Math Released Item Algebra 1. System of Inequalities VF648815

Transcription

1 Math Released Item 2016 Algebra 1 System of Inequalities VF648815

2 Prompt

3 Rubric Task is worth a total of 3 points. VF Rubric Part A Score Description 1 Student response includes the following element. Computation component = 1 point o Correct System of Equations Sample Student Response: 0 Student response is incorrect or irrelevant. VF Rubric Part B Score Description 2 Student response includes the following 2 elements. Reasoning component = 2 points o Valid reasoning about why all points in the first quadrant have coordinates that satisfy o Valid reasoning about why all points in the first quadrant have coordinates that satisfy Sample Student Response: All points (x,y) in quadrant I have a positive x-coordinate and a positive y-coordinate. Therefore is satisfied. Because all points (x,y) in quadrant I have a positive x-coordinate and a positive y-coordinate, the sum of x and y must also be positive. If is greater than 0, then must be greater than -2, and is satisfied. Note: The response does not have to include the identification (x,y); referring to the x- and y-coordinates in general is enough. To earn the second point, the student must make the connection that anything greater than 0 is also greater than -2. It is ok if the student uses a specific example; such as showing the point (2,3) meets both conditions. However, if only a specific point is used and the student never refers to all points in general, award at most 1 point for reasoning. 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant.

4 Anchor Set A1 A8 With Annotations

5 A1 Part A: Score Point 1 Part B: Score Point 2

6 Annotation Anchor Paper 1 Part A: Score Point 1 This response receives full credit. The student includes the required element. The response includes the correct system of inequalities (y > 0, x + y > -2) Part B: Score Point 2 This response receives full credit. The student includes both of the two required elements. The response satisfies condition one that the y coordinate is positive (the first quadrant is when both the y and the x values are positive. Every Y value in the in the first quadrant is greater than 0). The response satisfies condition two that the sum of the coordinates is greater than -2 (the first quadrant is when both the y and the x values are positive... and every x + y will be greater than 0. 0 is greater than -2). The description identifies both coordinate points, the y coordinate and x coordinate, as positive numbers and states that adding them is greater than the negative number. This is the minimal amount of specificity to earn credit for condition two in Part B.

7 A2 Part A: Score Point 1 Part B: Score Point 2

8 Annotation Anchor Paper 2 Part A: Score Point 1 This response receives full credit. The student includes the required element. The response includes the correct system of inequalities (y > 0, x + y > -2) Part B: Score Point 2 This response receives full credit. The student includes both of the two required elements. The response satisfies condition one that the y coordinate is positive (The only numbers that are greater than 0 are positive numbers, which means the y coordinate is above the x axis). The response satisfies condition two that the sum of the coordinates is greater than -2 (A positive number + a positive number is greater than the negative number, which means the x coordinate can be a positive number too. A point with both coordinate points positive is in Quadrant 1.) The description identifies both coordinate points, the y coordinate and x coordinate, as positive numbers and states that adding them is greater than the negative number. This is the minimal amount of specificity to earn credit for condition two in Part B.

9 A3 Part A: Score Point 1 Part B: Score Point 1

10 Annotation Anchor Paper 3 Part A: Score Point 1 This response receives full credit. The student includes the required element. The response includes the correct system of inequalities (y > -x-2, y > 0). y > -x-2 is an equivalent inequality to x+y > -2. Part B: Score Point 1 This response receives partial credit. The student includes one of the two required elements. The response satisfies condition one that the y coordinate is positive (points in the first quadrant are all positives any positive number is greater than 0). The response does not satisfy condition two, that the sum of the coordinates is greater than 2. While the description says positive values are greater than -2, which is true, there is no mention of adding the coordinates together; therefore, no credit is earned for condition two. There is also no specific mention that the coordinates are positive only that the points are all positives.

11 A4 Part A: Score Point 1 Part B: Score Point 1

12 Annotation Anchor Paper 4 Part A: Score Point 1 This response receives full credit. The student includes the required element. The response includes the correct system of inequalities (x+y>-2, y>0). Part B: Score Point 1 This response receives partial credit. The student includes one of the two required elements. The response satisfies condition one that the y coordinate is positive (y is anything greater than 0). The response does not satisfy condition two, that the sum of the coordinates is greater than -2. The description fails to note that the x-coordinate is positive in quadrant I. Therefore, no credit is earned for condition two.

13 A5 Part A: Score Point 1 Part B: Score Point 0

14 Annotation Anchor Paper 5 Part A: Score Point 1 This response receives full credit. The student includes the required element. The response includes the correct system of inequalities (y>0, y+x>- 2). Part B: Score Point 0 This response receives no credit. The student includes neither of the required elements. The response does not satisfy condition one, that the y coordinate is positive, or condition two, that the sum of the coordinates is greater than -2. The description the student provides is a repeat of information given in the prompt. It addresses neither the quadrant I condition nor the greater than 2 condition.

15 A6 Part A: Score Point 0 Part B: Score Point 1

16 Annotation Anchor Paper 6 Part A: Score Point 0 The response receives no credit. The student does not include the required element. The response does not provide the correct inequalities. Part B: Score Point 1 This response receives partial credit. The student includes one of the two required elements. The response satisfies condition one that the y coordinate is positive (Quadrant 1 contains positive, positive coordinates). The response does not satisfy condition two, that the sum of the coordinates is greater than 2. The description fails to make the connection that x+y>0; therefore, no credit is earned for condition two.

17 A7 Part A: Score Point 0 Part B: Score Point 0

18 Annotation Anchor Paper 7 Part A: Score Point 0 The response receives no credit. The student does not include the required element. The response does not provide the correct inequalities. Part B: Score Point 0 This response receives no credit. The student includes neither of the required elements. The response does not satisfy condition one that the y coordinate is positive (none of the numbers in quadrant 1 are negative). The answer does not account for 0, which is not a negative number, but is also not in Quadrant I. The response makes no attempt to respond to the elements associated with condition two.

19 A8 Part A: Score Point 0 Part B: Score Point 0

20 Annotation Anchor Paper 8 Part A: Score Point 0 The response receives no credit. The student does not include the required element. The response does not provide the correct inequalities. Part B: Score Point 0 This response receives no credit. The student includes neither of the required elements. The response does not satisfy condition one, that the y coordinate is positive or condition two, that the sum of the coordinates is greater than -2. The description is a repeat of information in the prompt.

21 Practice Set P101 - P105 No Annotations Included

22 P101

23 P102

24 P103

25 P104

26 P105

27 Practice Set Paper Score P101 0,1 P102 0,0 P103 1,1 P104 1,1 P105 0,1