KINDERGARTEN Mathematics

Summative Assessment

2012-2013

Administration Manual

STATE BOARD OF EDUCATION

The guiding mission of the North Carolina State Board of Education is that every public school student

will graduate from high school, globally competitive for work and postsecondary education and prepared for life in

the 21st Century.

WILLIAM COBEY

Chair :: Chapel Hill

A.L. COLLINS

Vice Chair :: Kernersville

DAN FOREST

Lieutenant Governor :: Raleigh

JANET COWELL

State Treasurer :: Raleigh

JUNE ST. CLAIR ATKINSON

Secretary to the Board :: Raleigh

BECKY TAYLOR

Greenville

REGINALD KENAN

Rose Hill

KEVIN D. HOWELL

Raleigh

GREG ALCORN

Salisbury

OLIVIA OXENDINE

Lumberton

JOHN A. TATE III

Charlotte

WAYNE MCDEVITT

Asheville

MARCE SAVAGE

Waxhaw

PATRICIA N. WILLOUGHBY

Raleigh

NC DEPARTMENT OF PUBLIC INSTRUCTION June St. Clair Atkinson, Ed.D., State Superintendent

301 N. Wilmington Street :: Raleigh, North Carolina 27601-2825

In compliance with federal law, the NC Department of Public Instruction administers all state-operated educational programs, employment

activities and admissions without discrimination because of race, religion, national or ethnic origin, color, age, military service, disability, or

gender, except where exemption is appropriate and allowed by law.

Inquiries or complaints regarding discrimination issues should be directed to:

Dr. Rebecca Garland, Chief Academic Officer :: Academic Services and Instructional Support

6368 Mail Service Center, Raleigh, NC 27699-6368 :: Telephone: (919) 807-3200 :: Fax: (919) 807-4065

Visit us on the Web :: www.ncpublicschools.org M0713

If you have questions or feedback please contact: Kitty Rutherford, kitty.rutherford@dpi.nc.gov

NC DEPARTMENT OF PUBLIC INSTRUCTION KINDERGARTEN 3

Administration Manual

Kindergarten Grade

Mathematics Summative Assessment

In response to North Carolina legislative and State Board requirements, the NC Department of

Public Instruction provides Local Education Agencies with state-developed assessments to be

implemented for Kindergarten, First and Second Grades. These assessments are to include

documented, on-going individualized assessments throughout the year and a summative evaluation

at the end of the year. These assessments monitor achievement of benchmarks in the North Carolina

Standard Course of Study: Common Core State Standards for Mathematics.

The intended purposes of these assessments are:

To provide information about progress of each student for instructional adaptations and early

interventions.

To provide next-year teachers with information about the status of each of their incoming

students.

To inform parents about the status of their children relative to grade-level standards at the end of

the year

To provide the school and school district information about the achievement status and progress

of groups of students in grades K, 1, and 2.

These state-developed assessment materials are aligned with the Common Core State

Standards for Mathematics and may be adopted or modified as appropriate for individual

school districts. The North Carolina Department of Public Instruction appreciates any

suggestions and feedback, which will help improve upon this resource. Feedback may be sent

to NCDPI Mathematics Consultants, Denise Schulz (denise.schulz@dpi.nc.gov) or Kitty

Rutherford (kitty.rutherford@dpi.nc.gov).

INTRODUCTION

The Kindergarten Mathematics Summative Assessment is designed to assess student proficiency on

selected standards from the Common Core State Standards for Mathematics at the end of the school

year. Items assessed in this document were established based on research and information from

numerous experts, including the Common Core State Standards authors.

The tasks in the student mathematics assessment booklet are designed to mirror tasks and

assessment items that students should be experiencing throughout the year. District leaders have the

option to use the assessment as presented or to adapt the assessment to best meet student needs and

district requirements.

The number of days used to administer the assessment is a District decision or a teacher-based

decision based on each class’ situation. However, the assessment is to be administered at the

end of the school year. Individual districts determine the timeline of the assessment.

NC DEPARTMENT OF PUBLIC INSTRUCTION KINDERGARTEN 4

ASSESSMENT MATERIALS

The required assessment materials are indicated below. Some assessment materials are provided with

the assessment, but may require preparation. Teachers may wish to create an “Assessment Kit”, using a

bag or a box to house all of the materials needed. Calculators are not used during this assessment.

Task ASSESSMENT MATERIALS Included Additional

1 None

2 Beach Image

3 Set of 20 counters (used for tasks 3, 5, & 8)

4 Domino Cards (cut apart)

You may substitute real dominoes if you prefer.

Quantity Cards (cut apart)

5 Set of 20 counters (used for tasks 3, 5, & 8)

Optional Recording Form

6 Color Tiles – at least 4 of one color and 4 of another

color; you may substitute another counter or colored

squares if you do not have access to color tiles.

