FIRST GRADEMid-Year Benchmark Assessment

Administration Manual & Scoring Guide

STATE BOARD OF EDUCATION

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NC DEPARTMENT OF PUBLIC INSTRUCTIONJune St. Clair Atkinson, Ed.D., State Superintendent301 N. Wilmington Street :: Raleigh, North Carolina 27601-2825

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First Grade Administration Manual and Scoring GuideMathematics 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 (kitty.rutherford@dpi.nc.gov).

INTRODUCTION

The First 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 national and state 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 themid-year point of the school year.

NC DEPARTMENT OF PUBLIC INSTRUCTION FIRST GRADE3

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

Pencil

Counters or cubes (approx 20)

Calculators are not used during this assessment.

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.

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Administrations Models

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

NC DEPARTMENT OF PUBLIC INSTRUCTION FIRST GRADE5

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 8-13

Student Summary Used for individual students to take notes, share at conferences, and plan instruction.

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 14

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.

NC DEPARTMENT OF PUBLIC INSTRUCTION FIRST GRADE6

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.

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2012-2013 Mid-Year Benchmark Assessment StandardsFirst Grade

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Common Core State Standard Mid-Year BenchmarkRepresent and solve problems involving addition and subtraction.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Solve problem-types to 12. Add To/Result Unknown Take From/Result Unknown

Solve problem-types to 10. Add to/Change Unknown Take from/Change Unknown Compare-Difference Unknown (more

and fewer)

Solve problem-types for 6, 7, & 8. Put Together/Take Apart- Both

Addends UnknownUnderstand and apply properties of operations and the relationship between addition and subtraction.1.OA.3 Apply properties of operations as strategies to add and subtract.

Explore True/False equations to 10.

Add and subtract within 20.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.

Add and subtract within 12 using multiple strategies.

Work with addition and subtraction equations.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Work with equations to 10.

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Extend the counting sequence.1.NBT.1 Count to 120, starting an any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Count and write numbers to 50, crossing over decades.

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Reason with shapes and their attributes.1.G.1 Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.

Distinguish rectangles from similar shapes.

1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Identify halves and partition shapes into halves.

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First Grade Proficiency Rubric

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

Tasks 1, 2 and 3NUMBER AND OPERATIONS IN BASE TEN

Extend the counting sequence.1.NBT.1 Count to 120, starting an any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

ANSWER KEY

1) 17, 18, 19, 20, 21, 2238, 39, 40, 41, 42, 43

2) Draws 12 circles.3) Counts 23 stars and writes the number “23”.

NOTE: The digits within each number need to be in correct order for the item to be counted correct (Ex. thirty-four is written as 34, not 43).Level I The student responds in 0-1 of the following ways:

Correctly writes the sequence of 5 numbers for 17. Correctly writes the sequence of 5 numbers for 38. Accurately draws the correct number of circles for 12. Accurately writes “23” for the number of stars.

Level II The student responds in 2 of the following ways: Correctly writes the sequence of 5 numbers for 17. Correctly writes the sequence of 5 numbers for 38. Accurately draws the correct number of circles for 12. Accurately writes “23” for the number of stars.

Level III The student responds in 3 of the following ways: Correctly writes the sequence of 5 numbers for 17. Correctly writes the sequence of 5 numbers for 38. Accurately draws the correct number of circles for 12. Accurately writes “23” for the number of stars.

Level IV The student answers all items correctly: Correctly writes the sequence of 5 numbers for both 17 and 38 AND Accurately draws the correct number of circles for 12 AND Accurately writes “23” for the number of stars.

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First Grade Proficiency Rubric

Tasks 4 and 5OPERATIONS AND ALGEBRAIC THINKING

Represent and solve problems involving addition and subtraction.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Problem-Type: Add to/Result UnknownProblem-Type: Take from/Result Unknown

Add and subtract within 20.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

ANSWER KEY

3) 8 + 4 = □ or 4 + 8 = □ 12 cubes4) 10 – 4 = □ or or 4 + □ = 10 or □ + 4 = 10 6 birds

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:

Writes a correct number sentence for task 4. Writes a correct number sentence for task 5. 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.

Level II The student responds in 3-5 of the following ways: Writes a correct number sentence for task 4. Writes a correct number sentence for task 5. 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.

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.

