ISTEP+: Grade 7 Mathematics. Released Items and Scoring Notes

Transcription

1 ISTEP+: Grade 7 Mathematics Released Items and Scoring Notes

2 Introduction Indiana students in Grades 3-8 participated in the ISTEP+ Spring 2013 administration. The test for ISTEP+ in Spring 2013 consisted of an Applied Skills section administered in March and a Multiple-Choice section administered in late April and early May. For all grades, the Applied Skills section of the assessment was handscored by trained evaluators. The Multiple-Choice section was machine-scored. Scores for the Applied Skills and Multiple-Choice sections are combined to generate a student s total score. Test results for both the Multiple-Choice and Applied Skills sections, as well as images of the Applied Skills student responses, are available online. It is the expectation of the Indiana Department of Education that schools will take this opportunity to have a conversation with parents and students about the results. As a springboard for this conversation, the Indiana Department of Education has created this document which outlines the released Applied Skills questions and includes brief scoring notes that describe the given score points and explain the scoring rules and expectations for the individual questions. This document consists of: a brief description of the types of questions assessed a short summary of scoring rules utilized by the trained evaluators access to rubrics used to score student responses a copy of the released Applied Skills questions anchor papers used by evaluators to distinguish between rubric scores NOTE: The Applied Skills operational questions are released at the end of each test administration. It is important to keep in mind that a significant portion of a student s score is calculated from the Multiple-Choice section of the assessment, which is not addressed within this document. Page 2 of 32

3 QUESTION TYPES This document addresses the Applied Skills section of ISTEP+, which allows students to demonstrate their understanding of content in a variety of ways. The Applied Skills Assessment consists of constructed-response (CR) and extended-response (ER) questions. CR and ER questions are cognitively more demanding than multiple-choice (MC) questions. ER questions are typically more complex and will likely require more steps to respond. SCORING For the Applied Skills Assessment, each question is scored according to a rubric. Rubrics clearly define the requirements for each score point. Each student response is evaluated individually to determine whether it is acceptable. This allows student scores to be reported as accurately as possible. To ensure consistency when scoring the ISTEP+ questions, CTB/McGraw-Hill works closely with assessment specialists at the Indiana Department of Education and teacher committees to set guidelines for scoring student responses. Committees look at several student papers and score them using the rubrics. Some of the student responses are selected as anchor papers and are used as clear examples of specific score points. Samples of anchor papers are presented within this document. Scoring supervisors then use anchor papers and approved, scored student responses to ensure that responses are evaluated appropriately and consistently. Individuals who evaluate and score ISTEP+ student responses must have a four-year college degree and pass a series of qualifying tests on specific questions before they can evaluate any student responses. If a response is unscorable, it is assigned one of the following condition codes: A B C D Blank/No Response/Refusal Illegible Written predominantly in a language other than English Insufficient response/copied from text For additional information regarding ISTEP+ or other student assessments, please contact the Indiana Department of Education by calling or writing via istep@doe.in.gov. Page 3 of 32

4 The chart below summarizes the question types used to measure a student s mastery of content, the assessment that contains the particular question type, the standards assessed in each assessment, and the scoring method used to evaluate a student s response given the question type. Scoring Note: All student responses to questions found in each Applied Skills Assessment are handscored using the specific rubric(s) outlined in the column labeled Scoring Method. As indicated in the chart, all multiple-choice questions are machine scored. Question Type Assessment Standards Assessed Scoring Method Constructed-Response (CR) Applied Skills Assessment 1,2,3,5,7 4-pt. CR Rubric (2-pts. Content and 2-pts. Problem Solving) Extended-Response (ER) Applied Skills Assessment 1,2,3,5,7 6-pt. ER Rubric (3-pts. Content and 3-pts. Problem Solving) Multiple-Choice (MC) Multiple-Choice Assessment All Machine-Scored More information is available regarding these assessment topics on the Office of Student Assessment homepage at Page 4 of 32

