
nd a
ftern
oon.
Ex. I
denti
fy a
ctivi
ty o
n sc
hedu
le a
nd re
late
to m
orni
ng (b
efor
e lu
nch)
to a
ftern
oon
(afte
r lu
nch)
.
120 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE5.
MD
.1.b
. Use
cus
tom
ary
units
to m
easu
re w
eigh
t and
le
ngth
of o
bjec
ts.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
MD
.1.b
. Use
two
cust
omar
y un
its to
mea
sure
wei
ght a
nd le
ngth
of o
bjec
ts.
Ex. W
eigh
an
obje
ct in
pou
nds a
nd w
eigh
aga
in u
sing
ounc
es.
Ex. W
eigh
obj
ects
in o
unce
s and
wei
gh a
gain
in p
ound
s.Ex
. Mea
sure
a v
arie
ty o
bjec
ts in
inch
es a
nd m
easu
re a
gain
in fe
et.
Ex. M
easu
re a
n ob
ject
usin
g fe
et a
nd m
easu
re a
gain
usin
g in
ches
.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
MD
.1.b
. Use
cus
tom
ary
units
to m
easu
re w
eigh
t and
leng
th o
f obj
ects
.Ex
. Wei
gh a
var
iety
of o
bjec
ts in
pou
nds.
Ex. W
eigh
a v
arie
ty o
f obj
ects
in o
unce
s.Ex
. Mea
sure
leng
th o
f obj
ects
usin
g fe
et.
Ex. M
easu
re le
ngth
of o
bjec
ts u
sing
inch
es.
Leve
l II A
A S
tude
nts
will
:EE
5.M
D.1
.b. I
denti
fy c
usto
mar
y un
its o
f mea
sure
men
t for
wei
ght a
nd le
ngth
.Ex
. Giv
en a
n ob
ject
, cho
ose
poun
ds o
r inc
hes t
o w
eigh
a p
erso
n.Ex
. Sho
wn
a sc
ale
and
a ru
ler,
choo
se c
orre
ct to
ol to
mea
sure
wei
ght o
f obj
ects
(use
inch
ru
ler i
f pos
sible
).
Leve
l I A
A S
tude
nts
will
:EE
5.M
D.1
.b. I
denti
fy w
hich
tool
s are
use
d to
wei
gh.
Ex. I
denti
fy w
hich
tool
you
use
to w
eigh
a p
erso
n.Ex
. Ind
icat
e w
hich
tool
is u
sed
to m
easu
re le
ngth
.Ex
. Ind
icat
e w
hich
tool
is u
sed
to m
easu
re fl
our a
nd su
gar i
n a
reci
pe.
Math | Kindergarten-5 Grade 121
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
EE5.
MD
.1.c
. Ind
icat
e re
lativ
e va
lue
of c
olle
ction
s of c
oins
.Le
vel I
V A
A S
tude
nts
will
:EE
5.M
D.1
.c. I
ndic
ate
rela
tive
valu
e of
coi
ns a
nd b
ills t
o ea
ch o
ther
.Ex
. Giv
en a
qua
rter
and
a c
olle
ction
of n
icke
ls, se
lect
five
nic
kels
to tr
ade
for o
ne q
uart
er.
Ex. G
iven
a d
olla
r and
offe
red
thre
e qu
arte
rs in
exc
hang
e, in
dica
te th
at th
e do
llar i
s wor
th
mor
e.Ex
. Giv
en a
dol
lar a
nd a
col
lecti
on o
f dim
es, s
elec
t 10
dim
es in
exc
hang
e fo
r the
dol
lar.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
MD
.1.c
. Ind
icat
e re
lativ
e va
lue
of c
olle
ction
s of c
oins
.Ex
. Whe
n as
ked
wha
t is w
orth
five
cen
ts, c
hoos
es a
nic
kel.
Whe
n as
ked
wha
t is w
orth
25
cent
s, c
hoos
e a
quar
ter.
Ex. G
iven
two
coin
s, id
entif
y th
e va
lue
of e
ach
and
indi
cate
whi
ch is
mor
e.Ex
. Giv
en 2
5 pe
nnie
s and
two
dim
es, i
ndic
ate
whi
ch se
t is w
orth
mor
e.
Leve
l II A
A S
tude
nts
will
:EE
5.M
D.1
.c. I
denti
fy c
oins
(pen
ny, n
icke
l, di
me,
qua
rter
) and
thei
r val
ues.
Ex. G
iven
two
coin
s, c
hoos
e co
rrec
t coi
n by
nam
e an
d va
lue.
Ex. S
how
n a
coin
, nam
es c
oin.
Ex. S
how
rela
tive
valu
es o
f pen
ny, n
icke
l, di
me,
qua
rter
by
arra
ngin
g th
em in
ord
er fr
om
leas
t to
mos
t.
Leve
l I A
A S
tude
nts
will
:EE
5.M
D.1
.c. M
atch
coi
ns th
at a
re a
like
(pen
ny, n
icke
l, di
me,
qua
rter
).Ex
. Giv
en a
gro
up o
f coi
ns, m
atch
coi
ns th
at a
re a
like.
Ex. G
iven
a p
ictu
re o
f a q
uart
er, c
hoos
e a
quar
ter f
rom
a g
roup
of c
oins
.
122 Common Core Essential Elements
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Repr
esen
t and
inte
rpre
t dat
a.
5.M
D.2
. Mak
e a
line
plot
to
disp
lay
a da
ta se
t of
mea
sure
men
ts in
frac
tions
of
a u
nit (
1/2,
1/4
, 1/8
). U
se
oper
ation
s on
frac
tions
for
this
grad
e to
solv
e pr
oble
ms
invo
lvin
g in
form
ation
pre
sent
ed
in li
ne p
lots
. Fo
r exa
mpl
e,
give
n di
ffere
nt m
easu
rem
ents
of
liqu
id in
iden
tical
bea
kers
, fin
d th
e am
ount
of l
iqui
d ea
ch
beak
er w
ould
con
tain
if th
e to
tal
amou
nt in
all
the
beak
ers
wer
e re
dist
ribut
ed e
qual
ly.
EE5.
MD
.2.a
. Rep
rese
nt a
nd
inte
rpre
t dat
a on
a p
ictu
re, l
ine
plot
, or b
ar g
raph
giv
en a
mod
el
and
a gr
aph
to c
ompl
ete.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
MD
.2.a
. Col
lect
, org
anize
, and
inte
rpre
t dat
a. C
reat
e a
grap
h us
ing
a gr
aph
tem
plat
e,
and
disp
lay
the
data
on
the
grap
h.Ex
. Cou
nt n
umbe
r of s
tude
nts w
ho li
ke d
ogs a
nd n
umbe
r who
like
cat
s. S
how
whe
re o
n th
e gr
aph
to p
ut th
e ba
r for
dog
s and
for c
ats a
nd w
here
to in
dica
te th
e nu
mbe
r of v
otes
an
d en
ter t
he re
sults
on
the
grap
h. D
eter
min
e if
the
resu
lt sh
own
seem
s rea
sona
ble
and
why
(e.g
., gr
aph
show
s tha
t stu
dent
s hav
e m
ore
snak
es a
s pet
s tha
n do
gs).
Ex. B
ased
on
clas
s obs
erva
tion
(how
man
y w
ore
red
toda
y), d
eter
min
e ho
w to
gra
ph d
ata
and
show
gra
ph te
lling
whi
ch w
as m
ore,
less
, or t
he sa
me.
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
MD
.2.a
. Rep
rese
nt a
nd in
terp
ret d
ata
on a
pic
ture
, lin
e pl
ot, o
r bar
gra
ph g
iven
a
mod
el a
nd a
gra
ph to
com
plet
e.Ex
. Giv
en d
ata,
plo
t dat
a po
ints
on
a gi
ven
grap
h. D
eter
min
e w
hich
has
mor
e, le
ss, o
r the
sa
me.
Ex. T
ake
give
n da
ta fr
om a
surv
ey a
nd p
ut th
e sa
me
data
on
a gi
ven
grap
h us
ing
a m
odel
. Te
ll on
e th
ing
the
grap
h sa
ys a
bout
the
surv
ey.
Leve
l II A
A S
tude
nts
will
:EE
5.M
D.2
.a. D
ispla
y da
ta o
n a
pict
ure,
line
plo
t, or
bar
gra
ph a
nd a
nsw
er q
uesti
ons a
bout
th
e gr
aph.
Ex. I
ndic
ate
whe
re d
ata
shou
ld g
o on
the
grap
h, a
nd sh
ade/
colo
r cor
rect
am
ount
of
spac
es o
n gi
ven
grap
h, a
nsw
er a
que
stion
abo
ut th
e gr
aph
(e.g
., Is
this
abou
t dog
s?).
Ex. U
se o
bjec
ts to
disp
lay
data
on
grap
h an
d in
dica
te ty
pe o
f gra
ph.
Leve
l I A
A S
tude
nts
will
:EE
5.M
D.2
.a. I
denti
fy a
sim
ple
grap
h.Ex
. Ide
ntify
a si
mpl
e pi
ctur
e gr
aph
or sc
hedu
le.
Ex. P
ick
out a
gra
ph w
hen
pres
ente
d w
ith a
gra
ph a
nd a
non
-gra
ph.
Math | Kindergarten-5 Grade 123
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Geo
met
ric
mea
sure
men
t:
unde
rsta
nd c
once
pts
of
volu
me
and
rela
te v
olum
e to
m
ulti
plic
ation
and
to a
dditi
on.
