G6 U7 Constructed Response
Name: ________________________________________ Date:_______________
Grade 6 Unit 7 Constructed Response Geometry TASK 1: Draw and Find the Area of Polygons on the Coordinate Grid (MC: 6.G.1, 6.G.3; MP: 1, 2, 3, 4, 6, 7, 8) 1. Justin and Mike had a fun Sunday afternoon riding around their neighborhood on their skateboards. They started off from Mike’s house at (-7, 2). a. Plot and label Mike’s house. b. Plot and label the points that represent their first stops: Skate Shop: (0, 2) Snack Shack: (0, -5)
c. The skate park was their third stop, and the vertex forms their path into a square. What are the coordinates of the skate park?
________________ d. If the coordinate grid represents neighborhood blocks, what is the perimeter of the square path the boys skated?
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 1
2. Samantha is creating a parallelogram-shaped floral centerpiece to decorate a rectangular table for a garden party.
a. Three of the vertices of her rectangular table are (-5, 3), (3, 3), and (3, -1). Plot these points and find the missing vertex.
________________
b. Find the area of Samantha’s table in square feet. ________________
c. Three of the vertices of the parallelogram-shaped floral arrangement are (-3, ½), (-2, 1½), and (0, ½). Plot these points and find the missing vertex.
________________ d. In square feet, find the area of Samantha’s table not covered by the centerpiece. Show your work. ________________
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 2
3. Use the polygons in the coordinate grid to solve the problems. a. Juanita found the area of the isosceles triangle. Here is her work. A =bxh A = 6 units x 6.5 units A = 39 units2 Explain and correct her error.
b. Find the area of the hexagon. Show your work and explain your steps.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 7 Constructed Response Geometry TASK 2: Find the Volume of Rectangular Prisms (MC: 6.G.2; MP: 1, 2, 3, 4, 6, 7, 8) 4. a. What is the volume of a ½-inch cube? Show your work.
b. Johnson told his classmate that it takes eight ½-inch cubes to equal the volume of one 1-inch cube. Is that true? Explain why or why not. Draw a model to support your answer.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 2, Page 4
5. Every year the 6th graders look forward to several activities to celebrate the end of their elementary school years. a. Sixth graders vote for teachers who have stood out in a variety of ways. Each ballot box is 13½ inches long, 9½ inches wide, and 5 inches high. What is the volume of one ballot box? Show your work.
Most School Spirit Funniest
Most Encouraging
b. This year the sixth graders bought a gift for the school that arrived in a carton that was 10¼ feet long, 2½ feet wide, and ¾ of a foot high. What is the volume of the carton? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 5
c. The cake for the end-of-the-year party arrived in a 25⅞ × 18⅙ × 4 inch box. What is the volume of the cake box? Show your work.
d. Each case of juice boxes for the end-of-the-year party is 13.3 × 8.6 × 4.5 inches. What is the total volume of one case? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 6
Name: ________________________________________ Date:_______________
Grade 6 Unit 7 Constructed Response Geometry TASK 3: Find the Surface Area of Solid Figures Using Nets (MC: 6.G.4; MP: 1, 2, 3, 4, 6, 7, 8) 6. Getting ready for the end of the year, PTA parents carefully unpacked the sixth graders’ gift to the school from its carton. a. Find the surface area of the carton. Show your work.
2½ ft ¾ ft 2½ ft ¾ ft
10¼ ft
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 7
b. The gift is a painted wooden sign to be hung facing the parking lot. To protect it from the weather, a volunteer will coat it with polyurethane before it is hung. The sign is 9¾ feet long, 2 feet tall, and ¼ of a foot thick. Sketch a net of the sign and find the total surface area. Show your work. 2 ft Lincoln LIONS
You can’t hide from our pride! 9¾ ft
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 8
¼ ft
7. The science teacher used a glass triangular prism to show students how light breaks up into the colors of the rainbow. This prism has equilateral triangles at each end.
1.2 in
7.8 in What is the surface area of this triangular prism? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 9
8. Examine this net with a square base.
3½ yd 2½ yd
a. What solid figure is formed by this net?
b. What is the surface area of the figure? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 10
9. Vebjorn found the surface area of this cube using its net. Here is his work.
¾m Surface Area of a cube = ¾ m × ¾ m × ¾ m Surface Area =
27/ 64
m3
Is Vebjorn’s work correct? Explain why or why not. If his work is incorrect, solve the problem correctly.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 11
Grade 6 Unit 7 Constructed Response Geometry TASK 1: Draw and Find the Area of Polygons on the Coordinate Grid (MC: 6.G.1, 6.G.3; MP: 1, 2, 3, 4, 6, 7, 8) 1. Justin and Mike had a fun Sunday afternoon riding around their neighborhood on their skateboards. They started off from Mike’s house at (-7, 2). a. Plot and label Mike’s house. b. Plot and label the points that represent their first stops: Skate Shop: (0, 2) Snack Shack: (0, -5)
c. The skate park was their third stop, and the vertex forms their path into a square. What are the coordinates of the skate park?
