# MA.6.GR.2.3

Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula.

### Clarifications

Clarification 1: Problem types include finding the volume or a missing dimension of a rectangular prism.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.GR.2.AP.3: Given a real-world problem, find the volume of a rectangular prism using a visual model and the formula.

## Related Resources

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

## 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

Cube Volume and Surface Area:

Students are asked to calculate the volume and surface area of a cube.

Type: Formative Assessment

## Lesson Plans

Solar Oven Bakery:

The students will investigate how radiation from the sun allows us to bake cookie dough. The students will also determine if the volume of the box determines the time it will take for the cookie dough to bake. The students will also create a graph of the data collected while the cookie dough is baking in the solar oven.

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

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

The Cost of Keeping Cool:

Students will find the volumes of objects. After decomposing a model of a house into basic objects students will determine the cost of running the air conditioning.

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

## Original Student Tutorials

Volume Part 3: Missing Dimensions:

Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.

This is part 3 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Volume Part 2:

Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.

This is part 2 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Volume Part 1:

Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.

This is part 1 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

KROS Pacific Ocean Kayak Journey: Food Storage Mass and Volume:

What do you do if you don't have room for all your gear on a solo ocean trek? You're gonna need a bigger boat...or pack smarter with math.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

NASA Space Flight Hardware Geometry:

If you want to take things to space, you have to have a place to put them. Just make sure they fit before you send them up.

Type: Perspectives Video: Professional/Enthusiast

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

## Tutorials

Find the Volume of an Object in a Rectangular Prism:

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

Volume of a Rectangular Prism Problem:

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: Tutorial

Volume of a Rectangular Prism: Fractional Cubes:

In this video, discover 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.

Type: Tutorial

Volume of a Rectangular Prism: Word Problem:

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

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

## 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.

Cube Volume and Surface Area:

Students are asked to calculate the volume and surface area of a cube.

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.

## Original Student Tutorials Mathematics - Grades 6-8

Volume Part 1:

Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.

This is part 1 in a three-part series. Click below to open the other tutorials in the series.

Volume Part 2:

Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.

This is part 2 in a three-part series. Click below to open the other tutorials in the series.

Volume Part 3: Missing Dimensions:

Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.

This is part 3 in a three-part series. Click below to open the other tutorials in the series.

## Student Resources

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

## Original Student Tutorials

Volume Part 3: Missing Dimensions:

Help Cindy find the missing dimension of a rectangular prism in her delivery services job with this interactive tutorial.

This is part 3 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Volume Part 2:

Follow Cindy as she explores fractional unit cubes and finds the volume of rectangular prisms that have rational number dimensions in this interactive tutorial.

This is part 2 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Volume Part 1:

Follow Cindy as she learns about the volume formulas to create boxes in this interactive tutorial.

This is part 1 in a three-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

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

Find the Volume of an Object in a Rectangular Prism:

Find the volume of an object, given dimensions of a rectangular prism filled with water, and the incremental volume after the object is dropped into the water.

Type: Tutorial

Volume of a Rectangular Prism Problem:

This video involves packing a larger rectangular prism with smaller ones which is solved in two different ways.

Type: Tutorial

Volume of a Rectangular Prism: Fractional Cubes:

In this video, discover 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.

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.