5.M
D.3
. Rec
ogni
ze v
olum
e as
an
att
ribut
e of
solid
figu
res a
nd
unde
rsta
nd c
once
pts o
f vol
ume
mea
sure
men
t.
A cu
be w
ith si
de le
ngth
1 u
nit,
calle
d a
“uni
t cub
e,”
is sa
id to
hav
e “o
ne
cubi
c un
it” o
f vol
ume,
and
can
be
used
to
mea
sure
vol
ume.
A
solid
figu
re, w
hich
can
be
pack
ed w
ithou
t gap
s or o
verla
ps u
sing
n un
it cu
bes,
is sa
id to
hav
e a
volu
me
of n
cu
bic
units
.
5.M
D.4
. Mea
sure
vol
umes
by
cou
nting
uni
t cub
es, u
sing
cubi
c cm
, cub
ic in
, cub
ic ft
, and
im
prov
ised
units
.
5.M
D.5
. Rel
ate
volu
me
to th
e op
erati
ons o
f mul
tiplic
ation
and
ad
ditio
n an
d so
lve
real
wor
ld
and
mat
hem
atica
l pro
blem
s in
volv
ing
volu
me.
Fi
nd th
e vo
lum
e of
a ri
ght
rect
angu
lar p
rism
with
who
le-n
umbe
r sid
e le
ngth
s by
pack
ing
it w
ith u
nit
cube
s, a
nd sh
ow th
at th
e vo
lum
e is
the
sam
e as
wou
ld b
e fo
und
by m
ultip
lyin
g th
e ed
ge le
ngth
s, e
quiv
alen
tly b
y m
ultip
lyin
g th
e he
ight
by
the
area
of
the
base
. Re
pres
ent t
hree
fold
who
le-
num
ber p
rodu
cts a
s vol
umes
, e.g
., to
re
pres
ent t
he a
ssoc
iativ
e pr
oper
ty o
f m
ultip
licati
on.
Ap
ply
the
form
ulas
V =
l ×
w
× h
and
V =
b ×
h fo
r rec
tang
ular
pris
ms
to fi
nd v
olum
es o
f rig
ht re
ctan
gula
r pr
isms w
ith w
hole
-num
ber e
dge
leng
ths
in th
e co
ntex
t of s
olvi
ng re
al w
orld
and
m
athe
mati
cal p
robl
ems.
Re
cogn
ize v
olum
e as
add
itive
. Fi
nd v
olum
es o
f sol
id fi
gure
s com
pose
d of
two
non-
over
lapp
ing
right
rect
angu
lar
prism
s by
addi
ng th
e vo
lum
es o
f the
no
n-ov
erla
ppin
g pa
rts,
app
lyin
g th
is te
chni
que
to so
lve
real
wor
ld p
robl
ems.
EE5.
MD
.3-5
. Det
erm
ine
volu
me
of a
cub
e by
cou
nting
uni
ts o
f m
easu
re.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
MD
.3-5
. N/A
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
MD
.3-5
. Det
erm
ine
volu
me
of a
cub
e by
cou
nting
uni
ts o
f mea
sure
.Ex
. Giv
en c
ubes
that
fill
a bo
x w
ith n
o ga
ps (s
mal
l num
ber,
how
man
y), d
eter
min
e by
co
untin
g th
e nu
mbe
r of c
ubes
nee
ded
to fi
ll th
e bo
x.Ex
. Giv
en a
cub
e 4
x 4
x 4
inch
es c
onst
ruct
ed o
f one
squa
re in
ch c
ube,
disa
ssem
ble
it to
de
term
ine
by c
ounti
ng h
ow m
any
cube
s wer
e re
quire
d.
Leve
l II A
A S
tude
nts
will
:EE
5.M
D.3
-5. I
denti
fy o
bjec
ts th
at h
ave
volu
me.
Ex. G
iven
a g
roup
of p
ictu
res (
cup,
rock
, for
k), c
hoos
e w
hich
one
can
be
fille
d.Ex
. Ide
ntify
obj
ects
in th
e ro
om th
at c
an b
e fil
led
(e.g
., cu
p, fi
sh ta
nk).
Ex. G
iven
a sq
uare
and
a c
ube,
indi
cate
cub
e.
Leve
l I A
A S
tude
nts
will
:EE
5.M
D.3
-5. D
emon
stra
te so
lid o
r liq
uid,
full
or e
mpt
y.Ex
. Giv
en a
gla
ss o
f wat
er a
nd a
pap
er w
eigh
t, in
dica
te w
hich
one
you
can
pou
r.Ex
. Giv
en a
gla
ss o
f wat
er a
nd a
pap
er w
eigh
t, de
mon
stra
te th
at th
e w
ater
is li
quid
by
pour
ing
into
ano
ther
con
tain
er.
Ex. G
iven
a g
lass
full
of w
ater
and
an
empt
y gl
ass,
indi
cate
whi
ch o
ne is
full
and
whi
ch o
ne
is em
pty.
124 Common Core Essential Elements
Fift
h G
rad
e M
ath
emat
ics
Stan
dar
ds:
Geo
met
ry
CCSS
Gra
de-L
evel
Clu
ster
sCo
mm
on C
ore
Esse
ntial
Ele
men
tsIn
stru
ction
al A
chie
vem
ent L
evel
Des
crip
tor
Gra
ph p
oint
s on
the
coor
dina
te
plan
e to
sol
ve re
al-w
orld
and
m
athe
mati
cal p
robl
ems.
5.G
.1. U
se a
pai
r of p
erpe
ndic
ular
nu
mbe
r lin
es, c
alle
d ax
es, t
o de
fine
a co
ordi
nate
syst
em, w
ith
the
inte
rsec
tion
of th
e lin
es (t
he
orig
in) a
rran
ged
to c
oinc
ide
with
th
e 0
on e
ach
line
and
a gi
ven
poin
t in
the
plan
e lo
cate
d by
usin
g an
or
dere
d pa
ir of
num
bers
, cal
led
its c
oord
inat
es.
Und
erst
and
that
th
e fir
st n
umbe
r ind
icat
es h
ow
far t
o tr
avel
from
the
orig
in in
th
e di
recti
on o
f one
axi
s, a
nd th
e se
cond
num
ber i
ndic
ates
how
far
to tr
avel
in th
e di
recti
on o
f the
se
cond
axi
s, w
ith th
e co
nven
tion
that
the
nam
es o
f the
two
axes
and
th
e co
ordi
nate
s cor
resp
ond
(e.g
., x-
axis
and
x-co
ordi
nate
, y-a
xis a
nd
y-co
ordi
nate
).
5.G
.2. R
epre
sent
real
wor
ld a
nd
mat
hem
atica
l pro
blem
s by
grap
hing
po
ints
in th
e fir
st q
uadr
ant o
f the
co
ordi
nate
pla
ne, a
nd in
terp
ret
coor
dina
te v
alue
s of p
oint
s in
the
cont
ext o
f the
situ
ation
.
5.G
.3. U
nder
stan
d th
at a
ttrib
utes
be
long
ing
to a
cat
egor
y of
two-
dim
ensio
nal fi
gure
s also
bel
ong
to
all s
ubca
tego
ries o
f tha
t cat
egor
y.
For e
xam
ple,
all
rect
angl
es h
ave
four
righ
t ang
les a
nd sq
uare
s are
re
ctan
gles
, so
all s
quar
es h
ave
four
rig
ht a
ngle
s.
5.G
.4. C
lass
ify tw
o-di
men
siona
l fig
ures
in a
hie
rarc
hy b
ased
on
prop
ertie
s.
EE5.
G.1
-5. S
ort t
wo-
dim
ensio
nal
figur
es a
nd d
escr
ibe
the
com
mon
att
ribut
es su
ch a
s an
gles
, num
ber o
f sid
es, c
orne
rs
(dim
ensio
n), a
nd c
olor
.
Leve
l IV
AA
Stu
dent
s w
ill:
EE5.
G.1
-5. S
ort i
nto
quad
rant
tabl
es a
nd d
escr
ibe
figur
es b
y tw
o co
mm
on a
ttrib
utes
.Ex
. Sor
t figu
res b
y co
lor a
nd sh
ape.
Ex. S
ort fi
gure
s by
cong
ruen
t and
non
-con
grue
nt.
Ex. S
ort fi
gure
s by
angl
e an
d nu
mbe
r of s
ides
.
Blue
cir
cles
Red
circ
les
Blue
squ
ares
Red
squa
res
Leve
l III
AA
Stu
dent
s w
ill:
EE5.
G.1
-5. S
ort t
wo-
dim
ensio
nal fi
gure
s and
des
crib
e th
e co
mm
on a
ttrib
utes
such
as
angl
es, n
umbe
r of s
ides
, cor
ners
(dim
ensio
n), a
nd c
olor
.Ex
. Giv
en sh
apes
, sor
t by
angl
es a
nd in
dica
te h
ow y
ou so
rted
them
.Ex
. Giv
en sh
apes
sort
ed b
ased
on
the
num
ber o
f sid
es, s
ort t
hem
by
anot
her a
ttrib
ute.
Leve
l II A
A S
tude
nts
will
:EE
5.G
.1-5
. Sor
t figu
res b
ased
on
a gi
ven
attrib
ute.
Ex. S
ort fi
gure
s by
shap
e.Ex
. Sor
t figu
res b
y siz
e.