5 Constructed Response Rubric Content Rubric 2 A score of two indicates a thorough understanding of the mathematical concepts embodied in the task. The response shows algorithms, computations, and other content related work executed correctly and completely. 1 A score of one indicates a partial understanding of the mathematical concepts embodied in the task. The response contains errors in the execution of algorithms, computations, and/or other content related work. 0 A score of zero indicates limited or no understanding of the mathematical concepts embodied in the task. Problem-Solving Rubric 2 A score of two indicates a thorough understanding of the problem-solving concepts embodied in the task. The response shows an appropriate strategy to solve the problem, and the strategy is executed correctly and completely. identifies all important elements of the problem and shows a complete understanding of the relationships among them. provides clear and complete explanations and/or interpretations when required. 1 A score of one indicates a partial understanding of the problem-solving concepts embodied in the task. The response contains one or more of the following errors. The response shows an appropriate strategy to solve the problem. However, the execution of the strategy contains errors and/or is incomplete. identifies some of the important elements of the problem and shows a general understanding of the relationships among them. provides incomplete, partial, or unclear explanations and/or interpretations when required. 0 A score of zero indicates limited or no understanding of the problem-solving concepts embodied in the task. Clarification and Implementation Guidance Correct answers ONLY, on all parts of the problem with no work shown, will receive a maximum of 1 point in content and a maximum of 1 point in Problem Solving. A student can receive the top score point in Problem Solving if the strategy used would result in a correct answer even though the response contains computation errors. A student can receive the top score point in Problem Solving if an error made in the content portion is used with an appropriate strategy to solve the problem. Page 5 of 32

6 Extended Response Rubric Content Rubric 3 A score of three indicates a thorough understanding of the mathematical concepts embodied in the task. The response shows algorithms, computations, and other content related work executed correctly and completely. 2 A score of two indicates a partial understanding of the mathematical concepts embodied in the task. The response shows an attempt to execute algorithms, computations, and other content related work correctly and completely; computation errors or other minor errors in the content related work may be present. 1 A score of one indicates a limited understanding of the mathematical concepts embodied in the task. The response contains major errors, or only a partial process. contains algorithms, computations, and other content related work which may only be partially correct. 0 A score of zero indicates no understanding of the mathematical concepts embodied in the task. Problem-Solving Rubric 3 A score of three indicates a thorough understanding of the problem-solving concepts embodied in the task. The response shows an appropriate strategy to solve the problem, and the strategy is executed correctly and completely. identifies all important elements of the problem and shows a complete understanding of the relationships among them. provides clear and complete explanations and/or interpretations when required. 2 A score of two indicates a partial understanding of the problem-solving concepts embodied in the task. The response contains one or more of the following errors. The response shows an appropriate strategy to solve the problem. However, the execution of the strategy lacks an essential element. identifies some of the important elements of the problem and shows a general understanding of the relationships among them. provides incomplete or unclear explanations and/or interpretations when required. 1 A score of one indicates a limited understanding of the problem-solving concepts embodied in the task. The response contains one or more of the following errors. The response shows an appropriate strategy to solve the problem. However, the execution of the strategy is applied incorrectly and/or is incomplete. shows a limited understanding of the relationships among the elements of the problem. provides incomplete, unclear, or omitted explanations and/or interpretations when required. 0 A score of zero indicates no understanding of the problem-solving concepts embodied in the task. Clarification and Implementation Guidance Correct answers ONLY, on all parts of the problem with no work shown, will receive a maximum of 2 points in content and a maximum of 2 points in Problem Solving. A student can receive the top score point in Problem Solving if the strategy used would result in a correct answer even though the response contains computation errors. A student can receive the top score point in Problem Solving if an error made in the content portion is used with an appropriate strategy to solve the problem. Page 6 of 32

7 Constructed Response Standard 5: Measurement Standard 7: Problem Solving Question 1 Ms. Thompson is installing a new tile floor in her kitchen. There are cabinets along two sides of the kitchen floor that are 1.5 feet wide, as shown in the diagram below. What is the area of the kitchen floor, not including the area covered with cabinets? Show All Work Answer square feet Page 7 of 32

8 Each 1-foot square tile costs $4.50, before tax. What would be the cost, before tax, to purchase enough 1-foot square tiles to cover the part of the kitchen floor that does not have cabinets on it, plus 10 extra tiles? Show All Work Answer $ Page 8 of 32

9 Exemplary Response: 104 square feet And $513 Sample Process: = = 8 A = lw = 13 x 8 = = x $4.50 = $513 Page 9 of 32

10 Question 1, Sample A Measurement Score Point 1; Problem Solving Score Point 2 Scoring Notes: This response shows a partial understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. There is only one flaw in this response. In part one, the correct area for the entire kitchen is found. However, the process shown to determine the kitchen area covered with cabinets is not valid which results in an incorrect answer for part one. The incorrect answer in part one is used correctly in part two. Page 10 of 32

