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Mathematics Diagnostic

Grade 6 Scoring Guide

Mathematics, Diagnostic Grade 6

1

Mathematics Grade 6

In participating districts, all students in grades 3–8, and high school Algebra I and Geometry, will take the LEAP 360 mathematics diagnostic assessments, which are designed to:

• identify the specific prerequisite skills individual students or groups of students need in order to be successful with major content for the current grade;

• help teachers to understand student performance on previous grade-level content that is prerequisite knowledge for the current grade; and

• assist teachers with meaningful, yet ambitious, goal setting for student learning targets.

The purpose of this Scoring Guide is to provide teachers with the necessary information, guidance, and tools to score and interpret students’ responses to Reasoning (Type II) and Modeling (Type III) Constructed-Response (CR) items that align to Louisiana Student Mathematics Standards. The CRs, scoring rubrics, and numerous samples of student responses have been selected to ensure that teachers score actual responses fairly, accurately, and consistently. This document provides the scoring information and practice scoring exercise for the two CRs in the Grade 6 Diagnostic Mathematics assessment:

Item 13: Modeling Item 42: Reasoning

There are 8 or 10 anchor papers selected to illustrate the types of student responses that earn each possible number of points, or score, for each item. Each anchor paper is annotated to describe the rationale for the earned score. Scorers should:

• Review the alignment of the item (Evidence Statement and Standard[s]) as well as the metadata (Point Value, Depth of Knowledge [DOK], and Difficulty).

• Review the item. • Review the rubric. • Read each bullet point and each score point descriptor carefully. • Read the student work and annotated scoring notes for each anchor paper.


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Mathematics Grade 6, Item 13

Alignment Task Type: Modeling (Type III) Evidence Statement: LEAP.III.6.2: Solve multi-step contextual problems with degree of difficulty appropriate to Grade 6, requiring application of knowledge and skills articulated in 5.NBT.B, 5.NF, 5.MD, and 5.G.A. Primary Standard: 5.NF.B.6: Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Secondary Standard: 5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

c. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are there in 2 cups of raisins?

Point Value: 3 DOK: 2 Difficulty: Low


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Constructed-Response Item Jessica and Alex use ribbon to decorate picture frames. Part A Jessica has 1

2 yard of ribbon.

• She uses this ribbon to decorate 3 picture frames. • She uses an equal amount of ribbon to decorate each picture frame.

How many yards of ribbon does Jessica use to decorate each picture frame?

A. 16

B. 1

C. 32

D. 6

Part B Alex uses 11

3 yards of ribbon to decorate each picture frame. He wants to decorate

6 picture frames.

• Determine how many yards of ribbon Alex needs to decorate the picture frames. • Show your work or explain your answer.


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Scoring Information Part A (1 point) Answer Key: A Rationale A: correct

Rationale B: multiplied 12

by 3, then interpreted result using whole-number component

of 112

Rationale C: multiplied 12

by 3

Rationale D: used reciprocal of 12

instead of 3

Part B (2 points)

• Correct answer (1 point) • Valid work or explanation (1 point)

Sample Student Response: Alex needs 8 yards of ribbon to decorate 6 frames.

1 4 241 6 6 83 3 3

3 The student earns 3 points. 2 The student earns 2 points. 1 The student earns 1 point. 0 The student’s response is incorrect, irrelevant to the skill or

concept being measured, or blank.


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Anchor Set

The sample Grade 6, Item 13, student responses—or anchor set—included in this section of the Scoring Guide are provided to ensure that teachers understand how to apply the rubrics reliably and consistently. The anchor set includes annotated references to both the rubric and specific examples from the student responses to exemplify why the response received a particular score.


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Anchor Paper #1

Score Information: 3 The response includes the correct answer to Part A (1), the correct answer to Part B (1), and valid work/explanation (1).

Part A.

1 1 1 132 2 3 6

A. correct answer Jessica uses 1

6 yards of ribbon to decorate each picture frame.

Part B.

1 4 6 241 6 83 3 1 3

Alex needs 8 yards of ribbon to decorate 6 picture frames using 11

3

yards for each frame. I know because 1 241 63 3

which is

equavilent to 8.


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Anchor Paper #2

Score Information: 3 The response includes the correct answer to Part A (1), the correct answer to Part B (1), and valid work/explanation (1).

Part A: Answer A Part B:

11 6 83

Alex needs 8 yards of ribbon. 113

per frame and there are 6 frames.


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Anchor Paper #3

Score Information: 2 The response includes the correct answer to Part A (1), the correct answer to Part B (1), and no work/explanation (0).

A. Jessica uses 16

yards of ribbon for each frame.

B. Alex will need 8 yards of ribbon.


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Anchor Paper #4

Score Information: 2 The response includes an incorrect answer to Part A (0), the correct answer to Part B (1), and valid work/explanation (1).