Leve
l I A
A S
tude
nts
will
:EE
5.G
.1-5
. Ind
icat
e tw
o-di
men
siona
l sha
pes n
amed
.Ex
. Tou
ch th
e ro
ugh
tria
ngle
.Ex
. Tou
ch th
e ci
rcle
.
Math | Kindergarten-5 Grade 125
Acute triangle. A triangle with all acute angles (acute means measuring less than 90°). See http://www.mathsisfun.com/definitions/acute-triangle.html
Angles. A shape formed by two lines or rays that diverge from a common point or vertex.
Area. The size of a region enclosed by the figure. Area is measured in square units (e.g., the area of this rectangle is six square units).
Associative property for addition. The sum of three or more numbers which are always the same when added together, no matter what order they are in. This is illustrated by a + (b + c) = (a + b) + c; 2 + (3 + 4) = (2 + 3) + 4.
Associative property for multiplication. The product of three or more numbers which are always the same when multiplied together, regardless of their grouping. This is illustrated by a(bc) = (ab)c; 2(3×4) = (2×3)4.
Attributes. For math purposes, “attributes” refer to characteristics of an object or geometric shape. These include qualities of shape, color, size, side, length, etc.
Base ten blocks. Blocks used to learn place value, addition, subtraction, multiplication, and division. Base ten blocks consist of cubes (ones place), rods (tens place), flats (hundreds place), and blocks (thousands place).
Categorical data. Types of data, which may be divided into groups such as race, sex, age group, and educational level when categorized into a small number of groups.
Commutative property of addition. The sum of numbers are always the same when added together, no matter if the order of the addends are changed. This is illustrated by a + b = b + a (2 + 1 = 1 + 2).
Commutative property of multiplication. The product of numbers are always the same when multiplied together, even if the order of factors are changed (i.e., if a and b are two real numbers, then a × b = b × a.)
Compose numbers. To combine parts/components to form a number (adding parts to obtain a number).
Congruent figures. Figures that have the same size and shape.
Congruent/congruence. The same.
Decompose numbers. The process of separating numbers into their components (to divide a number into smaller parts). Example: 456 can be decomposed as 456 = 400 + 50 + 6.
Denominator. The “bottom” number of a fraction; the number that represents the total number of parts into which one whole is divided (e.g., in 3/4, the 4 is the denominator and indicates that one whole is divided into 4 parts).
Dividend. The number that is being divided (e.g., In the problem, there are 550 pencils; each pack has 10 pencils; how many packs are there? 550 ÷ 10 = 55, 550 is the dividend because it tells how many pencils there are in all to be divided.).
GLOSSARY & EXAMPLES OF MATHEMATICS TERMS
126 Common Core Essential Elements
Divisor. A number by which another number is divided (e.g., In the problem, there are 550 pencils; each pack has 10 pencils; how many packs are there? 550 ÷ 10 = 55, 10 is the divisor because it tells how many times 550 is to be divided.
Edge. The line segment where two faces of a solid figure meet (i.e., a cube has 12 edges).
ELA. English Language Arts
Equation. A mathematical sentence of equality between two expressions; equations have an equal sign (e.g., n + 50 = 75 or 75 = n + 50 means that n + 50 must have the same value as 75).
Equilateral triangle. A triangle with all three sides of equal length, corresponding to what could also be known as a “regular” triangle – an equilateral triangle is therefore a special case of an isosceles triangle having not just two but all three sides equal. An equilateral triangle also has three equal angles. See http://www.mathsisfun.com/definitions/equilateral-triangle.html
Expression. An operation between numbers that represents a single numeric quantity; expressions do not have an equal sign (e.g., 4r, x+2, y-1).
Face. A plane surface of a three-dimensional figure.
Fact families. Sets of related math facts. For example:Addition fact family: 3 + 5 = 8; 8 - 3 = 5; 5 + 3 = 8; and 8 - 5 = 3Multiplication fact family: 5 x 4 = 20; 20 ÷ 5 = 4; 4 x 5=20; and 20 ÷ 4 = 5
Fair share. In division meaning splitting into equal parts or groups with nothing left over.
Frequency table. A table that lists items and uses tally marks to record and show the number of times they occur.
Functions. A special kind of relation where each x-value has one and only one y-value.
Function table. A table that lists pairs of numbers that show a function.
Inequality. A mathematical sentence in which the value of the expressions on either side of the relationship symbol are unequal; relation symbols used in inequalities include > (greater than) and < (less than) symbols (e.g., 7 > 3, x < y).
Input/output table. A table that lists pairs of numbers that show a function.
Integers. Positive and negative whole numbers.
Interlocking cubes. Manipulatives that help students learn number and math concepts - cubes represent “units” and link in one direction. Interlocking cubes are used for patterning, grouping, sorting, counting, numbers, addition, subtraction, multiplication, division, and measurement.
Intersecting lines. Lines that cross.
Inverse operations. Opposite/reverse operations (e.g., subtraction is the inverse operation of addition, which is why 4 + 5 = 9 and 9 – 5 = 4; division is the inverse operation of multiplication, which is why 4 x 5 = 20 and 20 ÷ 5 = 4).
Math | Kindergarten-5 Grade 127
Linear equation. An equation that is made up of two expressions set equal to each other (e.g., y = 2x + 5) - A linear equation has only one or two variables and graph as a straight line. See http://www.eduplace.com/math/mathsteps/7/d/index.html
Line graph. A graphical representation using points connected by line segments to show how something changes over time.
Lines of symmetry. Any imaginary line along which a figure could be folded so that both halves match exactly.
Manipulatives. Objects that are used to explore mathematical ideas and solve mathematical problems (e.g., tools, models, blocks, tiles cubes, geoboards, colored rods, M&M’s).
Mathematical structures.
Addition – compare-total unknownEx. If Anita has 10 sheets of paper and you have 10 more sheets than Anita. How many sheets do you have?
Addition – start unknownEx. Sam gave away 10 apples and has five apples left. How many apples did he start have before he gave 10 apples?
Addition join-part/part – wholeEx. Jessie had 20 cakes and bought five more. How many does he have now?
Subtraction – classic take awayEx. If Judy had $50 and spent $10, how much does she have left?
Subtraction – difference unknownEx. Sandi has 10 cats and 20 dogs. Which does she have more of, cats or dogs? How many more?
Subtraction – deficit missing amountEx. Sandy wants to collect 35 cards and she already has 15. How many more cards does she need?
Multiplication – repeated additionEx. James got paid $5 each day for five days. How much money did he have at the end of the five days?
Multiplication – arrayEx. Carlos wanted to cover his rectangular paper with one-inch tiles. If his paper is five inches long and four inches wide, how many tiles will it take to cover the paper?
Multiplication – fundamental counting principleEx. Julie packed four shirts and four jeans for her trip. How many outfits can she make?
Division – repeated subtractionEx. James pays $5 each day to ride the bus. How many days can he ride for $20?
Division – factor/area – side lengthEx. Tim wants to know the width of a rectangular surface covered in 20 one-inch tiles. He knows the length is five inches, but what is the width?
128 Common Core Essential Elements
Division – partitive/fair shareEx. Julie has 20 different outfits. She has five shirts – how many pair of jeans does she have to make 20 different outfits?
Mean. The “average” – To find the mean, add up all the numbers and then divide by the number of numbers.
Median. The “middle” value in the list of numbers - To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list.
Minuend. The number one is subtracting from (e.g., 9 in 9 – 2 = __).
Mode. The value that occurs most often - If no number is repeated, then there is no mode for the list. See http://www.purplemath.com/modules/meanmode.htm
Models. Pictorial or tactile aids used explore mathematical ideas and solve mathematical problems – Manipulatives can be used to model situations.
Non-numeric patterns. Using symbols, shapes, designs, and pictures to make patterns (e.g., □□ΔΔ◊◊□□ΔΔ◊◊).
Non-standard units of measure. Measurements that are neither metric nor English (e.g., number of footsteps used to measure distance or using a piece of yarn used to measure length).
Number line. A diagram that represents numbers as points on a line; a number line must have the arrows at the end.
Number sentence. An equation or inequality using numbers and symbols that is written horizontally (e.g., 5 < 7 or 5 +7+12).
Numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Numeric patterns. A pattern that uses skip counting, often starting with the number 1 or 2 – Counting by tens and twos may also be presented to students beginning with different numbers such as 7 or 23; this is more difficult for students but indicates a deeper understanding of skip counting (e.g., 7, 17, 27, 37, 47, . . . or 7, 9, 11, 13, 15, 17).
Numerical expression. A mathematical phrase that involves only numbers and one or more operational symbols.
Obtuse triangle. A triangle that has one obtuse angle (obtuse means measuring more than 90°). See http://www.mathsisfun.com/definitions/obtuse-triangle.html
Operations. Addition, subtraction, multiplication, and division.
Ordered pair. In the ordered pair (1, 3), the first number is called the x-coordinate; the second number is called the y-coordinate; this ordered pair represents the coordinates of point A.• The x-coordinate tells the distance right (positive) or left (negative).• The y-coordinate tells the distance up (positive) or down (negative).
Math | Kindergarten-5 Grade 129
Parallel Lines. Lines that are the same distance apart and that never intersect – Lines that have the same slope are parallel.
