Standard #: MAFS.6.G.1.2 (Archived Standard)


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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
Grade: 6
Domain-Subdomain: Geometry
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 Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1 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?

N/A EE: Equation Editor
Sample Item 2 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 =

N/A EE: Equation Editor


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Related Resources

Formative Assessments

Name Description
Prism Packing

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

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.

Bricks

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

Lesson Plans

Name Description
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.

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.

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.

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 positive rational number edge lengths. Students first design boxes and fill with Rubik's Cubes. They create a formula from the patterns they find. Using cubes with fractional edges requires students to apply fractional units to their formulas. 

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.

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. 

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.

How much can it hold?

This lesson uses a discovery approach to exploring the meaning of volume. The students will work with cubes as they construct and analyze the relationship between the length, width, and height to the total amount of cubes. Students will be able to apply this concept to real world applications of other right rectangular prisms and compare them to determine which will hold the most volume. 

 

Original Student Tutorials

Name Description
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.

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 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.

Problem-Solving Tasks

Name Description
Banana Bread

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

Name Description
Edcite: Mathematics Grade 6

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.

Tutorials

Name Description
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.

Volume of a Rectangular Prism: Word Problem

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

WebQuest

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
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.

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 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.

Problem-Solving Task

Name Description
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

Name Description
Edcite: Mathematics Grade 6:

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.

Tutorials

Name Description
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.

Volume of a Rectangular Prism: Word Problem:

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



Parent Resources

Problem-Solving Tasks

Name Description
Banana Bread:

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.



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