Mathematics Diagnostic Grade 3

Mathematics Diagnostic

Grade 3 Scoring Guide

Mathematics, Diagnostic Grade 3

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Mathematics Grade 3

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 3 Diagnostic Mathematics assessment:

Item 29: Reasoning Item 42: Modeling

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 3, Item 29

Alignment Task Type: Reasoning (Type II) Evidence Statement: LEAP.II.3.5: 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 2.NBT Primary Standard: 2.NBT.A.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Point Value: 4 DOK: 2 Difficulty: Medium


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Constructed-Response Item Part A Josh compares these numbers.

599 609 Josh says 599 is greater than 609 because there are two 9s in 599 and only one 9 in 609, but Josh’s reasoning is not correct. Explain why Josh’s reasoning is not correct. Explain how Josh could correct his reasoning and correctly compare the numbers. Part B Next, Josh will compare these numbers.

580 509 Write a comparison using <, =, or > to compare the numbers. Explain how you know your comparison is true.


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Scoring Information Part A (2 points)

• Correct explanation of incorrect reasoning (1 point) • Correct explanation of corrected reasoning (1 point)

Sample Student Response: Josh compared the value of digits, but did not think about place value of those digits. Using place value, he should start by comparing the digits in the hundreds place of each number. Since the 6 in 609 is greater than the 5 in 599, the number 609 is greater than 599. Part B (2 points)

• Correct comparison using symbolic notation (1 point) • Correct explanation of reasoning (1 point)

580 509> (or equivalent) Sample Student Response: Start by comparing the digits in the hundreds place. Since they are both 5, they have the same number of hundreds. Next, compare the digits in the tens place. Since 8 tens 0 tens> , the comparison 580 509> is true.

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 3, Item 29, 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 to Part A includes a correct explanation of incorrect reasoning (1) and a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1) and a correct explanation of reasoning (1).

Josh is wrong because 609 has 6 hundreds and 599 has 5 hundreds, so 609 599. Josh could say even though 599 has 2 9’s, it has 5 hundreds and 609 has 6 hundreds.

580 509 I know my comparison is correct because 580 has 8 tens and 509 has 0, so 580 is greater than 509.


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Anchor Paper #1


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Anchor Paper #2

Score Information: 4 The response to Part A includes a correct explanation of incorrect reasoning (1) and a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1) and a correct explanation of reasoning (1).

Part one 609 599 isn’t correct because in the tens place 9 0, but in the

hundreds place 6 5 Part two

580 509 because in the ones place 9 0 , but in the tens place 8 0 and in the hundreds 5 5


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Anchor Paper #2


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Anchor Paper #3

Score Information: 3 The response to Part A includes no explanation of incorrect reasoning (0), but a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1) and a correct explanation of reasoning (1).

Part A Josh is incorrect because the number 6 in 609 stands for 600 and the 5 in 599 stands for 500. 600 is greater than 500. So, 609 is greater than 599. Part B

580 509 580 is greater than 509 because when you look at the numbers the both numbers of the hundreds places are the same. So, you look at the tens place their is an 8 in 580 and a 0 in 509, and the 8 is greater than the 0. This is why 580 is greater than 509.


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Anchor Paper #3


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Anchor Paper #4

Score Information: 3 The response to Part A includes an incomplete explanation of incorrect reasoning (0), but a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1) and a correct explanation of reasoning (1).

609 599 10

580 509 Josh is incorrect because hundreds are more than tens and ones. 609 has a higher number than 599 so he is wrong. 580 has eight tens 0 ones and five hundreds. while 509 has five hundreds 0 tens and 9 ones.


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Anchor Paper #4


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Anchor Paper #5

Score Information: 2 The response to Part A includes no explanation of incorrect reasoning (0), but a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1), but no explanation of reasoning (0).

599 609 609 is geater because it haves a big hundred and if you count up you will get to 599 before 609 so it means 609 is geater

580 509 580 is geater than 509


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Anchor Paper #5


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Anchor Paper #6

Score Information: 2 The response to Part A includes no explanation of incorrect reasoning (0), but a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1), but an incorrect explanation of reasoning (0).