Pattern. Patterns with a minimum of three terms• using numbers by repeatedly adding or subtracting (i.e., 2, 4, 6, 8, 10, 12; 0, 3, 6, 9, 12, 15;
or 50, 45, 40, 35, 30, 25).• using objects, figures, colors, sound, etc. - a repeated pattern needs to be at least six terms.
Extend a pattern - When a student is asked to continue a pattern, the pattern is presented, and the student is asked, “What comes next?” before a student can extend or describe a pattern, the given pattern must be comprised of a minimum of three terms so that the student can see the regularities of the situation and extend or describe the pattern based on those regularities.
Percent. A way of expressing a fraction as “out of 100” (e.g., 50% means 50 out of 100 or 50/100).
Perpendicular lines. Lines that intersect, forming right angles.
Polygon. A closed plane figure made by line segments.
Prediction. A guess based on available information.
Quadrilateral. A four-sided polygon.
Rational numbers. Any number that can be expressed as a/b (b≠0) where a and b are integers; also, in decimal form, any terminating or ultimately repeating decimal.
Ratios. A comparison between two things. For instance, someone can look at a group of people and refer to the “ratio of boys to girls” in the class. Suppose there are 35 students, 15 of whom are boys; the ratio of boys to girls is 15 to 20. See http://www.purplemath.com/modules/ratio.htm
Real-life situations. Ways in which mathematical concepts are used in real life.
Real numbers. All numbers on a number line, including negative and positive integers, fractions, and irrational numbers.
Real-world applications. Ways in which mathematical concepts are used in real-life situations.
Rectangle. A four-sided polygon (a flat shape with straight sides) where every angle is a right angle (90°); opposite sides are parallel and of equal length.
Right triangle. A triangle that has one right angle (a right angle measures exactly 90°) – Only a single angle in a triangle can be a right angle or it would not be a triangle. A small square is used to mark which angle in the figure is the right angle.
Sets. A group or collection of things that go together (e.g., a group of four stars).
130 Common Core Essential Elements
Side. In most general terms, a line segment that is part of the figure - it is connected at either end to another line segment, which, in turn, may or may not be connected to still other line segments.
Similar figures. Figures that have the same shape but different sizes.
Similar shapes. Objects of the same shape but different sizes in which the corresponding angles are the same.
Slope. The steepness/incline/grade of a line.
Positive slope – the condition in which a line inclines from left to right.
Negative slope – the condition in which a line declines from left to right.
Square. A four-sided polygon (a flat shape with straight sides) where all sides have equal length and every angle is a right angle (90°).
Square root. A value that can be multiplied by itself to give the original number (e.g., the square root of 25 is 5 because 5 x 5 = 25).
Square root notation. Numbers written using a radical √.
Subitize. To judge the number of objects in a group accurately without counting.
Three-dimensional geometric figures. The study of solid figures in three-dimensional space: cube, rectangular prism, sphere, cone, cylinder, and pyramid.
Two-dimensional figures. The study of two-dimensional figures in a plane; drawings of square, rectangle, circle, triangle, pentagon, hexagon, and octagon.
Unknown fixed quantities. A constant that is a quantity; a value that does not change.
Variable. A symbol for an unknown number to be solved; it is usually a letter like x or y (e.g., in x + 3 = 7, x is the variable).
Venn diagram. Made up of two or more overlapping circles. It is often used in mathematics to show relationships between sets. A Venn diagram enables students to organize similarities and differences visually.
Vertex (vertices, pl.). The point(s) where two or more edges meet (corners).
Volume. The amount of three-dimensional space an object occupies; capacity.
Math | Kindergarten-5 Grade 131
Accommodations. Changes in the administration of an assessment, such as setting, scheduling, timing, presentation format, response mode, or others, including any combination of these that does not change the construct intended to be measured by the assessment or the meaning of the resulting scores. Accommodations are used for equity, not advantage, and serve to level the playing field. To be appropriate, assessment accommodations must be identified in the student’s Individualized Education Plan (IEP) or Section 504 plan and used regularly during instruction and classroom assessment.
Achievement descriptors. Narrative descriptions of performance levels that convey student performance at each achievement level and further defines content standards by connecting them to information that describes how well students are doing in learning the knowledge and skills contained in the content standards. (See also “performance descriptors.”)
Achievement levels. A measurement that distinguishes an adequate performance from a Level I or expert performance. Achievement levels provide a determination of the extent to which a student has met the content standards. (See also Performance levels.)
Achievement standard .A system that includes performance levels (e.g., unsatisfactory, Level III, advanced), descriptions of student performance for each level, examples of student work representing the entire range of performance for each level, and cut scores. A system of performance standards operationalizes and further defines content standards by connecting them to information that describes how well students are doing in learning the knowledge and skills contained in the content standards. (See also “performance standards.”)
Achievement test. An instrument designed to efficiently measure the amount of academic knowledge and/or skill a student has acquired from instruction. Such tests provide information that can be compared to either a norm group or a measure of performance, such as a standard.
Age appropriate. The characteristics of the skills taught, the activities and materials selected, and the language level employed that reflect the chronological age of the student.
Alignment. The similarity or match between or among content standards, achievement (performance) standards, curriculum, instruction, and assessments in terms of equal breadth, depth, and complexity of knowledge and skill expectations.
Alternate assessment. An instrument used in gathering information on the standards-based performance and progress of students whose disabilities preclude their valid and reliable participation in general assessments. Alternate assessments measure the performance of a relatively small population of students who are unable to participate in the general assessment system, even with accommodations, as determined by the IEP team.
Assessment. The process of collecting information about individuals, groups, or systems that relies upon a number of instruments, one of which may be a test. Therefore, assessment is a more comprehensive term than test.
Assessment literacy. The knowledge of the basic principles of sound assessment practice including terminology, development, administration, analysis, and standards of quality.
GLOSSARY OF SPECIAL EDUCATION TERMS
132 Common Core Essential Elements
Assistance (vs. support). The degree to which the teacher provides aid to the student’s performance that provides direct assistance in the content or skill being demonstrated by the student. That is, the assistance involves the teacher performing the cognitive work required. Assistance results in an invalidation of the item or score. (See also “support.”)
Assistive technology. A device, piece of equipment, product system, or service that is used to increase, maintain, or improve the functional capabilities of a student with a disability. (See 34 CFR §300.5 and 300.6.)
Cues. Assistance, words, or actions provided to a student to increase the likelihood that the student will give the desired response.
Curriculum. A document that describes what teachers do in order to convey grade-level knowledge and skills to a student.
Depth. The level of cognitive processing (e.g., recognition, recall, problem solving, analysis, synthesis, and evaluation) required for success relative to the performance standards.
Disaggregation. The collection and reporting of student achievement results by particular subgroups (e.g., students with disabilities, limited English Level III students) to ascertain the subgroup’s academic progress. Disaggregation makes it possible to compare subgroups or cohorts.
Essence of the standard. That which conveys the same ideas, skills, and content of the standard, expressed in simpler terms.
Essential Elements (EEs or CCEEs). The Common Core Essential Elements are specific statements of the content and skills that are linked to the Common Core State Standards (CCSS) grade level specific expectations for students with significant cognitive disabilities.
Grade Band Essential Element. A statement of essential precursor content and skills linked to the Common Core State Standards (CCSS) grade level clusters and indicators that maintain the essence of that standard, thereby identifying the grade-level expectations for students with significant cognitive disabilities to access and make progress in the general curriculum.
Grade level. The grade in which a student is enrolled.
Instructional Achievement Level Descriptors (IALDs). Describes student achievement and illustrates student performance. IALDs operationalize and further define Essential Elements by connecting them to information that describes how well students are doing in learning the knowledge and skills contained in the Essential Elements.
Individualized Education Program (IEP). An IEP is a written plan, developed by a team of regular and special educators, parents, related service personnel, and the student, as appropriate, describing the specially designed instruction needed for an eligible exceptional student to progress in the content standards and objectives and to meet other educational needs.
Linked. A relationship between a grade level indicator for Common Core State Standards (CCSS) and Common Core Essential Elements (EEs or CCEEs) that reflects similar content and skills but does not match the breadth, depth, and complexity of the standards.
Math | Kindergarten-5 Grade 133
Multiple measures. Measurement of student or school performance through more than one form or test.• For students, these might include teacher observations, performance assessments or
portfolios.• For schools, these might include dropout rates, absenteeism, college attendance or
documented behavior problems
Natural cue. Assistance given to a student that provides a flow among the expectations presented by the educator, opportunities to learn, and the desired outcome exhibited by the student.
Opportunity to learn. The provision of learning conditions, including suitable adjustments, to maximize a student’s chances of attaining the desired learning outcomes, such as the mastery of content standards.
Readability. The formatting of presented material that considers the organization of text; syntactic complexity of sentences; use of abstractions; density of concepts; sequence and organization of ideas; page format; sentence length; paragraph length; variety of punctuation; student background knowledge or interest; and use of illustrations or graphics in determining the appropriate level of difficulty of instructional or assessment materials.
Real-world application. The opportunity for a student to exhibit a behavior or complete a task that he or she would normally be expected to perform outside of the school environment.
Response requirements. The type, kind, or method of action required of a student to answer a question or testing item. The response may include, but is not limited to, reading, writing, speaking, creating, and drawing.
Stakeholders. A group of individuals perceived to be vested in a particular decision (e.g., a policy decision).
Standardized. An established procedure that assures that a test is administered with the same directions, and under the same conditions and is scored in the same manner for all students to ensure the comparability of scores. Standardization allows reliable and valid comparison to be made among students taking the test. The two major types of standardized tests are norm-referenced and criterion-referenced.
