common core essential elements alternate achievement...

&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.


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


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


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.


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


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.


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


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.


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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


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.


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.


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


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.”


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


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

)


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.


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.


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.


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

.


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.


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.


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

)


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.


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.


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


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.


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.


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.


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.


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)


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?

”).


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.)


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

.


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

.


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.


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

.


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?”


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.


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.


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

)


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.


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.


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

.


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.


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.


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.


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.


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.


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.


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


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.


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.


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

.


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

.


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.


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

.


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.


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)

.


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


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?

”


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

).


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

.


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

).


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.


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.


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.


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?

”


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.


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.


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.


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.


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

.


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.


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.)


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)

.


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).


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.


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.


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.


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.


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

.


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

.


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.


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.


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.


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.


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


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

.


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.


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.

)


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)

.


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 =.


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

.


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.


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.


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

.


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

).


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.


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.


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

.


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.

)


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.


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.


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.


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


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.


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.


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.


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.


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.


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

.


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.


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

.


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).


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)


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


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


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)

.


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.


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

.


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.


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

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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


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).


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?


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).


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).


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.


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


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.


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.


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)


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


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


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


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


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


APPENDIX A

SEA/STAKEHOLDER DEMOGRAPHICS


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


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


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


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


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


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


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


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

Asse

ssm

ent

Cons

ulta

nt

Spec

ial

Educ

ation

and

Ar

t K-1

2

22 y

ears

var

ied

expe

rienc

eCa

ucas

ian

21-2

5M

ED

Larr

y Ti

mm

MI

Spec

ial E

duca

tion

CI;

Indu

stria

l Ed

ucati

onM

iddl

e Sc

hool

CI

Mat

h 6-

8Ge

nera

l Ed

ucati

on 6

-8

Tech

Ed.

Mod

to M

ild C

.I.Ca

ucas

ian

16-2

0M

A

Mon

a Tj

aden

KSEl

emen

tary

K-9

; EM

R an

d TM

R Sp

ecia

l Ed

ucati

on K

-9;

Spec

ial E

duca

tion

Supe

rviso

r K-1

2;

Libr

ary

Med

ia K

-12

Spec

ial E

duca

tion

Prog

ram

Co

ordi

nato

r

Spec

ial

Educ

ation

Pr

ogra

m

Coor

dina

tor

Spec

ial E

duca

tion

Teac

her a

nd

Coor

dina

tor

Cauc

asia

n30

+M

S

Jani

ce To

rnow

WA

Gene

ral a

nd S

peci

al

Educ

ation

K-1

2W

A O

ffice

of

Supe

rinte

nden

t of

Publ

ic In

stru

ction

Spec

ial

Educ

ation

K-1

2Sp

ecia

l Edu

catio

n Te

ache

r and

Ad

min

istra

tor

Cauc

asia

n30

+M

ED


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

Jane

Van

DeZa

nde

MO

ELA

and

Spec

ial

Educ

ation

(H

andi

capp

ed

Lear

ner)

Dire

ctor

of

Asse

ssm

ent

5-8

Spee

ch a

nd

Lang

uage

and

LD

; ELA

and

So

cial

Stu

dies

9-

12

Chap

ter I

Dire

ctor

Mat

h an

d Re

adin

g, S

peci

al

Educ

ation

Irish

Am

eric

an16

-20

Oth

er

Degr

ee

Joyc

e Vi

scom

iVA

Elem

enta

ry K

-5

(rea

ding

, mat

h,

soci

al st

udie

s,

scie

nce)

Spec

ial E

duca

tion

Inte

llect

ually

Im

paire

d, M

ultip

le

Hand

icap

ped

and

OHI

Spec

ial

Educ

ation

–

preK

-12

Spec

ial E

duca

tion

Inte

llect

ually

Impa

ired,

M

ultip

le H

andi

capp

ed,

Seve

re a

nd P

rofo

und,

O

HI

Cauc

asia

n20

-25

BS

Nic

ole

War

ren

UT

Early

Chi

ldho

od

Educ

ation

; El

emen

tary

Mat

h En

dors

emen

t; ES

L En

dors

emen

t, Ad

min

. Cer

tifica

tion

Elem

enta

ry M

ath

Coac

h; G

ener

al

and

Spec

ial

Educ

ation

, fac

ilita

te

elem

enta

ry

endo

rsem

ent

clas

ses

Gene

ral

Educ

ation

Ki

nder

gart

en.

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Jorea M. Marple, Ed.D.State Superintendent of Schools