Mathematics Diagnostic Algebra I. Scoring Guide

Transcription

1 Mathematics Diagnostic Algebra I Scoring Guide

2 Mathematics Algebra I Mathematics, Diagnostic Algebra I 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 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 Algebra I Diagnostic Mathematics assessment: Item 54: Modeling Item 55: Reasoning There are 8 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. 1

3 Mathematics Algebra I, Item 54 Alignment Mathematics, Diagnostic Algebra I Task Type: Modeling (Type III) Evidence Statement: LEAP.III.A1.1: Solve multi-step contextual problems with degree of difficulty appropriate to the course, requiring application of knowledge and skills articulated in 7.RP.A, 7.NS.3, 7.EE, and/or 8.EE. Primary Standard: 8.EE.C.8: Analyze and solve pairs of simultaneous linear equations. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Secondary Standard: 8.EE.C.7: Solve linear equations in one variable. b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Point Value: 3 DOK: 2 Difficulty: Medium 2

4 Mathematics Algebra I, Item 54 Constructed-Response Item An airplane has a total of 414 packets of crackers, pretzels, and peanuts available for passengers. There are n packets of crackers. The number of packets of pretzels is 9 more than twice the number of packets of crackers. The number of packets of peanuts is 3 times the number of packets of pretzels. Part A Which equation can be used to determine the number of packets of crackers, n, on the airplane? A. 6n + 9 = 414 B n = 414 C. 9n + 36 = 414 D n = 414 Part B The airplane has seats for 144 passengers. The seats are arranged in 48 rows, with 3 seats in each row. There are 132 passengers on a certain flight. There are exactly 2 passengers in x rows. There are exactly 3 passengers in y rows. Write a system of linear equations that can be used to model the situation. Use your system to determine the number of rows with exactly 2 passengers and the number of rows with exactly 3 passengers. Show your work. 3

5 Mathematics Algebra I, Item 54 Scoring Information Mathematics, Diagnostic Algebra I Part A (1 point) Answer Key: C Rationale A: used 3x for the number of packets of peanuts Rationale B: used 3x for the number of packets of peanuts and switched the placement of the variable Rationale C: correct [ n+ 2n ( 2n+ 9) = 414 3n n+ 27 = 414 ] Rationale D: switched the placement of the variable Part B (2 points) Correct system of equations (1 point) Correct solution, with work shown (1 point) Sample Student Response: x + y = y = y = y = 132 y = 36 x + 36 = 48 x = 12 There are 12 rows with exactly 2 passengers. There are 36 rows with exactly 3 passengers. 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. 4

6 Mathematics Algebra I, Item 54 Anchor Set Mathematics, Diagnostic Algebra I The sample Algebra I, Item 54, 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. 5

7 Anchor Paper #1 Part A C Part B x y 48 3y 132 3y y x x x x x 4 3 x y 48 y 36 Score Information: 3 The response to Part A is correct (1). The response to Part B includes a correct system of equations (1), and a correct solution, with work shown (1). 6

8 Anchor Paper #2 A) choice C B) 3y 132 x y 48 x 48 y 2 48 y 3y y 3y y 132 y 36 x x rows of 2 and 36 rows of 3 Score Information: 3 The response to Part A is correct (1). The response to Part B includes a correct system of equations (1), and a correct solution, with work shown (1). 7

9 Anchor Paper #3 Part A: the answer I choose is A. Part B: the system of equations would be x y 48 3y 132 x y 48 x 48 y 3y y 3y y 3y y 132 y 36 y 36 so x 12 because Score Information: 2 The response to Part A is incorrect (0). The response to Part B includes a correct system of equations (1), and a correct solution, with work shown (1). 8

10 Anchor Paper #4 Part A C. Part B x y 48 3y 144 x y y 96 3y 144 2y 96 y 48 y 48, x 0 their are 0 rows with 2 passengers and 48 rows with 3 Score Information: 2 The response to Part A is correct (1). The response to Part B includes an incorrect system of equations (0), but a correct process to determine the solution, with work shown (1). 9

11 Anchor Paper #5 Part A: C. 9n Part B: 3y 132 x 1.5y y 66 3y 132 3y 66 3y 132 6y y 66 y 11 x x 82.5 Score Information: 1 The response to Part A is correct (1). The response to Part B includes only one equation (0), and an incorrect solution, with incorrect work shown (0). 10

12 Anchor Paper #6 A. The equation that can be used to determine the number of packets of crackers is C. 9n B. 3y 48 3y 144 Score Information: 1 The response to Part A is correct (1). The response to Part B includes an incorrect system of equations (0), and no solution or work shown (0). 11

