G4 U10 Constructed Response Rubric
Grade 4 Unit 10 Constructed Response Angles Description Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees.
MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8
2. Draw, Measure, and Estimate Angles
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8
3. Find Missing Angles
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
Task
1. Form and Measure Angles
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 1
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. Responses will vary by student. All responses must match the illustration the student draws in parts a-d.
Points
U K
E
a. Student draws and labels three points. (See sample above)
1
b. Student accurately connects two points with a ray and names it. (See sample above)
1 1
c. Student accurately connects two different points with another ray and names it. (See sample above)
1
d. Student accurately names the angle formed by the two rays. Sample response: ∠UKE
1
e. Student correctly identifies whether the angle is acute, obtuse, or right. Sample response: obtuse
1
f. Student makes a reasonable estimate of the measure of the angle formed and describes how the estimate was made. Sample response: I estimate angle ∠UKE is 135o because it is greater than 90o and the remaining part of the angle is about 45o (half of another 90o). 90o + 45o = 135o.
1
g. Student correctly measures and records the angle using a protractor. Sample response: 137 o 2. a. Student correctly measures and records ∠CAT: 70o
1
b. Student correctly measures and records ∠DOG: 70o
1
c. Student correctly compares ∠CAT and ∠DOG, and explains: ∠CAT = ∠DOG. The angle in the larger circle may look larger because it forms a larger slice than in the smaller circle. But, the measure of angles has nothing to do with the size of the circle or the area of the pie-shaped pieces. Instead, the angle represents the portion of the circular arc formed by the rays.
2
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 3
Total
3. a. Student gives a reasonable estimate. Sample response: ~45o
1
b. Student gives the correct answer: 90o
1
c. Student accurately labels the fuel gauge and gives a reasonable estimate of the angle: ~60o full
1
P
S
empty
G
A
4. a. Student gives an accurate measurement. 108o
1
b. Student draws ⃗⃗⃗⃗⃗⃗ 𝑨𝑩 to form a 63o angle. 40
50
1 60
30 B 20
70 R 80 90
10
0 mph C
A c. Student gives the correct answer: 35 mph
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 4
100 mph 1
5. a. Student draws an accurate angle.
1
3,000 2,000
4,000
5,000
1,000
6,000
v
0 RPM
7,000 1
b. Student gives the correct measure: 30o c. Student gives the correct answer and an accurate explanation: Wording may vary. Sample response: No, making sure the needle is never at an angle greater than 180o will not be enough to make sure Mike’s engine is safe. When the needle makes a 180o angle, it will be at 6,000 rpms which is much higher than 4,500. This may cause the engine to overheat and get damaged. He should make sure the angle formed by the needle is not greater than 135o. 6. Responses will vary by student. All responses must match the illustration the student draws in part a. a. Student forms and accurately draws ∠XYG. Responses will vary. Sample response: 158o
2
1
G X
Y
Z
b. Student accurately calculates ∠GYZ and shows work. Responses will vary. Sample response: 180o – 158o = 22o.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 5
1
7. a. Student accurately calculates ∠NLG and shows work: 111o
1
b. Student accurately calculates ∠AEN and shows work: 35o
1
c. Student accurately calculates ∠ANE and shows work: 55o
1
d. Student gives an accurate explanation: Wording may vary. Sample response: The sum of all the angles in a triangle is always 180o. I know the measure of ∠EAN is 90o because the square symbol shows the lines are perpendicular. Perpendicular lines form 90o angles. I already calculated the measure of ∠AEN to be 35o. The sum of the known angles is 125o. If I subtract that from 180o, I will find the measure of ∠ANE to be 55o.
2
8. Student gives the correct answer, an accurate explanation, and solves the problem correctly. Wording may vary. Sample response: No, Janette’s work is not correct because she subtracted only one of the known angles from 360o. She should have subtracted 112o and 90o from 360o. The measure of the missing angle is 158o. Total
2
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Standards for Mathematical Practice (MP)
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees.
