# MAFS.6.G.1.2

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
General Information
Subject Area: Mathematics
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Solve real-world and mathematical problems involving area, surface area, and volume. (Supporting 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
Test Item Specifications

• Assessment Limits :
Prisms in items must be right rectangular prisms. Unit fractional edge lengths for the unit cubes used for packing must have a numerator of 1.
• Calculator :

No

• Context :

Allowable

Sample Test Items (2)
• Test Item #: Sample Item 1
• Question: A right rectangular prism has a length of 4 ½ feet, a width of 6 ½ feet, and a height of 8 feet.

What is the volume of the prism?

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

• Test Item #: Sample Item 2
• Question: Alex has 64 cubes, with dimensions in feet (ft), like the one shown.

He uses all the cubes to fill a box shaped like a larger rectangular prism. There are no gaps between the cubes.

A. What is the volume, in cubic feet, of the larger rectangular prism?

Volume =

B. What is a possible set of dimensions, in feet, of the larger rectangular prism?

Length =

Width =

Height =

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

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101010: M/J Two-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101020: M/J Two-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101040: M/J Three-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101050: M/J Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
0101025: M/J Two-Dimensional Studio Art 2 & Career Planning (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond)
0101005: M/J Exploring Two-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101026: M/J Two-Dimensional Studio Art 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101035: M/J Exploring Three-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101060: M/J Three-Dimensional Studio Art 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))
0104110: M/J Drawing 2 (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0104200: M/J Painting (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0110100: M/J Printmaking (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.G.1.AP.2a: Find the fractional length and volume of a rectangular prism with edges using models.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 2 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 1 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Formative Assessments

Prism Packing:

Students are asked to determine the number of unit prisms needed to fill a larger prism with fractional dimensions.

Type: Formative Assessment

Clay Blocks:

Students are asked to explain the relationship between two approaches to finding the volume of a right rectangular prism.

Type: Formative Assessment

Moving Truck:

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Type: Formative Assessment

Bricks:

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Type: Formative Assessment

## Lesson Plans

Amazing Insulating Atmosphere:

In this Engineering Design Challenge, students will design a terrarium and then monitor the levels of water, gases, and temperature in the environment. The factor being changed will be the layers of plastic wrap covering the terrarium. Students will examine how the thickness of the atmosphere affects the health of the plants in the terrarium. Students will conduct research, work in teams, and then finally create a presentation to the class sharing their findings.

Type: Lesson Plan

Sound Is Not The Only Place You Hear About Volume!:

This lesson introduces the idea of finding volume. Volume in sixth grade math is very "rectangular" (cubes, rectangular prisms) and this lesson brings to light that volume is simply a measure of available space, but can take on many shapes or forms (cylinders for example - graduated cylinders and beakers) in science. Students will be left to design their own data collection and organizing the data that they collect. They will apply the skill of finding volume to using fractional parts of a number (decimals) and finding the product using the volume formula.

Type: Lesson Plan

How Many Rubik's Cubes Can You Pack?:

This two-day lesson uses a hands-on problem solving approach to find the volume of a right rectangular prism with fractional edges. Students first design boxes and fill with Rubik's Cubes. They create a formula from the patterns they found. Using cubes with fractional edges requires students to apply fractional units to their formula.

Type: Lesson Plan

The Classroom Money Vault:

This activity has students predict the number of one hundred dollar bills that can fit inside the classroom. The students use volume measurements to explain their estimation.

Type: Lesson Plan

Fill to Believe!:

In this lesson, students work cooperatively to find the volume of a right rectangular prisms, using whole and fraction units of measurement, using the volume formula, and using manipulatives to count the number of units necessary to fill the prisms, and compare it with the formula results.

Type: Lesson Plan

How Many Small Boxes?:

In this lesson students will extend their knowledge of volume from using whole numbers to using fractional units. Students will work with adding, multiplying, and dividing fractions to find the volume of right rectangular prisms, as well as, determining the number of fractional unit cubes in a rectangular prism.

Type: Lesson Plan

How much can it hold?:

This lesson uses a discovery approach to exploring the meaning of volume. The students will utilize math practice standards and cubes as they construct and analyze the relationship between the length, width, and height to the total amount of cubes. Since the students should already be able to use the formula on their own (from 5th grade standards), they will be able to apply it to real world applications of other right rectangular prisms and compare to determine which will hold the most volume.

Type: Lesson Plan

Who Wants To Carry a Million?:

"Students calculate the volume of a million dollars in 1\$ bills and the dimensions of a box large enough to hold a million dollars" (from the Beacon Lesson Plan Library).

Type: Lesson Plan

The purpose of this task is two-fold. One is to provide students with a multi-step problem involving volume. The other is to give them a chance to discuss the difference between exact calculations and their meaning in a context. It is important to note that students could argue that whether the new pan is appropriate depends in part on how accurate Leo's estimate for the needed height is.

Christo’s Building:

Students are asked to draw a scale model of a building and find related volume and surface areas of the model and the building which are rectangular prisms.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Volume of a Rectangular Prism: Fractional Cubes:

Another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism. Watch this explanation.

Type: Tutorial

Volume of a Rectangular Prism: Word Problem:

This video shows how to solve a word problem involving rectangular prisms.

Type: Tutorial

## WebQuest

Volume of Prisms:

This lesson is designed to develop students' understanding of volume and ability to find volumes of triangular prisms. It provides links to discussions and activities related to volume as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: WebQuest

## MFAS Formative Assessments

Bricks:

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Clay Blocks:

Students are asked to explain the relationship between two approaches to finding the volume of a right rectangular prism.

Moving Truck:

Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Prism Packing:

Students are asked to determine the number of unit prisms needed to fill a larger prism with fractional dimensions.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Christo’s Building:

Students are asked to draw a scale model of a building and find related volume and surface areas of the model and the building which are rectangular prisms.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Volume of a Rectangular Prism: Fractional Cubes:

Another way of finding the volume of a rectangular prism involves dividing it into fractional cubes, finding the volume of one, and then multiplying that area by the number of cubes that fit into the rectangular prism. Watch this explanation.

Type: Tutorial

Volume of a Rectangular Prism: Word Problem:

This video shows how to solve a word problem involving rectangular prisms.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.