SAMPLE TASKS. Concepts Embedded Skills Vocabulary. unit cube. unit cube volume side lengths
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1 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.3a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. Concepts Embedded Skills Vocabulary unit cube Explain a unit cube as having side length of one. Describe volume in terms of cubic units. Explain volume as multiplying side lengths. unit cube volume side lengths SAMPLE TASKS I How many cubic units are in the following figure? a. 5 b. 20 c. 10 d. 1
2 II Which figure has more cubic units? a. b. c. d.
3 III How many cubic units are in the following figure? Answer Explain how you found your answer.
4 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.3b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Concepts Embedded Skills Vocabulary packing solid figures Explain/show the volume of a solid figure through repeated addition of unit cubes. Explain the difference between 2D and 3D figures. repeated addition volume solid figure 2D figures 3D figures SAMPLE TASKS I Calculate the volume of the following figure. Answer
5 II What is the volume of the following rectangular prism? III Find the volume of the following figure. Answer Explain how you calculated the volume.
6 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Concepts Embedded Skills Vocabulary volume Calculate the volume of a solid figure by counting the unit cubes. Select the appropriate unit of measure for calculating the volume of a figure. Convert between units of measure when calculating volume. unit cube solid figure volume convert I Calculate the number of cubic units contained in the rectangular prism below. SAMPLE TASKS a. 15 b. 20 c. 60 d. 40
7 II Which rectangular prism has a volume of 60 of cubic units? A. Figure 1 B. Figure 2 C. Figure 3 D. Figure 4
8 III Part a - How many cubic units are in the rectangular prism shown? Answer: PartB Explain how you found your answer.
9 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.5a. 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. Concepts Embedded Skills Vocabulary volume with unit cubes Define right rectangular prism. right rectangular prism Calculate the volume of a right rectangular prism by unit cubes packing it with unit cubes. volume Calculate the volume of a right rectangular prism by using the formulas V = l x w x h and V = B x h (Area of the Base times the height.) Explain how finding the volume using the methods above result in the same solution. SAMPLE TASKS I Explain two ways to calculate volume for the rectangular prism below. A. B.
10 II Calculate the total volume of the storage unit. Answer III What is the volume of the storage unit below? a. 28 ft. b. 30 ft. c. 148 ft. d. 160 ft.
11 IV. A jewelry box shaped like a cube has sides that are 10 centimeters long. What is the volume of the jewelry box? A. 25 cm B. 100 cm C. 125 cm D. 525 cm
12 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.5b. Apply the formulas V = l w h and V = B h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Concepts Embedded Skills Vocabulary volume formulas Calculate the volume of a rectangular prism using the formulas: V=l x w x h and V=B x h Describe/show how l x w = B (length times width equals area of the base (B). Calculate the volume of a right rectangular prism in the context of a word problem. volume right rectangular prism base length width height Area of the base (B) SAMPLE TASKS I For the rectangular prism shown below, use the two formulas shown to tell the number of cubic units in it. A. V = L x W x H B. V = B x H
13 II What is the volume of the storage unit below? a. 168 ft. b ft. c. 128 ft. d. 30 ft.
14 III What is the volume of the juice box? Height = 8 inches Width = 2 inches Length = 6 inches a. 48 inches b. 12 inches c. 96 inches d. 90 inches
15 Common Core Learning Standards Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.5c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Concepts Embedded Skills Vocabulary volume as additive Calculate the volumes of non-overlapping right rectangular prisms and add them together. Solve word problems requiring the calculations of multiple volumes and adding them together. Volume right rectangular prism non-overlapping parts SAMPLE TASKS I What is the total volume of the figure below? a. 12,000mm b. 24,000mm c. 4,800mm d. 120,000mm
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