MAFS.5.MD.3.5Archived Standard

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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.

Remarks

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.
General Information
Subject Area: Mathematics
Grade: 5
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 Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

  • 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

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5020120: STEM Lab Grade 5 (Specifically in versions: 2016 - 2022, 2022 - 2024, 2024 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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

Formative Assessments

Volume Two Ways:

Students are asked to compare different strategies for finding the volume of a rectangular prism.

Type: Formative Assessment

Using Additive Reasoning When Finding Volume:

Students are asked to find the volumes of solids composed of rectangular prisms.

Type: Formative Assessment

Determining Dimensions:

Students are given the total volume of a rectangular prism and constraints on one dimension and asked to provide dimensions that would fit the constraints.

Type: Formative Assessment

Determining and Interpreting Volume:

Students are asked to determine the volumes of two right rectangular prisms given the dimensions of one and the base area and height of the other.

Type: Formative Assessment

Lesson Plans

Pump Up the Volume:

This is a lesson on volume relating specifically to using the formula V = B x h.

Type: Lesson Plan

States of Matter and Their Properties - Mass and Volume Lesson #2:

When matter changes state, its properties change, too. In most cases, volume will increase when matter is melted from a solid to a liquid. Water is an exception, as its volume decreases when melted from ice to water. If matter is not added or removed, its mass will remain the same when it changes state. In this lesson, students will use if/then logical thinking to bridge the science and computer science concepts. This is lesson 2 of 3 in the States of Matter Unit.

Type: Lesson Plan

Survive or Die:

In this technology-rich lesson, students will design a habitat in which a plant or animal can survive. Students will focus on the adaptations that allow certain plants and animals to live in specific habitats.

Type: Lesson Plan

Building Apartments: Connecting Volume of Centimeter Cubes to the Formula V = B x h:

Students will build "apartments" with centimeter cubes by packing boxes (template included).  In addition, they will use centimeter cubes to build a variety of rectangular prisms and record the area of the base (B) and height (h) on a worksheet.  They will use that information to complete the volume formula, V = B x h.  Students will think about how the volume changes as the height and base of rectangular prisms change.

Type: Lesson Plan

Lunchbox Volume:

This lesson focuses on the application of volume knowledge.  Students will need to add the volumes of individual right rectangular prisms to find total volumes.

Type: Lesson Plan

Volumize Your Brain To Its Capacity:

Students will be able to apply and understand the meaning of volume with shoe boxes and cereal boxes. 

Type: Lesson Plan

Bakery Boxes in the Mail:

Students need to make decisions about the correct bakery box to send cookies through the mail to fill orders. Students need to consider the capacity, dimensions, and volume of the boxes in terms of how many cookies each box will hold.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

MEA Bait Shop Baffle:

Students will first review rectangular prisms and the formula for finding the volume of rectangular prisms. After students have determined the volume of a given set of rectangular prisms (aquariums), the students will use that information to help Seymour Phish in determining which aquarium he should purchase for his minnows.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Volume: Let's Be Efficient:

This lesson provides a hands-on approach to develop the formula for finding the volume of a right rectangular prism. Students will apply the formula. Students will determine the volume of figures composed of two right rectangular-prism solids.  While students will decompose simple 3 D shapes into two rectangular prisms, this decomposition is not required in the standard.  It is used here to help deepened student understanding.

Type: Lesson Plan

Cereal Box Volume Varying Predicament:

Students will review rectangular prisms and the formula for finding the volume of rectangular prisms. Once students have determined the volume of a number of rectangular prisms (cereal boxes), the students will use that information to help a fictitious company in determining which cereal box they should use for their new product.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Building Pools:

I

In this Model Eliciting Activity, MEA, students will work in teams to determine a the most suitable pool for a home construction company to build. Students will need to calculate the volume of the pool, make decisions based on a table of data, and write a letter to the customer providing evidence for their decisions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Building Rectangular Prisms Part 2:

This is the second part of a two-part volume lesson. In the first Building Rectangular Prisms (attached) lesson, foundational volume concepts are taught and students count cubes to find volume. In this lesson, students will discover the volume formulas length x width x height and base x height as they build rectangular prisms. They will use the formulas to find volume in real world situations.

Type: Lesson Plan

Shoe Closet MEA:

In this open-ended problem, students will work in teams to determine a procedure for ranking shoe closet styles for a person’s dream closet. Students will need to calculate the perimeter and cost for the closet, make decisions based on a table of data, and write a letter to the client providing evidence for their decisions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Finding Volume (Utah Education Network):

In this lesson students will learn how to calculate and compare volumes of rectangular prisms.

