FOR TEACHERS ONLY. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA

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1 FOR TEACHERS ONLY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesday, June 17, :15 a.m. to 12:15 p.m., only SCORING KEY Mechanics of Rating The following procedures are to be followed f scing student answer papers f the Regents Examination in Integrated Algebra. Me detailed infmation about scing is provided in the publication Infmation Booklet f Scing the Regents Examination in Integrated Algebra. Use only a No. 2 pencil in rating the Regents Examination in Integrated Algebra. Do not attempt to crect the student s wk by making insertions changes of any kind. Scing overlays have been included in the package of scing materials and must be used to sce Part I, the multiple-choice section. When scing the examination: cut out the rectangular space on the bottom of the scing overlay to recd the total Part I sce do not punch holes in the scing overlay do not make any marks on the answer sheet, other than in the spaces provided f recding sces do not machine scan the answer sheets. Marking up scanning these answer sheets will interfere with the sce collection. Unless otherwise specified, mathematically crect variations in the answers will be allowed. Units need not be given when the wding of the questions allows such omissions. Each student s answer paper is to be sced by a minimum of three mathematics teachers. On the back of the student s answer sheet, raters must enter their initials in the boxes next to the questions they have sced and also write their name in the box under the heading Rater s/scer s Name. Raters should recd the student s sces f all questions and the total raw sce on the student s answer sheet. Make a careful recd to be retained in the school of the total raw sce earned by each student. The State Education Department will provide a recdkeeping fm f this purpose as part of the detailed directions f administering and scing the June 2008 Regents Examination in Integrated Algebra. The conversion chart f the Regents Examination in Integrated Algebra will be posted on the Department s web site no later than Rating Day, Thursday, June 26, 2008.

2 Part I Allow a total of 60 credits, 2 credits f each of the following: (1) 1 (9) 2 (17) 3 (25) 3 (2) 4 (10) 4 (18) 2 (26) 4 (3) 1 (11) 1 (19) 3 (27) 4 (4) 1 (12) 3 (20) 3 (28) 1 (5) 4 (13) 4 (21) 2 (29) 4 (6) 2 (14) 1 (22) 3 (30) 2 (7) 1 (15) 4 (23) 4 (8) 3 (16) 2 (24) 2 [2] [OVER]

3 Updated infmation regarding the rating of this examination may be posted on the New Yk State Education Department s web site during the rating period. Check this web site and select the link Examination Scing Infmation f any recently posted infmation regarding this examination. This site should be checked befe the rating process f this examination begins and several times throughout the Regents examination period. General Rules f Applying Mathematics Rubrics I. General Principles f Rating The rubrics f the constructed-response questions on the Regents Examination in Integrated Algebra are designed to provide a systematic, consistent method f awarding credit. The rubrics are not to be considered all-inclusive; it is impossible to anticipate all the different methods that students might use to solve a given problem. Each response must be rated carefully using the teacher s professional judgment and knowledge of mathematics; all calculations must be checked. The specific rubrics f each question must be applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters must follow the general rating guidelines in the publication Infmation Booklet f Scing the Regents Examination in Integrated Algebra, use their own professional judgment, confer with other mathematics teachers, and/ contact the consultants at the State Education Department f guidance. During each Regents examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools befe each administration period. II. Full-Credit Responses A full-credit response provides a complete and crect answer to all parts of the question. Sufficient wk is shown to enable the rater to determine how the student arrived at the crect answer. When the rubric f the full-credit response includes one me examples of an acceptable method f solving the question (usually introduced by the phrase such as ), it does not mean that there are no additional acceptable methods of arriving at the crect answer. Unless otherwise specified, mathematically crect alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; i.e., an algebraic solution a graphic solution. A crect solution using a method other than the one specified is awarded half the credit of a crect solution using the specified method. III. Appropriate Wk Full-Credit Responses: The directions in the examination booklet f all the constructed-response questions state: Clearly indicate the necessary steps, including appropriate fmula substitutions, diagrams, charts, etc. The student has the responsibility of providing the crect answer and showing how that answer was obtained. The student must construct the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used. Responses With Errs: Rubrics that state Appropriate wk is shown, but are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errs, whether computational, rounding, graphing, conceptual. If the response is incomplete, i.e., an equation is written but not solved an equation is solved but not all of the parts of the question are answered, appropriate wk has not been shown. Other rubrics address incomplete responses. IV. Multiple Errs Computational Errs, Graphing Errs, and Rounding Errs: Each of these types of errs results in a 1-credit deduction. Any combination of two of these types of errs results in a 2-credit deduction. No me than 2 credits should be deducted f such mechanical errs in any response. The teacher must carefully review the student s wk to determine what errs were made and what type of errs they were. Conceptual Errs: A conceptual err involves a me serious lack of knowledge procedure. Examples of conceptual errs include using the increct fmula f the area of a figure, choosing the increct trigonometric function, multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual err can receive no me than half credit. If a response shows repeated occurrences of the same conceptual err, the student should not be penalized twice. If the same conceptual err is repeated in responses to other questions, credit should be deducted in each response. If a response shows two ( me) different maj conceptual errs, it should be considered completely increct and receive no credit. If a response shows one conceptual err and one computational, graphing, rounding err, the teacher must award credit that takes into account both errs, i.e., awarding half credit f the conceptual err and deducting 1 credit f each mechanical err (maximum of two deductions f mechanical errs). [3] [OVER]

4 Part II F each question, use the specific criteria to award a maximum of two credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (31) [2] Ann s, and appropriate wk is shown to justify the answer. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown calculating gas mileage of both vehicles, but no further crect wk is shown. [0] Ann s, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. (32) [2] , and appropriate wk is shown. [1] Appropriate wk is shown, but one computational err is made. [1] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown, but the answer is not expressed in terms of. [1] 36 9, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [4] [OVER]

