Sample Item Extended Constructed Response Item for Grade 5
 Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic Topic A. Knowledge of Number and Place Value Indicator 1. Apply knowledge of fractions, decimals, and place value Objective c. Identify and determine equivalent forms of proper fractions Assessment limit: Use denominators that are factors of 100, decimals, or percents (0 – 200)
 Michele took a 20-question quiz in her mathematics class. She answered of the questions correctly on the quiz. Step A What is Michele's score written as a percent? Step B Explain how you found the percent that is equivalent to the fraction form of Michele's score. Use what you know about fractions and percents in your explanation. Use words, numbers, and/or symbols. Michele took a 25-question quiz in her science class. She answered of the questions correctly. Is the score on her science quiz the same or different than her math score? Explain why your answer is correct. Use what you know about fractions and percents in your explanation. Use words, numbers, and/or symbols. Step A is scored 0 (Incorrect) or 1 (Correct) and assesses 6.A.1.c. Step B is scored with a 4 point (0, 1, 2, 3) rubric and assesses Processes of Mathematics. Note: 20 "Sample Student Responses" follow below. Each response appears on its own separate page and includes scoring information. The "Sample Student Responses" represent a range of score points. Correct Answer Step A85% Sample Student Response #1 Score for Sample Student Response #1: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 0 Annotation for Step B, Using the Rubric: This response is completely incorrect. Sample Student Response #2 Score for Sample Student Response #2: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 0 Annotation for Step B, Using the Rubric: This response is completely incorrect. While the correct score, 85%, is given, the process for how it was determined is completely incorrect. The justification for the answer of "no" for the comparison of the mathematics and science scores is missing. Sample Student Response #3 Score for Sample Student Response #3: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The correct fraction for the score is given, but it is not written as a percent. However, the explanation for the process used to find the score (multiplying the fraction 17/20 by 5/5) indicates a partial application of a strategy in the context of the problem. The justification for the comparison of the mathematics and science scores is irrelevant. Sample Student Response #4 Score for Sample Student Response #4: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The explanation for how to find Michele's score is missing. The connection between the mathematics quiz score and the science quiz score is partial: "on her mathematics test... each problem is 5 points... on her science test... the points are lower... because the science test has more questions than the mathematics test." Sample Student Response #5 Score for Sample Student Response #5: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The explanation for how to find the score is missing. The connection between the relationships of the first score and the second score is partial: "25 question is more question than part A so it will be a lower percent." The justification is overly general: "17/20 is better than 17/25." Sample Student Response #6 Score for Sample Student Response #6: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 2 Annotation for Step B, Using the Rubric: This response demonstrates a general understanding and analysis of the problem. The explanation of the process used to determine Michele's score supports the answer is Step A but is only partially developed: "20X5=100. Then... 17X5=85. So the percentage is 85/100." The connection between Michele's mathematics quiz score and science quiz score is overly general: "there's more she could have right and she had the same right." Sample Student Response #7 Score for Sample Student Response #7: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 2 Annotation for Step B, Using the Rubric: This response demonstrates a general understanding and analysis of the problem. An application of a reasonable strategy for finding Michele's score is indicated. The explanation for the process used to find the percent that represents Michele's test score is clear: "I looked at how may questions there were... 5X20=100 so each question is worth five points... -15 points from 100%=85%." The connection between Michele's mathematics quiz score and science quiz score is clear, "88%>85%... Michele's two scores are different." Appropriate supportive numbers are provided. However justification for why "each question was 4 points" on the science test is missing. Sample Student Response #8 Score for Sample Student Response #8: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation for how to find Michele's mathematics score is clear and logical, "this is because 20 times 5 is 100 and 17 times 5 is 85. The top number of this fraction converts to a percent." The connection between Michele's mathematics quiz score and science quiz score is clear, "Michele's score is 85%... Michele's science score is 68%." The justification for the science score is clear and logical, "25 times 4 is 100 and 17 times 4 is 68%. The top number once again converts." Appropriate supportive information and numbers are provided. Sample Student Response #9 Score for Sample Student Response #9: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation of how to find Michele's score is clear, fully developed and logical, "Say you multiplied 20X5=100 then you would have to multiply the top number by 5... So the answer would be 85% or 85 out of 100." The connection between Michele's mathematics quiz score and science quiz score is clear and stated explicitly, "[I] got 85% (math) and 68% (science)." Appropriate supportive numbers are provided. Sample Student Response #10 Score for Sample Student Response #10: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation for how to find Michele's mathematics score is clear, fully developed and logical, "one answer equals 5%...3X5=15... 100%-15%=85%." The connection between the mathematics and science scores is clear and stated explicitly, "85% math>68% science." The justification for the comparison of scores is clear, fully developed and logical. Appropriate numbers are provided as support for the justification. Sample Student Response #11 Score for Sample Student Response #11: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 2 Annotation for Step B, Using the Rubric: This response demonstrates a general understanding and analysis of. the problem. An application of a reasonable strategy for finding Michele's score is indicated. The explanation for the process used to find the percent that represents Michel's test score is clear, "I know 20 right is 100% so 10 right must be 50%... I know 100+20=5. I added 5... I continued this pattern until 17/20=85%." Supportive numbers are provided. The connection between Michele's mathematics quiz score and science quiz score is clear, "17/25<17/20." The justification for the comparison is partial, "Because she missed 3 on the math test and 8 on the science... she did worse on the science." The connection between the different denominators and the points per question is missing. Compare to Sample Student Response #7. Sample Student Response #12 Score for Sample Student Response #12: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The correct decimal for the score is given, but it is not written as a percent. The explanation of how to find the score is missing. The supportive mathematics (17/20=10R3), is incorrect. The justification for the math and science test scores being different is partial, "Now she has 25 on the second test, five more questions than the math test she took. Compare to Sample Student Response #3. Sample Student Response #13 Score for Sample Student Response #13: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation for how to find Michele's mathematics score is clear, fully developed and logical, "The 20 is equal to 100%. Well, if every question is worth 5 points you have to multiply 17X5=85%." The connection between the mathematics and science scores is clear and stated explicitly, "No, because the points for scoring are different and the percent is different." The justification, with appropriate supportive numbers, for the comparison of scores is clear, fully developed and logical, "17 X 4points for every answer correct=68 percent." Compare to Sample Student Response #10. Sample Student Response #14 Score for Sample Student Response #14: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 0 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The explanation for how to find Michele's score is missing. The connection between the math quiz score and the science quiz score is partial, "The score is not the same...because she got 8 wrong and on the 20 question quiz she got three wrong." Compare to Sample Student Response #3. Sample Student Response #15 Score for Sample Student Response #15: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 2 Annotation for Step B, Using the Rubric: This response demonstrates a general understanding and analysis of the problem. The explanation of the process used to determine Michele's score is clear, "if each question is worth 5 points5X3=15 and 100-15=85... 20X5=100." The justification for Michele's different science quiz score is flawed, "her score would be 60 because 8X5=40 and 100-40=60." Compare to Sample Student Response #6. Sample Student Response #16 Score for Sample Student Response #16: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 0 Annotation for Step B, Using the Rubric: This response is completely incorrect. Compare to Sample Student Response #1. Sample Student Response #17 Score for Sample Student Response #17: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation for how to find Michele's math score is clear and logical, "5X20=100% and 17X5 would equal 85%." Although technically a justification, this information fully supports the explanation. The justification for Michele's science quiz score is also clear and logical, "68% is correct because 4X25=100% and 17X4 would equal 68%." The fact that 68% is a different score than 85% is never directly stated; however this is seen as a minor error and does not detract from the overall comprehensive level of understanding demonstrated in this response. Compare to Sample Student Response #8. Sample Student Response #18 Score for Sample Student Response #18: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The explanation for Michele's mathematics quiz score is partial, "100-15=85." The connection between Michele's mathematics quiz score and science quiz score is overly general, "She got a better percentage on her math... She got pretty bad on her science." The justification is logically flawed and lacks support, "73% out of 100%." Compare to Sample Student Response #5. Sample Student Response #19 Score for Sample Student Response #19: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 3 Annotation for Step B, Using the Rubric: This response demonstrates a comprehensive understanding and analysis of the problem. The application of a reasonable strategy for determining the percent in the context of the problem is indicated. The explanation for how to find Michele's mathematics score is clear, fully developed and logical, " X 20=100...20-17=3... 3X5=15... 100-15=85%." The connection between the mathematics and science scores is clear and stated explicitly, "we already know that her math score is 85%, and...100-32=68%. The justification for Michele's science quiz score is clear, fully developed and logical. Appropriate numbers are provided as support for the justification. Compare to Sample Student Response #9. Sample Student Response #20 Score for Sample Student Response #20: Step A - Content (Knowledge of Number Relationships and Computation/Arithmetic): 1 Step B - Processes of Mathematics: 1 Annotation for Step B, Using the Rubric: This response demonstrates a minimal understanding and analysis of the problem. The explanation for Michele's mathematics quiz score is partial, "You count by 5's 17 times." The explanation of the relationship between Michele's mathematics quiz score and science quiz score is incorrect. Supportive information and/or numbers are not provided. Compare to Sample Student Response #5.

