Math Released Item Grade 8. Justify Parallel Lines VF525280

Transcription

1 Math Released Item 2017 Grade 8 Justify Parallel Lines VF525280

2 Anchor Set A1 A8 With Annotations

3 Prompt

4 Rubric VF Rubric Score Description 3 Student response includes the following 3 elements. Reasoning component = 3 points o The component has 3 parts, each worth 1 point. Part 1: The student explains why the sum of the measures of angles 4 and 5 is 180 degrees. For example: The angles 4 and 5 are on the same side of a transversal that cuts two parallel lines. Therefore, sum of the measures of angle 5 and angle 4 is 180 degrees. Note: The student must use correct mathematical language (e.g. same side interior angles ) in his or her reasoning to receive the point for this part. Part 2: The student explains why the sum of the measures of angles 9 and 10 is 180 degrees. For example: The angles 9 and 10 form a straight line. Therefore, the sum of the measures of angle 10 and angle 9 is 180 degrees. Note: The student must use correct mathematical language (e.g. linear pair ) in his or her reasoning to receive the point for this part. Part 3: The student explains that since the sum of the measures of angles 4 and 5 is 180 degrees, and that the sum of the measures of angles 9 and 10 is 180 degrees, then m 4 + m 5 = m 10 + m 9. Notes: If a student provides only the following equations, the total points earned would not be greater than 1 point. m 4 + m 5 = 180 o m 10 + m 9 = 180 o so m 4 + m 5 = m 10 + m 9 2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements. 0 Student response is incorrect or irrelevant.

5 A1 Score Point 3

6 Annotation Anchor Paper 1 Score Point 3 This response receives full credit. It includes each of the three required elements: The response explains why the sum of the measures of angles 4 and 5 is 180 degrees (because angle 4 plus angle 5 equals 180 degrees because of the consecutive angle theorem). The response explains why the sum of the measures of angles 9 and 10 is 180 degrees (angles 10 and 9 are adjacent angles that form a straight angle which equals 180 degrees). The response explains why m 4 + m 5 = m 10 + m 9 (yes, angle 4 plus angle 5 equals angle 10 plus angle 9, and that equals 180 degrees).

7 A2 Score Point 3

8 Annotation Anchor Paper 2 Score Point 3 This response receives full credit. It includes each of the three required elements: The response explains why the sum of the measures of angles 4 and 5 is 180 degrees (seince 4 5 are sime side interir angles they equel 180 o ). The response explains why the sum of the measures of angles 9 and 10 is 180 degrees ( 9 10 are a liner pair which also equal 180 o ). The response explains why m 4 + m 5 = m 10 + m 9 (she is correct they equel 180º which also equal 180º). Although the response does not explicitly demonstrate m 4 + m 5 = m 10 + m 9, stating (she is correct) and showing both pairs of angle equal 180 o makes it clear that the sums of the two pairs of angles are equal.

9 A3 Score Point 2

10 Annotation Anchor Paper 3 Score Point 2 This response receives partial credit. It includes two of the three required elements: The response explains why the sum of the measures of angles 4 and 5 is 180 degrees (m 4 and m 5 are consecutive interior angles meaning they are supplementary). Indicating that the two angles are supplementary and equal 180 o is redundant. By definition, indicating that two angles are supplementary, their sum is 180 o. The response explains why m 4 + m 5 = m 10 + m 9 (m 4 and m 5 equal 180 o [and] m 10 andm 9 equal 180 o [and] Amy is correct]. Although there is not a valid reason provided for why m 10 and m 9 equal 180 o, recognizing that their sum is 180 o and that the sum of m 4 and m 5 equal 180 o is sufficient to earn credit for this element. The explanation for why the sum of the measures of angles 9 and 10 is 180 degrees is incorrect (m 10 and m 9 are adjacent).

11 A4 Score Point 2

12 Annotation Anchor Paper 4 Score Point 2 This response receives partial credit. It includes two of the three required elements: The response explains why the sum of the measures of angles 9 and 10 is 180 degrees ( 9 and 10 for a straight line which makes them equal 180 degrees). The response explains why m 4 + m 5 = m 10 + m 9 (Amy is correct because 4 and 5 equal 180 and 9 and 10 equal 180). The explanation for why the sum of the measures of angles 4 and 5 is 180 degrees is too vague to receive any credit (since lines k and l are parallel). The fact that lines k and l are parallel is given in the prompt.

13 A5 Score Point 1

14 Annotation Anchor Paper 5 Score Point 1 This response receives partial credit. It includes one of the three required elements: The response explains why m 4 + m 5 = m 10 + m 9 (Amy is correct because m<4 + m<5 will have to equal 180 o [and] m<10 + m<9 will have to equal 180 o ). Indicating the sum of the measures of angles 4 and 5 equal 180 o and the sum of the measures of angles 9 and 10 equal 180 o is sufficient for the response to earn credit. The explanation for why the sum of the measures of angles 4 and 5 is 180 degrees is incomplete (m<4 + m<5 will have to equal 180 o because the are interior angles). To make the response complete, it must indicate that angles 4 and 5 are consecutive or same side interior angles. The explanation for why the sum of the measures of angles 9 and 10 is 180 degrees is missing.

15 A6 Score Point 1

16 Annotation Anchor Paper 6 Score Point 1 This response receives partial credit. It includes one of the three required elements: The response explains why m 4 + m 5 = m 10 + m 9 (Amy is correct. 10 and 9 are supplementary so they will add up to 180 degrees) and (4 and 5 are supplementary and the angles will come to 180 o ). The explanation for why the sum of the measures of angles 4 and 5 is 180 degrees is incorrect (4 is the alternate exterior of 6 which is supplementary to 5). Angle 4 and angle 6 are alternate interior angles. Also, there is no reason given why angle 6 and angle 5 are supplementary. The explanation for why the sum of the measures of angles 9 and 10 is 180 degrees is missing.

17 A7 Score Point 0

18 Annotation Anchor Paper 7 Score Point 0 This response receives no credit. It includes none of the three required elements: The explanation for why the sum of the measures of angles 4 and 5 is 180 degrees is missing. The explanation for why the sum of the measures of angles 9 and 10 is 180 degrees is missing. The explanation for why m 4 + m 5 = m 10 + m 9 is incorrect (m 4 + m 5 is not congruent to m 10 + m 9 because one is same side interior angles and the other is alternate interior angles).

19 A8 Score Point 0

20 Annotation Anchor Paper 8 Score Point 0 This response receives no credit. It includes none of the three required elements: The explanation for why the sum of the measures of angles 4 and 5 is 180 degrees is incorrect (angle 4 and angle 5 are alternate interior angles). Angle 4 and angle 5 are consecutive interior angles. The explanation for why the sum of the measures of angles 9 and 10 is 180 degrees is missing. The explanation for why m 4 + m 5 = m 10 + m 9 is incorrect (no).

21 Practice Set P101 - P105 No Annotations Included

22 P101

23 P102

24 P103

25 P104

26 P105

27 Practice Set Paper Score P101 1 P102 0 P103 1 P104 2 P105 0