7 Student Image Cards (cut apart)

Ten Frames

Set of 10 counters

8 Set of 20 counters (used for tasks 3, 5, & 8)

Ten Frame Example

9 Pool Image

10 Shape Images (cut apart)

11 Birthday Party Image

12 Recording Sheet (one per student)

General

Items

Paper

Pencil

Assessment Kit “To Do” List

Printing Locate Copy & Cut

Beach Image (1 copy) 1 set of 20 counters Domino Cards (1 set)

Task 5 Recording Forms

(optional)

Color Tiles – at least 4 of one

color and 4 of another color

Quantity Cards (1 set)

Ten Frame Example (1 copy) Building Materials for 3-D shapes Student Image Cards (1 set)

Pool Image (1 copy) Paper & pencil Shape Images (1 set)

Birthday Party Image (1 copy)

Task 12 Recording Sheet (1 copy

per child)

ADMINISTERING THE ASSESSMENT

Preparing the students

Because the assessment tasks are similar to the tasks used for daily instruction and on-going

formative assessment, no special preparation for students is necessary. However, teachers may want

to explain to the students that these tasks provide a way to see what each student knows and what

each student still needs to learn. The teacher may also want to explain that the students will need to

answer each question on their own, without support from other classmates or the teacher.

As during daily instruction, students should have a relaxed atmosphere in which to do the tasks.

This assessment is not timed. Students should have as much time as needed, within reason.

Selecting the tasks The tasks can be administered in a sequence that best fits the learning environment. The tasks do

not need to be administered in the order presented. District leaders(s) may decide a particular order

for assessment administration or the decision may be left to the individual teacher. However, some

tasks may have multiple parts that will need to be administered together.

Administration models

The assessment can be administered in several ways. The District Leader(s) may designate a uniform

administration process for all teachers to follow within the LEA/District or the teachers may be asked to

decide on one or more assessment models to use based on their particular students and unique situations.

When assessing young children, it is important to remember that they frequently know more than they

can record in traditional, symbolic formats. “Age, fluency with language, and experiences influence

how successful students are likely to write a strong explanation or offer an explanation orally” (Joyner

& Muri, 2011). Therefore, Individual and Small Group are suggested models for administration.

Individual: The classroom teacher presents a series of assessment tasks to one student

and carefully listens to the student’s responses and observes the student’s

strategies and thinking as the student works.

Since both correct answers and appropriate processes are valued in mathematics,

teachers find that observing students and talking with them are ideal ways to

provide students with opportunities to demonstrate what they know and can apply

in new situations. Thus, the teacher is encouraged to ask the student clarifying

questions during the assessment or after the assessment to gain a more accurate

picture of what the student knows and understands. Insight into children’s

thinking helps teachers build on what students understand, not just what they can

do by memorizing processes.

CAUTION: Asking clarifying questions is different from asking leading

questions. Be sure that the questions asked provide information about student

thinking rather than coach or lead students towards a solution.

Small Group: The teacher reads the directions for each task aloud to a small group of students.

A small group of students complete the same items at the same time. This model allows students in the same room to be working on different work at

the same time. Teachers need to read the directions aloud to the students and

observe students as they work, so it is possible that some of the students are

completing assessment tasks while other students are working on other classroom

tasks and activities. Teachers may decide to set up various centers/stations of

which the students move through, thus many students complete particular

assessment tasks after an entire rotation is completed.

The teacher reads aloud all directions and all questions to the students. If a student(s) asks for

clarification, the teacher may reread the directions and questions aloud as often as needed or may

substitute a familiar word for an unfamiliar word (e.g., “number sentence” for “equation”).

However, since the teacher is seeking information about what the student can do independently, the

teacher may not coach or instruct a student on how to answer a question.

Monitoring Students at Work

While students are working, the teacher observes the student carefully and makes notes about the

manner in which student accomplishes the tasks. The teacher is encouraged to find out as much as

possible about what students are thinking and how they go about working on tasks. As the teacher

works with a student, s/he asks the student questions to gain insight into his/her understanding and

makes notes about student’s responses. For example, the teacher might say, “Tell me about the

picture you have drawn.” or “What are you doing with the counters?” or “What else can you tell

me?” Discussions with students offer rich information about the student’s understandings.

If students do not understand a question and ask, “What does this mean?” or say, “I don’t get it.” the

teacher may simply repeat the directions, substitute a familiar word for an unfamiliar word if

necessary, and say, “Do the best you can.”

SCORING THE ASSESSMENT

What does Proficient mean?

When students are proficient with a particular standard/cluster, then they:

can model and explain the concepts,

use the mathematics appropriately & accurately, and

are fluent and comfortable in applying mathematics.

