G4 U10 Constructed Response
Name: ________________________________________ Date:_______________
Grade 4 Unit 10 Constructed Response Angles TASK 1: Form and Measure Angles (MC: 4.G.1, 4.MD.5ab; MP: 1, 2, 4, 5, 6, 7, 8) 1. Show your work in the box below.
a. Draw and label three points. b. Connect two points with a ray. Name the ray: _____________ c. Connect two different points with a ray. Name the ray: _____________ d. Name the angle formed by the two rays: _____________ e. Is the angle acute, obtuse, or right? _____________ f. Estimate the measure of the angle. _____________ Describe how you made your estimate.
g. What is the measure of the angle using a protractor? _____________ Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 1, Page 1
2. Examine ∠CAT and ∠DOG, which are angles of differently sized circles.
G
D
T O C A
______________ ∠CAT
______________ ∠DOG
a. Find the measure of ∠CAT using a protractor. _____________ b. Find the measure of ∠DOG using a protractor. _____________ c. Compare the measures of angles CAT and DOG. Use , or =. Explain the comparison.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 1, Page 2
Name: ________________________________________ Date:_______________
Grade 4 Unit 10 Constructed Response Angles TASK 2: Draw, Measure, and Estimate Angles (MC: 4.MD.6; MP: 1, 2, 3, 4, 5, 6, 7, 8) 3. Gasoline-powered automobiles have a fuel gauge that shows how much gas is in the tank. full
S
empty
G
A
a. The needle in this fuel gauge shows the tank is half full. Estimate the measure of ∠GAS. _____________ b. The needle moves as the gas tank is filled or emptied. What would be the measure of ∠GAS if the tank was full? _____________ ̅̅̅̅ and vertex ∠A, draw a ray that shows c. Using line segment AG 2 approximately where the needle would fall when the gas tank is full. 3 Label the ray with point P. Estimate the measure of ∠GAP. _____________ Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 3
4. A speedometer is a gauge that shows the speed of a car in miles per hour (mph). The needle moves as the car’s speed changes.
50
40
60
30
70 R
20
80 90
10
0 mph
100 mph C
A
a. The needle in this speedometer shows the car is moving 60 miles per hour (mph). Use a protractor to find the measure of ∠CAR.
_____________ b. Using line segment ̅̅̅̅ AC and vertex ∠A, draw a ray that forms a 63o angle on the speedometer above. Label the ray with point B. Use a protractor.
c. What speed is shown by ∠CAB?
_____________
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 4
5. A tachometer is another gauge found in a car. It tells the number of times the engine’s crankshaft rotates per minute (rpm). The more rotations per minute, the harder the engine is working. 3,000 2,000
4,000
5,000
0 rpm
v
1,000
6,000
7,000
a. When a car is parked with the engine running, the engine is idling. Mike has an old car. Its tachometer shows 1,000 rpms when the engine is idling. Draw the angle formed when the needle shows 1,000 rpms. b. Use a protractor to find the measure of the angle that indicates 1,000 rpms.
_____________ c. If an engine works too hard for too long, it could overheat and be damaged. Mike’s old car should not be run over 4,500 rpms. He says he’ll make sure the angle formed by the needle is never greater than 180o. Will this keep his engine safe? Explain your thinking.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 5
Name: ________________________________________ Date:_______________
Grade 4 Unit 10 Constructed Response Angles TASK 3: Find Missing Angles (MC: 4.G.1, 4.MD.7; MP: 1, 2, 3, 4, 6, 7, 8) 6. Show your work in the box below.
X
Y
Z
a. Draw ray ⃗⃗⃗⃗⃗ YG to form an angle of your choice from vertex ∠Y. Use a protactor to measure the angle of ∠XYG. _____________ b. Calculate the measure of ∠GYZ. Show your work.
