Alabama Reading and Mathematics Test. Annotated Packet. for Mathematics Grade 7

Transcription

1 Alabama Reading and Mathematics Test Annotated Packet for Mathematics Grade 7 Dr. Joseph B. Morton State Superintendent of Education Alabama State Department of Education Montgomery, Alabama NCS Pearson, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright owner except for the printing of complete pages with the copyright notice, for instructional use and not for resale. Portions of this work were previously published. Printed in the United States of America.

2 TABLE OF CONTENTS Introduction 3 Glossary of Common Terms 4 Math Grade 7 Question Question with description of an accurate response 5 Question Rubric 6 Question Samples of responses with annotations 7 Math Grade 7 Question Question 17 Description of an accurate response with question rubric 18 Question Samples of responses with annotations 19 2

3 INTRODUCTION This document provides specific information about the open-ended questions on the Alabama Reading and Mathematics Test (ARMT). It is intended to give an overview of how responses to open-ended questions are scored and to provide responses at each score point. This document includes two open-ended questions from previous administrations of the ARMT. Each open-ended question is followed by the scoring rubric and three responses for each score point. Sample responses will include annotations and explanations on scoring decisions. 3

4 GLOSSARY OF COMMON TERMS Annotations: A brief explanation of why a paper has received the score it has, emphasizing the specific ways it is representative of that score point and sometimes pointing out what is lacking that may have made it a higher score point. Invalids: Refers to student responses which do not meet criteria for scorability. For example, blank papers; off-task and/or off-topic papers; papers containing only irrelevant marks or images. These papers receive a score of zero. Item: A question for which a score or set of scores is to be recorded based on the response. Logic: The correct operation performed on the correct numbers. An error in transcription or omission of numbers from a list leads to a lack of full logic. Incorrect numbers resulting from a computation, transcription, or omission error in an early part of a response are considered part of correct logic when appropriately used in subsequent sections of the response. Open-ended response: Complex assessment items/tasks that can be approached or solved in more than one way and have more than one accurate response. Students are asked to include reasons for their conclusions. Rubric: Written descriptions of the performance evidence or behaviors expected at each level or score point on the scale for open-ended items. Score point: A numerical value representing the level of success a constructed response achieves in relation to the rubric and the descriptors for each score point. 4

5 QUESTION Accurate Response(s): a. When ordered, the scores are: 97, 98, 99, 99, 100, 108, 108, 110, 110, 110, 111, 112, 118, 121, 121, 123. The 8th and 9th positions are 110. The median is 110. b. The scores total = The mean is 109. c. The bowling score that occurs the most often, 3 times, is is the mode. 5

6 RUBRIC Score Points All correct. RESPONSE ATTRIBUTES The logics are correct and two answers are correct. OR The logics for two parts are correct and three answers are correct. OR All logics are correct. OR Parts a and b are correct. The logic for one part is correct. OR The logics are missing or incomplete but one to three answers are correct. 0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.) 6

7 Sample Paper 1 Score Point 1 A---Median-The logic, placing the numbers in order, is partially correct. The student doesn t use or take into account the repeat numbers. This leads to an incorrect median. B---Mean-The response doesn t demonstrate understanding of mean. C---Mode-The response shows correct logic for mode and the correct selection. This response receives a score point of 1 for a correct logic and answer in part c. 7

8 Sample Paper 2 Score Point 1 A---Median-The logic demonstrates understanding of median, but is incomplete (orders a set of 14 numbers instead of 16). The correct answer 110 is circled twice. B---Mean-The response appears to understand mean. A set of numbers is added together and divided by 16. The set of numbers added is incomplete, leading to an incorrect answer. C---Mode-The response doesn t demonstrate understanding of mode. The logic is partially correct for two parts, median and mean. This earns a score point of 1 since only one answer is correct. 8

9 Sample Paper 3 Score Point 1 A---Median-This logic is considered incomplete since the median was found for the individual bowler and not the entire group. B---Mean-This logic is considered incomplete since the mean was found for the individual bowler and not the entire group. C---Mode-The correct answer 110 is written. The logic is unclear. The response receives a score point of 1 for correct answers, with incomplete logic. 9

10 Sample Paper 4 Score Point 2 A---Median-The logic, placing the numbers in order, is partially correct. An incorrect answer is given due to a copy error. There should be only two 108 s and there should be a 100 in the list. B---Mean-The logic is correct when it s based on the copy error in part a, leading to a correct answer. C---Mode-Correct answer for mode based on a consistent copy error. The response is penalized only once for the copy error. This response earns a score point of 2 because all logics are correct. 10

11 24 Sample Paper 5 Score Point 2 A---Median-The logic, placing the numbers in order, is correct for median (based on a set of 16 numbers), yielding a correct median of 110. B---Mean-The logic is correct. The 16 numbers added together equal Then they are divided by 16 to reach a correct mean of 109. C---Mode-The correct answer 110 is written. This response earns a score point of 2 because both parts a and b are correct. 11

12 Sample Paper 6 Score Point 2 A---Median-The logic, placing the numbers in order, is correct for median (based on a set of 16 numbers), yielding a correct median of 110. B---Mean-The response appears to understand mean. A set of numbers is added together and divided by 16. The set of numbers added is incomplete, leading to an incorrect answer. C---Mode-The correct answer of 110 is written. The logic number(s) that appears most is a correct definition. This earns a score point of 2 because all three logics are correct. 12

