Unit 1 Finding Volume — Unit Plan

Title	Assessment
Lesson 1 What Is Volume?	Which Has More Volume? Which object has a greater volume? Explain or show your reasoning. A B Show Solution B. Sample response: B is made of 9 cubes and A is made of 8 cubes.
Lesson 2 Measure Volume	Volume of a Rectangular Prism Find the volume of the rectangular prism. Explain or show your reasoning. Show Solution 30 unit cubes. Sample responses: $5\times6=30$ , $5\times3=15$ and $15\times2=30$ , or $3\times2=6$ and $6\times5=30$
Lesson 3 Volume of Prism Drawings	Jada’s Prism Jada’s prism has 4 layers and each layer has 9 unit cubes. Circle the prism that is Jada's. A B C D Find the volume of Jada’s prism. Explain or show your reasoning. Show Solution B 36 unit cubes. Sample responses: There are 4 layers with 9 unit cubes in each layer so there are 36 unit cubes, $4\times9=36$ .
Lesson 4 Use Layers to Determine Volume	Use Expressions If the rectangular prism was filled completely, how many cubes could it hold? Explain or show how the expression $3 \times 8$ represents the volume of the prism. Show Solution 60 unit cubes. Sample response: One of the layers has 8 unit cubes, and there are 3 of those layers.
Section A Check Section A Checkpoint	Problem 1 Which figure has greater volume? Explain your reasoning. A B Show Solution A. Sample response: Figure A is 10 unit cubes and Figure B is only 9 unit cubes, so Figure A takes up more space. Problem 2 Find the volume of each prism. Explain or show your reasoning. a. b. Show Solution 30 unit cubes (or equivalent). Sample response: There are 2 layers of 15 cubes. 60 unit cubes (or equivalent). Sample response: The base layer has 20 cubes and there are 3 layers in the full prism. Problem 3 Explain or show how the expression $4 \times 6$ represents the volume of the rectangular prism in cubes. Show Solution Sample response: The layer of cubes the prism sits on has 6 cubes. There are 4 of these layers in the prism. So the volume is $4 \times 6$ unit cubes.

Lesson 5 Side Lengths of Rectangular Prisms	Determine the Volume Here is a base of a rectangular prism. What is the volume of the prism if it has a height of 3 units? Show Solution 36 unit cubes
Lesson 6 Expressions for Volume	Choose the Expression Which of these expressions does not represent the volume of the rectangular prism in cubic units? Explain or show your reasoning. $4\times5\times8\times4$ $20\times8$ $(4\times5)\times8$ $4\times40$ Choose one of the expressions from above and explain why it represents the volume of the prism in cubic units. Show Solution $4\times5\times8\times4$ . Sample response: Once we find the area of the base $4\times5$ , we only need to multiply it by the height, 8. Sample responses: $20\times8$ , because 20 represents the area of a base and 8 is the height of the prism with that base. $(4\times5)\times8$ , because $4\times5$ are the side lengths of a base and 8 is the height of the prism with that base. $4\times40$ , because 40 is the area of one of the bases and 4 is the height of the prism with that base.
Lesson 7 Cubic Units of Measure	Find the Volume Priya’s family rented a moving truck to move their belongings to their new house. The space inside the back of the moving truck is 15 feet long, 5 feet wide, and 8 feet tall. What is the volume of the back of the moving truck? Explain or show your reasoning. (Remember to include the cubic unit of measure.) Show Solution 600 cubic feet. Sample response: $8 \times 5 \times 15 = 40 \times 15 = (40 \times 10) + (40 \times 5) = 400 + 200 = 600$
Section B Check Section B Checkpoint	Problem 1 Find the volume of the rectangular prism. Explain or show your reasoning. Show Solution 140 cubic inches. Sample response: The base area is $7 \times 4$ or 28 square inches, and I multiplied that by the height, $28 \times 5 = 140$ . Problem 2 Explain or show how the expression $4 \times 48$ represents the volume of the rectangular prism in cubic units. Show Solution Sample response: The base that the prism sits on has an area of $8 \times 6$ or 48 square units. There are 4 layers of 48 unit cubes in the prism, so its volume is $4 \times 48$ cubic units. Problem 3 A box is shaped like a rectangular prism. Its measurements are 6 centimeters by 2 centimeters by 15 centimeters. Select all expressions that represent the volume of the box in cubic centimeters. A. $6 \times 2 \times 15$ B. $2 \times 90$ C. $12 \times 30$ D. $8 \times 15$ E. $15 \times 12$ Show Solution A, B, E

