These state-developed assessment materials are...

SECOND GRADEMid-Year Benchmark Assessment

Administration Manual and Scoring Guide

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 preparedfor life in the 21st Century.

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Administration Manual and Scoring GuideSecond 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 GRADE1

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 studentsBecause 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 tasksThe 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 modelsThe 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 WorkWhile 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, andare 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 UnderstandingThe 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 SummaryUsed 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 SummaryOnce 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 AssessmentAs 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 StandardsSecond Grade

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Common Core State Standard Mid-Year BenchmarkRepresent 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

Num

ber

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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 100s2.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.

Solve one-step problem-types to 100. Add To-Result Unknown Take From-Change Unknown Compare-Bigger Unknown: More

Mea

sure

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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.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.

Solve one-step problem-types to 20. Compare- Smaller Unknown:

More Compare- Bigger Unknown:

Fewer

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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 3MEASUREMENT AND DATAMeasure 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 inchesb: 4 inchesc: 5 inchesd: 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.Level IV n/a


Second Grade Proficiency Rubric

Tasks 4 and 5OPERATIONS AND ALGEBRAIC THINKINGRepresent 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-stepCompare- Bigger Unknown: Fewer, One-step

MEASUREMENT AND DATARelate 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

KEY4) 13 + 6 = □; 6 + 13 = □ 19 feet5) 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. Writes a correct number sentence for task 5.

Level II The student responds in 3-5 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. Writes a correct number sentence for task 5.

Level III The student correctly solves both problem-types, ANDThe student accurately uses pictures, number or words and correct number sentences to represent and/or solve both problems.

Level IV n/a

NOTE: Students may write equations before, during or after solving a problem. Students are not required to write an equation before solving a problem.



Tasks 6 and 7OPERATIONS AND ALGEBRAIC THINKINGRepresent 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-stepAdd To-Start Unknown, One-step

ANSWER KEY

6) □ – 6 = 11 ; 11 + 6 = □ 17 nuts7) □ + 8 = 19; 19 – 8 = □ 11 students

Note: Symbols may vary.Note: Number sentences can be written in a different format, such as 8 = 7 + 1.Level I The student responds in 0-2 of the following ways:

Correctly solves task 6. Correctly solves task 7. Uses accurate pictures, numbers, or words for task 6. Uses accurate pictures, numbers or words for task 7. Writes a correct number sentence for task 6. Writes a correct number sentence for task 7.

Level II The student responds in 3-5 of the following ways: Correctly solves task 6. Correctly solves task 7. Uses accurate pictures, numbers, or words for task 6. Uses accurate pictures, numbers or words for task 7. Writes a correct number sentence for task 6. Writes a correct number sentence for task 7.

Level III The student correctly solves both problem-types, ANDThe student accurately uses pictures, number or words and correct number sentences to represent and/or solve both problems.

Level IV n/a




Task 8 and 9NUMBER AND OPERATIONS IN BASE TENUnderstand 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 booksb) 300 + 70 + 8

9)a) 125, 130, 135, 140, 145, 150, 155b) 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.Level IV n/a



Tasks 10 and 11NUMBER AND OPERATIONS IN BASE TENUnderstand 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. 38b. 700c. 320d. 2 hundreds + 1 ten + 9 onese. 21 tens + 9 onesf. 219 onesg. 465h. 723

11)a. <b. <c. <d. >

Level I The student correctly answers 0-4 of the 12 items within the 2 tasks.Level II The student correctly answers 5-8 of the 12 items within the 2 tasks.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.


Second Grade Proficiency Rubric Task 12-14

OPERATIONS AND ALGEBRAIC THINKINGRepresent and solve problems involving addition and subtraction2.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

NUMBER AND OPERATIONS IN BASE TENUnderstand 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

8) 70 + 15 = □ ; 15 + 70 = □ 85 yards9) 99 - □ = 50 ; 50 + □ = 99 49 stickers10) 24 + 31 = □ ; 31 + 24 = □ 55 pennies

Note: Symbols may vary.Note: Number sentences can be written in a different format, such as □ = 7 + 1.Level I The student responds in 0-3 of the following ways:

Writes a correct number sentence for task 12. Writes a correct number sentence for task 13. Writes a correct number sentence for task 14. Correctly solves task 12. Correctly solves task 13. Correctly solves task 14. Uses accurate pictures, numbers, or words for task 12. Uses accurate pictures, numbers or words for task 13. Uses accurate pictures, numbers or words for task 14.

Level II The student responds in 4-6 of the following ways: Writes a correct number sentence for task 12. Writes a correct number sentence for task 13. Writes a correct number sentence for task 14. Correctly solves task 12. Correctly solves task 13. Correctly solves task 14. Uses accurate pictures, numbers, or words for task 12. Uses accurate pictures, numbers or words for task 13. Uses accurate pictures, numbers or words for task 14.

Level III The student responds in 7-8 of the following ways: Writes a correct number sentence for task 12. Writes a correct number sentence for task 13. Writes a correct number sentence for task 14. Correctly solves task 12. Correctly solves task 13. Correctly solves task 14. Uses accurate pictures, numbers, or words for task 12. Uses accurate pictures, numbers or words for task 13. Uses accurate pictures, numbers or words for task 14.

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.



Second Grade Proficiency Rubric Task 15, 16, 17, and 18

GEOMETRYReason 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) Hexagon17) X

18) A quadrilateral has 4 sidesA quadrilateral has 4 angles.

Level I The student correctly answers 0-4 of the 12 items within the 4 tasks.Level II The student correctly answers 5-8 of the 12 items within the 4 tasks.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 SummaryMathematics Mid-Year Benchmark Assessment

Measurement and Data

Operations and Algebraic Thinking Number & Operations in Base Ten

GeometryMeasurement & Data

Operations & Algebraic Thinking

Measure and estimate lengths

in standard units.

2.MD.12.MD.22.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.12.NBT.22.NBT.3


2.NBT.12.NBT.32.NBT.4


2.NBT.52.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 LevelsB

EY

ON

D

Level IVAdvanced in Performance and UnderstandingConsistently demonstrates advanced conceptual mathematical understandingsConsistently generates tasks that make connections between and among mathematical ideasConsistently applies strategies to unique situationsConsistently demonstrates confidence to approach tasks beyond the proficiency level for gradeConsistently initiates mathematical investigations

CO

NSI

STE

NT

Level IIIProficient in Performance and UnderstandingConsistently demonstrate understanding of mathematical standards and cluster at the grade levelConsistently demonstrates conceptual understandingConsistently applies multiple strategies flexibly in various situationsUnderstands and fluently applies procedures with understandingConsistently demonstrates perseverance and precisionConstructs logical mathematical arguments for thinking and reasoningUses mathematical language correctly and appropriately

INC

ON

SIST

EN

T

Level IINot Yet Proficient in Performance and UnderstandingInconsistently uses tools appropriately and strategicallyDemonstrates inconsistent understanding of key mathematical ideas at grade levelDemonstrates inconsistent conceptual understanding of key mathematical ideas at grade levelInconsistent in understanding and application of grade level appropriate strategiesDepends upon the assistance of teacher and/or peers to understand and complete tasksNeeds additional time to complete tasksApplies models of mathematical ideas inconsistently

SEL

DO

M

Level 1Limited Performance and UnderstandingExhibits minimal understanding of key mathematical ideas at grade levelRarely demonstrates conceptual understandingSeldom provides precise responsesSeldom uses appropriate strategiesConsistently requires assistance and alternative instructionUses tools inappropriately to model mathematics


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