Standards. There are two types of standards, content and achievement (performance).• Content standards. Statements of the subject-specific knowledge and skills that schools are
expected to teach students, indicating what students should know and be able to do.• Achievement (Performance) standards. Indices of qualities that specify how adept or
competent a student demonstration must be and consist of the following four components:levels that provide descriptive labels or narratives for student performance (i.e.,
advanced, Level III, etc.);descriptions of what students at each particular level must demonstrate relative to the
task;examples of student work at each level illustrating the range of performance within each
level; andcut scores clearly separating each performance level.
134 Common Core Essential Elements
Standards-based assessments. Assessments constructed to measure how well students have mastered specific content standards or skills.
Test. A measuring device or procedure. Educational tests are typically composed of questions or tasks designed to elicit predetermined behavioral responses or to measure specific academic content standards.
Test presentation. The method, manner, or structure in which test items or assessments are administered to the student.
Universal design of assessment. A method for developing an assessment to ensure accessibility by all students regardless of ability or disability. Universal design of assessment is based on principles used in the field of architecture in which user diversity is considered during the conceptual stage of development.
*Adapted from the Glossary of Assessment Terms and Acronyms Used in Assessing Special Education Students: A Report from the Assessing Special Education Students (ASES) State Collaborative on Assessment and Student Standards (SCASS)
Math | Kindergarten-5 Grade 135
Council of Chief State School Officers (CCSSO). (2003). Glossary of assessment terms and acronyms used in assessing special education students: A report from the Assessing Special Education Students (ASES) State Collaborative on Assessment and Student Standards (SCASS). Washington, DC: Author. Retrieved from http://www.ccsso.org/Documents/2006/Assessing_Students_with_Disabilities_Glossary_2006.pdf
Education Commission of the States. (1998). Designing and implementing standards-based accountability systems. Denver, CO: Author. Retrieved from http://www.eric.ed.gov/PDFS/ED419275.pdf
Hansche, L. (1998). Handbook for the development of performance standards: Meeting the requirements of Title I. Washington, DC: U.S. Department of Education (ED) and CCSSO. Retrieved from http://www.eric.ed.gov/PDFS/ED427027.pdf
Jaeger, R. M., & Tucker, C. G. (1998). Analyzing, disaggregating, reporting, and interpreting students’ achievement test results: A guide to practice for Title I and beyond. Washington, DC: CCSSO.
Johnstone, C. J. (2003). Improving validity of large-scale tests: Universal design and student performance (Technical Report 37). Minneapolis, MN: University of Minnesota, National Center on Educational Outcomes (NCEO). Retrieved from http://www.cehd.umn.edu/nceo/onlinepubs/technical37.htm.
Lehr, C.,& Thurlow, M. (2003). Putting it all together: Including students with disabilities in assessment and accountability systems (Policy Directions No. 16). Minneapolis, MN: University of Minnesota, NCEO. Retrieved from http://www.cehd.umn.edu/NCEO/onlinepubs/Policy16.htm
Linn, R. L., & Herman, J. L. (1997). A policymaker’s guide to standards-led assessment. Denver, CO: National Center for Research on Evaluation, Standards, and Student Testing (CRESST) & Education Commission of the States (ECS) Distribution Center. Retrieved from http://www.eric.ed.gov/PDFS/ED408680.pdf
McKean, E. (Ed.). (2005). The New Oxford American Dictionary (2nd ed.). New York, NY: Oxford University Press.
Quenemoen, R., Thompson, S., & Thurlow, M. (2003). Measuring academic achievement of students with significant cognitive disabilities: Building understanding of alternate assessment scoring criteria (Synthesis Report 50). Minneapolis, MN: University of Minnesota, NCEO. Retrieved from http://www.cehd.umn.edu/NCEO/onlinepubs/Synthesis50.html
Rabinowitz, S., Roeber, E., Schroeder, C., & Sheinker, J. (2006). Creating aligned standards and assessment systems. Washington, DC: CCSSO. Retrieved from http://www.ccsso.org/Documents/2006/Creating_Aligned_Standards_2006.pdf
Roeber, E. (2002). Setting standards on alternate assessments (Synthesis Report 42). Minneapolis, MN: University of Minnesota, NCEO. Retrieved from http://www.cehd.umn.edu/nceo/OnlinePubs/Synthesis42.html
BIBLIOGRAPHY OF DEVELOPMENT PROCESS
136 Common Core Essential Elements
Sheinker, J. M. (2004, April 26). Achievement standards for alternate assessments: What is standard setting? Teleconference presentation for the National Center for Educational Outcomes to 38 State Departments of Education, Minneapolis, MN. Retrieved from http://www.cehd.umn.edu/nceo/teleconferences/tele08/default.html
Sheinker, J. M., & Redfield, D. L. (2001). Handbook for professional development on assessment literacy. Washington, DC: CCSSO.
Thompson, S. J., Johnstone, C. J., & Thurlow, M. L. (2002). Universal design applied to large scale assessments (Synthesis Report 44). Minneapolis, MN: University of Minnesota, NCEO. Retrieved from http://www.cehd.umn.edu/nceo/onlinepubs/Synthesis44.html
Ysseldyke, J., Krentz, J., Elliott, J., Thurlow, M. L., Erickson, R., & Moore, M. L. (1998). NCEO framework For educational accountability. Minneapolis, MN: University of Minnesota, NCEO. Retrieved from http://www.cehd.umn.edu/NCEO/onlinepubs/archive/Framework/FrameworkText.html
Math | Kindergarten-5 Grade 137
Blaha, R., & Cooper, H. (2009, February 12-14). Academic learners with deafblindness: Providing access to the general curriculum. Paper presented at the Purpose, Satisfaction, and Joy in the Lives of Students with Deafblindness and the People Who Care Conference, Austin, TX. Retrieved from http://www.tsbvi.edu/attachments/handouts/feb09/BlahaCooperAcademAccessGenEd_handout.doc
Browder, D. M. & Spooner, F. (Eds.). (2006). Teaching language arts, math, and science to students with significant cognitive disabilities. Baltimore, MD: Brookes Publishing Co. Retrieved from http://www.brookespublishing.com/store/books/browder-7985/index.htm
Burris, C., Heubert, J., & Levin, H. (2004). Math acceleration for all. Educational Leadership: Improving Achievement in Math and Science, 61(5), 68-71. Alexandria, VA: Association for Supervision and Curriculum Development (ASCD). Retrieved from http://www.ascd.org/publications/educational-leadership/feb04/vol61/num05/Math-Acceleration-for-All.aspx
Clements, D. H. (1999, March). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5(7), 400-405. Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/publications/article.aspx?id=20890
Clements, D. H. (1999, January). Teaching length measurement: Research challenges. School Science and Mathematics, 99(1), 5-11. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/ssm.1999.99.issue-1/issuetoc
Clements, D. H., & Sarama, J. (2010). Technology. In V. Washington & J. Andrews (Eds.), Children of 2020: Creating a better tomorrow (pp. 119-123). Washington, DC: Council for Professional Recognition/National Association for the Education of Young Children.
Clements, D. H., Sarama, J., & Wolfe, C. B. (2011). Tools for early assessment in mathematics (TEAM). Columbus, OH: McGraw-Hill Education. Retrieved from https://www.mheonline.com/program/view/4/4/335/007TEAM
Cooney, S., & Bottoms, G. (2002). Middle grades to high school: Mending a weak link (Research brief). Atlanta, GA: Southern Regional Education Board. Retrieved from http://publications.sreb.org/2002/02V08_Middle_Grades_To_HS.pdf
Daro, P. (2011, February). Unlocking the common core: Common core state standards. Webinar for the Common Core Virtual Conference, sponsored by Pearson Education. Retrieved from http://commoncore.pearsoned.com/index.cfm?locator=PS1324
Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2006). Learning disabilities: From identification to intervention. New York, NY: Guilford Press.
Ford, R. (2006, January). High school profiles of mathematically unprepared college freshmen. Paper presented at the fourth annual International Conference on Education, Honolulu, HI.
Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficult. Journal of Educational Psychology, 97(3), 493-513.
Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., Schatschneider, C., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98(1), 29-43.
BIBLIOGRAPHY FOR MATHEMATICS CONTENT
138 Common Core Essential Elements
Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., & Fletcher, J. M. (2008). Intensive intervention for students with mathematics disabilities: seven principles of effective practice. Learning Disability Quarterly, 31(2), 79-92. Retrieved from http://www.mendeley.com/research/intensive-intervention-students-mathematics-disabilities-seven-principles-effective-practice-4/
Fuchs, L. S., Powell, S. R., Seethaler, P. M., Fuchs, D., Hamlett, C. L., Cirino, P., & Fletcher, J. M. (2007). Intensive intervention on number combination and story problem deficits in third graders with math difficulties, with and without concurrent reading difficulties. Manuscript submitted for publication.