13 Anchor Paper #7 Part A = B. Part B = 144 total passengers 48 rows 3 seats Score Information: 0 The response to Part A is incorrect (0). The response to Part B includes only one (incorrect) equation (0), and no solution or work shown (0). 12

14 Anchor Paper #8 Part A: A. 6n Part B: y 132 x 3y 132 6y y y x 44 Score Information: 0 The response to Part A is incorrect (0). The response to Part B includes an incorrect system of equations (0), and an incorrect solution, with incorrect work shown (0). 13

15 Mathematics Algebra I, Item 54 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. 14

16 Mathematics Algebra I, Item 54, Practice Scoring Exercise Paper Score Justification for Score #1 #2 #3 #4 #5 15

17 Practice Paper #1 Part A D. Part B y 132 y x x x x 12 8x x

18 Practice Paper #2 Part A - C Part B x y 48 3y 132 y 48 x 3y y 44 x x 44 x x x 3 12 x 12 y 48 y 36 17

19 Practice Paper #3 Part A Answer: C. Part B x y 48 3x 2y 132 x y y 96 3x 2y 132 2y 96 x y 48 y 12 there are 12 rows with 3 passengers and 36 rows with 2 passengers 18

20 Practice Paper #4 Part A A Part B 3y x 144 x y y 132 3y 126 y rows have 2 passengers and 42 rows have 3 passengers. 19

21 Practice Paper #5 Part A: C.) 9n Part B: 3y

22 Mathematics Algebra I, Item 54 Practice Scoring Exercise Key Paper Score Justification for Score #1 0 The response to Part A is incorrect (0). The response to Part B includes an incorrect system of equations (0), and an incorrect solution, with incorrect work shown (0). #2 3 The response to Part A is correct (1). The response to Part B includes a correct system of equations (1), and a correct solution, with work shown (1). #3 2 #4 1 The response to Part A is correct (1). The response to Part B includes an incorrect system of equations (0), but a correct process to determine the solution, with work shown (1). The response to Part A is incorrect (0). The response to Part B includes an incorrect system of equations (0), but a correct process to determine the solution, with work shown (1). #5 1 The response to Part A is correct (1). The response to Part B includes only one equation (0), and no solution or work shown (0). 21

23 Mathematics Algebra I, Item 55 Alignment Mathematics, Diagnostic Algebra I Task Type: Reasoning (Type II) Evidence Statement: LEAP.II.A1.10: Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures about linear equations in one or two variables. Content scope: 8.EE.B Primary Standard: 8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Point Value: 3 DOK: 2 Difficulty: Medium 22

24 Mathematics Algebra I, Item 55 Constructed-Response Item Joslyn earns money working part-time at a grocery store. This table shows the amounts of money that she earns for working different numbers of hours. Part A Explain why the information in the table is a proportional relationship. As part of your explanation, determine the amount, in dollars, Joslyn earns per hour. Show your work. Part B Kate also has a part-time job. After working x hours, she earns y dollars. Her total earnings can be described by the equation y = 11.25x. Explain why Joslyn s total earnings will always be greater than Kate s total earnings when Joslyn and Kate work the same number of hours. 23

25 Mathematics Algebra I, Item 55 Scoring Information Mathematics, Diagnostic Algebra I Part A (2 points) Correct explanation (1 point) Correct amount per hour, with work shown (1 point) Sample Student Response: Each pair of values in the table forms equivalent ratios because 25 2 = 12.5, 50 4 = 12.5, = 12.5, = Since all the ratios are equivalent, they form a proportional relationship. The ratio : 1 is the unit rate for the proportional relationship and describes the amount Joslyn earns per hour, $ Part B (1 point) Correct explanation Sample Student Response: The equation represents a line with a slope of that passes through the origin. That meets the criteria for a proportional relationship. The unit rate for the proportion is the same as the slope of the line, 11.25, and represents Kate's earnings of $11.25 per hour. Joslyn earns $12.50 per hour. Since > 11.25, when they work the same number of hours, Joslyn s total earnings will always be greater than Kate s total earnings. 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. 24

26 Mathematics Algebra I, Item 55 Anchor Set Mathematics, Diagnostic Algebra I The sample Algebra I, Item 55, 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. 25

27 Anchor Paper #1 Part A The relationship is proportional because the rate is the same for each hours. Part B - Joselyn s earnings will be greater because y 11.25x means the rate is $11.25 per hour and Joselyns rate is $12.50 per hour. Score Information: 3 The response includes a correct explanation for Part A (1), the correct amount per hour (in the Part B explanation), with work shown (1), and a correct explanation for Part B (1). 26