### Extended Constructed Response (ECR) Rubric

Print: Scoring Rubric

Score 3

The response demonstrates a comprehensive understanding and analysis of a problem.

• Application of a reasonable strategy in the context of the problem is indicated.
• Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is clear, fully developed, and logical.
• Connections and/or extensions made within mathematics or outside of mathematics are clear and stated explicitly.
• Supportive information and/or numbers are provided as appropriate. 3

Score 2

The response demonstrates a general understanding and analysis of a problem.

• Application of a reasonable strategy in the context of the problem is indicated.
• Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is feasible, but may be only partially developed.
• Connections and/or extensions made within mathematics or outside of mathematics are partial or overly general, or may be implied.
• Supportive information and/or numbers are provided as appropriate. 3

Score 1

The response demonstrates a minimal understanding and analysis of a problem.

• Partial application of a strategy in the context of the problem is indicated.
• Explanation1 of and/or justification2 for the mathematical process(es) used to solve a problem is logically flawed or missing.
• Connections and/or extensions made within mathematics or outside of mathematics are flawed or missing.
• Supportive information and/or numbers may or may not be provided as appropriate.3

Score 0

The response is completely incorrect, irrelevant to the problem, or missing.4

Note 1:

Explanation refers to students' ability to communicate how they arrived at the solution for an item using the language of mathematics.

Note 2:

Justification refers to students' ability to support the reasoning used to solve a problem, or to demonstrate why the solution is correct using mathematical concepts and principles.

Note 3:

Students need to complete rubric criteria for explanation, justification, connections and/or extensions as cued for in a given problem.

Note 4:

Merely an exact copy or paraphrase of the problem will receive a score of "0".

Rubric Document Date: August 2003

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