SECOND GRADE
Mid-Year Benchmark Assessment
Administration Manual and Scoring Guide
STATE BOARD OF EDUCATION
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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 ().
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 7for a description of the benchmark expectationsevaluated 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.
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 / AdditionalStudent 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 asksthe 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 appropriatelyaccurately, 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 StudentSummary 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.
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NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
2012-2013 Mid-Year Benchmark Assessment Standards
Second Grade
Operations and Algebraic Thinking / Common Core State Standard / Mid-Year BenchmarkRepresent and solve problems involving addition and subtraction.
2.OA.1Use 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
- Add To-Result Unknown
- Take From-Change Unknown
- Compare-Bigger Unknown: More
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; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens – called a “hundred.”
- 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.3Read 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
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. / 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
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.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.
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NC DEPARTMENT OF PUBLIC INSTRUCTION SECOND GRADE
Second GradeProficiency Rubric
The Second Grade Mathematics Mid-year Assessment Tasks are scored using the following Proficiency Rubric.
Tasks 1, 2 and 3MEASUREMENT AND DATA
Measure and estimate lengths in standard units.
2.MD.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.2Measure 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.4Measure 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.
Level IV / n/a
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.
- 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, AND
The 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.