SECOND GRADE - NC Mathematics - homemaccss.ncdpi.wikispaces.net/file/view/2nd Mid-Year... · · 2013-08-01SECOND GRADE Mathematics Mid-Year Benchmark Assessment 2012-2013 ... NC

SECOND GRADE Mathematics

Mid-Year Benchmark 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 C. HARRISON

Chairman :: Fayetteville

WAYNE MCDEVITT

Vice Chair :: Asheville

WALTER DALTON

Lieutenant Governor :: Rutherfordton

JANET COWELL

State Treasurer :: Raleigh

JEAN W. WOOLARD

Plymouth

REGINALD KENAN

Rose Hill

KEVIN D. HOWELL

Raleigh

SHIRLEY E. HARRIS

Troy

CHRISTINE J. GREENE

High Point

JOHN A. TATE III

Charlotte

ROBERT “TOM” SPEED

Boone

MELISSA E. BARTLETT

Roxboro

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, NC Public Schools 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 M0910

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 Mid-Year Benchmark 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 Mid-Year Benchmark Assessment is designed to assess student

proficiency on selected standards from the Common Core State Standards for Mathematics at the mid-

year point within the school year. The benchmarks assessed in this document were established based

on research and information from numerous experts, including the Common Core State Standards

authors. Please refer to the 2012-213 Mid-year Benchmark Assessment Standards table on page 7 for a

description of the benchmark expectations evaluated in this assessment.

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 mid-year

point 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

Counters or cubes (approx 30)

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 and 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.

The teacher also needs to ensure that there is an adequate supply of counters or cubes

for each student in the class to use during the assessment.

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

counters 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 are you doing with the counters?”

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.

A benchmark assessment is like a snapshot- it provides a picture of a student’s performance at one

point in time. This snapshot is combined with other “pictures” to create a comprehensive photo album

of a student’s mathematics performance (Joyner, 2012).

Therefore, this Mid-Year Benchmark 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 Mid-Year Benchmark 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 8-14

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 15

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 Mid-Year Benchmark Assessment

As stated earlier, the Mid-Year Benchmark 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 Mid-Year Benchmark 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 Mid-Year Benchmark Assessment Standards

Second Grade


Op

era

tio

ns

an

d A

lgeb

raic

Th

ink

ing

Common Core State Standard Mid-Year Benchmark

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

Solve one-step problem-types to 20.

Take From-Start Unknown

Add To-Start Unknown

Solve one-step problems to 100.

Add To-Result Unknown

Take From-Change Unknown

Compare-Bigger Unknown: More

Nu

mb

er a

nd

Op

era

tio

ns

in B

ase

Ten

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.

Count a collection of objects using

100, 10s and 1s.

Write 3-digit numbers in number

form and expanded form.

Make and compare true equations

from numbers written in number

form and expanded form.

Skip count by 5s and 10s to 300.

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.9 Explain why addition and subtraction strategies work,

using place value and the properties of operations.


Add To-Result Unknown

Take From-Change Unknown

Compare-Bigger Unknown: More

Mea

sure

men

t a

nd

Da

ta

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

another, expressing the length difference in terms of a standard

length unit.

Use inch ruler to measure length.

Determine difference between 2

objects (within 10).

Identify how a measurement relates

to the unit used.

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.


Compare- Smaller Unknown:

More

Compare- Bigger Unknown:

Fewer

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.

Draw shape with given attributes.

Use attribute clues to determine

shape.

Identify quadrilaterals and attributes

of quadrilaterals.

Second Grade Proficiency Rubric


The Second Grade Mathematics Mid-year Assessment Tasks are scored using the following Proficiency Rubric.

Tasks 1, 2 and 3 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.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

1) While the intent is for the pencils to be the following lengths, printing may have

slightly altered the pictures. Please check the graphics before disseminating

and scoring.

a: 6 inches

b: 4 inches

c: 5 inches

d: 3 inches

2) 3 inches

3) Multiple explanations possible. Justification needs to indicate awareness that a

centimeter is a much smaller unit than an inch. Therefore, there are more

centimeters than inches.

Example of justification: Mr. Vance measured the pencil using centimeters and

centimeters are much smaller than inches. That’s why his number is bigger

than Mrs. Smith’s measurement.

Level I The student correctly answers 0-2 items within the 3 tasks.

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

Level III The student correctly answers all 6 items within the 3 tasks.



Tasks 4 and 5

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, e.g., by using drawings and equations with a symbol for the unknown number to

represent the problem.

Compare-Smaller Unknown: More, One-step

Compare- Bigger Unknown: Fewer, One-step

MEASUREMENT AND DATA

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 and equations with a symbol for the unknown

number to represent the problem.

ANSWER

KEY

4) 13 + 6 = □; 6 + 13 = □ 19 feet

5) 9 – 5 = □; 5 + □ = 9 4 inches

Note: Symbols may vary.

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

Level I The student responds in 0-2 of the following ways:

Correctly solves task 4.

