mathematics diagnostic grade 7 - caddo math department

Mathematics Diagnostic

Grade 7 Scoring Guide

Mathematics, Diagnostic Grade 7

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Mathematics Grade 7

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 7 Diagnostic Mathematics assessment:

Item 43: Reasoning Item 44: 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 7, Item 43

Alignment Task Type: Reasoning (Type II) Evidence Statement: LEAP.II.7.6: Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. Content Scope: Knowledge and skills articulated in 6.NS.C, 6.EE.A, 6.EE.B. Primary Standard: 6.NS.C.7: Understand ordering and absolute value of rational numbers.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3ºC > –7ºC to express the fact that –3ºC is warmer than –7ºC.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

Point Value: 4 DOK: 2 Difficulty: Medium


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Constructed-Response Item The beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail.

• The elevation of the first rest stop is 10 feet. • The elevation of the second rest stop is 15 feet. • The elevation of the third rest stop is 12 feet.

Jack compares the elevations, in feet, of the first two rest stops by writing the inequality

10 15 . Jack states that the inequality he wrote is correct because 10 is less than 15. Part A Explain whether the inequality Jack writes is correct or incorrect. In your explanation, include a description of each value in the inequality in terms of what it represents. Part B The change in elevation is greatest between the beginning of the trail and which rest stop? Explain your reasoning.


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Scoring Information Part A (2 points)

• Identification of comparison as incorrect, with valid explanation (1 point) • Valid description of what values represent (1 point)

Sample Student Response: The inequality Jack writes is incorrect because he compared the negative numbers as if they were positive. The number 10 is actually greater than the number 15 . In this inequality, 10 feet and 15 feet above sea level can also be interpreted as 10 feet and 15 feet below sea level. This means that the first rest stop is at a higher elevation than the second rest stop. Part B (2 points)

• Identification of the greatest change in elevation (1 point) • Valid explanation (1 point)

Sample Student Response: The change in elevation is greatest between the beginning of the trail and the second rest stop. Between the beginning of the trail (sea level) and the second rest stop there is a difference of 15 feet, while the differences between sea level and the other two rest stops are 10 feet and 12 feet, and 15 is greater than 10 and 12.

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 7, Item 43, 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 identification of the comparison as incorrect, with explanation (1), a valid description of what the values represent (1), identification of the greatest change in elevation (1), and a valid explanation (1).

A) The inequality Jack wrote is incorrect because 10 feet is greater than 15 feet. The comparison of the two depends on their absolute value, or their distance from zero (sea level). 10 is ten feet below sea level. So, the absolute value of 10 is 10. 15 is fifteen feet below sea level. So, the absolute value of 15 is 15. This information means that 10 is closer to sea level, or closer to zero. So, 10 15 . B) The change in elevation is greatest between the beginning of the trail, and the second rest stop. This is because of the absolute value, or the distance from the sea level. The beginning of the trail is exactly at zero, so the number with the greatest absolute value is the farthest. The first stop has an absolute value of 10, the second is 15, and the third is 12. The greatest is 15, so it is greatest from the beginning to the second stop.


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Anchor Paper #2

Score Information: 4 The response includes identification of the comparison as incorrect, with explanation (1), a valid description of what the values represent (1), identification of the greatest change in elevation (1), and a valid explanation (1).

Part A: Jacks inequality is incorrect because the values are negative. When values are negative the one closest to zero is greater. In this case 10 is greater than 15 because it is closer to zero, which is sea level. 10 is 10 feet below sea level and 15 is 15 feet below. Part B: The greastest distance is between the beginning of the trail and the second rest stop. This is because absolute value is the distance of a numer from zero. Sea level is 0 and 2nd rest stop is 15 which is 15ft. This makes this the greatest distance.


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Anchor Paper #3

Score Information: 3 The response includes identification of the comparison as incorrect, with explanation (1), no valid description of what the values represent (0), identification of the greatest change in elevation (1), and a valid explanation (1).

A. The inequality Jack writes is incorrect BC 10 is closer to 0 so it is greater then 15 which gives you the inequality of 10 15 . B. The change in elevation is greatest between the beginning of the trail and stop #2 which is 15. This is so BC 15 is 15 feet below 0 and it is farther away from 0 than 10 and 12.