_____________
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 6
7. Use the illustration to solve the problems. A
N G
E
55o
42o
x
27o
L
a. Calculate the measure of ∠NLG. Show your work.
b. Calculate the measure of ∠AEN. Show your work.
c. The sum of all angles in a triangle is always 180o. Calculate the measure of ∠ANE. Show your work.
d. Explain how you found the measure of ∠ANE.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 7
8. Mrs. Rodriguez asked the class to find the measure of the missing angle.
112o
y
This is Janette’s work. 360o – 112o = 248o y = 248o Is Janette’s work accurate? Explain why or why not. If her answer is wrong, solve the problem correctly.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 8
Grade 4 Unit 10 Constructed Response Angles TASK 1: Form and Measure Angles (MC: 4.G.1, 4.MD.5ab; MP: 1, 2, 4, 5, 6, 7, 8) 1. Show your work in the box below.
a. Draw and label three points. b. Connect two points with a ray. Name the ray: _____________ c. Connect two different points with a ray. Name the ray: _____________ d. Name the angle formed by the two rays: _____________ e. Is the angle acute, obtuse, or right? _____________ f. Estimate the measure of the angle. _____________ Describe how you made your estimate.
g. What is the measure of the angle using a protractor? _____________ Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 1, Page 1
2. Examine ∠CAT and ∠DOG, which are angles of differently sized circles.
G
D
T O C A
______________ ∠CAT
______________ ∠DOG
a. Find the measure of ∠CAT using a protractor. _____________ b. Find the measure of ∠DOG using a protractor. _____________ c. Compare the measures of angles CAT and DOG. Use , or =. Explain the comparison.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 1, Page 2
Name: ________________________________________ Date:_______________
Grade 4 Unit 10 Constructed Response Angles TASK 2: Draw, Measure, and Estimate Angles (MC: 4.MD.6; MP: 1, 2, 3, 4, 5, 6, 7, 8) 3. Gasoline-powered automobiles have a fuel gauge that shows how much gas is in the tank. full
S
empty
G
A
a. The needle in this fuel gauge shows the tank is half full. Estimate the measure of ∠GAS. _____________ b. The needle moves as the gas tank is filled or emptied. What would be the measure of ∠GAS if the tank was full? _____________ ̅̅̅̅ and vertex ∠A, draw a ray that shows c. Using line segment AG 2 approximately where the needle would fall when the gas tank is full. 3 Label the ray with point P. Estimate the measure of ∠GAP. _____________ Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 3
4. A speedometer is a gauge that shows the speed of a car in miles per hour (mph). The needle moves as the car’s speed changes.
50
40
60
30
70 R
20
80 90
10
0 mph
100 mph C
A
a. The needle in this speedometer shows the car is moving 60 miles per hour (mph). Use a protractor to find the measure of ∠CAR.
_____________ b. Using line segment ̅̅̅̅ AC and vertex ∠A, draw a ray that forms a 63o angle on the speedometer above. Label the ray with point B. Use a protractor.
c. What speed is shown by ∠CAB?
_____________
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 4
5. A tachometer is another gauge found in a car. It tells the number of times the engine’s crankshaft rotates per minute (rpm). The more rotations per minute, the harder the engine is working. 3,000 2,000
4,000
5,000
0 rpm
v
1,000
6,000
7,000
a. When a car is parked with the engine running, the engine is idling. Mike has an old car. Its tachometer shows 1,000 rpms when the engine is idling. Draw the angle formed when the needle shows 1,000 rpms. b. Use a protractor to find the measure of the angle that indicates 1,000 rpms.
_____________ c. If an engine works too hard for too long, it could overheat and be damaged. Mike’s old car should not be run over 4,500 rpms. He says he’ll make sure the angle formed by the needle is never greater than 180o. Will this keep his engine safe? Explain your thinking.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 2, Page 5
Name: ________________________________________ Date:_______________
Grade 4 Unit 10 Constructed Response Angles TASK 3: Find Missing Angles (MC: 4.G.1, 4.MD.7; MP: 1, 2, 3, 4, 6, 7, 8) 6. Show your work in the box below.
X
Y
Z
a. Draw ray ⃗⃗⃗⃗⃗ YG to form an angle of your choice from vertex ∠Y. Use a protactor to measure the angle of ∠XYG. _____________ b. Calculate the measure of ∠GYZ. Show your work.
_____________
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 6
7. Use the illustration to solve the problems. A
N G
E
55o
42o
x
27o
L
a. Calculate the measure of ∠NLG. Show your work.
b. Calculate the measure of ∠AEN. Show your work.
c. The sum of all angles in a triangle is always 180o. Calculate the measure of ∠ANE. Show your work.
d. Explain how you found the measure of ∠ANE.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 7
8. Mrs. Rodriguez asked the class to find the measure of the missing angle.
112o
y
This is Janette’s work. 360o – 112o = 248o y = 248o Is Janette’s work accurate? Explain why or why not. If her answer is wrong, solve the problem correctly.
Copyright © Swun Math Grade 4 Unit 10 Constructed Response, Task 3, Page 8
