# MA.5.GR.3.2

Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula.

### Clarifications

Clarification 1: Instruction includes finding the volume of right rectangular prisms by packing the figure with unit cubes, using a visual model or applying a multiplication formula.

Clarification 2: Right rectangular prisms cannot exceed two-digit edge lengths and responses include the appropriate units in word form.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Related Courses

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

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.5.GR.3.AP.2: Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes. Explore that the volume is the same as what would be found by multiplying the edge lengths

## Related Resources

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

## Formative Assessments

Measuring Volume:

Students are asked to determine the volume of a rectangular prism by using both a formula and counting cubic units.

Type: Formative Assessment

Volume Two Ways:

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

Type: Formative Assessment

Find the Volume:

Students are asked to count unit cubes to determine the volume of a right rectangular prism.

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

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

Getting the Top Mini-Fridge not a Small Deal:

In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost.  In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money.  Students will also determine the volume of a rectangular prism using a formula.

Type: Lesson Plan

Volume, Mass, and Density Boxes:

This activity was designed for blind learners, but all types of learners can utilize it to investigate volume, mass, and density. The learner will create several boxes with different materials in each. They will then compare the sizes and masses and do the math to figure the densities. Educators could also create a data collection chart for this activity.

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

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

Pump Up the Volume:

In this 5E lesson, the students will explore the concept of volume. The students will build rectangular prisms, identify the dimensions of the prism and discover the volume of the prism.

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

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

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

## 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

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.

## 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

## 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

## STEM Lessons - Model Eliciting Activity

Getting the Top Mini-Fridge not a Small Deal:

In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost.  In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money.  Students will also determine the volume of a rectangular prism using a formula.

## 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.

Find the Volume:

Students are asked to count unit cubes to determine the volume of a right rectangular prism.

Measuring Volume:

Students are asked to determine the volume of a rectangular prism by using both a formula and counting cubic units.

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

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.

## 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.