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Anchor Paper #4

Score Information: 3 The response includes identification of the comparison as incorrect, with explanation (1), no valid description of what the values represent (0), identification of the greatest change in elevation (1), and a valid explanation (1).

Part A: Jack is incorrect, because although 15 is greater than 10, 10 is closer to 0 than 15. If jack would have said that the absolute value of 15 is greater than 10, Jack would have been correct. Part B: The change in elevation is greatest between the beginning of the trail and the 2nd rest stop. At the beginning of the trail, the amount of elevation is 0 feet, at rest stop 2, the amount of elevation was at 15 feet. Therefore, the amount of elevation decreased by 15 feet.


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Anchor Paper #5

Score Information: 2 The response includes identification of the comparison as incorrect, with no explanation (0), no valid description of what the values represent (0), identification of the greatest change in elevation (1), and a valid explanation (1).

The inequality Jack wote is in correct bcause 10 is not less than 15. The greates elevation change is betwen the beggining and rest stop 2 becase it is a 15 foot change and all the other rest stops the change is less than 15.


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Anchor Paper #6

Score Information: 2 The response includes identification of the comparison as incorrect, with explanation (1), a valid description of what the values represent (1), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

Part A: The inequality Jack writes is incorrect because they’re negative numbers, and while it is true 10 is less than 15 when it’s a negative number, the larger the negative number the less its value. The number is 10 because it’s 10 feet below sea level, and 15 because it’s 15 feet below sea level, making 15 below 10. Part B: The change in elevation is greatest when it changes from 15 to 12 because in order to become an even number it would have to increase by 15 and 15 plus 12 is 27, which is the largest number of change.


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Anchor Paper #7

Score Information: 1 The response includes identification of the comparison as incorrect, with explanation (1), no valid description of what the values represent (0), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

A. Jack is wrong about the inequality because he used absolute value instead of the real value. B. The change is greatest from the beginning of the trail to the third rest stop. The change is 12 feet.


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Anchor Paper #8

Score Information: 1 The response includes identification of the comparison as incorrect, with explanation (1), no valid description of what the values represent (0), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

A) Jack is incorrect because 10 isn’t as far from zero then 15 so it’s bigger. B) The beginning of the trail and the third rest stop because it travels 22 feet instead of 5 feet from 10 to 15feet.


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Anchor Paper #9

Score Information: 0 The response includes identification of the comparison as correct (0), no valid description of what the values represent (0), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

Part A: Jack is correct, because 10 15 is saying 15 is greater than 10 or 10 is less than 15. Part B: The greatest elevation between his two stops is 15 to 12 because 15 12 is 27 and 10 12 is 22, 27 is greater.


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Anchor Paper #10

Score Information: 0 The response includes identification of the comparison as correct (0), no valid description of what the values represent (0), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

the inequality jack wrote is correct because the biggest part of the symbol goes to the bigger number. So ten is less then fifteen. the biggest change in elevation is rest stop 12. because it is 12 feet above sea level.


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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 7, Item 43, Practice Scoring Exercise

Paper Score Justification for Score

#1

#2

#3

#4

#5


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Practice Paper #1

Part A: The inequality is incorrect because 10 is greater than, 15, not less than 15. Part B: The change in elevation is greatest between the beginning of trail and the second rest stop. The begining of the trail is at sea level. The elevation is 0 feet. The elevation of the second rest stop is 15 feet. 15 feet is 15 feet away from 0 feet, which is greater than the other rest stops’ distance from sea level.


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Practice Paper #2

Part A. Jack’s inequality is correct. His inequality is right because 15 is 15 feet below sea level, and 10 is below sea level too but 15 is deeper than 10 and the sign “eats” the bigger number so that is why the inequality is correct. Part B. The greatest number is 12 because since 10 and 15 are below sea level they are negative but since 12 is about sea level it passes both of the numbers and it is above 12 is the greatest number.


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Practice Paper #3

A. Jack is incorect, 10 is not less than 15. 15 is 15 units less than 0, while 10 is only 10 less than 0. B. The greatest change in elevation from the beginning is the second rest stop. Sea leval is 0, then the Absolute value of 12 is 12, of 10 is 10, a 15 is 15. 15 is obviously the longest in between 0 and itself.