Type: Lesson Plan

Formulating Volume:

Students will use situational stories to help them apply the formulas V = l × w × h and V = B × h  to find the volumes of right rectangular prisms with whole-number edge lengths.

Type: Lesson Plan

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

Original Student Tutorial

Video Game Store: Volume!:

Help solve the problem of shipping video games and accessories to customers by calculating the volume of the containers needed in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Computing Volume Progression 4:

Students are asked to apply knowledge of volume of rectangular prisms to find the volume of an irregularly shaped object using the principle of displacement.

Type: Problem-Solving Task

Surface Area and Volume:

In this activity, students adjust the dimensions of either a rectangular or triangular prism and the surface area and volume are calculated for those dimensions. Students can also switch into compute mode where they are given a prism with certain dimensions and they must compute the surface area and volume. The application keeps score so students can track their progress. This application allows students to explore the surface area and volume of rectangular and triangular prisms and how changing dimensions affect these measurements. This activity also includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Problem-Solving Task

Teaching Idea

Volume of Rectangular Prisms:

This lesson is designed to introduce students to the concept of volume and how to find the volume of rectangular prisms. This lesson 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: Teaching Idea

Tutorials

Volume through Decomposition:

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula. 

Type: Tutorial

Volume: Decomposing a Solid Figure Example:

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

Unit/Lesson Sequence

Three Dimensional Shapes:

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.

Type: Unit/Lesson Sequence

STEM Lessons - Model Eliciting Activity

Bakery Boxes in the Mail:

Students need to make decisions about the correct bakery box to send cookies through the mail to fill orders. Students need to consider the capacity, dimensions, and volume of the boxes in terms of how many cookies each box will hold.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Building Pools:

I

In this Model Eliciting Activity, MEA, students will work in teams to determine a the most suitable pool for a home construction company to build. Students will need to calculate the volume of the pool, make decisions based on a table of data, and write a letter to the customer providing evidence for their decisions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Cereal Box Volume Varying Predicament:

Students will review rectangular prisms and the formula for finding the volume of rectangular prisms. Once students have determined the volume of a number of rectangular prisms (cereal boxes), the students will use that information to help a fictitious company in determining which cereal box they should use for their new product.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

MEA Bait Shop Baffle:

Students will first review rectangular prisms and the formula for finding the volume of rectangular prisms. After students have determined the volume of a given set of rectangular prisms (aquariums), the students will use that information to help Seymour Phish in determining which aquarium he should purchase for his minnows.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Shoe Closet MEA:

In this open-ended problem, students will work in teams to determine a procedure for ranking shoe closet styles for a person’s dream closet. Students will need to calculate the perimeter and cost for the closet, make decisions based on a table of data, and write a letter to the client providing evidence for their decisions.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

MFAS Formative Assessments

Determining and Interpreting Volume:

Students are asked to determine the volumes of two right rectangular prisms given the dimensions of one and the base area and height of the other.

Determining Dimensions:

Students are given the total volume of a rectangular prism and constraints on one dimension and asked to provide dimensions that would fit the constraints.

Using Additive Reasoning When Finding Volume:

Students are asked to find the volumes of solids composed of rectangular prisms.

Volume Two Ways:

Students are asked to compare different strategies for finding the volume of a rectangular prism.

Original Student Tutorials Mathematics - Grades K-5

Video Game Store: Volume!:

Help solve the problem of shipping video games and accessories to customers by calculating the volume of the containers needed in this interactive tutorial.

Student Resources

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

Original Student Tutorial

Video Game Store: Volume!:

Help solve the problem of shipping video games and accessories to customers by calculating the volume of the containers needed in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Computing Volume Progression 4:

Students are asked to apply knowledge of volume of rectangular prisms to find the volume of an irregularly shaped object using the principle of displacement.

Type: Problem-Solving Task

Tutorials

Volume through Decomposition:

This Khan Academy tutorial video illustrates how to find the volume of an irregular solid figure by dividing the figure into two rectangular prisms and finding the volume of each.  Although the tutorial works from a drawing, individual volume cubes are not drawn so students must work from the formula. 

Type: Tutorial

Volume: Decomposing a Solid Figure Example:

This Khan Academy tutorial video illustrates finding the volume of an irregular figure made up of unit cubes by separating the figure into two rectangular prisms and finding the volume of each part.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Computing Volume Progression 4:

Students are asked to apply knowledge of volume of rectangular prisms to find the volume of an irregularly shaped object using the principle of displacement.

Type: Problem-Solving Task