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# MAFS.5.MD.3.5

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

1. 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.
2. 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.
3. 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.
Subject Area: Mathematics
Domain-Subdomain: Measurement and Data
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Remarks/Examples

Examples of Opportunities for In-Depth Focus

Students work with volume as an attribute of a solid figure and as a measurement quantity. Students also relate volume to multiplication and addition. This work begins a progression leading to valuable skills in geometric measurement in middle school.

### TEST ITEM SPECIFICATIONS

• Item Type(s): This benchmark may be assessed using: MS , EE item(s)

• Assessment Limits :
Items may not contain fraction or decimal dimensions or volumes. Items may contain no more than two non-overlapping prisms – non-overlapping means that two prisms may share a face, but they do not share the same volume.

Items assessing MAFS.5.MD.3.5b may not contain the use or graphic of unit cubes.

Items assessing MAFS.5.MD.3.5c must contain a graphic of the figures.

• Calculator :

No

• Context :

Allowable

### SAMPLE TEST ITEMS (3)

• Test Item #: Sample Item 1
• Question: A shipping box in the shape of a rectangular prism has the dimensions shown.

V = l × w × h

What is the volume, in cubic feet, of the box?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 2
• Question: Select all the options that could be the dimensions of a rectangular prism with a volume of 384 cubic feet (ft).

• Difficulty: N/A
• Type: MS: Multiselect

• Test Item #: Sample Item 3
• Question:

For MAFS.5.MD.3.5b:

A right rectangular prism has a volume of 144 cubic centimeters and a height of 4 centimeters.

What are a possible length and width, in centimeters, of the prism?

V = l × w × h

• Difficulty: N/A
• Type: EE: Equation Editor