G3 U10 Constructed Response
Name: ________________________________________ Date:_______________
Grade 3 Unit 10 Constructed Response Measurement TASK 1: Finding the Area of Rectangles (MC: 3.MD.5ab, 6, 7ab; MP: 1, 3, 4, 6, 7, 8) 1. The principal wants a new four-square court painted on the playground. She drew a sketch for the painter showing him the court should be 18 feet long on each side. a. Count to find the area of one of the playing squares in square feet.
Area = ______________________________
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 1, Page 1
b. The painter prefers to measure in yards, so he redrew the principal’s sketch. Count to find the area of one playing square in square yards.
Area = ______________________________ c. Draw the square units in another playing square. Write and solve a multiplication equation that represents the area of both playing squares in square yards.
d. Write and solve a multiplication equation that represents the area of the entire four-square court in square yards.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 2
2. The principal would also like to have lines painted for a new handball court. She wants the area of the handball court to be 35 square yards. The ball wall is 5 yards wide, so that’s how wide the court will be.
Wall = 5 yards
a. The principal started a sketch for the painter, but she got distracted by a phone call. Finish her sketch to show the painter how long the sides of the handball court should be.
b. Write and solve an equation that represents the area of the handball court.
c. Does your drawing in Part A match the solution you found in Part B? Explain why or why not.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 3
3. The principal will ask the painter to repaint the room numbers on the blacktop. The painter will lay stencils on the blacktop and paint over them. Each number stencil is a square with a side length of 1 foot.
a. What is the area of one stencil?
38 4 7
b. If he places them side-by-side without any gaps or overlaps, what will be the total area of the blacktop covered by the stencils when he paints the number for room 834?
Prove your answer with a drawing.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 4
c. The painter has a total of 10 number stencils, one for each number zero through nine. He told a third grader all ten stencils would always form a shape with an area of 10 ft2, no matter how he arranged them, as long as there were no gaps or overlaps. Is he right? Explain your answer.
d. Draw at least two sketches to illustrate your answer for Part C.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 5
Name: ________________________________________ Date:_______________
Grade 3 Unit 10 Constructed Response Measurement TASK 2: Find the Area of Rectangles using the Distributive Property and Decomposition (MC: 3.MD.7cd; MP: 1, 2, 3, 4, 6, 7, 8) 4. Use the Distributive Property to find the total area of each half-court. a. On a volleyball half-court, the distance from the net to the attack line is 10 ft. The distance from the attack line to the back line is 20 ft. A volleyball half-court is 30 ft wide. Net
Attack Line
Back Line
30 ft
10 ft
20 ft
(30 × _______) + (30 × _______) = _______
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 6
b. On a singles tennis half-court, the distance from the net to the service line is 7 yards. The distance from the service line to the baseline is 6 yards. A singles tennis half-court is 9 yards wide.
Net 7 yd Service Line 6 yd
9 yd
Baseline
(9 × _______) + (9 × _______) = _______
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 7
c. On my grandpa’s backyard badminton half-court, the distance from the net to the short service line is 2 yards. The distance from the short service line to the long service line is 5 yards. The half-court is 7 yards wide. Grandpa says the area of the half-court is 45 yd2. Here are his calculations.
Long Short Service Line Service Line Net (7 yd × 5 yd) + (5 yd × 2 yd) 35 yd2 + 10 yd2 45 yd2
7 yd
5 yd
Did Grandpa find the correct area? Explain why or why not.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 8
2 yd
5. Mrs. Schilling’s classroom is a portable bungalow. The painter will paint all four exterior walls. Help him find the total area to be painted on each wall. a. The north-facing wall is 5 meters wide and 3 meters high. It has an air conditioning unit attached to it, which will not be painted. What is the total area of this wall that will be painted? Show your work.