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Practice Paper #4

Part A: Jack is not correct because he left his 3rd rest stop out which supposed to be In, but the correct way is 10 15 12 so it would be negitive 10 less than negitive 15 and 12 is greater than negitive 15. Part B: The elevation is greatest between the beginning of the trail and Rest stop 3 because It comes all the way from negitive 15 to 12 which is 23 numbers away from 10 to positve 12.


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Practice Paper #5

Part A: Jack is incorrect. 15 is 15 ft. below sea level. 10 ft. is 10 ft. below sea level. 15 is 15 numbers to the left of 0 on a number line. 10 is 10 numbers away from 0 on a number line. Part B: The change is the greatest from the beginning of the trail to the Second rest stop. In this case you compare the absolute values. 15 is greater than 10 and 12.


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Mathematics

Grade 7, Item 43 Practice Scoring Exercise Key


#1 2 The response includes identification of the comparison as incorrect, with no explanation (0), no valid description of what the values represent (0), identification of the greatest change in elevation (1), and a valid explanation (1).

#2 1 The response includes identification of the comparison as correct (0), a valid description of what the values represent (1), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

#3 3 The response includes identification of the comparison as incorrect, with explanation (1), no valid description of what the values represent (0), identification of the greatest change in elevation (1), and a valid explanation (1).

#4 0

The response includes identification of the comparison as incorrect, with an incorrect explanation (0), no valid description of what the values represent (0), incorrect identification of the greatest change in elevation (0), and an incorrect explanation (0).

#5 4 The response includes identification of the comparison as incorrect, with explanation (1), a valid description of what the values represent (1), identification of the greatest change in elevation (1), and a valid explanation (1).


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Alignment

Task Type: Modeling (Type III) Evidence Statement: LEAP.III.7.2: Solve multi-step contextual problems with degree of difficulty appropriate to grade 7, requiring application of knowledge and skills articulated in 6.RP.A, 6.EE.C, 6.G. Primary Standard: 6.EE.C.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Secondary Standard: 6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

b. Solve unit rate problems including those involving unit pricing and constant speed.

Point Value: 3 DOK: 2 Difficulty: Medium


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Constructed-Response Item Maude and Ahmed each drove their cars for 4.6 hours. In that time, Maude drove 230 miles. Ahmed drove 10 miles per hour slower than Maude drove. Write an equation that can be used to determine the distance, y, in miles, that Ahmed drove in h hours. Use your equation to determine how many more miles Maude drove in h hours than Ahmed drove. Show your work.


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Scoring Information 3 points

• Correct equation, in terms of y (1 point) • Correct answer (1 point) • Work shown to determine answer (1 point)

Sample Student Response: Maude drove at 50 miles per hour. I got that by dividing the 230 miles she drove by the 4.6 hours she spent driving. Ahmed drove 10 miles per hour less than Maude, which is 40 miles per hour, so my equation is 40y h .

4040 4.6184

y hyy

230 184 46 Maude drove 46 more miles than Ahmed. NOTE: Accept any answer that is 10 times as great as a defined value of h.

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 7, Item 44, 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 a correct equation in terms of y (1), a correct answer (1), and work shown (1).

Maude drove 50 miles every hour. Ahmed drove 40 miles every hour. Ahmed drove 184 miles in 4.6 hours. Maude drove 46 more miles than Ahmed.

40 h y or 40h y

230 4.6 5040 4.6 184.0230 184 46


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Anchor Paper #2

Score Information: 3 The response includes a correct equation in terms of y (1), a correct answer (1), and work shown (1).

40h y 230 4.6 10 40 miles per hour

40 4.6 184 miles 230 184 46

Ahmed drove 184 miles in 4.6 hours. Maude drove 46 more miles than Ahmed.


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Anchor Paper #3

Score Information: 2 The response includes no equation in terms of y (0), a correct answer (1), and work shown (1).