13 Sample Paper 7 Score Point 3 A---Median-The logic, placing the numbers in order, is correct for median (based on a set of 16 numbers), yielding a correct median of 110. For part a, the process is slightly flawed, seven crossed out on the left and eight on the right. B---Mean-The logic is correct. The 16 numbers added together equal Then they are divided by 16 to reach a correct mean of 109. (The actual calculated mean is An answer of 109, with or without discussion of the rounding is acceptable.) C---Mode-The correct answer of 110 is written. The logic number repeated most is a correct definition. This response earns a score point of 3 because of correct answers for all three parts (110, 109, 110) with adequate logic (explanation) for determining each measure of central tendency (median, mean, and mode). 13

14 Sample Paper 8 Score Point 3 Annotation on Next Page 14

15 A---Median-The logic, placing the numbers in order, is correct for median (based on a set of 16 numbers), yielding a correct median of 110. B---Mean-The logic is correct. The 16 numbers added together equal Then they are divided by 16 to reach a correct mean of C---Mode-The correct answer 110 is written. The logic by finding the most occurring number... is a correct definition. This response earns a score point of 3 because of correct answers for all three parts (110, , 110), with complete logic (explanation or work) for determining each measure of central tendency (median, mean, and mode). 15

16 Sample Paper 9 Score Point 3 A---Median-The logic, placing the numbers in order, is correct for median (based on a set of 16 numbers), yielding a correct median of 110. B---Mean-The logic is correct. The 16 numbers added together equal Then they are divided by 16 to reach a correct mean of C---Mode-The correct answer 110 is written. The logic is correct, identifying the most by circling the three 110 s. This response earns a score point of 3 because of correct answers for all three parts (110, , 110), with complete logic (work shown) for determining each measure of central tendency (median, mean, and mode). 16

17 QUESTION 17

18 Accurate Response(s): Wallace is correct, even though he did not predict the actual probability. The probability is the same every time Anna conducts the experiment, even if she does it 100 times in a row. The compound probability of any single outcome is: = 12 1 and that is between 0 and 50%. RUBRIC Score Points All correct. RESPONSE ATTRIBUTES The logic supporting the correct answer is complete. OR Partial logic is demonstrated and the answer is correct. The answer is correct. OR Partial logic is demonstrated. 0 None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.) 18

19 Sample Paper 10 Score Point 1 The correct answer (Wallace) is selected without logic. This response earns a score point of 1 for the correct answer. 19

20 Sample Paper 11 Score Point 1 The answer is correct (Wallace). The explanation is insufficient to be accepted as even partial logic. For the quarter, it is correct that there is a 1/2 chance of landing on tails. For the cube, it is correct that there is a 1/6 chance of rolling a 3 in Experiment Number 5. The response correctly notes that this is between 0 and 50 but fails to address compound probability. This response earns a score point of 1 because the answer is correct. 20

21 Sample Paper 12 Score Point 1 The answer is correct (Wallace). The explanation is insufficient to be accepted as even partial logic. For the quarter, it is correct that there is a 1/2 chance of landing on tails. For the cube, it is correct that there is a 1/6 chance of rolling a 3 in Experiment Number 5. However, the response fails to address compound probability. The response earns a score point of 1 because the answer is correct. 21

22 Sample Paper 13 Score Point 2 The answer is correct (Wallace). For the quarter, it is correct that there is a 1/2 chance of landing on tails. For the cube, it is correct that there is a 1/6 chance of rolling a 3 in Experiment Number 5. Partial logic is demonstrated because the response recognizes compound probability but does not solve for compound probability. Partial logic and the correct answer earn this response a score point of 2. 22

23 Sample Paper 14 Score Point 2 The answer is correct (Wallace). For the quarter, it is correct that there is a 1/2 chance of landing on tails. For the cube, it is correct that there is a 1/6 chance of rolling a 3 in Experiment Number 5. Partial logic is demonstrated because the response recognizes compound probability but solves incorrectly, making a calculation error. Partial logic and the correct answer earn this response a score point of 2. 23

24 Sample Paper 15 Score Point 2 The answer is correct (Wallace). For the quarter, it is correct that there is a 1/2 chance of landing on tails. For the cube, it is correct that there is a 1/6 chance of rolling a 3 in Experiment Number 5. Partial logic is demonstrated because the response recognizes compound probability giving the correct probability of 1/12. The response doesn t show the calculation of times 1/6 to equal 1/12 so the logic is not considered complete. Partial logic and the correct answer earn this response a score point of 2. 24

25 Sample Paper 16 Score Point 3 The answer is correct (Wallace). 1 For the quarter, it is correct that there is a chance of landing on tails. 2 1 For the cube, it is correct that there is a chance of rolling a 3 in 6 Experiment Number 5. 1 The logic correctly illustrates compound probability calculating that times equals. The response does not need to explain how or was derived. The response receives a score point of 3 for all correct. 25

26 Sample Paper 17 Score Point 3 The answer is correct (Wallace). 1 For the quarter, it is correct that there is a chance of landing on tails. 2 1 For the cube, it is correct that there is a chance of rolling a 3 in 6 Experiment Number 5. 1 The logic correctly illustrates compound probability, calculating that times equals The response receives a score point of 3 for all correct. 26

27 3 Sample Paper 18 Score Point 3 The answer is correct (Wallace). 1 The logic illustrates compound probability correctly calculating that times equals. Also, this response shows why the other classmates are 6 12 not correct. The response receives a score point of 3 for all correct. 27