New York State Testing Program Common Core Mathematics Test

Transcription

1 New York State Testing Program Common Core Mathematics Test Performance Level Descriptions Grade 4 August 2013

2 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY New York State Testing Program Common Core Mathematics Test Performance Level Descriptions GRADE 4 Policy-Level Performance Level Definitions For each grade, there are students performing along a proficiency continuum with regard to the skills and knowledge necessary to meet the demands of grade-specific Common Core Standards for Mathematics. There are students who are above proficiency, students who are proficient, students who are not quite proficient, and students who are well below proficient at each grade level. New York State assessments are designed to classify students into one of four proficiency categories; these proficiency categories are defined as: NYS Level 4 Students performing at this level excel in standards for their grade. They demonstrate knowledge, skills, and practices embodied by the New York State P-12 Common Core Learning Standards for Mathematics that are considered more than sufficient for the expectations at this grade. NYS Level 3 Students performing at this level are proficient in standards for their grade. They demonstrate knowledge, skills, and practices embodied by the New York State P-12 Common Core Learning Standards for Mathematics that are considered sufficient for the expectations at this grade. NYS Level 2 Students performing at this level are below proficient in standards for their grade. They demonstrate knowledge, skills, and practices embodied by the New York State P-12 Common Core Learning Standards for Mathematics that are considered partial but insufficient for the expectations at this grade. NYS Level 1 Students performing at this level are well below proficient in standards for their grade. They demonstrate limited knowledge, skills, and practices embodied by the New York State P-12 Common Core Learning Standards for Mathematics that are considered insufficient for the expectations at this grade. 2

3 Performance Level Descriptions Performance Level Descriptions (PLDs) describe the range of knowledge and skills students should demonstrate at a given performance level. How were the PLDs developed? The New York State Education Department (NYSED) convened the state's English Language Arts (ELA) and Math Content Advisory Panels (CAPs) to develop the initial draft PLDs for grades 3-8. The CAPs are classroom teachers from elementary, middle and high school, school and district administrators, English Language Learner (ELL) and students with disabilities (SWD) specialists, and higher education faculty members from across the state. The draft PLDs from the CAPs then went through additional rounds of review and edit from a number of content experts and assessment experts under NYSED supervision. In developing PLDs, the CAPs considered policy-level definitions of the performance levels (see above) and the expectations for each grade level in the Common Core State Standards. Drafting PLDs began with Level 3, the proficiency level, to determine the content knowledge and skill necessary at a given grade level and content standard to be considered proficient according to the rigor and demand of the Common Core. CAP members then drafted PLDs at Levels 4 (excel) and 2 (partial but insufficient for proficiency). Finally, Level 1 PLDs describe a wide range of students, including both those who are just below meeting the requirements for Level 2 and those who attempted but did not answer any questions correctly. Because of the range of students covered in Level 1, these PLDs were developed last and will be released in the next version of this document. The next version of this document, to be released in September 2013, will include Level 1 PLDs for the Major Clusters and PLDs for the Supporting and Additional Clusters for all levels. How are the PLDs used in Assessment? PLDs are essential in setting standards for the New York State Grades 3-8 assessments. Standard setting panelists use PLDs to determine the threshold expectations for students to demonstrate the knowledge and skills necessary to attain just barely a Level 2, Level 3, or Level 4 on the assessment. These discussions then influence the panelists in establishing the cut scores on the assessment. PLDs are also used to inform item development, as each test needs questions that distinguish performance all along the continuum. How can the PLDs be used in Instruction? PLDs help communicate to students, families, educators and the public the specific knowledge and skills expected of students to demonstrate proficiency and can serve a number of purposes in classroom instruction. They are the foundation of rich discussion around what students need to do to perform at higher levels and to explain the progression of learning within a subject and grade level. We encourage the use of the PLDs for a variety of purposes, such as differentiating instruction to maximize individual student outcomes, creating classroom assessments and rubrics to help in identifying target performance levels for individual or groups of students, and tracking student growth along the proficiency continuum as described by the PLDs. 3