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First Grade Proficiency Rubric

Tasks 6, 7, 8 and 9OPERATIONS AND ALGEBRAIC THINKING

Represent and solve problems involving addition and subtraction.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Problem-Type: Add To/Change UnknownProblem-Type: Take From/Change UnknownProblem-Type: Compare/Difference Unknown- “How many fewer?” versionProblem-Type: Compare/Difference Unknown- “How many more” version

Add and subtract within 20.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

ANSWER KEY

6) 5 + □ = 7 or 7 – 5 = □2 jump ropes

7) 8 - □ = 2 or 2 + □ = 86 leaves

8) 5 – 3 = □ or 3 + □ = 52 jellybeans

9) 3 + □ = 9 or 9 – 3 = □6 grapes

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:

Writes a correct number sentence for 0-1 tasks OR Correctly solves 0-1 tasks and uses accurate pictures, numbers, or words

for 0-1 tasks.Level II The student responds the following ways:

Writes a correct number sentence for 2-3 tasks OR Correctly solves 2-3 tasks and uses accurate pictures, numbers, or words

for 2-3 tasks.Level III The student responds in the following ways:

Writes a correct number sentence for 4 tasks OR Correctly solves 4 tasks and uses accurate pictures, numbers, or words

for 4 tasks.Level IV The student:

Writes a correct number sentence for all tasks AND Correctly solves all tasks, AND Uses accurate pictures, numbers or words for all tasks.

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

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First Grade Proficiency Rubric

Task 10OPERATIONS AND ALGEBRAIC THINKING

Understand and apply properties of operations and the relationship between addition and subtraction.1.OA.3 Apply properties of operations as strategies to add and subtract.

Work with addition and subtraction equations.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.ANSWER

KEY10)

(a) FalsePossible corrections could include: 6 = 7 – 1 or 9 = 8 – 1 or 6 = 8 – 2Possible justifications could include: 6 does not equal 8 – 1; 8 – 1 equals 7, not 6

(b) TruePossible justifications could include: 5 + 4 is 9 and 4 + 5 is 9; both sides have equal amounts (quantities)

(c) FalsePossible corrections could include: 3 + 2 = 2 + 3 or 4 + 2 = 2 + 4Possible justifications could include: 3 + 2 is 5 and 2 + 4 is 6; 5 and 6are not equal

NOTE: In order for an item to be counted correct, it must have all parts of the item correct. For example, Item (a) must state false, provide a correct alternative equation, and provide sound reasoning in order to be counted correct.Level I The student correctly answers 0 of the items.Level II The student correctly answers 1 of the items.Level III The student correctly answers 2 of the items.Level IV The student correctly answers all 3 items.

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First Grade Proficiency Rubric

Tasks 11, 12, and 13OPERATIONS AND ALGEBRAIC THINKING

Represent and solve problems involving addition and subtraction.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, and comparing with unknowns in all positions.Problem-Type: Put Together-Take Apart/Both Addends Unknown

Add and subtract within 20.1.OA.3 Apply properties of operations as strategies to add and subtract.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

ANSWER KEY

11) 1 + 5 = 6 &/or 5 + 1 + 62 + 4 = 6 &/or 4 + 2 = 63 + 3 = 6

12) 1 + 7 = 8 &/or 7 + 1 = 82 + 6 = 8 &/or 6 + 2 = 83 + 5 = 8 &/or 5 + 3 = 84 + 4 = 8

13) 0 + 7 = 7 &/or 7 + 0 = 71 + 6 = 7 &/or 6 + 1 = 72 + 5 = 7 &/or 5 + 2 = 73 + 4 = 7 &/or 4 + 3 = 7

NOTE: In order for an item to be considered correct, at least 3 accurate equations need to be written.Level I The student correctly answers 0-1 items.Level II The student correctly answers 2 items.Level III The student correctly answers 3 items.Level IV The student writes all possible combinations for 6, 7 and 8.

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First Grade Proficiency Rubric

Task 14GEOMETRY

Reason with shapes and their attributes.1.G.1 Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.

ANSWER KEY

Level I The student correctly identifies 0-2 of the rectangles.Level II The student correctly identifies 3-4 of the rectangles.Level III The student correctly identifies all of the rectangles.Level IV n/a

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First Grade Proficiency Rubric

Task 15 and 16GEOMETRY

Reason with shapes and their attributes.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

ANSWER KEY

Level I The student correctly identifies 0-4 of the pictures as partitioned into halves ANDThe student correctly partitions 0-3 of the shapes into halves.

Level II The student correctly identifies 0-4 of the pictures as partitioned into halves ORThe student correctly partitions 0-3 of the shapes into halves.

Level III The student correctly identifies all of the pictures that were partitioned into halves ANDThe student correctly partitions all of the shapes into halves.

Level IV n/a

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First Grade Class SummaryMathematics Mid-Year Benchmark Assessment

Number and Operations in

Base TenOperations and Algebraic Thinking Geometry

Extend the Counting Sequence

Represent and solve problems involving addition

and subtraction.

Add and subtract

within 20.

Represent and solve problems

involving addition and subtraction.

Add and subtract within

20.

Understand and apply

properties or operations and

the relationship

between addition and subtraction.

Work with addition and subtraction equations.

Represent and solve problems

involving addition and subtraction.

Add and subtract within 20.

Reason with shapesand their attributes

Student Names Tasks 1, 2 & 3 Task 4 & 5 Tasks 6, 7, 8 & 9 Task 10 Tasks 11, 12, & 13 Task 14 Task15 & 16

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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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