11 Question 1, Sample B Measurement Score Point 1; Problem Solving Score Point 1 Scoring Notes: This response shows a partial understanding of the content skills and a partial understanding of the problem-solving concepts within the question. In part one, the correct area for the entire kitchen is found. However, the process shown to determine the kitchen area covered with cabinets is not valid which results in an incorrect answer for part one. The incorrect answer in part one is used correctly in part two; however, the process to include the cost of 10 extra tiles is incorrect. Page 11 of 32

12 Question 1, Sample C Measurement Score Point 0; Problem Solving Score Point 2 Scoring Notes: This response shows limited or no understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. In part one, the perimeter is found instead of the area. In part two, the work and answer are correct based on the incorrect answer in part one. Page 12 of 32

13 Question 1, Sample D Measurement Score Point 0; Problem Solving Score Point 1 Scoring Notes: This response shows limited or no understanding of the content skills and a partial understanding of the problem-solving concepts within the question. In part one, the work and answer are both incorrect. In part two, the incorrect answer from part one is used correctly, however, the cost of 10 extra tiles is not included. Page 13 of 32

14 Constructed Response Standard 5: Measurement Standard 7: Problem Solving Question 2 Angela is using water from her well to fill a fish tank that is shaped like a rectangular prism, as shown in the diagram below. Angela is going to fill the fish tank to a level that is 3 inches below the top of the tank. Angela s well pumps 8 gallons of water per minute. How many minutes will it take to fill the fish tank? Show All Work Answer minutes Page 14 of 32

15 Exemplary Response: 9.84 minutes Sample Process: 2 feet 3 inches = 1.75 feet 1.75 x 4 x 1.5 = 10.5 cubic feet 10.5 x 7.5 = gallons minutes Page 15 of 32

16 Question 2, Sample A Measurement Score Point 1; Problem Solving Score Point 2 Scoring Notes: This response shows a partial understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. The only flaw in this response is that the volume of water needed to fill the tank should have accounted for the tank only being filled to 3 inches below the top. Everything else is correct. Page 16 of 32

17 Question 2, Sample B Measurement Score Point 1; Problem Solving Score Point 1 Scoring Notes: This response shows a partial understanding of the content skills and a partial understanding of the problem-solving concepts within the question. The volume of water needed to fill the entire tank is found correctly. However, an incorrect process is used (12 3) when trying to account for the tank only being filled to 3 inches below the top. Next, the volume of water is correctly converted to gallons; however, this value should have been divided by 8 to determine the number of minutes needed to fill the tank. Page 17 of 32

18 Question 2, Sample C Measurement Score Point 0; Problem Solving Score Point 2 Scoring Notes: This response shows a limited or no understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. An incorrect process is used ( ) to determine the volume of water needed to fill the tank. All of the steps shown after that are correct. A correct process to convert from cubic feet to gallons is shown as well as a correct process to determine the number of minutes. Page 18 of 32

19 Question 2, Sample D Measurement Score Point 1; Problem Solving Score Point 0 Scoring Notes: This response shows a partial understanding of the content skills and limited or no understanding of the problem-solving concepts within the question. A correct process to determine the volume of water in the entire tank is shown. Page 19 of 32

20 Constructed Response Standard 3: Algebra & Functions Standard 7: Problem Solving Question 3 Emily is playing a game. She needs 300 points to win the game. She scored 34 points on her first turn, 27 points on her second turn, and 23 points on her third turn. Write an equation that can be used to determine the number of turns, n, Emily needs to win the game if she scores 27 points on each remaining turn. Equation The maximum number of points that can be scored on 1 turn is 40 points. How many fewer turns will it take Emily to win the game if she scores 40 points on each of her remaining turns than if she only scores 27 points? Show All Work Answer fewer turns Page 20 of 32

21 Exemplary Response: 27n + 84 = 300 (Or other valid equation.) And 2 fewer turns Sample Process: = 84 27n + 84 = n = n = 216 n = n = 8 turns = turns 8 6 = 2 fewer turns Page 21 of 32

