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SECOND GRADE 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, [email protected]

http://www.ncpublicschools.org/

mailto:[email protected]

Administration Manual and Scoring Guide

Second 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 Consultant, Kitty Rutherford ([email protected]).

INTRODUCTION

The Second Grade Mathematics Summative Assessment is designed to assess student proficiency on

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

grade. The tasks 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.

NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE 2

ASSESSMENT MATERIALS

Each student will need a student booklet and a pencil. Each student will also need access to counters

or cubes throughout the assessment. The counters or cubes can be provided to each student in

individual bags or boxes, or they can be located in a central space from which the children can access

as needed.

ASSESSMENT MATERIALS Included Additional

Student Booklet

Inch Ruler

Pencil

4 crayons (red, blue, yellow, and green)

Calculators are not used during this assessment.

*NOTE: It is possible that printing may have caused graphics to shift. Please check measurement

graphics for accuracy.

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.


Whole Class: The teacher reads the directions for each task aloud to the entire class ad all

students complete the same items in their student booklet at the same time.

The teacher needs to consider the varying abilities of the students and select items to be

presented in this format that are most likely answered in approximately the same

amount of time. This prevents situations in which students who need additional time to

complete the task are rushed, or students who are ready to move on to the next question

are waiting for other classmates to finish.

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 in their student booklet 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, 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 completing many of the

assessment tasks after an entire rotation is completed.

Individual: Depending on the students’ needs, the teacher may opt to read the directions for

each task aloud to one student.

This model allows for students who may have been absent from assessment

administration or students who require more one-on-one support for the completion of

the assessment.

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 in their mathematics assessment booklet, teachers may make notes as needed

about the manner in which students accomplish tasks. For example, a teacher may note if a student uses

counting strategies for simple computation or if the student has an alternative strategy. They may note if

the student works with confidence on all of the tasks or if there some aspects that seem more difficult.

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 circulates, s/he asks the students questions to gain

insight into their understanding and makes notes about students’ responses. For example, the teacher

might say, “Tell me about the picture you have drawn.” or “What else can you tell me?” Discussions

with students offer rich information about students’ 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.

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.

Scoring Tool Purpose Page #

Proficiency Rubric Used to determine proficiency in performance and

understanding for each task or collection of tasks. Page 8-18

Student Summary Used to take notes, plan instruction, and share at

conferences for individual students.

Last page of

student booklet

Class Summary

Used to compile all students’ proficiency levels with

each task or collection of tasks for instructional

groupings and planning.

Page 19

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 determining the next instructional steps.

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 15) 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 on-going assessment of

students. 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.

2012-2013 Summative Assessment Standards

Second Grade


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Common Core State Standard Summative

Represent and solve problems involving addition and subtraction. 2.OA.1 Use addition and subtraction within 100 to solve one- and

two-step word problems involving situations of adding to, taking

from, putting together, taking apart, and comparing, with

unknowns in all positions, e.g., by using drawings and equations

with a symbol for the unknown number to represent the problem

Tasks 1, 2, 3, and 4

Add and Subtract within 20

2.OA.2 Fluently add and subtract within 20 using mental

strategies.

Task 6

Work with equal groups of objects to gain foundations for multiplication

2.OA.3 Determine whether a group of objects (up to 20) has an

odd or even number of members; Write an equation to express an

even number as a sum of two equal addends.

2.OA.4 Use addition to find the total number of objects arranged

in rectangular arrays with up to 5 rows and up to 5 columns; write

an equation to express the total as a sum of equal addends.

Task 7

Task 8

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Understand place value. 2.NBT.1 Understand that the three digits of a three-digit number

represent amounts of hundreds, tens, and ones; e.g., 706 equals 7

hundreds, 0 tens, and 6 ones. Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens – called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900

refer to one, two, three, four, five, six, seven, eight, or nine

hundreds (and 0 tens and 0 ones).

2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s

2.NBT.3 Read and write numbers to 1000 using base-ten numerals,

number names, and expanded form.

2.NBT.4 Compare two three-digit numbers based on meanings of

the hundreds, tens, and ones digits, using <, =, and > symbols to

record the results of comparisons.

Task 9

Task 10

Task 11

Task 11

Use place value understanding and properties of operations to add and subtract.

2.NBT.5 Fluently add and subtract within 100 using strategies

based on place value, properties of operations, and/or the

relationship between addition and subtraction.

2.NBT.6 Add up to four two-digit numbers using strategies based

on place value and properties of operations.

2.NBT.7 Add and subtract within 1,000, using concrete models or

drawings and strategies based on place value, properties of

operations, and /or the relationship between addition and

subtraction; relate strategy to a written method. Understand that in

adding or subtracting three-digit numbers, one adds or subtracts

hundreds and hundreds, tens and tens, ones and ones; and

sometimes it is necessary to compose or decompose tens or

hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and

mentally subtract 10 or 100 from a given number 100-900.

