armt grade 5 mathematics

Alabama Reading and Mathematics Test Annotated Packet for

Mathematics Grade 5

Dr. Joseph B. Morton State Superintendent of Education Alabama State Department of Education Montgomery, Alabama

Copyright © 2008 by Alabama State Department of Education. Copyright © 2008 by 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.

ARMT GRADE 5 MATHEMATICS TABLE OF CONTENTS Introduction

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Glossary of Common Terms

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Math Grade 5 Question Question with description of an accurate response Question Rubric Question Samples of responses with annotations

5 6 7

Math Grade 5 Question Question with description of an accurate response Question Rubric Question Samples of responses with annotations

16 17 18

2 Copyright © 2008 by Alabama State Department of Education. Copyright © 2008 by NCS Pearson, Inc. All rights reserved. Printed in the United States of America.

ARMT GRADE 5 MATHEMATICS 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.

Copyright © 2008 by Alabama State Department of Education. Copyright © 2008 by NCS Pearson, Inc. All rights reserved. Printed in the United States of America.

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ARMT GRADE 5 MATHEMATICS 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.


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ARMT GRADE 5 MATHEMATICS QUESTION

Accurate Response(s): a. Chocolate stars, jawbreakers, licorice sticks: 1.082 + 1.004 + 0.998 = 3.084 b. Peppermints, licorice sticks, chocolate stars: 0.921 + 0.998 + 1.082 = 3.001 Any other correct answers will be accepted.


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ARMT GRADE 5 MATHEMATICS RUBRIC Score

RESPONSE ATTRIBUTES

Points 3

All correct.

2

All logics are correct. OR All of part a or all of part b is correct. One logic is correct. OR One or more answers are correct. OR One logic and one answer are correct. None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)

1

0


6

ARMT GRADE 5 MATHEMATICS Sample Paper 1 Score Point 1

A---The logic (addition of 3 feasible numbers) is correct and one answer (the total) is correct, but no list is given. The student adds the weights of the chocolate stars (1.092), jawbreakers (1.004), and peppermints (0.921). The combined weight of these three candy selections is 3.017, which is over 3 pounds. There is a transcription error, the chocolate stars weigh 1.082, not 1.092 pounds, but the answer is consistent with that mistake. B---The logic and answer are missing. The student states “There is no other way.” According to the rubric, this response earned a score point of 1 because “One logic and one answer are correct.”


7


A---The logic (addition of 3 feasible numbers) is correct and one answer (the total) is correct, but no list is given. The student adds the weights of the chocolate stars (1.082) and the licorice sticks (0.998). This totals to 2.080. The student then adds the weight of the peppermints (0.921). This gives a correct answer of 3.001. B---The logic (subtraction) is incorrect, and the answer is incorrect. The student subtracts the weight of the gumballs (0.573) from the weight of the licorice sticks (.998), reaching an answer of .425. The student then subtracts this weight (.425) from the weight of the peppermints (0.921). Even though the subtraction is done correctly in both steps of part b, no credit may be given for a correct answer because the logic is faulty. According to the rubric, this response earned a score point of 1 because “One logic and one answer are correct.”


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A---The logic (addition of 3 feasible numbers) is correct, but the answer (total) is incorrect, plus no list is given. The student adds the weights of the licorice sticks (0.998), chocolate stars (1.082), and peppermints (0.921). The total is incorrect and the list is missing. B---The logic and answers are missing. According to the rubric, this response earned a score point of 1 because “One logic is correct.”


9


A---The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student listed three candies, along with three candy weights. The student adds chocolate stars (1.082), jawbreakers (1.004), and licorice sticks (0.998) to a correct total of 3.084, which is over 3 pounds. B---Part b is not attempted. The “b” shown in the answer refers to the addition of the part a candies. According to the rubric, this response earned a score point of 2 because “All of part a or all of part b is correct.”

Copyright © 2008 by Alabama State Department of Education. Copyright © 2008 by 10 NCS Pearson, Inc. All rights reserved. Printed in the United States of America.


A---The logic (addition of 3 feasible numbers) is correct and one answer (total) is correct. The student adds the weights of the chocolate stars (1.082), licorice sticks (0.998), and peppermints (0.921). The combined weight of these three candy selections when added together is 3.001, which is over 3 pounds. No list is given. B---The logic (addition of 3 feasible numbers) is correct and one answer (total) is correct. The student adds the weights of the licorice sticks (0.998), jawbreakers (1.004), and chocolate stars (1.082). The combined weight of these three candy selections when added together is 3.084, which is over 3 pounds. Again, no list is given. According to the rubric, this response earned a score point of 2 because “All logics are correct.”