Fuson, K. C., Clements, D. H., & Beckmann, S. (2010). Focus in Grade 1: Teaching with the curriculum focal points. Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/catalog/product.aspx?id=13628
Ginsburg, A., & Leinwand, S. (2009). Informing Grades 1-6 mathematics standards development: What can be learned from high-performing Hong Kong, Korea, and Singapore? Washington, DC: American Institutes for Research. Retrieved from http://www.air.org/files/MathStandards.pdf
James B. Hunt Jr. Institute for Educational Leadership and Policy. (n.d.). Common core state standards – General brief. Retrieved from http://www.edweek.org/media/fordham_event.pdf
Kroesbergen, E. H., & Van Luit, J.E.H. (2003). Mathematics interventions for children with special needs: A meta-analysis. Remedial and Special Education, 24(2), 97-114. Retrieved from http://rse.sagepub.com/content/24/2/97.abstract
Maccini, P., Mulcahy, C. A., & Wilson, M. G. (2007). A follow-up of mathematics interventions for secdonary students with learning disabilities. Learning Disabilities Research and Practice, 22(1), 58-74. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5826.2007.00231.x/abstract
Miller, S. P., & Hudson, P.J. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research and Practice, 22(1), 47-57. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5826.2007.00230.x/abstract
Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research and Practice, 22(1), 75-83. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5826.2007.00232.x/abstract
National Governors Association for Best Practices (NGA Center) & Council of Chief State School Officers (CCSSO). (2011). The standards: Mathematics. Retrieved from http://www.corestandards.org/the-standards/mathematics.
NGA Center & CCSSO. (2010). Common core state standards for mathematics. Appendix A: Designing high school mathematics courses based on the common core state standards. Retrieved from http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf
Math | Kindergarten-5 Grade 139
Sarama, J., & Clements, D. H. (2010). The mathematical lives of young children. In V. Washington & J. Andrews (Eds.), Children of 2020: Creating a better tomorrow (pp. 81-84). Washington, DC: Council for Professional Recognition/National Association for the Education of Young Children.
Sarama, J., & Clements, D. H. (2009). Teaching math in the primary grades: The learning trajectories approach. Young Children, 64(2), 63-65. Retrieved from http://www.naeyc.org/files/yc/file/Primary_Interest_BTJ.pdf
Schmidt, B., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 1-18. Retrieved from http://www.aft.org/pdfs/americaneducator/summer2002/curriculum.pdf
Swanson, H. L. (2006). Cross-sectional and incremental changes in working memory and mathematical problem solving. Journal of Educational Psychology, 98, 265-281.
Thompson, S. J., Morse, A. B., Sharpe, M., & Hall, S. (2005). Accommodations manual: How to select, administer and evaluate use of accommodations and assessment for students with disabilities (2nd ed.). Washington, DC: CCSSO. Retrieved from http://www.ccsso.org/Documents/2005/Accommodations_Manual_How_2005.pdf
Washington Office of the Superintendent of Public Instruction. (2008). Guidelines for accelerating students into high school mathematics in grade 8. Olympia, WA: Author. Retrieved from http://www.k12.wa.us/Mathematics/Standards/Compression.pdf
Wiley, A., Wyatt, J. & Camara, W. J. (2010). The development of a multidimensional college readiness index (Research Report No. 2010-3). New York, NY: The College Board. Retrieved from http://professionals.collegeboard.com/profdownload/pdf/10b_2084_DevMultiDimenRR_WEB_100618.pdf
140 Common Core Essential Elements
Math | Kindergarten-5 Grade 141
APPENDIX A
SEA/STAKEHOLDER DEMOGRAPHICS
142 Common Core Essential Elements
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Barb
ara
Adam
sIA
No
resp
onse
K-12
Mat
hem
atics
Cu
rric
ulum
Co
ordi
nato
r
No
resp
onse
No
resp
onse
Cauc
asia
n20
-25
PhD
Roul
a Al
Mou
abbi
MI
Seco
ndar
y M
ath
6-12
; Bili
ngua
l Ar
abic
/Fre
nch
6-12
HS B
iling
ual
Alge
bra/
Geom
etry
. Co
llege
Alg
ebra
9-11
and
Co
llege
Arab
ic, F
renc
h, A
fric
anCa
ucas
ian
20-2
5M
A
Robi
n Ba
rbou
rN
CAl
l Sub
ject
s 4-6
; 6-9
M
ath
and
Scie
nce;
AI
G ce
rtific
ation
Seco
ndar
y M
ath
Cons
ulta
nt fo
r NC
Dept
. of P
ublic
In
stru
ction
7-8
Mat
h;
9th
Phys
ical
Sc
ienc
e; A
lgeb
ra
1; In
tegr
ated
M
ath
Gene
ral E
duca
tion
with
in
clus
ion
expe
rienc
eCa
ucas
ian
20-2
5M
A
Tam
ara
Barr
ient
osM
IK-
5 El
emen
tary
; 6-8
M
ath/
Scie
nce
Dire
ctor
, Sag
inaw
Va
lley
Stat
e U
nive
rsity
Reg
iona
l M
athe
mati
cs a
nd
Scie
nce
Cent
er
6-8
Mat
hN
/AHi
span
ic11
-15
MA
DiRa
e Bo
ydKS
Core
Con
tent
Mes
h K-
6; E
lem
enta
ry
K-9;
LD
K-9;
MR
K-9;
SPE
D EL
A K-
9;
SPED
Hist
ory
and
Gove
rnm
ent K
-9;
SPED
Mat
h K-
9; S
PED
Scie
nce
K-9
Func
tiona
l 6-8
inte
r-re
late
d te
ache
r Sp
ecia
l Ed
ucati
on 6
-8;
Sum
mer
Sch
ool
to K
-12
Spec
ial
Educ
ation
MR;
S/P
; Auti
sm; E
D;
DB; M
D: H
I; O
HI; T
BI; L
DCa
ucas
ian
16-2
0BA
Lynd
a Br
own
UT
ESL/
Elem
Mat
h/Ea
rly C
hild
hood
En
dors
emen
t
Mat
h Co
ach
K-6
(4
scho
ols,
gen
eral
and
sp
ecia
l ed.
)
2-6
Gene
ral
Educ
ation
Spec
ial E
duca
tion
and
Incl
usio
nCa
ucas
ian
30+
MED
Sue
Burg
erN
JEl
emen
tary
/ Te
ache
r of
Hand
icap
ped
Spec
ial E
duca
tion/
Cu
rric
ulum
Sp
ecia
list
HS R
esou
rce
HS R
esou
rce;
Auti
sm;
OHI
; MLD
; BD;
Pr
esch
ool D
isabl
ed
Cauc
asia
n30
+BA
Jenn
ifer B
urns
OK
Spec
ial E
duca
tion
– al
l con
tent
sAs
sess
men
t Co
ordi
nato
r for
Sp
ecia
l Edu
catio
n Se
rvic
es fo
r Sta
te
Dept
. of E
d.
Spec
ial
Educ
ation
Pre
-K
and
6-8
S/P;
MI/
MO
Cauc
asia
n6-
10M
ED/
MS
John
But
zIA
Mat
h K-
8; K
-6
Elem
enta
ry
Educ
ation
2nd
grad
e te
ache
r5t
h gr
ade
Inst
ructi
on o
f Spe
cial
Ed
ucati
on in
Gen
eral
Ed
ucati
on c
lass
room
Cauc
asia
n16
-20
BA
Math | Kindergarten-5 Grade 143
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Laur
el C
akin
berk
IASp
ecia
l Edu
catio
n St
rate
gist
IISp
ecia
l Edu
catio
nM
iddl
e/HS
MO
/S/P
Cauc
asia
n11
-15
MA
Shar
on C
ampi
one
MO
LD 1
-8; M
H/BD
K-9
; Sp
ec E
d Ad
min
K-1
2;
Prin
cipa
l K-1
2
Func
tiona
l, Li
fe
Skill
s, S
elf-c
onta
ined
4-
6
Mid
dle
Scho
ol
7-8/
Spec
ial
Educ
ation
SSD
Coor
dina
tor;
Teac
her A
ssist
seve
re
popu
latio
n
Cauc
asia
n16
-20
MS
Wen
dy C
arve
rU
TCo
mm
unic
ation
Di
sord
ers/
Spec
ial
Educ
ation
K-1
2+;
Spee
ch L
angu
age
Path
olog
y,
Psyc
holo
gy, M
ild/
Mod
Dis,
ELA
Spec
ial E
duca
tion
Asse
ssm
ent
Spec
ialis
t
Spec
ial
Educ
ation
K-1
2+ M
I/M
O/S
Cauc
asia
n30
+M
S
Beth
Cip
oletti
WV
Mat
h 7-
12As
sista
nt
Dire
ctor
, Offi
ce o
f As
sess
men
t and
Ac
coun
tabi
lity
Mat
h 7-
12
and
colle
ge;
taug
ht te
ache
r pr
epar
ation
co
urse
s (m
athe
mati
cs)
Incl
usio
n Cl
asse
sCa
ucas
ian
30+
EdD
Emily
Com
bsM
OM
ath
5-9/
ELA
5-9
Mat
h 7t
h gr
ade
Gene
ral
Educ
ation
Gra
de
6
Incl
usio
n; sp
ecia
l se
rvic
e, IE
PCa
ucas
ian
11-1
5M
S
Sidn
ey C
oole
yKS
Mat
h; S
peci
al
Educ
ation
Stat
e M
athe
mati
cs
Cons
ulta
ntGe
nera
l Ed
ucati
on 7
-12
Inte
grat
ed M
ath
grad
es
7-9;
Sta
te L
D co
nsul
tant
Cauc
asia
n30
+Ph
D
Shirl
ey C
oope
rN
JM
ath
Stat
e M
athe
mati
cs
Coor
dina
tor
Gene
ral
Educ
ation
Incl
usio
nAf
rican
Am
eric
an30
+M
S
Jeff
Craw
ford
WA
Mat
hHS
Mat
h, 9
-12
Colle
ge
Mat
hem
atics
Low
SES
Cauc
asia
n16
-20
MS
Amy
Daug
hert
yO
KSp
ecia
l Edu
catio
n –
All c
onte
nts
Asso
ciat
e St
ate
Dire
ctor
for S
peci
al
Educ
ation
Ser
vice
s,
Stat
e De
pt. o
f Ed.
