The New York City Department of Education. Grade 4 Mathematics Benchmark Assessment. Teacher Guide Fall 2012
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1 The New York City Department of Education Grade 4 Mathematics Benchmark Assessment Teacher Guide Fall 2012 November 26, 2012 January 11,
2 Table of Contents Test Design and Instructional Purpose... 3 Limitations... 3 Test Content... 4 Rubrics for Scoring Short-Response & Extended-Response/ Performance Task Items... 7
3 Test Design and Instructional Purpose The Mathematics Benchmark Assessment is designed to help you collect some information about your students progress toward meeting the Common Core expectations for fourth grade. This information can provide insights around your students mathematical proficiency, specifically their fluency with skills, their conceptual understanding, and their ability to apply concepts and skills in novel settings. Consequently, the results from the Benchmark Assessment may influence your plans for targeting instruction to meet your students needs. There are two Mathematics Benchmark Assessments available for the school year. Both assessments are aligned to units from the New York City Department of Education s Curriculum Maps. The first Grade 4 Mathematics Benchmark Assessment, designed to be administered in the fall, focuses on Unit 1, Unit 2 and part of Unit 3. The second Grade 4 Mathematics Benchmark Assessment, designed to be administered in the winter, focuses on the remainder of Unit 3 and Unit 4. The assessments contain various item types: multiple choice, true-false (for the purpose of assessing fluency), short response, and constructed response/performance tasks. Items may partially align to a single standard, several standards, a cluster, or a domain, or may require synthesis across clusters and/or domains. The Benchmark Assessments are meant to provide a lens to identify some of the skills and concepts that may need to be taught or reinforced if students are to meet the Common Core expectations for fourth grade. The results of this assessment will best support your instruction and your students learning if you are familiar with the Common Core Learning Standards, including the fluency expectations, key advances, and culminating standards. Limitations Neither Benchmark Assessment is an exhaustive test. While each Benchmark reflects the Common Core Standards in the units that comprise its blueprint, Common Core Standards contain a breadth of skills and concepts that cannot be fully assessed by any single measure. Additionally, each Benchmark Assessment is limited to a maximum of three units and covers approximately 25 40% of the year s instruction. Accordingly, the Benchmark Assessments do not reflect the work of the entire grade. As a result, this assessment is best used as part of a comprehensive set of evaluative measures that include teacher observation, classwork, homework, and school- or teachermade assessments. If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 3
4 Test Content Unit 1 focuses on Place Value, Rounding, and Fluency with Addition and Subtraction Algorithms of Whole Numbers. Unit 2 focuses on Unit Conversions and Addition and Subtraction of Length, Weight, and Capacity. Unit 3 focuses on Multiplication and Division of Up to a 4-Digit Number by Up to a 1-Digit Number Using Place Value. Content of Benchmark 1 Unit Domain Cluster Standard Items Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten Generalize place understanding for multi-digit whole numbers. Generalize place understanding for multi-digit whole numbers. Generalize place understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. 10, 14, 19 4, 5, 11, 15 6, 12, 27 1, 2, 3 If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 4
5 3 3 1, 3 3 Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Use the four operations with whole numbers to solve problems. Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. 4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4.OA.4. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. 13, 20, 21 17, 22, 29 24, 25, 26, 30 7, 18, 23 If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 5
6 2 2 Measurement and Data Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 8, 16, 28 9 If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 6
7 Rubrics for Scoring Short-Response and Extended-Response/Performance Task Items Item # 26 Key Elements N/A Criteria 3 Meets Standard (Meets criteria at grade level) 3 correct elements 1 point for setting up equation 1 point for correct answer 1 point for process 2 Near Standard (Mostly meets criteria) 2 correct elements 1 point for setting up equation 1 point for correct answer 1 point for process 1 Approaching standard (Partially meets criteria) 1 correct element 1 point for setting up equation 1 point for correct answer 1 point for process 0 Far Below Standard Incorrect response Exemplar 3 Part A c = Other valid equation Part B = / 15 = 5 Remainder 9 Other valid process If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 7
8 Item # 27 Key Elements N/A Criteria 3 Meets Standard (Meets criteria at grade level) 3 correct elements Rounds the number correctly Explains a process to find an approximate total number of members Concludes that 28,000 is not close to Sasha's estimate 2 Near Standard (Mostly meets criteria) 2 correct elements Rounds the number correctly Explains a process to find an approximate total number of members Rounds the number correctly Concludes that the total number of members rounded to the nearest thousand is not the same as Sasha's estimate Explains a process to find an approximate total number of members Concludes that 28,000 is not close to Sasha's estimate 1 Approaching standard (Partially meets criteria) 1 correct element Rounds the number correctly Explains a process to find an approximate total number of members Concludes that 28,000 is not close to Sasha's estimate 0 Far Below Standard Incorrect response Exemplar 3 15,000 I round 13,452 to the nearest thousand and add it to 15, ,452 rounded to the nearest thousand is 13,000. Adding the two, 15, ,000 is 28, ,000 is not close to 40,000 so Sasha's estimate is too large. If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 8
9 Item # 28 Key Elements N/A Criteria 3 Meets Standard (Meets criteria at grade level) 5 correct elements Completes 5 equations correctly 2 Near Standard (Mostly meets criteria) 3 or 4 correct elements Completes 3 or 4 equations correctly 1 Approaching standard (Partially meets criteria) 1 correct element Completes 1 equation correctly 0 Far Below Standard Incorrect response Exemplar 3 1 kilogram = 1,000 grams 10 grams = 1,000 centigrams 10 centimeters = 100 millimeters 1 liter = 1,000 milliliters 1 kiloliter = 1,000 liters Item # 29 Key Elements N/A Criteria 6 Meets Standard (Meets criteria at grade level) 6 correct elements 2 points for a correct equation or model to show the multiplicative comparison between Bob and Leah 1 point for the number of old newspapers Leah collected 2 points for the correct equation to show the multiplicative comparison between Bob and Nathan 1 point for the stating the multiplicative comparison between Bob and Nathan 5 5 correct elements 4 4 correct elements 3 3 correct elements 2 2 correct elements If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 9
10 1 1 correct element 0 Far Below Standard Incorrect response Exemplar 6 If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 10
11 Item # 30 N/A Key Elements Criteria 6 Meets Standard (Meets criteria at grade level) 6 correct elements 1 point for correct number of teams 1 point for correct process 1 point for correct number of additional players 1 point for correct process 1 point for disagree 1 point for correct explanation 5 5 correct elements 4 4 correct elements 3 3 correct elements 2 2 correct elements 1 1 correct element 0 Far Below Standard Incorrect response Exemplar 6 Part A = 9 Remainder 3 9 teams can be formed Part B 18 3 = more players are needed Part C Disagree If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 11
12 Part D If there are 13 vans and each van holds 12 players then only 12 x 13 or 156 players would be able to fit in the vans. Other correct explanation If you have any questions, contact the NYC Acuity Helpdesk at 866 NYC 6550 or NYCAcuity@ctb.com. 12
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16 The New York City Department of Education Grade 4 Mathematics Benchmark Assessment Teacher Guide Fall 2012 November 26, 2012 January 11, 2013
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