Correctly solves task 5

Uses accurate pictures, numbers, or words for task 4.

Uses accurate pictures, numbers or words for task 5.

Writes a correct number sentence for task 4.


Level II The student responds in 3-5 of the following ways:


Correctly solves task 5





Level III The student correctly solves both problem-types, AND

The student accurately uses pictures, number or words and correct number sentences to

represent and/or solve both problems.

NOTE: Students may write equations before, during or after solving a problem.



NOTE: Students may write equations before, during or after solving a problem.

Tasks 6 and 7

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, e.g., by using drawings and equations with a symbol for the unknown number to

represent the problem.

Take From- Start Unknown, One-step

Add To-Start Unknown, One-step

ANSWER

KEY

6) □ – 6 = 11 ; 11 + 6 = □ 17 nuts

7) □ + 8 = 19; 19 – 8 = □ 11 students


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















Level III The student correctly solves both problem-types, AND

The student accurately uses pictures, number or words and correct number sentences to

represent and/or solve both problems.



Task 8 and 9

NUMBER AND OPERATIONS IN BASE TEN

Understand place value.

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

tens and 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.

ANSWER

KEY

8)

a) 378 books

b) 300 + 70 + 8

9)

a) 125, 130, 135, 140, 145, 150, 155

b) 234, 244, 254, 264, 274, 284, 294

Level I The student correctly answers 0-1 of the 4 items within the 2 tasks.

Level II The student correctly answers 2-3 of the 4 items within the 2 tasks.

Level III The student correctly answers all 4 items within the 2 tasks.



Tasks 10 and 11


Understand place value.

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

tens and ones.

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 >, =, < symbols to record the results of comparisons.

ANSWER

KEY

10)

a. 38

b. 700

c. 320

d. 2 hundreds + 1 ten + 9 ones

e. 21 tens + 9 ones

f. 219 ones

g. 465

h. 723

11)

a. <

b. <

c. <

d. >



Level III The student correctly answers 9-11 of the 12 items within the 2 tasks.

Level IV The student correctly answers all 12 items within the 2 tasks.



Task 12-14 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, e.g., by using drawings

and equations with a symbol for the unknown number to represent the problem.

Add To-Result Unknown, One-step


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

ANSWER

KEY

12) 70 + 15 = □ ; 15 + 70 = □ 85 yards

13) 99 - □ = 50 ; 50 + □ = 99 49 stickers

14) 24 + 31 = □ ; 31 + 24 = □ 55 pennies


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





















Level III The student responds in 7-8 of the following ways:










Level IV The student correctly solves all 3 problem-types, AND the student accurately uses pictures, number or

words and correct number sentences to represent and/or solve all 3 problems. NOTE: Students may write equations before, during or after solving a problem.



Task 15, 16, 17, and 18

GEOMETRY

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

ANSWER

KEY

15) A triangle is drawn (can be equilateral, isosceles, scalene, or right)

Triangle

16) Hexagon

17) X

18) A quadrilateral has 4 sides

A quadrilateral has 4 angles.



Level III The student correctly answers 9-11 of the 12 items within the 4 tasks.

Level IV The student correctly answers all 12 items within the 4 tasks.


Second Grade Class Summary Mathematics Mid-Year Benchmark Assessment

Measurement

and Data

Operations and

Algebraic Thinking Number & Operations in Base Ten

Geometry Measurement

& Data

Operations &

Algebraic

Thinking

Measure and

estimate lengths

in standard

units.

2.MD.1

2.MD.2

2.MD.4

Represent

and solve

problems

involving

addition and

subtraction.

2.OA.1

Relate

addition and

subtraction to

length.

2.MD.5

Represent and

solve problems

involving

addition and

subtraction

2.OA.1

Understand

place value.

2.NBT.1

2.NBT.2

2.NBT.3

Understand

place value.

2.NBT.1

2.NBT.3

2.NBT.4

Understand place

value.

2.NBT.5

2.NBT.9

Represent and solve

problems involving

addition and

subtraction

2.OA.1

Reason with shapes

and their attributes.

2.G.1

Student Names Tasks 1, 2 & 3 Task 4 & 5 Tasks 6 & 7 Tasks 8 & 9 Tasks 10 & 11 Tasks 12, 13 & 14 Tasks 15, 16, 17 & 18


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

BE

YO

ND

Level IV

Advanced in Performance and Understanding

Consistently demonstrates advanced conceptual mathematical understandings

Consistently generates tasks that make connections between and among mathematical ideas

Consistently applies strategies to unique situations

Consistently demonstrates confidence to approach tasks beyond the proficiency level for grade

Consistently initiates mathematical investigations

Documents

SECOND GRADE - NC Mathematics - homemaccss.ncdpi.wikispaces.net/file/view/2nd Mid-Year... · · 2013-08-01SECOND GRADE Mathematics Mid-Year Benchmark Assessment 2012-2013 ... NC