Spec
ial
Educ
ation
K-1
2S/
P; E
moti
onal
Di
stur
bed
Cauc
asia
n6-
10BS
John
DeB
ened
ettiW
ASp
ecia
l Edu
catio
n4-
5 Ex
tend
ed
Reso
urce
N/A
Spec
ial E
duca
tion
teac
her
Cauc
asia
n6-
10BS
144 Common Core Essential Elements
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Thom
as D
eete
rIA
NA
Lead
Con
sulta
nt
(Gen
eral
Edu
catio
n)
Asse
ssm
ent,
Acco
unta
bilit
y,
Prog
ram
Eva
luati
on
Gene
ral
Educ
ation
Asia
n-Ca
ucas
ian
20-2
5Ph
D
Jenn
ie D
eFrie
zU
TAd
min
istra
tive/
Su
perv
isory
Ce
rtific
ation
; Lev
el 2
M
ath
endo
rsem
ent;
Leve
l 2 E
lem
enta
ry
Educ
ation
Lic
ense
, m
iddl
e le
vel
educ
ation
Uta
h St
ate
Offi
ce
of E
duca
tion
Elem
enta
ry M
ath
Asse
ssm
ent
Spec
ialis
t/As
sista
nt
Spec
ial E
duca
tion
Asse
ssm
ent
Spec
ialis
t
Gene
ral
Educ
ation
Gr
ades
4-7
; M
ath/
Scie
nce
Assis
tant
to S
tate
Sp
ecia
l Edu
catio
n As
sess
men
t Spe
cial
ist
Cauc
asia
n11
-15
MED
Kirs
ten
Dlug
oW
A6-
8 EL
A, M
ath,
Re
adin
g an
d Sp
ecia
l Ed
ucati
on
Spec
ial E
duca
tion
Teac
her 6
-8, L
ife
Skill
s Cla
ssro
om
Ung
rade
d cl
assr
oom
for
blin
d ag
es 1
2-16
VI; D
B; A
ut; M
D; L
D;
BD, I
DCa
ucas
ian
6-10
MED
Ambe
r Eck
esW
IEl
emen
tary
Ed
ucati
on a
nd L
D;
Read
ing
Teac
her
Spec
ial E
duca
tion
Man
ager
Gra
des 6
-8Re
adin
g 6-
8;
Mat
h 6-
8 an
d su
mm
er c
lass
es
K-3
Spec
ial E
duca
tion
man
ager
/tea
cher
Cauc
asia
n6-
10BS
John
Eise
nber
gVA
Spec
ial E
duca
tion
Virg
inia
Dep
artm
ent
of E
duca
tion
Dire
ctor
of
Inst
ructi
onal
Su
ppor
t and
Rel
ated
Se
rvic
es
Spec
ial
Educ
ation
ASD;
SD;
IDCa
ucas
ian
11-1
5M
S
Lin
Ever
ettM
OK-
5 Ad
min
istra
tor/
Prin
cipa
l; 4-
8 SS
; K-8
Ge
nera
l Edu
catio
n:
Life
time
Certi
ficat
e;
4-8
Mid
dle
Scho
ol
Adm
in/P
rinci
pal;
Supe
rinte
nden
t’s
certi
ficati
on, K
-12
MO
Dep
t. of
Ed
ucati
on A
ssist
ant
Dire
ctor
of
Asse
ssm
ent/
Offi
ce
of C
CR
Self-
cont
aine
d 1-
4; E
LA M
iddl
e;
Prin
cipa
l K-8
, M
etho
ds fo
r pr
e-se
rvic
e te
ache
rs/
Uni
vers
ity
Spec
ial E
d Co
ordi
nato
rCa
ucas
ian
30+
EdS
Math | Kindergarten-5 Grade 145
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Dagn
y Fi
dler
IADi
rect
or o
f Spe
cial
Ed
ucati
on; P
K-12
Pr
inci
pal;
PK-1
2 Sp
ecia
l Edu
catio
n Su
perv
isor
Vice
-Prin
cipa
l/Sp
ecia
l Edu
catio
n Su
perv
isor (
focu
s on
stud
ents
with
SCD
)
Spec
ial
Educ
ation
K-
12, C
olle
ge
inst
ructi
on
Focu
s on
stud
ents
with
sig
nific
ant d
isabi
lities
Cauc
asia
n30
+Ph
D
Kim
Fra
ttoU
TU
nder
revi
ewDi
stric
t Lev
el
Teac
her S
peci
alist
fo
r Stu
dent
s w/
Sign
ifica
nt C
ogni
tive
Disa
biliti
es
K-6
Spec
ial
Educ
ation
K-6
Reso
urce
Teac
her;
Incl
usio
n Sp
ecia
list;
Spec
ial E
duca
tion
Coor
dina
tor;
Teac
her
spec
ialis
t K-1
2+,
Teac
her S
peci
alist
, st
uden
ts w
ith S
CD
Cauc
asia
n11
-15
MS
Rose
mar
y Ga
rdne
rW
IEl
emen
tary
Ed
ucati
on 1
-8; S
SLD
PreK
-12;
Prin
cipa
l; Di
rect
or o
f Spe
cial
Ed
ucati
on; P
upil
Serv
ices
Spec
ial E
duca
tion;
Ed
ucati
onal
Pr
ogra
mm
er
Gene
ral
Educ
ation
1 &
2,
and
Spe
cial
Ed
ucati
on
inte
rmed
iate
an
d m
iddl
e sc
hool
Spec
ial E
duca
tion
Teac
her/
Supp
ort A
dmin
Cauc
asia
n26
-30
MS
Mel
issa
Ghol
son
WV
Mul
ti-Su
bjec
ts K
-8;
Men
tal I
mpa
irmen
ts,
Autis
m, B
ehav
ior
Diso
rder
s, S
peci
fic
LD K
-21;
Prin
cipa
l an
d Su
perin
tend
ent
WV
Dept
. of
Educ
ation
, Offi
ce
of A
sses
smen
t and
Ac
coun
tabi
lity,
Al
tern
ate
Asse
ssm
ent a
nd
Acco
mm
odati
ons
Elem
enta
ry
(gen
eral
an
d sp
ecia
l ed
ucati
on),
Mid
dle
Scho
ol
(spe
cial
ed
ucati
on);
High
Sc
hool
(gen
eral
an
d sp
ecia
l ed
ucati
on),
, Co
llege
(tea
cher
pr
epar
ation
co
urse
s)
Supe
rviso
r of S
peci
al
Educ
ation
; Spe
cial
ed
ucati
on te
achi
ng
expe
rienc
e w
ith a
utism
, m
ild, m
oder
ate,
seve
re
and
prof
ound
, men
tal
impa
irmen
ts, b
ehav
ior
diso
rder
s, g
ifted
and
le
arni
ng d
isabi
lities
Cauc
asia
n16
-20
MA
Debr
a Ha
wki
nsW
AES
EA S
choo
l Ps
ycho
logy
Dire
ctor
Cla
ssro
om
Asse
ssm
ent
Inte
grati
on
Gene
ral
Educ
ation
Pos
t-Se
cond
ary
Leve
l
Prof
ound
ly M
enta
lly
Hand
icap
ped
Cauc
asia
n20
-25
EdD
146 Common Core Essential Elements
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Lind
a Ho
wle
yM
ISt
ate
Educ
ation
As
sess
men
t Re
pres
enta
tive
Stat
e Ed
ucati
on
Asse
ssm
ent
Repr
esen
tativ
e
Cauc
asia
n11
-15
MS
Ange
lita
Jagl
aW
AEl
emen
tary
K-8
; Te
ache
r of E
nglis
h as
a
Seco
nd L
angu
age;
Re
adin
g an
d M
ath
M.S
. Ed;
NBC
T
Gene
ral E
duca
tion–
4t
h gr
ade
Spec
ial E
duca
tion,
low
SE
S, E
LLM
exic
an-
Amer
ican
6-10
MS
Bria
n Jo
hnso
nW
ISp
ecia
l Edu
catio
nSp
ecia
l Edu
catio
nCD
; Auti
sm; E
BDCa
ucas
ian
6-10
MS
Mar
yAnn
Jose
phN
JN
BCT;
Mid
dle
Child
hood
Ge
nera
list;
Spec
ial
Educ
ation
K-1
2
Spec
ial E
duca
tion
Cons
ulta
nt N
JDO
E/O
SEP
Spec
ial
Educ
ation
Se
vere
/Pr
ofou
nd,
Mid
dle
Scho
ol;
5-6
In C
lass
Re
sour
ce
Plan
ning
(s
peci
al e
d),
self-
cont
aine
d cl
assr
oom
age
s 7-
11; G
ener
al
and
Spec
ial
Educ
ation
Pr
e-K-
1
Seve
re/P
rofo
und;
Le
arni
ng D
isabl
ed K
-8Ca
ucas
ian
30+
MED
Sara
Kin
gM
ON
o re
spon
seSp
ecia
l Edu
catio
n ag
es 1
8-20
Spec
ial
Educ
ation
age
s 14
-20
Spec
ial E
duca
tion
Cauc
asia
n6-
10M
A
Tere
sa K
raft
KSEd
ucati
on o