Part A C

1 1 1 3 112 2 2 2 2

Part B

1 1 1 1 1 1 61 1 1 1 1 1 6 83 3 3 3 3 3 3

She will need 8 yards of ribbon because if you add 11

3 6 times you

get 8 yards.


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Anchor Paper #5

Score Information: 1 The response includes the correct answer to Part A (1), an incorrect answer to Part B (0), and incorrect work (0).

Part A A Part B

113

(make improper) 6

313

3 1 43 3 3

1 13 3

4 63

keep, change, flip

4 1 4 23 6 18 2

29

29

yards of ribbon per frame


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Anchor Paper #6

Score Information: 1 The response includes the correct answer to Part A (1), an incorrect answer to Part B (0), and incorrect work (0).

Part A A Part B Alex needs 1 yard to decorate the 6 picture frames 36 inches = 1 yard 6 inches 6 = 36 inches = 1 yard


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Anchor Paper #7

Score Information: 0 The response includes an incorrect answer to Part A (0), an incorrect answer to Part B (0), and incorrect work/explanation (0).

D

1 6 32

113

1 3 1 44 6 24

She needs 24 yards of ribbion in order to decorate 6 picture frames. To get my answer I did 1 3 1 from the fraction 11

3 and got 4,

then got 6 which is how many picture frames she wanted to decorate, and multiplied 4 6 and got 24.


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Anchor Paper #8

Score Information: 0 The response includes an incorrect answer to Part A (0), an incorrect answer to Part B (0), and incorrect work/explanation (0).

C

3 1 31 2 211 63

Alexes needed 3 yards of ribbion for 6 picture frames.

1 and 13

times 61

to get 61 23

1 2 3 to get 3 yards


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Practice Scoring Exercise

Five (5) sample responses have been selected and presented here to help scorers calibrate their expectations and judgments and to ensure student responses are accurately and consistently scored. Scorers should:

• Review the rubric again. • Read each bullet point and each score point descriptor carefully. • Read each sample response. • Give each sample response a score based on the rubric. • Compare your scores with the key, noting any differences in how the responses

were scored. • Begin scoring student responses when confident that the rubric can be applied

accurately and consistently.


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Mathematics Grade 6, Item 13, Practice Scoring Exercise

Paper Score Justification for Score

#1

#2

#3

#4

#5


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Practice Paper #1

Part A: A

1 1 1 3 16 6 6 6 2

Part B: So Alex is using 11

3 yards of ribbon for each picture frame

so then you just do 11 63

to find out the total amount he will need

in all which is 8.

1 6 61 6 236 2 8


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Practice Paper #2

Part A:

1 1 1 132 2 3 6

A. 1

6

Part B:

1 4 4 1 41 6 63 3 3 6 18

Alex will need 4

18 yard of ribbon to decorate the picture frames.


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Practice Paper #3

Part A: 3 1 3 2 6 61 2 1 1 1

Answer = D

Part B:

1 61 6 6 83 3

Alex would need 8 yards of ribbon to decorate the picture frames. I figured this out because I multiplied

11 63

to see how much ribbon

would be used and I got 663

then I simplified that to 8 yards of

ribbon for all 6 picture frames.


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Practice Paper #4

Part A: C, 32

Part B: Alex needs 61

3 yards of ribbon to decorate the pictrue

frames.

1 6 61 13 1 3


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Practice Paper #5

Part A: D 3 2 61 1

Part B:

4 6 24 83 1 3

He would need 8 yards.


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Practice Scoring Exercise Key


#1 3 The response includes the correct answer to Part A (1), the correct answer to Part B (1), and valid work/explanation (1).

#2 1 The response includes the correct answer to Part A (1), an incorrect answer to Part B (0), and incorrect work/explanation (0).

#3 2 The response includes an incorrect answer to Part A (0), the correct answer to Part B (1), and valid work/explanation (1).

#4 0 The response includes an incorrect answer to Part A (0), an incorrect answer to Part B (0), and incorrect work (0).

#5 2 The response includes an incorrect answer to Part A (0), the correct answer to Part B (1), and valid work (1).


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Alignment

Task Type: Reasoning (Type II) Evidence Statement: LEAP.II.6.9: Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed ‘student’ reasoning is presented and the task is to correct and improve it.) Content Scope: Knowledge and skills articulated in 5.NBT, 5.MD.C. Primary Standard: 5.NBT.A.3: Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Point Value: 4 DOK: 2 Difficulty: Medium


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Constructed-Response Item Melissa compares the numbers 0.058 and 0.21. She thinks that 0.058 0.21 because 58 21 , but the reasoning that Melissa used is incorrect.

• Identify the incorrect reasoning that Melissa used. Explain why the reasoning is incorrect.