________________ d. If the coordinate grid represents neighborhood blocks, what is the perimeter of the square path the boys skated?
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 1
2. Samantha is creating a parallelogram-shaped floral centerpiece to decorate a rectangular table for a garden party.
a. Three of the vertices of her rectangular table are (-5, 3), (3, 3), and (3, -1). Plot these points and find the missing vertex.
________________
b. Find the area of Samantha’s table in square feet. ________________
c. Three of the vertices of the parallelogram-shaped floral arrangement are (-3, ½), (-2, 1½), and (0, ½). Plot these points and find the missing vertex.
________________ d. In square feet, find the area of Samantha’s table not covered by the centerpiece. Show your work. ________________
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 2
3. Use the polygons in the coordinate grid to solve the problems. a. Juanita found the area of the isosceles triangle. Here is her work. A =bxh A = 6 units x 6.5 units A = 39 units2 Explain and correct her error.
b. Find the area of the hexagon. Show your work and explain your steps.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 3
Name: ________________________________________ Date:_______________
Grade 6 Unit 7 Constructed Response Geometry TASK 2: Find the Volume of Rectangular Prisms (MC: 6.G.2; MP: 1, 2, 3, 4, 6, 7, 8) 4. a. What is the volume of a ½-inch cube? Show your work.
b. Johnson told his classmate that it takes eight ½-inch cubes to equal the volume of one 1-inch cube. Is that true? Explain why or why not. Draw a model to support your answer.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 2, Page 4
5. Every year the 6th graders look forward to several activities to celebrate the end of their elementary school years. a. Sixth graders vote for teachers who have stood out in a variety of ways. Each ballot box is 13½ inches long, 9½ inches wide, and 5 inches high. What is the volume of one ballot box? Show your work.
Most School Spirit Funniest
Most Encouraging
b. This year the sixth graders bought a gift for the school that arrived in a carton that was 10¼ feet long, 2½ feet wide, and ¾ of a foot high. What is the volume of the carton? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 5
c. The cake for the end-of-the-year party arrived in a 25⅞ × 18⅙ × 4 inch box. What is the volume of the cake box? Show your work.
d. Each case of juice boxes for the end-of-the-year party is 13.3 × 8.6 × 4.5 inches. What is the total volume of one case? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 1, Page 6
Name: ________________________________________ Date:_______________
Grade 6 Unit 7 Constructed Response Geometry TASK 3: Find the Surface Area of Solid Figures Using Nets (MC: 6.G.4; MP: 1, 2, 3, 4, 6, 7, 8) 6. Getting ready for the end of the year, PTA parents carefully unpacked the sixth graders’ gift to the school from its carton. a. Find the surface area of the carton. Show your work.
2½ ft ¾ ft 2½ ft ¾ ft
10¼ ft
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 7
b. The gift is a painted wooden sign to be hung facing the parking lot. To protect it from the weather, a volunteer will coat it with polyurethane before it is hung. The sign is 9¾ feet long, 2 feet tall, and ¼ of a foot thick. Sketch a net of the sign and find the total surface area. Show your work. 2 ft Lincoln LIONS
You can’t hide from our pride! 9¾ ft
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 8
¼ ft
7. The science teacher used a glass triangular prism to show students how light breaks up into the colors of the rainbow. This prism has equilateral triangles at each end.
1.2 in
7.8 in What is the surface area of this triangular prism? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 9
8. Examine this net with a square base.
3½ yd 2½ yd
a. What solid figure is formed by this net?
b. What is the surface area of the figure? Show your work.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 10
9. Vebjorn found the surface area of this cube using its net. Here is his work.
¾m Surface Area of a cube = ¾ m × ¾ m × ¾ m Surface Area =
27/ 64
m3
Is Vebjorn’s work correct? Explain why or why not. If his work is incorrect, solve the problem correctly.
Copyright © Swun Math Grade 6 Unit 7 Constructed Response, Task 3, Page 11