2.NBT.9 Explain why addition and subtraction strategies work,

using place value and the properties of operations.

Tasks 1, 2, 3, and 4

Task 5

Task 12

Task 6

Tasks 1, 2, 3

2012-2013 Summative Assessment Standards

Second Grade


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Measure and estimate lengths in standard units. 2.MD.1 Measure the length of an object by selecting and using

appropriate tools such as rulers, yardsticks, meter sticks, and

measuring tapes.

2.MD.2 Measure the length of an object twice, using length units

of different lengths for the two measurements; describe how the

two measurements relate to the size of the unit chosen.

2.MD.3 Estimate lengths using units of inches, feet, centimeters,

and meters.

2.MD.4 Measure to determine how much longer one object is than

another, expressing the length difference in terms of a standard

length unit.

Task 13

Task 13

Task 13

Task 13

Relate addition and subtraction to length. 2.MD.5 Use addition and subtraction within 100 to solve word

problems involving lengths that are given in the same units, e.g.,

by using drawings (such as drawings of rulers) and equations with

a symbol for the unknown number to represent the problem.

2.MD.6 Represent whole numbers as lengths from 0 on a number

line diagram with equally spaced points corresponding to the

numbers 0, 1, 2,… and represent whole-number sums and

differences within 100 on a number line diagram.

Task 1

Task 3

Work with time and money. 2.MD.7 Tell and write time from analog and digital clocks to the

nearest five minutes, using a.m. and p.m.

2.MD.8 Solve word problems involving dollar bills, quarters,

dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Task 10

Represent and interpret data. 2.MD.9 Generate measurements data by measuring lengths of

several objects to the nearest whole unit, or by making repeated

measurements of the same object. Show the measurements by

making a line plot, where the horizontal scale is marked off in

whole-number units.

2.MD.10 Draw a picture graph and a bar graph (with single-unit

scale) to represent a data set with up to four categories. Solve

simple put together, take-apart, and compare problems using

information presented in a bar graph.

Geo

met

ry

Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such

as a given number of angles or a given number of equal faces.1

Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

2.G.2 Partition a rectangle into rows and columns of same-size

squares and count to find the total number of them.

2.G.3 Partition circles and rectangles into two, three, or four equal

shares, describe the shares using the words halves, thirds, half of, a

third of, etc., and describe the whole as two halves, three thirds,

four fourths,. Recognize that equal shares of identical wholes need

not have the same shape.

Task 14

Task 8

Task 15

NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE

8

The Second Grade Mathematics Summative Assessment Tasks are scored using the following Proficiency Rubric.

Task 1 OPERATIONS AND ALGEBRAIC THINKING

Represent and solve problems involving addition and subtraction.

2.OA.1 Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding

to, taking from putting together, taking apart, and comparing, with unknowns in all positions.

NUMBER AND OPERATIONS IN BASE TEN


2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the


2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

MEASUREMENT AND DATA

Relate addition and subtraction to length.

2.MD.5 Use addition and subtraction strategies within 100 to solve word problems involving lengths that are given in the

same units.

ANSWER

KEY

16 inches

54-38 = ; 38 + = 54

Note: Symbols may vary.

Note: Number sentences can be written in a different format, such as 8 = 7 + 1.

Level I The student responds the following way:

Incorrectly solves.

Level II The student responds the following ways:

Correctly solves using accurate pictures, numbers, or words OR

Writes a correct equation.

Level III The student:

Correctly solves AND

Writes a correct equation AND

Uses accurate pictures, numbers or words.


9









2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

ANSWER

KEY

9 degrees

45-36 = ; 36 + = 45; + 36 = 45




Incorrectly solves.
















ANSWER

KEY

15 centimeters

91 – 76 = ; 76 + = 91; + 76 = 91



Level I Student answers incorrectly and does not correctly represent the problem on the number

line.

Level II The student answers 15 and does not correctly represent the problem on the number line

OR correctly represents the problem on the number line but gets the answer 15.

Level III The student answers 15 and correctly represents the problem on the number line.


10









ANSWER

KEY

1. 82 pennies

2. Not enough

3. 18 pennies

Possible strategy: 34 + 48 = 82 then 100 – 82 =18, 100 – 34 + 48 =



Level I The student correctly answers 0-1 of the items.

Level II The student correctly answers 2 of the items.

Level III The student correctly answers 3 of the items.

Task 5 NUMBER AND OPERATIONS IN BASE TEN


2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

ANSWER

KEY

93 cans

One possible strategy: 28 + 36 + 12 + 17 =




Incorrectly solves.









11

Task 6

Read problems orally to students:

8 + 7

9 + 6

18 – 9

10 – 6

348 + 10

348 + 100

700 – 10

700 - 100 OPERATIONS AND ALGEBRAIC THINKING

Add and subtract within 20.