4 Cluster Performance Level 4 Performance Level 3 Performance Level 2 Performance Level 1* Students use the four operations with whole numbers to solve problems. (4.OA.1-3) Interpret multiplication equations as comparisons, and represent statements of multiplicative comparisons as multiplicative equations. Interpret multiplication equations as comparisons or represent statements of multiplicative comparisons as multiplicative equations. Interpret multiplication equations as comparisons or represent statements of multiplicative comparisons as multiplicative equations. Use multiplication or division to solve multi-step word problems involving multiplicative comparisons. Create real-world problems that could be solved using multiplicative comparison. Solve multi-step word problems using the four operations with whole numbers (multiplying a three- or four-digit number by a one-digit number, multiplying a two-digit number by a two-digit number, or dividing a three- or four-digit dividend by one-digit divisors), including problems in which remainders must be interpreted. Represent multi-step word problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding. Use multiplication or division to solve word problems involving multiplicative comparisons. Solve two-step word problems using the four operations with whole numbers (multiplying a three-digit number by a onedigit number, multiplying a twodigit number by a two-digit number, or dividing a threedigit dividend by one-digit divisors), including problems in which remainders must be interpreted. Represent multi-step word problems using equations with a letter standing in for the unknown quantity. Use multiplication or division to solve scaffolded problems involving multiplicative comparisons. Solve one-step word problems using the four operations with whole numbers (multiplying a three-digit number by a onedigit number or dividing a twodigit dividend by one-digit divisors). 4

5 Cluster Performance Level 4 Performance Level 3 Performance Level 2 Performance Level 1* Students generalize place value understanding for multi-digit whole numbers. (4.NBT.1-3) In any multi-digit whole number, determine that a digit in one place represents ten times as much as it represents in the place to its right. In any multi-digit whole number, determine that a digit in one place represents ten times as much as it represents in the place to its right. In any three-digit whole number, determine that a digit in one place represents ten times as much as it represents in the place to its right. Read, write, and compare multidigit whole numbers using base-ten numerals, number names in expanded form, and inequality symbols (>, <, =). Round multi-digit whole numbers to any place value, and choose an appropriate rounded number given a context. Read, write, and compare multi-digit whole numbers using base-ten numerals, number names in expanded form, and inequality symbols (>, <, =). Round multi-digit whole numbers to any place value. Read, write, and compare threedigit whole numbers using baseten numerals, number names in expanded form, and inequality symbols (>, <, =). Round three-digit whole numbers to any place value. 5

6 Cluster Performance Level 4 Performance Level 3 Performance Level 2 Performance Level 1* Students use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.5,6) Multiply a four-digit number by a one-digit whole number or a two-digit number by two-digit number based on place value and the properties of operations. Multiply a four-digit number by a one-digit whole number or a two-digit number by two-digit number based on place value and the properties of operations. Multiply a three-digit number by a one-digit whole number based on place value and the properties of operations. Illustrate and explain the product by using equations, rectangular arrays, and/or area models. Divide whole numbers up to four-digit dividends and onedigit divisors based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the quotient by using equations, rectangular arrays, and/or area models. Divide whole numbers up to four-digit dividends and onedigit divisors based on place value, the properties of operations, and/or the relationship between multiplication and division. Divide whole numbers up to two-digit dividends and one-digit divisors based on place value, the properties of operations, and/or the relationship between multiplication and division. 6

7 Cluster Performance Level 4 Performance Level 3 Performance Level 2 Performance Level 1* Students extend understanding of fraction equivalence and ordering. (4.NF.1,2) Generate equivalent fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. Generate equivalent fractions using visual models with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. Identify equivalent fractions using visual models with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. Compare two fractions, with like or unlike numerators or denominators, by creating common denominators and comparing to a benchmark fraction. Compare two fractions, with like or unlike numerators or denominators, by creating common denominators and comparing to a benchmark fraction. Given a visual model, compare two fractions, with like or unlike numerators or denominators, by comparing to a benchmark fraction. Students build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3,4) Record the results of comparisons with symbols >, =, or <. Create and solve mathematical and word problems involving the addition and subtraction of fractions and mixed numbers with like denominators by joining and separating parts. Record the results of comparisons with symbols >, =, or <. Solve mathematical and word problems involving the addition and subtraction of fractions and mixed numbers with like denominators by joining and separating parts. Record the results of comparisons with symbols >, =, or <. Using visual models, solve mathematical problems involving the addition and subtraction of fractions with like denominators by joining and separating parts. Decompose a fraction into a sum of fractions with the same denominator in more than one way. Decompose a fraction into a sum of fractions with the same denominator in more than one way. Using a visual model, decompose a fraction into a sum of fractions with the same denominator in more than one way. Create a visual fraction model, and solve mathematical and word problems by recognizing that fraction a is a multiple of b 1 and use that construct to b multiply a fraction by a whole number. Solve mathematical and word problems by recognizing that fraction a b is a sum of unit fractions 1 and use that b construct to multiply a fraction by a whole number. Using visual models, solve mathematical problems by recognizing that fraction a b is a multiple of 1 and use that b construct to multiply a fraction by a whole number. 7

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