22 Question 3, Sample A Algebra & Functions Score Point 2; Problem Solving Score Point 1 Scoring Notes: This response shows a thorough understanding of the content skills and a partial understanding of the problem-solving concepts within the question. The only flaw in this response is that 216 divided by 40 is 5.4. In this context, 5.4 should be rounded up to 6 instead of down to 5 in order to have enough points to win the game. Everything else is correct. Page 22 of 32

23 Question 3, Sample B Algebra & Functions Score Point 1; Problem Solving Score Point 2 Scoring Notes: This response shows a partial understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. The written equation is incorrect; however, everything else in this response is correct. The equation does not take into account that 27 points would be scored on each remaining turn which could be represented by 27n. Page 23 of 32

24 Question 3, Sample C Algebra & Functions Score Point 2; Problem Solving Score Point 0 Scoring Notes: This response shows a thorough understanding of the content skills and limited or no understanding of the problem-solving concepts within the question. This response shows a strong understanding of the content assessed in this question. The written equation is correct, and the equation is solved correctly. Page 24 of 32

25 Question 3, Sample D Algebra & Functions Score Point 1; Problem Solving Score Point 0 Scoring Notes: This response shows a partial understanding of the content skills and limited or no understanding of the problem-solving concepts within the question. This response shows a correct equation only. Page 25 of 32

26 Extended Response Standard 5: Measurement Standard 7: Problem Solving Question 4 A company is having 2 rectangular signs made to place in front of their building. A diagram of sign A is shown below. Sign B is similar to sign A. The dimensions of sign B are dimensions of sign A. The company will be charged in the following manner to have the signs made. $18 per square foot for signs over 20 square feet $13 per square foot for signs 20 square feet and under What will be the total cost for the company to have both signs made? the Show All Work Answer $ The company is thinking about having a third rectangular sign made to put on the side of their building. They want the sign to have the greatest area possible and still be charged at the $13 rate instead of the $18 rate. What is a possible length and width of the third sign? Length feet Width feet Page 26 of 32

27 Exemplary Response: $1,050 And Length: 5 feet Width: 4 feet Or other valid dimensions Sample Process: 9 3 = 3 feet 6 3 = 2 feet Sign B is 3 feet by 2 feet Sign B: A = lw = 3 x 2 = 6 square feet 6 x 13 = $78 Sign A: A = lw = 9 x 6 = 54 square feet 54 x $18 = $972 $972 + $78 = $1,050 Page 27 of 32

28 Question 4, Sample A Measurement Score Point 2; Problem Solving Score Point 3 Scoring Notes: This response shows a partial understanding of the content skills and a thorough understanding of the problem-solving concepts within the question. The only flaw in this response is a computation error when multiplying 13 and 6. Everything else is correct. Page 28 of 32

29 Question 4, Sample B Measurement Score Point 3; Problem Solving Score Point 1 Scoring Notes: This response shows a thorough understanding of the content skills and a limited understanding of the problem-solving concepts within the question. This response shows a strong understanding of the content assessed in this question. The dimensions of sign B are found as well as the area of both signs. However, limited understanding is shown to determine the cost of sign A and sign B, and the dimensions given for the third sign do not give the greatest area while being charged at the $13 rate. Page 29 of 32

30 Question 4, Sample C Measurement Score Point 1; Problem Solving Score Point 2 Scoring Notes: This response shows a limited understanding of the content skills and a partial understanding of the problem-solving concepts within the question. The area of sign A is found; however, the dimensions and area of sign B are not determined. This results in a Content Score of one point. This response also shows an understanding of the relationship between the costs and areas of the signs; however, the dimensions given for the third sign do not give the greatest area while being charged at the $13 rate. This results in a Problem Solving Score of two points. Page 30 of 32

31 Question 4, Sample D Measurement Score Point 1; Problem Solving Score Point 1 Scoring Notes: This response shows a limited understanding of the content skills and a limited understanding of the problem-solving concepts within the question. This response gives the correct area and cost of sign A; however, there is nothing else correct in this response. Page 31 of 32

32 Question 4, Sample E Measurement Score Point 1; Problem Solving Score Point 0 Scoring Notes: This response shows a limited understanding of the content skills and no understanding of the problem-solving concepts within the question. This response gives the correct area of sign A; however, there is nothing else correct in this response. Page 32 of 32