2m
Area
3m 1m 5m
b. The south-facing wall is 5 meters wide and 3 meters high. It has a door and a window, which will not be painted. What is the total area of this wall that will be painted? Show your work. 5m
1m
3m 2m
1m
Area
1m
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 9
c. The east-facing wall is 9 meters wide and 3 meters high. It has two large windows that will not be painted. What is the total area of this wall that will be painted? Show your work. 9m
3m
1m
1m 3m
3m
Area
d. The west-facing wall is 9 meters wide and 3 meters high. It has a large mural that will not be painted. What is the total area of this wall that will be painted? Show your work. 9m 7m 3m 2m
Area
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 10
6. A strip of sidewalk leading to the classroom door divides the grass into two sections. a. Find the total area of the yard in front of the classroom door by using either the Distributive Property or by decomposing the rectangle. Show your work.
grass
sidewalk
grass
4 ft
3 ft
5 ft
9 ft
b. Explain how you solved the problem.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 11
Name: ________________________________________ Date:_______________
Grade 3 Unit 10 Constructed Response Measurement TASK 3: Area and Perimeter of Rectangles and Complex Figures (MC: 3.MD.7d, 8; MP: 1, 2, 4, 6, 7, 8) 7. The school’s volleyball net is 3 feet tall and 30 feet long. 30 ft 3 ft
a. Find the perimeter of the volleyball net. Show your work.
b. Find the area of the volleyball net. Show your work.
c. Explain how perimeter and area are related.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 12
8. The perimeter of the volleyball scorekeeper’s official scorebook cover is 44 inches. It is 12 inches wide. 12 in
?
a. Find the length of the scorebook cover. Show your work.
b. Find the area of the scorebook cover. Show your work.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 13
9. The principal wants a new hopscotch game painted on the playground. She drew a sketch of the way she wanted it set up. Each square is 2 feet long on each side. 2 ft
a. Find the perimeter of the hopscotch game. Show your work.
10 8
9 7
5
6 4
2
3 1
b. Find the area of the hopscotch game. Show your work.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 14
c. Draw a different polygon with the same area as the hopscotch game.
d. Find the perimeter of your polygon.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 15
Grade 3 Unit 10 Constructed Response Measurement TASK 1: Finding the Area of Rectangles (MC: 3.MD.5ab, 6, 7ab; MP: 1, 3, 4, 6, 7, 8) 1. The principal wants a new four-square court painted on the playground. She drew a sketch for the painter showing him the court should be 18 feet long on each side. a. Count to find the area of one of the playing squares in square feet.
Area = ______________________________
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 1, Page 1
b. The painter prefers to measure in yards, so he redrew the principal’s sketch. Count to find the area of one playing square in square yards.
Area = ______________________________ c. Draw the square units in another playing square. Write and solve a multiplication equation that represents the area of both playing squares in square yards.
d. Write and solve a multiplication equation that represents the area of the entire four-square court in square yards.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 2
2. The principal would also like to have lines painted for a new handball court. She wants the area of the handball court to be 35 square yards. The ball wall is 5 yards wide, so that’s how wide the court will be.
Wall = 5 yards
a. The principal started a sketch for the painter, but she got distracted by a phone call. Finish her sketch to show the painter how long the sides of the handball court should be.
b. Write and solve an equation that represents the area of the handball court.
c. Does your drawing in Part A match the solution you found in Part B? Explain why or why not.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 3
3. The principal will ask the painter to repaint the room numbers on the blacktop. The painter will lay stencils on the blacktop and paint over them. Each number stencil is a square with a side length of 1 foot.
a. What is the area of one stencil?
38 4 7
b. If he places them side-by-side without any gaps or overlaps, what will be the total area of the blacktop covered by the stencils when he paints the number for room 834?