This Summative Assessment is designed to provide additional evidence of students’ independent

work and will be included with other information gathered about the student. This assessment is

not intended to provide a complete picture of a student’s mathematics understandings. When

determining overall student proficiency levels, this assessment should be combined with additional

documentation such as student products, formative assessment tasks, checklists, notes, and other

anecdotal information.

Rather than assessing each micro-skill or concept, the Summative Assessment is designed to assess

students’ proficiency at the cluster level. Therefore, some tasks are grouped together for scoring in

order to gain an accurate picture of a student’s proficiency within a particular cluster(s). Multiple

tasks, rather than a single task, also provide more insight into the consistency of a student’s

understanding and a more accurate picture of a student’s overall proficiency.

Determining Proficiency in Performance and Understanding

The Summative Assessment is scored using the Proficiency Rubric. As the teacher scores each

student’s booklet, the teacher may record notes and observations for that student on the Student

Summary form. A Class Summary form is provided to gain a global understanding of the class’

proficiency and for assisting with instructional groupings and planning.

Tool Purpose Page #

Proficiency Rubric Used to determine proficiency in performance and

understanding for each task or collection of tasks.

Included with the

Task Directions

Student Response

Sheet

Used to take notes, plan instruction, and share at

conferences for individual students.

Pages 10-11

Class Summary Used to compile all students’ proficiency levels with

each task or collection of tasks for instructional

groupings and planning.

Page 12

When scoring each student’s response, the teacher needs to pay particular attention to what the

student does and does not understand. Both are equally important.

In addition, the teacher needs to look beyond whether an item’s answer was correct or incorrect by

looking carefully at the types of mistakes that were made. Some mistakes that children make come

from a lack of information. At other times mistakes reflect a lack of understanding. There is logic

behind students’ answers. The teacher must look for the reasons for the responses and identify any

misconceptions that may exist.

Student Summary

Once the student’s work has been carefully reviewed and the proficiency scores have been

determined using the Proficiency Rubric, the teacher summarizes the student’s strengths and areas

of focus for each of the domains on the Student Summary form. The information on this form can

then be used to guide instruction, to share with families during conferences, to inform support staff,

and to discuss in Professional Learning Communities.

Proficiency Beyond the Summative Assessment

As stated earlier, the Summative Assessment is one piece of data collected to determine a student’s

mathematics understanding. When determining overall proficiency for a particular standard or

cluster, a variety of evidence is collected. In addition to the collection of evidence, the following

Mathematics Proficiency Levels rubric (page 11) can help solidify to what degree a student has

reached overall proficiency in mathematics.

SUMMARY

This Summative Assessment has been provided to help efforts to conduct a formalized end-of-year

assessment of students’ understanding. These items and tasks within this assessment are not

intended to provide a complete picture of a student’s mathematics understandings. Combined with

additional documentation, teachers will be able to make inferences about student achievement and

support each student’s development as a competent mathematician.

Standards and Tasks

Co

un

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nd

Ca

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ty

Common Core State Standard Summative Know number names and count sequence.

K.CC.1 Count to 100 by ones and tens.

K.CC.2 Count forward beginning from a given number within the known sequence

(instead of having to begin at 1).

K.CC.3 Write numbers from 0-20. Represent a number of objects with a written

numeral 0-20 (with 0 representing a count of no objects).

Task 1

Task 1

Task 12

Count to tell the number of objects.

K.CC.4 Understand the relationship between numbers and quantities; connect

counting to cardinality.

K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged

in a line, a rectangular array, or a circle, or as many as 10 things in a scattered

configuration’ given a number from 1-20, count out that many objects.

Tasks 2, 3

Tasks 2, 3

Compare numbers.

K.CC.6 Identify whether the number of objects in one group is greater than, less than,

or equal to the number of objects in another group, e.g., by using matching and

counting strategies. (Note: Including groups with up to ten objects.)

K.CC.7 Compare two numbers between 0 and 10 presented as written numerals.

Task 4

Task 4

Op

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on

s an

d A

lgeb

raic

Th

ink

ing

Understand addition as putting together and adding to, and understand subtraction as taking apart

and taking from.

K.OA.1 Represent addition and subtraction with objects, fingers, mental images,

drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10

by using objects or drawings to represent the problem.

K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way,

e.g., by using objects or drawings, and record each decomposition by a drawing or

equation.

K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the

given number, e.g., by using objects or drawings, and record the answer with a

drawing or equation.

K.OA.5 Fluently add and subtract within 5.

Task 5

Task 5

Task 6

Task 7

Task 12

Nu

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d

Op

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s

in B

ase

Ten

Work with numbers 11-19 to gain foundations for place value.