Both drove 4.6 hours Maude drove 230 miles Ahmed drove 10 miles slower

230 4.6 50 miles per hour

40 4.6 184 miles total 230 (Maude) – 184 (Ahmed) = 46 Maude drove 46 miles more than Ahmed.


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Anchor Paper #4

Score Information: 2 The response includes no equation in terms of y (0), a correct answer (1), and work shown (1).

4.6 M 230 (M = miles per hour for Maude.)

4.6 M 10 mile per hour slower than Maude. We have to figure out how many miles per hour Maude drove and to do this we must divide 230 by 4.6 and that equals 50 so

4.6 50 230 , Maude drove 50 miles per hour. If Ahmad drove 10 miles per hour slower than Maude we have to subtract 10 from 50 which is 40. So 4.6 40 184 So in the 4.6 hours Ahmad drove 184 miles. To find how many more miles Maude drove than Ahmed we have to Subtract 184 from 230 which is 46 so Maude drove 46 miles more than Ahmed.


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Anchor Paper #5

Score Information: 1 The response includes an incorrect equation in terms of y (0), a correct answer (1), and no work shown (0).

Ahmed drove 184 miles

184 4.6 230y h maude drove 46 more miles than ahmed


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Anchor Paper #6

Score Information: 1 The response includes no equation in terms of y (0), an incorrect answer (0), but correct process shown to determine rates (1).

4.6 hours M – 230/50mph A – 40mph/184 Maude: 230m/total 50m/ph Ahmed: 184m/total 40m/ph

230 180 Maude drove 50 more miles than Ahmed in 4.6 hours.


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Anchor Paper #7

Score Information: 0 The response includes no equation in terms of y (0), no correct answer (0), and no work shown (0).

Part A: 4.6 hours 230 miles Drove 10 miles So basically the equation would most likely be 230 miles as the number outside the equal sign and then 4.6 would be the 1st number and then you would times that to 10 miles. So basically visual it would be like this you’ll do 4.6 10 230h m miles and then that would be your equation because 4.6 hours comes in the problem first.


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Anchor Paper #8

Score Information: 0 The response includes no equation in terms of y (0), an incorrect answer (0), and incorrect work shown (0).

Ahmed drove 220. Equation that can be used to determine the distance, y, in miles, that Ahmed drove in h hours is 10 230 Ahmed needs to drive 10 more miles to get to Maude miles.


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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 7, Item 44, Practice Scoring Exercise


#1

#2

#3

#4

#5


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Practice Paper #1

4.6h/230 miles … 230 4.6 60.something.

60 10 6

230 46 60 (Maude) 60 10 6 (Ahmed)


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Practice Paper #2

A. 230 miles = 4.6 hours 50 miles = 1 hour

( 10) 4.6(50 10) 4.640 4.6 184

50 4.6 230

230 184 46

y hh

Maude drove 46 more miles per hour than Ahmed.


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Practice Paper #3

2.

40230 4.6 5050 10 4040 4.6 184

h y

Maude Goes 50 miles per hour, while Ahmed goes 40 miles per hour. In 4.6 hours, Ahmeed would have drove 184 miles. Maude drove 46 more miles than Ahmed in 4.6 hours.


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Practice Paper #4

Work

230 4.6 5050 10 4040 4.6 184

M 50 / hA 40 / h

230 184 46

Answer

40 4.6 184 That is how many miles Ahmed drove in 4.6. Maude drove 46 more miles than Ahmed.


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Practice Paper #5

230 504.6 1

Ahmed drove 40 miles per hour. 40y h

Maude drove 10 miles more than Ahmed per hour.

50 10 40


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Practice Scoring Exercise Key


#1 0 The response includes no equation in terms of y (0), an incorrect answer (0), and incorrect work shown (0).

#2 1 The response includes an incorrect equation in terms of y (0), an incorrect answer (due to inclusion of “per hour”) (0), but correct process shown to determine rates (1).

#3 3 The response includes a correct equation in terms of y (1), a correct answer (1), and work shown (1).

#4 2 The response includes no equation in terms of y (0), a correct answer (1), and work shown (1).

#5 3 The response includes a correct equation in terms of y (1), a correct answer (since “per hour” defines h as one) (1), and work shown (1).

mathematics diagnostic grade 7 - caddo math department

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