2.OA.2 Fluently add and subtract within 20 using mental strategies.



2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-

900.

ANSWER

KEY

8 + 7 = 15

9 + 6 = 15

18 – 9 =9

10 - 6 = 4

348 + 10 = 358

348 + 100 = 448

700 - 10 = 690

700 - 100 = 600


Level II The student correctly answers 3-5 of the items.

Level III The student correctly answers 6-8 of the items.

Level IV n/a


12


Work with equal groups of objects to gain foundations for multiplication.

2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members; Write an equation to

express an even number as a sum of two equal addends.

ANSWER

KEY

Even

Justifications will vary. The student should show or describe partners, pairing in

groups of two, or explain that 7 students at one table can evenly pair with 7 students

at another table. Accept any reasonable description.

Level I The student does not correctly identify the number as even.

Level II The student correctly identifies the number as even but does not give evidence that the

concept of odd and even is understood.

Level III The student identifies the number as even and gives ample evidence that the concept of

odd and even is understood and generalized.


Work with equal groups of objects to gain foundations for multiplication.

2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5

columns; write an equation to express the total as a sum of equal addends.

GEOMETRY

Reason with shapes and their attributes.

2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

ANSWER

KEY

Part A: 12

3 + 3 + 3 + 3 or 4 + 4 + 4

Note: 1 + 1 + 1 + 1 + 1 + 1 etc… is not an appropriate strategy

Part B: The rectangle divided into 4 columns and 2 rows; 8





Understand place value.

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

ANSWER

KEY

100 bottles are in each box.

768 bottles

9 boxes will be delivered to the recycling center.



Level III The student correctly answers 3of the items.


13



2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s

MEASUREMENT AND DATA

Work with time and money.

2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols

appropriately.

ANSWER

KEY

Part A: 53 ¢

Any reasonable combination of coins that equal a total of 38¢

Part B: 497, 498, 499

392, 402, 412




Level IV n/a



2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using <, =, and >

symbols to record the results of comparisons.

ANSWER

KEY

<

=

>

<

>

=



Level III The student correctly answers 5-6 of the items.


14



2.NBT.7 Add and subtract within 1,000, using concrete models or drawings and strategies based on place value,

properties of operations, and /or the relationship between addition and subtraction; relate strategy to a written method.

Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens,

ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

ANSWER

KEY

205

610

Students should use concrete models NOT the algorithm. If student uses the

algorithm then ask them to show another strategy to solve the problem.

Level I The student does not give an accurate answer for either item

Level II The student answers each problem accurately and is able to show at least one strategy per

problem. OR, The students answers the problems incorrectly, but is able to show two

strategies for solving each problem.

Level III The student answers each problem accurately and can show two strategies for solving

each problem.

Task 13 MEASUREMENT AND DATA

Measure and estimate lengths in standard units.

2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks,

and measuring tapes.

2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe

how the two measurements relate to the size of the unit chosen.

2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a

standard length unit.

ANSWER

KEY

While the intent is for the bracelets to be the following lengths, printing may have

slightly altered the pictures. Please check the graphics before disseminating and scoring.

Part A:

Reasonable estimate

Part B:

3”

5”

2” difference

Part C:

Multiple explanations possible. Justification needs to indicate awareness that it

takes more smaller units than larger units to measure the same distance.

(compensatory principle )

Level I The student neither correctly answers part B, nor provides an explanation for part C.

Level II The student answers at least 1 item in part B AND has a partial understanding of how

two measurements relate to the size of the unit chosen.

Level III Reasonably estimates length of bracelet, the student correctly answers all 3 items in part

A AND explains how the bracelet can be measured by either using more of a smaller-

sized unit or less of a larger-sized unit.


15

Task 14 GEOMETRY


2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of

equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

ANSWER

KEY

trapezoid, square

triangle, rectangle



Level III The student correctly answers all 4 of the items.

Task 15 GEOMETRY


2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves,

thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths,. Recognize that equal shares

of identical wholes need not have the same shape.

ANSWER

KEY

A-C. Accept any drawings that accurately represent the flag descriptions. The

pieces do not have to be congruent, but the size should be (relatively) equal.

D. Yes, the pieces are equal. Accept explanations that show that students recognize

that equal shares of identical wholes need not have the same shape.

Level I The student incorrectly partitions shapes A-C OR does not correctly identify D as

partitioned into equal pieces

Level II The student correctly partitions shapes A-C and correctly identifies D as partitioned into

equal pieces, but does not provide an explanation that demonstrates understanding of the

concept.

Level III The student correctly partitions shapes A-C, correctly identifies D as partitioned into

equal pieces and gives ample evidence that the concept of equal shares is understood and

generalized.


16

Second Grade Class Summary Mathematics Summative Assessment Include (standard number)

Std Names

Tasks A

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


17

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

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