28 Anchor Paper #2 PART A: The information on the table is a proportional relationship because: The amount of dollars Joslyn earns per hour is $ PART B. Kate y 11.25x Joslyn y 12.5x Joslyn s total earnings will always be greater than Kate s total earnings even if they worked for the same # of hours because Kate earns $11.25 per hour while Joslyn earns $12.5 per hour. Score Information: 3 The response includes a correct explanation for Part A (1), the correct amount per hour, with work shown (1), and a correct explanation for Part B (1). 27

29 Anchor Paper #3 Part A Joslyn earns $12.50 per hour. Part B. Joslyn s total will always be greater than Kate s total earning because of $12.50 is greater than $ Score Information: 2 The response includes no explanation for Part A (0), but the correct amount per hour, with work shown (1), and a correct explanation for Part B (1). 28

30 Anchor Paper #4 Part A: The information is porpotinal because it has a constant rate of 12.5, which means 12.5 gets added every hour. For one hour Joslyn works she makes $12.50, so she makes $12.50 an hour. Part B: Joslyn s earnings will always be greater than Kates because Kate makes $11.25 an hour and Joslyn makes $ Score Information: 2 The response includes a correct explanation for Part A (1), the correct amount per hour, but with no work shown (0), and a correct explanation for Part B (1). 29

31 Anchor Paper #5 Part A It is a porportional relationship because every 2 hours it goes up b 25. Part B Yes becaus Joslyn makes more money then Kate Score Information: 1 The response includes a correct explanation for Part A (1), no correct amount per hour, and no work shown (0), and an incomplete explanation for Part B (0). 30

32 Anchor Paper #6 Part A a hour Part B = Joslyn s total earnings will always be greater than Kate s total earnings b/c Joslyn has a greater amount per hour than Kate. Score Information: 1 The response includes no explanation for Part A (0), the correct amount per hour with work shown (1), and an incomplete explanation for Part B (0). 31

33 Anchor Paper #7 A) $ / / B) Because Joslyn has a higer starting value than Kate does Score Information: 0 The response includes no explanation for Part A (0), an incorrect amount per hour, with incorrect work shown (0), and an incomplete explanation for Part B (0). 32

34 Anchor Paper #8 Part A $12.50 Part B Because joslyn has a job that pays more money witch means her total earnings will increase faster than Kate s Score Information: 0 The response includes no explanation for Part A (0), the correct amount per hour, but with incomplete work shown (0), and an incomplete explanation for Part B (0). 33

35 Mathematics Algebra I, Item 55 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. 34

36 Mathematics Algebra I, Item 55, Practice Scoring Exercise Paper Score Justification for Score #1 #2 #3 #4 #5 35

37 Practice Paper #1 Part A he/she earns about $12.50 an hour. and yes it is porportinal because none of the numbere of houres repeated. Part B because she makes more money an hour 36

38 Practice Paper #2 A. Each amount is divided by number of hours worked. Each amount drops to B. With Kates hers is , , etc hers is down by five compared to Joslyn s earnings. 37

39 Practice Paper #3 Part A: The table is a proportional relationship because every number of hours worked can be multiplied by the same rate to get the amount earned. Joslyn earns $12.50 per hour Part B: y 11.25x Joslyn s total earning will always be greater because Joslyn earns more per hour. $11.25 $

40 Practice Paper #4 A) 25 x x = $12.50 per hour B) Because Kate earns more money adding her money w/ the part time job. 39

41 Practice Paper #5 Part A Joslyn earns $12.50 per hour because what I did was just take the first given amount of money and divide it by 2 hours because that s what she made in 2 hours. Also it works if you divide any of then by their hours like 50.00, etc. That is why its 4 5 proportional Part B Well its because Joslyn s job pays her just a few more than Kates job does even though they both work a part time job for same amount of hours. 40

42 Mathematics Algebra I, Item 55 Practice Scoring Exercise Key Paper Score Justification for Score #1 0 The response includes an incorrect explanation for Part A (0), the correct amount per hour, but with no work shown (0), and an incomplete explanation for Part B (0). #2 2 The response includes a correct explanation for Part A (1), no correct amount per hour, and no work shown (0), and a correct explanation for Part B (1). #3 3 The response includes a correct explanation for Part A (1), the correct amount per hour, with work shown (1), and a correct explanation for Part B (1). #4 1 The response includes no explanation for Part A (0), the correct amount per hour, with work shown (1), and an incorrect explanation for Part B (0). #5 2 The response includes a correct explanation for Part A (1), the correct amount per hour, with work shown (1), and an incomplete explanation for Part B (0). 41