A---The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student adds the weights of the chocolate stars (1.082), licorice sticks (0.998), and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.084, which is over 3 pounds. B---The logic (addition of 3 feasible numbers) is correct but the answers (total and list) are partially correct. The student adds the weights of the chocolate stars (1.082), peppermints (0.921), and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.007, which is over 3 pounds. The answer is missing the decimal point and therefore wrong. According to the rubric, this response earned a score point of 2 because “All of part a or all of part b is correct.”



A---The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student adds the weights of the licorice sticks (0.998), chocolate stars (1.082), and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.084, which is over 3 pounds. B---The logic is correct and the answers are correct. The student adds the weights of the peppermints (0.921), chocolate stars (1.082), and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.007, which is over 3 pounds. According to the rubric, this response earned a score point of 3 because all logics and answers are correct.


ARMT GRADE 5 MATHEMATICS Sample Paper 8 Score Point 3 A---The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student adds the weights of the chocolate stars (1.082), licorice sticks (0.998) and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.084, which is over 3 pounds.

B---The logic is correct and the answers are correct. The student adds the weights of the peppermints (0.921), chocolate stars (1.082), and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.007, which is over 3 pounds. According to the rubric, this response earned a score point of 3 because all logics and answers are correct. Note: Crossed out portions signify a “guess-and-check” method and are ignored.



A---The logic (addition of 3 feasible numbers) is correct and the answers (total and list) are correct. The student adds the weights of the chocolate stars (1.082), licorice sticks (0.998) and jawbreakers (1.004). The combined weight of these three candy selections when added together is 3.084, which is over 3 pounds. B---The logic is correct and the answers are correct. The student adds the weights of the chocolate stars (1.082), jawbreakers (1.004), and peppermints (0.921). The combined weight of these three candy selections when added together is 3.007, which is over 3 pounds. According to the rubric, this response earned a score point of 3 because all logics and answers are correct.


ARMT GRADE 5 MATHEMATICS QUESTION

Accurate Response(s): a. Fish b. Reason 1: Some pets are easier to take care of than others, so classes choose those pets as class pets. Reason 2: The area available in the classroom may determine what pet a class could have. Any other plausible reasons consistent with the data shown are acceptable.


ARMT GRADE 5 MATHEMATICS RUBRIC Score

RESPONSE ATTRIBUTES

Points 3

All correct.

2

Both logics are correct. OR One logic is correct and the answer is correct. OR Partial logics are correct and the answer is correct. One logic is correct. OR The answer is correct. None correct. (Also, blanks, rewrites problem, foreign language, illegible, refusals, off tasks, etc. scored as invalid.)

1 0



A---The answer (fish) is correct. B---The logics (two plausible explanations) are not valid. The prompt asks for reasons that could explain why students have different types of pets, not why fish may be popular pets. According to the rubric, a correct answer earns a score point of 1.



A---The answer is not attempted. B---One logic (plausible explanation) is correct: “…because some people like different pets and some like the same pets.” The other explanation is not attempted. According to the rubric, one correct logic earns a score point of 1.



A---The answer (fish) is correct. B---The logics (two plausible explanations) are not attempted. According to the rubric, a correct answer earns a score point of 1.



A---The answer (fish) is correct. B---One logic (plausible explanation) is correct: “because everone doesn’nt like the same animals.” The other explanation is not attempted. According to the rubric, a correct logic and answer earns a score point of 2.



A---The answer of “mouse” is incorrect. B---The logics (two plausible explanations) are correct: 1) “The oppinion might be different who wanted what...” 2) “…maybe the some of the students that he surveyed were afraid or allergic to that animal.” According to the rubric, both logics correct earns a score point of 2.



A---The answer (fish) is correct. B---One logic (plausible explanation) is correct: “They wher having a pet show.” The other explanation is not attempted. According to the rubric, a correct logic and answer earns a score point of 2.



A---The answer (fish) is correct. B---The logics (two plausible explanations) are correct: 1) “They could be having show and tell day.” 2) “They could be working in groups to see the differences in their pets.” According to the rubric, having all correct earns a score point of 3.



A---The answer (fish) is correct. B---The logics (two plausible explanations) are correct: 1) “Because it gives studants more classroom helping jobs.” 2) “because it makes the classroom more entertainable.” (This explanation was considered weak, but acceptable.) According to the rubric, having all correct earns a score point of 3.



A---The answer (fish) is correct. B---The logics (two plausible explanations) are correct: 1) “...Someone might be alergic...” 2) “…the class might of voted on a different animal”. According to the rubric, having all correct earns a score point of 3.