Part A Josh is not correct because 599 is 10 less than 609. So 609 is greater than 599. Josh could correct his reasoning by saying that 609 is 10 more 599 so it would bei less. Josh would correctly compare the numbers by saying 599 609. Part B

580 509 089580 509

I know my compararison is true because i subtracted 509 from 580 and got 89. So 509 is 89 less than 580.

509 89 580


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Anchor Paper #6


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Anchor Paper #7

Score Information: 1 The response to Part A includes no explanation of incorrect reasoning (0) and no explanation of corrected reasoning (0). The response to Part B includes a correct comparison using symbolic notation (1), but no explanation of reasoning (0).

Step1 599 609

599 is Lester Then 609. 609 is Greater Then 599 Thats What Made Josh awser Wrong. Step1

580 509 580 is Greater Then 509 Key 599 609 580 509


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Anchor Paper #7


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Anchor Paper #8

Score Information: 1 The response to Part A includes an incorrect explanation of incorrect reasoning (0) and no explanation of corrected reasoning (0). The response to Part B includes a correct comparison using symbolic notation (1), but no explanation of reasoning (0).

A. in part A Jhon is not corected becas if you add 609 599 1198 it will be rong but Part B has 580 509


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Anchor Paper #8


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Anchor Paper #9

Score Information: 0 The response to Part A includes no explanation of incorrect reasoning (0) and no explanation of corrected reasoning (0). The response to Part B includes a correct comparison, but without symbolic notation (0), and an incomplete explanation of reasoning (0).

A. Josh is not correct Because 609 is grater than 599. he can Be correct Becas he Jaust hat say 609 is gater thean 599 B. 580 is grater than 509 Becaus it is the 80 in 580


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Anchor Paper #9


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Anchor Paper #10

Score Information: 0 The response to Part A includes no explanation of incorrect reasoning (the response restates the prompt) (0) and no explanation of corrected reasoning (0). The response to Part B includes no correct comparison (0) and an incomplete explanation of reasoning (0).

Josh’s reasoning is incorrect because in 599 there are two nines and in 609 there is one nine. 580 509 I know it because I used a number line.


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Anchor Paper #10


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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 3, Item 29, Practice Scoring Exercise

Paper Score Justification for Score

#1

#2

#3

#4

#5


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Practice Paper #1


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Practice Paper #2


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Practice Paper #3


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Practice Paper #4


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Practice Paper #5


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Mathematics

Grade 3, Item 29 Practice Scoring Exercise Key


#1 1

The response to Part A includes no explanation of incorrect reasoning (0) and a vague explanation of corrected reasoning (0). The response to Part B includes a correct comparison using symbolic notation (1), but an incomplete explanation of reasoning (0).

#2 4

The response to Part A includes a correct explanation of incorrect reasoning (1) and a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1) and a correct explanation of reasoning (1).

#3 2

The response to Part A includes no explanation of incorrect reasoning (0), but a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1), but no explanation of reasoning (0).

#4 0 The response to Part A includes a vague explanation of incorrect reasoning (0) and a vague explanation of corrected reasoning (0). The response to Part B includes no correct comparison (0) and an incorrect explanation of reasoning (0).

#5 3

The response to Part A includes a correct explanation of incorrect reasoning (1) and a correct explanation of corrected reasoning (1). The response to Part B includes a correct comparison using symbolic notation (1), but no explanation of reasoning (0).


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Alignment

Task Type: Modeling (Type III) Evidence Statement: LEAP.III.3.2: Solve multi-step contextual problems with degree of difficulty appropriate to Grade 3, requiring application of knowledge and skills articulated in 2.OA.A, 2.OA.B, 2.NBT, and/or 2.MD.B. Primary Standard: 2.OA.A.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Secondary Standard: 2.MD.B.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. Point Value: 3 DOK: 2 Difficulty: Medium


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Constructed-Response Item Mike is using blue paper, yellow paper, and stickers for an art project. The point on this number line shows the total number of pieces of paper Mike uses for the project.

Part A Mike uses 8 pieces of blue paper for the project. How many pieces of yellow paper does Mike use for the project? Part B Mike has three sheets of stickers. This list shows the number of stickers on each sheet.