K.NBT.1 Compose and decompose numbers from 11-19 into ten ones and some further

ones, e.g., by using objects or drawings, and record each composition or decomposition by a

drawing or equation (e.g., 18=10 + 8); understand that these numbers are composed of ten

ones and one, two, three, four, five, six, seven, eight or nine ones.

Task 8

M

easu

rem

ent

an

d D

ata

Describe and compare measurable attributes

K.MD.1 Describe measurable attributes of objects, such as length or weight.

Describe several measurable attributes of a single object.

K.MD.2 Directly compare two objects with a measurable attribute in common to

see which object has “more of”/”less of” the attribute, and describe the

difference.

Task 9

Task 9

Geo

met

ry

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones,

cylinders, and spheres).

K.G.1. Describe objects in the environment using shapes and describe the

relative position of these objects using terms such as above, below, beside, in

front of, behind, and next to.

K.G.2 Correctly name shapes regardless of their orientations or overall size.

K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-

dimensional (“solid”).

Task 11

Task 11

Task 10

Analyze, compare, create, and compose shapes

K.G.4 Analyze and compare two-and three -dimensional shapes, in different

sizes and orientations, using informal language to describe their similarities,

differences, parts and other attributes.

Task 10

Student ____________________________________________________________________ Date________________________________________________

Kindergarten Student Response Sheet Mathematics Summative Assessment

Task

Std

Task Description

Student Response

Level

1 K.CC.1

K.CC.2 Rote counting by tens

Rote counting by ones

1 2 3

2 K.CC.4

K.CC.5 Counting objects in straight lines

Counting objects in a rectangular array

Counting scattered objects (to 5)

Counting scattered objects (to 10)

1 2 3 4

3 K.CC.4

K.CC.5 Counting out 8

Knows “1 more”

1 2 3

4 K.CC.6

K.CC.7 Comparing amounts

Comparing numbers

1 2 3

5

part 1

K.OA.1

K.OA.2 Adding

1 2 3

5

part 2

K.OA.1

K.OA.2 Subtracting

1 2 3

6 K.OA.3 Composing 4

1 2 3 4

7 K.OA.4 Making 10

1 2 3

8 K.NBT.1 Decomposing 14 into tens & ones

1 2 3

9 K.MD.1

K.MD.2 Measurable Attributes

Comparing lengths

1 2 3

10 K.G.3

K.G.4 Analyzing & comparing shapes

1 2 3

11 K.G.1

K.G.2

Positional words

Identifying shapes

1 2 3

12 K.CC.3

K.OA.5 Fluency

Writing Numbers

1 2 3

Kindergarten Class Summary Mathematics Summative Assessment

CC – Counting & Cardinality

OA – Operations & Algebraic Thinking

NBT – Number and Operations in Base Ten

MD – Measurement & Data

G – Geometry

CC OA NBT MD MD/G G CC

OA

Rote

Counti

ng

Counti

ng O

bje

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Cou

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ng O

ut

/

One

More

Com

par

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Num

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s

Addit

ion &

Subtr

acti

on

Addit

ion &

Subtr

acti

on

Dec

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ng

Num

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Mak

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0

Pla

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Mea

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ID

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&

Anal

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Shap

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ID

/ C

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Shap

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Flu

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&

Wri

ting #

s

Std. Names Task

1

Task

2

Task

3

Task

4

Task

5a

Task

5b

Task

6

Task

7

Task

8

Task

9

Task

10

Task

11

Task

12

Mathematics Proficiency Levels

SE

LD

OM

Level 1

Limited Performance and Understanding

Exhibits minimal understanding of key mathematical ideas at grade level

Rarely demonstrates conceptual understanding

Seldom provides precise responses

Seldom uses appropriate strategies

Consistently requires assistance and alternative instruction

Uses tools inappropriately to model mathematics

INC

ON

SIS

TE

NT

Level II

Not Yet Proficient in Performance and Understanding

Inconsistently uses tools appropriately and strategically

Demonstrates inconsistent understanding of key mathematical ideas at grade level

Demonstrates inconsistent conceptual understanding of key mathematical ideas at grade level

Inconsistent in understanding and application of grade level appropriate strategies

Depends upon the assistance of teacher and/or peers to understand and complete tasks

Needs additional time to complete tasks

Applies models of mathematical ideas inconsistently

CO

NS

IST

EN

T

Level III

Proficient in Performance and Understanding

Consistently demonstrate understanding of mathematical standards and cluster at the grade level

Consistently demonstrates conceptual understanding

Consistently applies multiple strategies flexibly in various situations

Understands and fluently applies procedures with understanding

Consistently demonstrates perseverance and precision

Constructs logical mathematical arguments for thinking and reasoning

Uses mathematical language correctly and appropriately