• Using expanded form, show or explain how to correct the reasoning that Melissa used. In your explanation, correctly compare the numbers.


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Scoring Information 4 points

• Identification of incorrect reasoning (1 point) • Valid explanation of incorrect reasoning (1 point) • Correct expanded form of each number (1 point) • Sufficient work or explanation, including a correct comparison (1 point)

Sample Student Response: The reasoning Melissa used is incorrect because she compared the non-zero digits in the numbers as though they were whole numbers. She did not use the place value of each digit when comparing. 0.058 0 0.1 5 0.01 8 0.0010.21 2 0.1 1 0.01

By starting with the greatest place value, Melissa would have seen that the tenths place is the first place in which there are different digits. The number 0.058 has 0 tenths and the number 0.21 has 2 tenths, so 0.21 must be greater than 0.058.

4 The student earns 4 points. 3 The student earns 3 points. 2 The student earns 2 points. 1 The student earns 1 point. 0 The student’s response is incorrect, irrelevant to the skill or

concept being measured, or blank.


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Anchor Set

The sample Grade 6, Item 42, student responses—or anchor set—included in this section of the Scoring Guide are provided to ensure that teachers understand how to apply the rubrics reliably and consistently. The anchor set includes annotated references to both the rubric and specific examples from the student responses to exemplify why the response received a particular score.


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Anchor Paper #1

Score Information: 4 The response includes an identification of incorrect reasoning (1), a valid explanation of the incorrect reasoning (1), correct expanded form of each number (1), and a correct comparison with explanation (1).

The Reasoning is incorrect because Melissa just only compared 58 and 21 but does numbers werent the same as 0.058 and 0.21 so her Reasoning will be wrong. What she should have done is set them up like this 0.058 0.21 and if she did she would have saw their was a difference in the tenths place and she would have also saw that 2 is grater than 0. So her answer should have came out like this 0.058 0.21 not this

0.058 0.21. Also she could have used expanded form

1 1 10 1 0 5 810 100 1000

1 10 1 2 110 100

and she would still find 12

10 is grater

than 10

10.


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Anchor Paper #2

Score Information: 4 The response includes an identification of incorrect reasoning (1), a valid explanation of the incorrect reasoning (1), correct expanded form of each number (1), and a correct comparison with explanation (1).

The reasoning that Melissa used is that 0.058 is greater than 0.21 because she saw that in 0.058 there is a 58 and in 0.21 there is a 21 and 58 is greater than 21. That is incorrect, because in 0.058 there are three digit number after the decimal and 0.21 have two digit number the decimal so Melissa should look at the same place value first. In the tenths place for 0.058 it is zero and in 0.21 it is 2 so 0.21 is greater than 0.058. Expanded Form:

0.058 0.05 0.0080.21 0.2 0.01

0.05 0.2 2 in the tenths place is greater than 0 in the tenths place in 0.05 in expanded form.


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Anchor Paper #3

Score Information: 3 The response includes no identification of incorrect reasoning (restates information from prompt) (0), a valid explanation of the incorrect reasoning (1), correct expanded form of each number (1), and a correct comparison with explanation (1).

Part A Melissa’s reasoning is incorrect because even though 58 21

0.058 0.21 because it has more decimal places in front of the 5. Part B 0 1 0 0.1 5 0.01 8 0.001 0 1 2 0.1 1 0.01

0.058 0.21

There is a zero in the tenths place in 0.058 making it less than 0.21 with the 2 in the tenths place


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Anchor Paper #4

Score Information: 3 The response includes an identification of incorrect reasoning (1), no explanation of the incorrect reasoning (0), correct expanded form of each number (1), and a correct comparison with explanation (1).

The reasoning for Melissa’s answer is incorrect. It is incorrect because 58 21 is correct but 0.058 0.21 is incorrect. To compare the two, you must add a zero in the thousandths place of 0.21. Making it 0.210 and changing the appearance while not changing the value. 0.210 0.058. In expanded form 0.210 is 0 .2 .01 .000 0.210. In expanded form 0.058 is .05 .008 0.058. 210 58 so that makes Melissa’s reasoning

incorrect.


30

Anchor Paper #5

Score Information: 2 The response includes an identification of incorrect reasoning (1), no explanation of the incorrect reasoning (0), no expanded form of each number (0), and a correct comparison (in Part A) with explanation (1).

Part A. The incorrect reasoning is she thought they were whole numbers. They are decimals 0.210 is thousanths and so is 0.058. 0.210 is greater than 0.058 so that’s why she is wrong. Part B. To correct it you need to put a 0 after 0.21 to make it thousanths, then compare.


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Anchor Paper #6

Score Information: 2 The response includes an insufficient identification of incorrect reasoning (0), no valid explanation of the incorrect reasoning (0), correct expanded form of each number (1), and a correct comparison with explanation (1).