25, 19, 20 Mike needs a total of 100 stickers for the project. How many more stickers does Mike need for the project? Show your work using an equation or equations.


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Scoring Information Part A (1 point)

• Correct answer (1 point) 4 (pieces of yellow paper) Part B (2 points)

• Correct equation(s) to show work (1 point) • Correct answer (1 point)

36 (stickers) Sample Student Response: 25 19 4444 20 64100 64 36

+ =+ =− =

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 3, 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: 3 The response to Part A includes the correct answer (1). The response to Part B includes correct equations to show work (1) and the correct answer (1).

Mike uses 4 pieces of yellow paper.

25 19 20 64100 64 36

36 64 100


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Anchor Paper #1


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Anchor Paper #2

Score Information: 3 The response to Part A includes the correct answer (1). The response to Part B includes correct equations to show work (1) and the correct answer (1).

Part A He uses 4 yellow peices of paper I used a number line to check. I put a point at 8 for the blue peices of paper. I counted 4 numbers up to 12, the pices in all. 1 1 1 1 4

Part B

25 19 4444 20 6464 36 100

He needs 36 more stickers to have 100 stickers in all.


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Anchor Paper #2


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Anchor Paper #3

Score Information: 2 The response to Part A includes an incorrect answer (0). The response to Part B includes correct equations to show work (1) and the correct answer (1).

Part A: 15 8 7. He uses 7 yellow papers since 15 8 7. Part B: Mike needs 36 more stickers since 25 19 20 64 and

100 64 36 .

25 19 20 64100 64 36


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Anchor Paper #3


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Anchor Paper #4

Score Information: 2 The response to Part A includes the correct answer (1). The response to Part B includes one correct equation to show work (1), but an incorrect answer (0).

he has 4 pecices of yellow paper

25 20 19 64 64


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Anchor Paper #4


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Anchor Paper #5

Score Information: 1 The response to Part A includes an incorrect answer (0). The response to Part B includes one correct equation to show work (1), but an incorrect answer (0).

Part A 10 B. 64 more stikers!

25 20 19 64


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Anchor Paper #5


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Anchor Paper #6

Score Information: 1 The response to Part A includes an incorrect answer (0). The response to Part B includes some correct equations to show work (1), but an incorrect answer due to a calculation error (0).

25 19 4444 20 6060 40 100

Mike needs 40 more sickers

15 8 7 He uses 7 pecices of yellow paper


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Anchor Paper #6


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Anchor Paper #7

Score Information: 0 The response to Part A includes an incorrect answer (0). The response to Part B includes no equations to show work (0) and an incorrect answer (0).

Part B Mike has three sheets of stickers. So if he needs 100 stickers on his project he needs 25 stickers on each one. 25 25 25 Part A Mike has 5 pieces of yellow paper because Mike was using 8 pieces of paper. Mike had 13 pieces of paper left.


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Anchor Paper #7


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Anchor Paper #8

Score Information: 0 The response to Part A includes an incorrect answer (0). The response to Part B includes no equations to show work (0) and an incorrect answer (0).

Part A Mike use 5 for the project Part B Mikeo need 81 for his project 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100


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Anchor Paper #8


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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 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 3, Item 42, Practice Scoring Exercise


#1

#2

#3

#4

#5


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Practice Paper #1


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Practice Paper #2


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Practice Paper #3


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Practice Paper #4


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Practice Paper #5


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Practice Scoring Exercise Key


#1 1 The response to Part A includes an incorrect answer (0). The response to Part B includes some correct equations to show work (1), but an incorrect answer (0).

#2 0 The response to Part A includes an incorrect answer (0). The response to Part B includes no equations to show work (0) and an incorrect answer (0).

#3 3 The response to Part A includes the correct answer (1). The response to Part B includes correct equations to show work (1) and the correct answer (1).

#4 2 The response to Part A includes the correct answer (1). The response to Part B includes some correct equations to show work (1), but an incorrect answer due to a calculation error (0).

#5 3 The response to Part A includes the correct answer (1). The response to Part B includes correct equations to show work (1) and the correct answer (1).

Documents

Mathematics Diagnostic Grade 3