f the
De
afCu
rric
ulum
and
As
sess
men
t Co
ordi
nato
r, KS
Sc
hool
for t
he D
eaf
Deaf
/HO
H/M
ulti-
hand
icap
ped;
Visu
al
Impa
irmen
ts
Cauc
asia
n30
+M
ED
Trac
ey L
ank
NJ
Spec
ial E
duca
tion
Spec
ial E
duca
tion
3-5
grad
esSp
ecia
l Ed
ucati
on 1
, 2,
and
6th
grad
es
Mul
tiple
Disa
biliti
esCa
ucas
ian
1-5
Rond
a La
yman
NC
Spee
ch L
angu
age;
EC
Adm
inist
ratio
nEC
Lea
d Te
ache
r/SL
P-Au
tism
and
low
in
cide
nce
Autis
m; S
ever
e/Pr
ofou
ndCa
ucas
ian
20-2
5M
ED
Math | Kindergarten-5 Grade 147
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Wes
ley
Lilly
WV
Spec
ial E
duca
tion
K-Ad
ult (
MI,
LD,
BD, A
utism
, Sev
ere
Men
tal D
isabi
lities
; Se
cond
ary
Educ
ation
; K-1
2 (P
hysic
al E
duca
tion)
Seco
ndar
y Sp
ecia
l Ed
ucati
on M
I/Se
vere
/Auti
sm
Spec
ial
Educ
ation
K-8
M
I/Se
vere
/Au
tism
/LD/
BD
MI/
Seve
re/
Autis
m/L
D/BD
; wor
ked
with
des
igni
ng a
ltern
ate
asse
ssm
ent
Cauc
asia
n6-
10M
A
Dian
e Lu
cas
VAEl
emen
tary
Rea
ding
, M
ath,
Soc
ial S
tudi
es,
and
Scie
nce
Spec
ial E
duca
tion
Clas
sroo
m R
esou
rce
Teac
her (
AT Te
am
Lead
er)
Early
Chi
ldho
od
Spec
ial
Educ
ation
Spec
ial E
duca
tion
pre
K-12
, ID,
SD,
Auti
sm, L
DCa
ucas
ian
30+
MS
Mic
hele
Luk
saKS
Seve
re D
isabi
lities
Spec
ial E
duca
tion
Cons
ultin
g Te
ache
r fo
r Ele
men
tary
Spec
ial
Educ
ation
Co
nsul
ting
Teac
her 5
-12
Seve
re D
isabi
lities
; De
af-B
lind,
Auti
smCa
ucas
ian
26-3
0M
A
Debo
rah
Matt
hew
sKS
Stud
ents
with
Si
gnifi
cant
Cog
nitiv
e Di
sabi
lities
and
Ear
ly
Child
hood
Kans
as S
tate
De
part
men
t of
Educ
ation
Early
chi
ldho
od-
high
scho
olEa
rly C
hild
hood
; St
uden
ts w
ith
Sign
ifica
nt C
ogni
tive
Disa
biliti
es
Cauc
asia
n20
-25
MS
Mel
issa
Mob
ley
WV
Autis
m/M
enta
l Im
pairm
ent
Supe
rviso
r of
Spec
ial E
duca
tion
– Au
tism
and
all
leve
ls of
men
tal
impa
irmen
t
Autis
m K
-8Au
tism
; Men
tal
Impa
irmen
ts P
reK-
Adul
tCa
ucas
ian
6-10
MA
Lisa
New
WV
Mat
h 7-
12; B
usin
ess
Prin
cipl
es 7
-12
HS A
lgeb
ra I,
Al
gebr
a su
ppor
t te
ache
r
Gene
ral
Educ
ation
Gr
ades
5-1
2
Team
teac
her;
incl
usio
n;
item
writi
ng fo
r al
tern
ate
asse
ssm
ent
Cauc
asia
nN
ative
Am
eric
an
20-2
5M
S
Kare
n Pa
ceM
OM
ath
7-12
HS M
ath
Teac
her
Gene
ral
Educ
ation
Mat
h 7-
9
LD, B
D, E
LL, l
ow S
ESCa
ucas
ian
30+
MED
148 Common Core Essential Elements
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Brai
n Pi
anos
iM
ISe
lf-co
ntai
ned
Elem
enta
ry 6
-8
Mat
h/Sc
ienc
e; K
-12
Spec
ial E
d.; C
ogni
tive
Impa
irmen
t Ad
min
istra
tion
– ce
rtifie
d el
emen
tary
pr
inci
pal,
supe
rviso
r an
d di
rect
or
certi
ficati
ons i
n sp
ecia
l ed.
Dire
ctor
of a
Ce
nter
-bas
ed sc
hool
se
rvin
g st
uden
ts
with
Mod
erat
e to
Se
vere
Cog
nitiv
e,
seve
re m
ultip
le
impa
irmen
ts,
autis
m; b
ehav
ior
need
s
Gene
ral
Educ
ation
3rd
gr
ade;
Spe
cial
Ed
ucati
on
HS C
ross
Ca
tego
rical
Deaf
son;
Dau
ghte
r with
LD
; Spe
cial
Oly
mpi
cs
volu
ntee
r
Cauc
asia
n20
-25
MA
Mar
y Ri
char
dsW
IW
I Edu
cato
r Gra
des
1-8
Mat
h Co
ach
PK-8
Gene
ral
Educ
ation
K-6
; Ti
tle I
Mat
h 1-
4; G
ifted
and
Ta
lent
ed G
rade
s 1-
5
Incl
usio
nCa
ucas
ian
30+
MS
Laur
a Sc
earc
eVA
Mat
h Sp
ecia
list K
-8M
ath
Coac
h K-
5In
clus
ion
Grad
es
3 an
d 5
Incl
usio
n; G
ifted
and
Ta
lent
edCa
ucas
ian
11-1
5M
ED
Lisa
Sei
pert
UT
MI/
MO
D/Se
vere
Sp
ecia
l Edu
catio
nID
/SID
self-
cont
aine
d Gr
ades
7-
9
LD/C
D Se
lf-co
ntai
ned
Grad
es 7
-9
LD/I
D/SI
DCa
ucas
ian
11-1
5BS
Katie
Sla
neN
JM
ath
and
LA7t
h Gr
ade
Spec
ial
Educ
ation
, sel
f-co
ntai
ned
and
incl
usiv
e
Spec
ial
Educ
ation
2-5
se
lf-co
ntai
ned
LD a
nd A
utism
Cauc
asia
n1-
5BA
Jane
t Soc
kwel
lN
CSe
vere
/Pro
foun
d K-
12; M
enta
lly
hand
icap
ped
K-12
; B/
E Ha
ndic
appe
d K-
12; L
D K-
12; B
irth
- Ki
nder
gart
en
Spec
ial E
duca
tion
Pres
choo
l Co
ordi
nato
r and
Su
ppor
t for
ID-
Mod
/Sev
ere
Spec
ial
Educ
ation
K-1
2 m
oder
ate
to
prof
ound
Mod
erat
e/se
vere
/pr
ofou
nd, b
ehav
ior-
emoti
onal
dist
urbe
d,
pre-
scho
ol
Cauc
asia
n21
-25
BS
Chris
tie
Step
hens
onO
KM
I/M
od; S
ever
e/Pr
ofou
ndEl
emen
tary
Sp
ecia
l Edu
catio
n Su
perv
isor
K-12
LD. I
D. M
D Au
tism
, OHI
Cauc
asia
n6-
10BS
Math | Kindergarten-5 Grade 149
Nam
eSt
ate
Are
a of
Certi
ficati
onCu
rren
t A
ssig
nmen
tO
ther
Gra
des
Taug
htSp
ecia
l Pop
ulati
on
Expe
rien
ceEt
hnic
ity
Year
s of
Ex
peri
ence
Hig
hest
D
egre
e
Deen
a Sw
ain
WV
Mul
ti-su
bjec
ts K
-8;
BD; a
utism
/adm
inRE
SA D
irect
or o
f Sp
ecia
l Edu
catio
nGe
nera
l Ed
ucati
on
K-8;
Mat
h an
d Sc
ienc
e at
Alt.
Sc
hool
/Juv
enile
De
tenti
on
Cent
er G
rade
s 7-
9; A
utism
K-1
2
Expe
rienc
e te
achi
ng
stud
ents
with
ASD
, Tr
aine
r of t
each
ers a
nd
adm
inist
rato
rs o
n SE
iss
ues
Cauc
asia
n16
-20
MA
Emily
Tha
tche
rIA
K-12
Str
at I
MD;
K-1
2 St
rat I
I MD.
Mul
ti-ca
t 6-
12; B
D K-
6; S
ever
e an
d Pr
ofou
nd K
-12;
Sp
ecia
l Edu
catio
n Co
nsul
tant
Iow
a De
pt. o
f Ed.
, Bu
reau
of S
tude
nt
and
Fam
ily S
uppo
rt
Serv
ices
(SPE
D),
Inst
ructi
onal
Co
nten
t Res
ourc
e an
d Al
tern
ate
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152 Common Core Essential Elements
Math | Kindergarten-5 Grade 153
Jorea M. Marple, Ed.D.State Superintendent of Schools