0.058 is smaller than 0.21 becacuse .21 is bigger than .058. There’s a zero in front of 58 making the number smaller, there is no zero in front of 21, which makes .21 bigger than .058. 0 0.0 .050 .008 0.058

and 0 .20 .01 0.21


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Anchor Paper #7

Score Information: 1 The response includes no identification of incorrect reasoning (0), a valid explanation of the incorrect reasoning (1), no expanded form of each number (0), and a correct comparison with insufficient work or explanation (0).

Melissa’s reasoning is incorrect because there is more than one zero in front of 58 and theres only one zero in front of 21 so 0.058 is smaller than 0.21 this is true because if the zeros were behind the 58 it would be greater than 0.21

0.21 0.058


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Anchor Paper #8

Score Information: 1 The response includes identification of incorrect reasoning (1), an incorrect explanation of the incorrect reasoning (0), no expanded form of each number (0), and a correct comparison with no work or explanation (0).

A- She is incorrect because 0.058 is not 58, it is .058 hundreths. And 0.21 is .21 tenths. B- The answer is 0.058 0.21.


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Anchor Paper #9

Score Information: 0 The response includes a vague identification of incorrect reasoning (0), no explanation of the incorrect reasoning (0), no expanded form of each number (0), and an incorrect comparison with an incorrect explanation (0).

A. 0.058 is biger but she forgot to add the zeros you can’t use just the 58 you need to add the zeros. B. 0.058 is bigger then 0.21 because it has more sylibils/numbers then 0.21


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Anchor Paper #10

Score Information: 0 The response includes no identification of incorrect reasoning (0), no explanation of the incorrect reasoning (0), no expanded form of each number (0), and an incorrect comparison with an incorrect explanation (0).

0.058 ? 0.21 0.058 0.21 0.058 is gratr then 0.21 because it have this in the nuber 58 then the two zeros.


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Practice Scoring Exercise

Five (5) sample responses have been selected and presented here to help scorers calibrate their expectations and judgments and to ensure student responses are accurately and consistently scored. Scorers should:

• Review the rubric again. • Read each bullet point and each score point descriptor carefully. • Read each sample response. • Give each sample response a score based on the rubric. • Compare your scores with the key, noting any differences in how the responses

were scored. • Begin scoring student responses when confident that the rubric can be applied

accurately and consistently.


37

Mathematics Grade 6, Item 42, Practice Scoring Exercise


#1

#2

#3

#4

#5


38

Practice Paper #1

0.058 0.21 because the first number that is not zero in 0.058 is in the huderths and 0.21 is in the tenths. The tenths are bigger.


39

Practice Paper #2

She is incorrect because shes using whole numbers when shes supose to not. You are supose to look at the teenths. Place to see, so you would do 0.058 0.21 because 0.21 has a bigger first number.


40

Practice Paper #3

Part A: Her reasoning was wrong because when you are comparing decimals, you have to compare each place value and the numbers in each. Part B: I think that 0.058 0.21 because when I look at the numbers in the tenths place, there is a 0 and a 2 and 0 2 so, 0.058 0.21


41

Practice Paper #4

Melissa reasoning is incorrect because she thinks that 0.058 0.21 58 21. Melissa reasoning is incoret because it is less than.

expanded form

0.058 0.210.058 0.21


42

Practice Paper #5

A. Melissa is incorrect because the decimal place value is different and you can't compare the numbers 58 and 21 because the digits have different place values. Tenths is the highest place value in the decimal place value. Also when you compare decimals you go down the number. So in the ones place both decimals have a zero. Then in the tenths place, one has a 0 the other has a 2. Two has a higher value than 0, so the decimal with the two is greater than the other one.

0.000 0.000 0.050 0.008 0.00 0.00 0.20 0.01


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Practice Scoring Exercise Key


#1 1 The response includes no identification of incorrect reasoning (0), no explanation of the incorrect reasoning (0), no expanded form of each number (0), and a correct comparison with explanation (1).

#2 3 The response includes an identification of incorrect reasoning (1), a valid explanation of the incorrect reasoning (1), no expanded form of each number (0), and a correct comparison with explanation (1).

#3 2 The response includes no identification of incorrect reasoning (0), a valid explanation of the incorrect reasoning (1), no expanded form of each number (0), and a correct comparison with explanation (1).

#4 0

The response includes no identification of incorrect reasoning (restates prompt) (0), no explanation of the incorrect reasoning (0), incorrect expanded form of each number (0), and both correct and incorrect comparisons with no work or explanation (0).

#5 4 The response includes an identification of incorrect reasoning (1), a valid explanation of the incorrect reasoning (1), correct expanded form of each number (1), and a correct comparison with explanation (1).

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