# MAFS.5.MD.3.3

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
1. 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.
2. 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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Measurement and Data
Cluster: Level 1: Recall
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
Test Item Specifications
Also Assesses:
MAFS.5.MD.3.4

• Assessment Limits :
Items may contain right rectangular prisms with whole-number side lengths. Figures may only be shown with unit cubes. Labels may include cubic units (i.e. cubic centimeters, cubic feet, etc.) or exponential units (i.e., cm3 , ft3 , etc.). Items requiring measurement of volume by counting unit cubes must provide a key of the cubic unit.
• Calculator :

No

• Context :

Allowable

Sample Test Items (4)
• Test Item #: Sample Item 1
• Question: Ellen is shopping for boxes. Which measurement should she use to determine the amount the box will hold?

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question:

A rectangular prism is shown. What is the volume in cubic inches (in.), of the rectangular prism?

• 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 (current), 2022 and beyond)
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond (current))
5020120: STEM Lab Grade 5 (Specifically in versions: 2016 and beyond (current))
5012065: Accelerated Mathematics Plan Grade 4 (Specifically in versions: 2019 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.5.MD.3.AP.3a: Use packing to recognize volume of a solid figure.

## Related Resources

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

## Assessments

Sample 4 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Sample 3 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Sample 2 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Sample 1 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

## Formative Assessments

How Do We Determine Volume?:

Students are asked to determine how a unit cube can be used to measure the volume of a rectangular prism.

Type: Formative Assessment

Determining Volume:

Students analyze a rectangular prism that contains one layer of unit cubes and are asked to explain how to determine the volume of the entire prism using only the information given.

Type: Formative Assessment

How Do You Find the Volume?:

Students discuss the volume of a prism measured in cubic units with gaps between the unit cubes used to measure its volume.

Type: Formative Assessment

## Lesson Plans

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

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

Volume: It's All About the Count:

In this lesson, students will learn the concept of volume as an attribute of solid figures, using unit cubes in various arrangements with a focus on rectangular prisms.

Type: Lesson Plan

Hands-On! Rectangular Prisms:

Students create surface area nets with graph paper and work with manipulative cubes to decide if there is a relationship between surface area and volume in rectangular prisms.

Type: Lesson Plan

Manipulating Cubic Units:

Students will recognize volume as an attribute of solid figures and understand concepts of volume measurement. They will measure volumes by counting unit cubes, using cubic centimeters and cubic inches.

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

Finding Volume (Utah Education Network):

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

Type: Lesson Plan

Building Rectangular Prisms Part 1:

This is the first part of a two-part volume lesson. In this lesson, students will build foundational concepts for volume and and count cubes to find volume. In the second part lesson Building Rectangular Prisms Part 2 (attached), 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

## Original Student Tutorials

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

Building Blocks of Volume :

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

Type: Original Student Tutorial

Working for Wonka:

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume.

Type: Original Student Tutorial

Computing Volume Progression 1:

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Box of Clay:

This purpose of this task is to help students understand what happens when you scale the dimensions of a right rectangular solid. This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them. These relative volumes can be calculated geometrically, filling the larger box with smaller boxes, or arithmetically using the given dimensions.

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.

## Professional Development

What Does It Mean To Measure?:

This is a professional development session from the Learning Math series from Annenberg. Learners will begin to explore the questions "What can be measured?" and "What does it mean to measure something?" Learners identify measurable properties of objects such as weight, surface area, and volume, and discuss which metric units are appropriate for measuring these properties. Learners will also learn that measurement is, by its nature, approximate. Finally, learners will consider how to make measurements using nonstandard units. This session features a number of problems for learners to solve and open-ended questions to discuss, videos that demonstrate measurement techniques, and an interactive activity that asks learners to construct shapes using different size triangles to foster understanding of area and perimeter. There are also nine homework problems in which learners are asked to generate different measurements, graph measurements, and evaluate the appropriateness of the measurements generated using a data chart. Many of the professional development activities can be used directly in the classroom.

Type: Professional Development

## 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: How to Measure It:

This Khan Academy tutorial video describes measurement in one, two, and three dimensions.

Type: Tutorial

Volume:

This interactive applet demonstrates volume as the number of unit cubes needed to fill a rectangular solid. The learner sees an animation and answers questions about the capacity of a box. The student can then ask for other problems where just the 3D dimensions are given and the volume is requested.

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

## Virtual Manipulative

Houses with Height Numbers:

This applet allows students to freely build shapes by stacking cubes and "explore the relation between a building (house) consisting of cubes and the height numbers representing the height of the different parts of the building." This exercise helps students visualize and understand the concepts of volume and three-dimensional, measurable space

Type: Virtual Manipulative

## MFAS Formative Assessments

Determining Volume:

Students analyze a rectangular prism that contains one layer of unit cubes and are asked to explain how to determine the volume of the entire prism using only the information given.

How Do We Determine Volume?:

Students are asked to determine how a unit cube can be used to measure the volume of a rectangular prism.

How Do You Find the Volume?:

Students discuss the volume of a prism measured in cubic units with gaps between the unit cubes used to measure its volume.

## Original Student Tutorials Mathematics - Grades K-5

Building Blocks of Volume :

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive 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.

Working for Wonka:

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume.

## Student Resources

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

## Original Student Tutorials

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

Building Blocks of Volume :

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

Type: Original Student Tutorial

Working for Wonka:

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume.

Type: Original Student Tutorial

Computing Volume Progression 1:

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Box of Clay:

This purpose of this task is to help students understand what happens when you scale the dimensions of a right rectangular solid. This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them. These relative volumes can be calculated geometrically, filling the larger box with smaller boxes, or arithmetically using the given dimensions.

## Tutorials

Volume: How to Measure It:

This Khan Academy tutorial video describes measurement in one, two, and three dimensions.

Type: Tutorial

Volume:

This interactive applet demonstrates volume as the number of unit cubes needed to fill a rectangular solid. The learner sees an animation and answers questions about the capacity of a box. The student can then ask for other problems where just the 3D dimensions are given and the volume is requested.

Type: Tutorial

## Virtual Manipulative

Houses with Height Numbers:

This applet allows students to freely build shapes by stacking cubes and "explore the relation between a building (house) consisting of cubes and the height numbers representing the height of the different parts of the building." This exercise helps students visualize and understand the concepts of volume and three-dimensional, measurable space

Type: Virtual Manipulative

## Parent Resources

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