Prove your answer with a drawing.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 4
c. The painter has a total of 10 number stencils, one for each number zero through nine. He told a third grader all ten stencils would always form a shape with an area of 10 ft2, no matter how he arranged them, as long as there were no gaps or overlaps. Is he right? Explain your answer.
d. Draw at least two sketches to illustrate your answer for Part C.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 5
Name: ________________________________________ Date:_______________
Grade 3 Unit 10 Constructed Response Measurement TASK 2: Find the Area of Rectangles using the Distributive Property and Decomposition (MC: 3.MD.7cd; MP: 1, 2, 3, 4, 6, 7, 8) 4. Use the Distributive Property to find the total area of each half-court. a. On a volleyball half-court, the distance from the net to the attack line is 10 ft. The distance from the attack line to the back line is 20 ft. A volleyball half-court is 30 ft wide. Net
Attack Line
Back Line
30 ft
10 ft
20 ft
(30 × _______) + (30 × _______) = _______
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 6
b. On a singles tennis half-court, the distance from the net to the service line is 7 yards. The distance from the service line to the baseline is 6 yards. A singles tennis half-court is 9 yards wide.
Net 7 yd Service Line 6 yd
9 yd
Baseline
(9 × _______) + (9 × _______) = _______
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 7
c. On my grandpa’s backyard badminton half-court, the distance from the net to the short service line is 2 yards. The distance from the short service line to the long service line is 5 yards. The half-court is 7 yards wide. Grandpa says the area of the half-court is 45 yd2. Here are his calculations.
Long Short Service Line Service Line Net (7 yd × 5 yd) + (5 yd × 2 yd) 35 yd2 + 10 yd2 45 yd2
7 yd
5 yd
Did Grandpa find the correct area? Explain why or why not.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 8
2 yd
5. Mrs. Schilling’s classroom is a portable bungalow. The painter will paint all four exterior walls. Help him find the total area to be painted on each wall. a. The north-facing wall is 5 meters wide and 3 meters high. It has an air conditioning unit attached to it, which will not be painted. What is the total area of this wall that will be painted? Show your work.
2m
Area
3m 1m 5m
b. The south-facing wall is 5 meters wide and 3 meters high. It has a door and a window, which will not be painted. What is the total area of this wall that will be painted? Show your work. 5m
1m
3m 2m
1m
Area
1m
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 9
c. The east-facing wall is 9 meters wide and 3 meters high. It has two large windows that will not be painted. What is the total area of this wall that will be painted? Show your work. 9m
3m
1m
1m 3m
3m
Area
d. The west-facing wall is 9 meters wide and 3 meters high. It has a large mural that will not be painted. What is the total area of this wall that will be painted? Show your work. 9m 7m 3m 2m
Area
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 10
6. A strip of sidewalk leading to the classroom door divides the grass into two sections. a. Find the total area of the yard in front of the classroom door by using either the Distributive Property or by decomposing the rectangle. Show your work.
grass
sidewalk
grass
4 ft
3 ft
5 ft
9 ft
b. Explain how you solved the problem.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 2, Page 11
Name: ________________________________________ Date:_______________
Grade 3 Unit 10 Constructed Response Measurement TASK 3: Area and Perimeter of Rectangles and Complex Figures (MC: 3.MD.7d, 8; MP: 1, 2, 4, 6, 7, 8) 7. The school’s volleyball net is 3 feet tall and 30 feet long. 30 ft 3 ft
a. Find the perimeter of the volleyball net. Show your work.
b. Find the area of the volleyball net. Show your work.
c. Explain how perimeter and area are related.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 12
8. The perimeter of the volleyball scorekeeper’s official scorebook cover is 44 inches. It is 12 inches wide. 12 in
?
a. Find the length of the scorebook cover. Show your work.
b. Find the area of the scorebook cover. Show your work.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 13
9. The principal wants a new hopscotch game painted on the playground. She drew a sketch of the way she wanted it set up. Each square is 2 feet long on each side. 2 ft
a. Find the perimeter of the hopscotch game. Show your work.
10 8
9 7
5
6 4
2
3 1
b. Find the area of the hopscotch game. Show your work.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 14
c. Draw a different polygon with the same area as the hopscotch game.
d. Find the perimeter of your polygon.
Copyright © Swun Math Grade 3 Unit 10 Constructed Response, Task 3, Page 15