Lesson 8 Figures Made of Prisms	Volume of a Figure Made of Prisms Find the volume of the figure. Explain or show your reasoning. Show Solution 56 cubic units. Sample response: I cut the shape horizontally to make a 2-unit-by-2-unit-by-4-unit prism and a 4-unit-by-2-unit-by-5-unit prism. So that’s 16 and 40 more, making 56 unit cubes altogether.
Lesson 9 Measure Figures Made from Prisms	Find the Volume of a Figure Find the volume of the figure. Explain or show your reasoning. 6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 6 feet. Right side rises 2 feet, then goes left 4 feet, goes up 3 feet, then goes left 2 feet, then goes down 5 feet. Width shown as 3 feet. Show Solution 28 cubic feet. Sample responses: Cutting the figure vertically makes a 5-foot-by-4-foot-by1-foot prism on the left and a 4-foot-by-2-foot-by-1-foot prism on the right. The total volume is $(5 \times 4 \times 1) + (4 \times 2 \times 1)$ , which is $20 + 8$ or 28 cubic feet. Cutting the figure horizontally makes a 3-foot-by-4-foot-by-1-foot prism on top and an 8-foot-by-2-foot-by-1-foot prism on the bottom. The volume is $(3 \times 4 \times 1) + (8 \times 2 \times 1)$ cubic feet, which is $12 + 16$ or 28 cubic feet.
Lesson 10 Represent Volume with Expressions	Expressions as Volume Write an expression to represent the volume of the figure. 6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 6 feet. Right side rises 3 feet, then goes left an unlabeled length, goes up an unlabeled length, then goes left 4 feet, then goes down 8 feet. Width shown as 2 feet. Find the volume of the figure, in cubic feet. Show Solution Sample responses: $(4 \times 8 \times 2) + (2 \times 3 \times 2)$ or $(4 \times 5 \times 2) + (6 \times 3 \times 2)$ (or equivalent) 76 cubic feet
Lesson 11 All Kinds of Prisms	The Volume of a Sandbox A preschool is building a sandbox. Here is a diagram that shows the side lengths of the sandbox. 6-sided rectangular prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, 10 feet. Right side rises 5 feet, then goes left an unlabeled length, goes up an unlabeled length, then goes left 6 feet, then goes down 7 feet. Width shown as 2 feet. What is the volume of the sandbox? Explain or show your reasoning. Show Solution 124 cubic feet. Sample response: There is a 10-foot-by-5-foot-by-2-foot prism and a 6-foot-by-2-foot-by-2-foot prism, so that’s $(10 \times 5 \times 2) + (6 \times 2 \times 2)=124$ .
Lesson 12 Tons and Tons of Garbage	No cool-down
Section C Check Section C Checkpoint	Problem 1 Find the volume of each figure. Explain or show your reasoning. a. b. 6-sided prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, unlabeled length. Right side rises 6 inches, then goes left 8 inches, goes up 2 inches, then goes left 6 inches, then goes down an unlabeled length. Width shown as 4 inches. Show Solution Sample responses: 28 cubic units. Sample response: I cut this figure into a 2-unit-by-3-unit-by-4-unit rectangular prism that has a volume of 24 cubic units, and there are 4 more cubes, so that's 28 cubic units. 384 cubic inches. Sample response: I can cut this figure into two rectangular prisms. One prism has side lengths 8 inches by 6 inches by 4 inches and the other prism is 6 inches by 8 inches by 4 inches. Each has a volume of $8 \times 6 \times 4$ or 192 cubic inches. The total volume is 384 cubic inches. Problem 2 A jewelry box is shaped like a rectangular prism. The base of the box has an area of 200 square centimeters and its height is 6 centimeters. What is the volume of the jewelry box? Explain or show your reasoning. Show Solution 1,200 cubic centimeters. Sample response: I multiplied the area of the base by the height, $200 \times 6 = 1,200$ .