5 (33) [2] 0 t 40 an equivalent answer. [1] Appropriate wk is shown, but one conceptual err is made, such as 0 < t < t 50. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [5] [OVER]

6 Part III F each question, use the specific criteria to award a maximum of three credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (34) [3] d 75 an equivalent inequality and 33, and appropriate wk is shown. [2] Appropriate wk is shown, but one computational rounding err is made. [1] Appropriate wk is shown, but two me computational rounding errs are made. [1] Appropriate wk is shown, but one conceptual err is made. [1] An increct inequality of equal difficulty is solved appropriately. [1] d 75, but no further crect wk is shown. [1] 33, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [6] [OVER]

7 (35) [3] 3 18 and % % equivalent answers, and $13.50, and appropriate wk is shown. [2] Appropriate wk is shown, but one rounding err is made, such as 16.6%, 16.7%, 17%. [2] An increct fractional rate of discount is found, but an appropriate percent is stated, and $13.50 is found. [2] Appropriate wk is shown, but only two crect answers are found. [1] Appropriate wk is shown, but one conceptual err is made. [1] Appropriate wk is shown, but only one crect answer is found. [1] 3 18, %, and $13.50, but no wk is shown. [0] 3 18, %, $13.50, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [7] [OVER]

8 (36) [3] The crect graph is drawn, and 1 and 3 are found. [2] Appropriate wk is shown, but one graphing err is made, but appropriate roots are identified. [2] The graph of the parabola is drawn crectly, but no further crect wk is shown. [1] Appropriate wk is shown, but two me graphing errs are made, but appropriate roots are identified. [1] Appropriate wk is shown, but one conceptual err is made. [1] 1 and 3 are stated, but no wk is shown. [0] 1 3 is stated, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [8] [OVER]

9 Part IV F each question, use the specific criteria to award a maximum of four credits. Unless otherwise specified, mathematically crect alternative solutions should be awarded appropriate credit. (37) [4] An appropriate equation is written, width = 3, length = 18, and appropriate wk is shown. [3] Appropriate wk is shown, but one computational facting err is made. [3] Appropriate wk is shown, but the length and width are not labeled are labeled increctly. [3] Appropriate wk is shown to find either the length the width of the walkway, but no further crect wk is shown. [2] Appropriate wk is shown, but two computational facting errs are made. [2] Appropriate wk is shown, but one conceptual err is made. [2] An appropriate quadratic equation in standard fm (set equal to zero) is written, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational facting err are made. [1] An appropriate equation is written, but no further crect wk is shown. [1] Width = 3 and length = 18, but no wk is shown. [0] Width = 3 length = 18, but no wk is shown. [0] 3 and 18, but no wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [9] [OVER]

10 (38) [4] , , and 0.008, and appropriate wk is shown, and an appropriate justification is given. [3] Appropriate wk is shown, but one computational rounding err is made. [3] , , and 0.008, and appropriate wk is shown, but no justification is given. [2] Appropriate wk is shown, but two me computational rounding errs are made. [2] Appropriate wk is shown, but one conceptual err is made, such as dividing by [1] Appropriate wk is shown, but one conceptual err and one computational rounding err are made. [1] and , and appropriate wk is shown, but no further crect wk is shown. [1] , , and 0.008, but no wk is shown. [0] , and appropriate wk is shown, but no further crect wk is shown. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [10] [OVER]

11 (39) [4] Mean = 315,000, median = 180,000, and the median is stated to be the best measure of central tendency, an appropriate justification is given, and appropriate wk is shown. [3] Appropriate wk is shown, but one computational err is made, but an appropriate measure of central tendency is stated, and an appropriate justification is given. [3] Mean = 315,000, median = 180,000, and the median is stated to be the best measure of central tendency, but no further crect wk is shown. [2] Appropriate wk is shown, but two computational errs are made, but an appropriate measure of central tendency is stated, and an appropriate justification is given. [2] Appropriate wk is shown, but one conceptual err is made. [2] Appropriate wk is shown to find mean = 315,000 and median = 180,000, but no further crect wk is shown. [1] Appropriate wk is shown, but one conceptual err and one computational err are made. [1] Appropriate wk is shown to find mean = 315,000 median = 180,000, but no further crect wk is shown. [1] Mean = 315,000 and median = 180,000, but no further crect wk is shown, and no justification is given. [0] Mean = 315,000 median = 180,000, but no further crect wk is shown, and no justification is given. [0] A zero response is completely increct, irrelevant, incoherent is a crect response that was obtained by an obviously increct procedure. [11] [OVER]

12 INTEGRATED ALGEBRA concluded Map to Learning Standards Key Ideas Item Numbers Number Sense and Operations 8, 28, 35 Algebra 4, 6, 7, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 30, 33, 34, 37 Geometry 1, 9, 11, 27, 29, 32, 36 Measurement 31, 38 Probability and Statistics 2, 3, 5, 19, 22, 39 Regents Examination in Integrated Algebra June 2008 Chart f Converting Total Test Raw Sces to Final Examination Sces (Scaled Sces) The Chart f Determining the Final Examination Sce f the June 2008 Regents Examination in Integrated Algebra will be posted on the Department s web site on Thursday, June 26, Submitting Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an imptant contribution to the test development process. The Department provides an online evaluation fm f State assessments. It contains spaces f teachers to respond to several specific questions and to make suggestions. Instructions f completing the evaluation fm are as follows: 1. Go to 2. Select the test title. 3. Complete the required demographic fields. 4. Complete each evaluation question and provide comments in the space provided. 5. Click the SUBMIT button at the bottom of the page to submit the completed fm. [12] [OVER]