Math assessment

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes,

e.g., to represent the associative property of multiplication.

b. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find of solving real- world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real-world problems.

Multiple-Choice Question (3 points each)

1. A piece of glass is shaped like a rectangular prism and has a volume of 32 cubic units.

The length of the piece of glass is 4 units. It has a width of 4 units. Determine the height.

A. 4 units

B. 8 units

C. 2 units

D. 14 units

2. A pack of Mountain Dews has 6 cans. Each can hold 473 ml of soda. What is the total number of liters in the pack?

A. 9.00 liters

B. 30.0 liters

C. 2.8 liters

D. 28.38 liters

3. Which measurement is equal to 3 meters?

A. 12 centimeters

B. 36 centimeters

C. 300 centimeters

D. 51 centimeters

4. The kid’s pool at Six Flags is made to look like a right rectangular prism. The pool is 24 feet long and 24 feet wide. How many cubic feet of water is needed to fill the pool to a depth of 2 feet?

A. 400 cubic feet

B. 640 cubic feet

C. 100 cubic feet

D. 150 cubic feet

5. A small wedding column has a square base with side lengths of 8 centimeters and a height of 4 centimeters. What is the volume of the column?

A. 35 centimeters

B. 32 centimeters

C. 70 centimeters

D. 140 centimeters

6. A bucket has a volume of 50 cubic meters. One of the dimensions is 5 meters. Which could be the other dimension of the bucket?

A. 10 meters B. 5 meters

C. 20 meters

D. 4 meters

7. Our corner store is constructing a candy display with two rectangular prisms. The base of each prism is square with a length of 5 inches. One prism is 24 inches tall and the other is twice as tall. What do you think the total volume of the candy display will be?

A. 32 cubic inches

B. 50 cubic inches

C. 120 cubic inches

D. 180 cubic inches

8. In our math lesson, we determined that the volume of a rectangular prism is 24 cubic meters with a height of 2 meters, and a length of 6 meters. Can you recall what the width was?

A. 6 meters

B. 4 meters

C. 8 meters

D. 12 meters

9. A statue at Rigley Park has a base of 8 feet by 6 feet by 4 feet and its edges are 4 feet long. What is the volume of this statue?

A. 42 cubic feet

B. 25 cubic feet

C. 56 cubic feet

D. 80 cubic feet

10. An action figure is 2 feet by 1 foot by 2 feet. What is the volume of this action figure?

A. 30 cubic feet

B. 32 cubic feet

C. 37 cubic feet

D. 72 cubic feet

11. Tell me, what is the volume of a box of Frosty Flakes that is 4 inches long, 6 inches tall, and 6 inches wide?

A. 22 cubic inches

B. 16 cubic inches

C. 96 cubic inches

D. 122 cubic inches

12. Thomas is building with cube shaped blocks. His structure is 12 blocks high and each level has the same shape and number of blocks. Can you figure out what the volume of his structure will be in cubic units?

A. 24 cubic units

B. 12 cubic units

C. 18 cubic units

D. 24 cubic units

13. The equation for volume is

A. V = L x W

B. W = V x L

Constructed Response Question (3 points each)

14. Kiya makes a picture frame with 12 square inches tiles. She puts the tiles in 2 equal rows.What are the side lengths of the frame? Use words, pictures, and numbers to support your answer.

15. I want to build a box to organize my hair products. I have a roller box that is 6 inches wide that needs to lay flat on the box. The box must also be no taller than 2 inches. Name one way I could build a box with a volume of 36 cubic inches.

16. Destiny’s she shed is a rectangular prism and it has dimensions of 12 meters by 6 meters by 24 meters. If Destiny were to double these dimensions, she believes she would only double the volume. Is she correct? Explain. Include a drawing in your explanation.

17. Elvie uses a 10 square inch cardboard box as the base of her project. Her box is 6 inches tall.

What would the volume of the box be? Show your work.

18. If a cereal box has a total volume of 30 cubic feet. What could be the four different sets of measurements?

___feet x ___ feet x __ feet

___feet x ___ feet x __ feet

___feet x ___ feet x __ feet

___feet x ___ feet x __ feet

19. The bakery made a two-layer wedding cake. Each layer is a rectangular prism that is 4 inches high. The base of the bottom layer of the cake is 50 square inches. The base of the top layer is 32 square inches. What is the total volume of the cake? Show your work.

20. The music store had 3,200 CD’s stored on 24 shelves. If the same number of CD’s were stored on each shelf, how many CD’s were stored on each shelf? Show your work.

21. A set of stairs at school are made of two blocks of cement. One block is a rectangular prism 3 feet long, 2 feet wide, and 1 foot tall. The other block is twice as tall as the first and the other dimensions are the same. What is the total volume of the cement used to make the stairs? Show your work.

22. The width of Timothy’s porch is 10 feet. Its area is 80 square feet. How long is the porch?

Show your work.

Performance Question (2 points each)

23. Shayla needs more storage for her volleyball equipment. Her current storage box measures 3 feet long by 4 feet wide by 4 feet high. She needs to replace it with a box 24 cubic feet of storage, so she doubles the width.

a. Will she achieve her goal if she does this? Explain.

b. If she wants to keep the height the same, what could the other dimensions be for a 32cubic-foot storage box?

c. If she uses the dimensions in part (b), what is the area of the new storage box’s floor?

d. How has the area of the bottom in her new storage box changed? Explain how you know.

24. Patrick makes a rectangle sidewalk with 48 square centimeter tiles. There are 6 equal rows of tiles.

a. How many tiles are in each row?

b. Can Patrick arrange all the tiles into 8 equal rows? Explain your answer.

25. Keysha desperately needs a shed to store her items. She needs a shed that measures 12 feet long by 10 feet wide by 16 feet high. She realizes she needs a shed with 960 cubic feet of storage.

a. Will she achieve her goal if she doubles each dimension? Why or why not?

b. If she wants to keep the height the same, what could the other dimensions be for her to get the volume she wants?

c. If she uses the dimensions in part (b), what could be the area of the new shed’s floor?

26. Sharon and Paul are having a discussion in class about how to find the volume of a rectangular prism. Sharon says that to find volume you must know the length, height, and width of the figure. Paul says that you only need to know the base and height of the figure.

a. Which student is correct and why?

b. Design a rectangular prism with dimensions. How would each find the volume?

27. Draw one rectangular prism with centimeter cubes.

a. Show the number of centimeters on each edge.

b. Answer the following questions.

How many cubes does the bottom layer have?

How many layers does it have?

c. What is the total volume of the rectangle prism?

28. Sheila has a box that is 8 inches tall, 6 inches long, and 2 inches wide.

a. Draw a diagram of the box, include the dimensions.

b. What did you determine the volume of the box was?

References

Mississippi Department of Education. (2016). Mississippi College-and-Career-Readiness

Standards for Mathematics.