MP.1 MP.2 MP.4 MP.5 MP.6 MP.7 MP.8
2. Draw, Measure, and Estimate Angles
4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
MP.1 MP.2 MP.3 MP.4 MP.5 MP.6 MP.7 MP.8
3. Find Missing Angles
4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
MP.1 MP.2 MP.3 MP.4 MP.6 MP.7 MP.8
Task
1. Form and Measure Angles
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 1
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 2
Scoring Rubric Question 1. Responses will vary by student. All responses must match the illustration the student draws in parts a-d.
Points
U K
E
a. Student draws and labels three points. (See sample above)
1
b. Student accurately connects two points with a ray and names it. (See sample above)
1 1
c. Student accurately connects two different points with another ray and names it. (See sample above)
1
d. Student accurately names the angle formed by the two rays. Sample response: ∠UKE
1
e. Student correctly identifies whether the angle is acute, obtuse, or right. Sample response: obtuse
1
f. Student makes a reasonable estimate of the measure of the angle formed and describes how the estimate was made. Sample response: I estimate angle ∠UKE is 135o because it is greater than 90o and the remaining part of the angle is about 45o (half of another 90o). 90o + 45o = 135o.
1
g. Student correctly measures and records the angle using a protractor. Sample response: 137 o 2. a. Student correctly measures and records ∠CAT: 70o
1
b. Student correctly measures and records ∠DOG: 70o
1
c. Student correctly compares ∠CAT and ∠DOG, and explains: ∠CAT = ∠DOG. The angle in the larger circle may look larger because it forms a larger slice than in the smaller circle. But, the measure of angles has nothing to do with the size of the circle or the area of the pie-shaped pieces. Instead, the angle represents the portion of the circular arc formed by the rays.
2
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 3
Total
3. a. Student gives a reasonable estimate. Sample response: ~45o
1
b. Student gives the correct answer: 90o
1
c. Student accurately labels the fuel gauge and gives a reasonable estimate of the angle: ~60o full
1
P
S
empty
G
A
4. a. Student gives an accurate measurement. 108o
1
b. Student draws ⃗⃗⃗⃗⃗⃗ 𝑨𝑩 to form a 63o angle. 40
50
1 60
30 B 20
70 R 80 90
10
0 mph C
A c. Student gives the correct answer: 35 mph
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 4
100 mph 1
5. a. Student draws an accurate angle.
1
3,000 2,000
4,000
5,000
1,000
6,000
v
0 RPM
7,000 1
b. Student gives the correct measure: 30o c. Student gives the correct answer and an accurate explanation: Wording may vary. Sample response: No, making sure the needle is never at an angle greater than 180o will not be enough to make sure Mike’s engine is safe. When the needle makes a 180o angle, it will be at 6,000 rpms which is much higher than 4,500. This may cause the engine to overheat and get damaged. He should make sure the angle formed by the needle is not greater than 135o. 6. Responses will vary by student. All responses must match the illustration the student draws in part a. a. Student forms and accurately draws ∠XYG. Responses will vary. Sample response: 158o
2
1
G X
Y
Z
b. Student accurately calculates ∠GYZ and shows work. Responses will vary. Sample response: 180o – 158o = 22o.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response Rubric, Page 5
1
7. a. Student accurately calculates ∠NLG and shows work: 111o
1
b. Student accurately calculates ∠AEN and shows work: 35o
1
c. Student accurately calculates ∠ANE and shows work: 55o
1
d. Student gives an accurate explanation: Wording may vary. Sample response: The sum of all the angles in a triangle is always 180o. I know the measure of ∠EAN is 90o because the square symbol shows the lines are perpendicular. Perpendicular lines form 90o angles. I already calculated the measure of ∠AEN to be 35o. The sum of the known angles is 125o. If I subtract that from 180o, I will find the measure of ∠ANE to be 55o.
2
8. Student gives the correct answer, an accurate explanation, and solves the problem correctly. Wording may vary. Sample response: No, Janette’s work is not correct because she subtracted only one of the known angles from 360o. She should have subtracted 112o and 90o from 360o. The measure of the missing angle is 158o. Total
2
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