G.1.2

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.

Assessment Banner - Assessment Questions Now Available!
Formative Assessments
Formative Assessments
Assessment Logo. Includes a gray clipboard on a blue background.
CPALMS: Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Bricks

Assessment Logo. Includes a gray clipboard on a blue background.
CPALMS: Students are asked to determine the number of unit prisms needed to fill a larger prism with fractional dimensions.

Prism Packing

Assessment Logo. Includes a gray clipboard on a blue background.
CPALMS: Students are asked to explain the relationship between two approaches to finding the volume of a right rectangular prism.

Clay Blocks

Assessment Logo. Includes a gray clipboard on a blue background.
CPALMS: Students are asked to determine the volume of a right rectangular prism given fractional edge lengths.

Moving Truck

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
Virtual Manipulatives Logo includes a laptop on a yellow background.
Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.

“Finding Surface Area and Volume” by NCTM Illuminations

Virtual Manipulatives Logo includes a laptop on a yellow background.
This interactive gives students the opportunity to find the surface area and volume of a box by clicking on the flattened sides, adding cubes, rows and layers of cubes where they can see what it looks like when the sides are folded up.

“Cubes” NCTM Illuminations

Content Coming Soon Logo
We're currently looking for great content to go here!
Change Me To Real Text
Assessment Questions
Assessment Questions
Assessments Logo. Includes 3 gray question marks on a purple background.
Click on this text to download this document.
Equation Editor
Content Coming Soon Logo
We are currently looking for great content to go here.

Change Me To Real Text

Content Coming Soon Logo
We are currently looking for great content to go here.

Change Me To Real Text

Videos of Expert Instruction
Videos of Expert Instruction
Decorative Light Bulb. Image includes gray lightbulb on purple background.
This Wiki Space has several geometry instructional videos that are made by teachers for teachers. The title mentioned is approx. 5:30 min and uses a virtual model in order to explain how to find the surface area and volume of a prism. The formula for volume is explained.

“Rectangular Prism Surface Area and Volume” Grade6Geometry Wiki Space

Decorative Light Bulb. Image includes gray lightbulb on purple background.
In this video, (approx. 12:30 min) Rob explains the meaning of volume and how 3D figures ``extend`` from 2D polygons. He models how to calculate volume from the initial conceptual understanding. Sixth grade would not need the parts on volume of cylinders and cones.

“Volume” by Math Antics

Decorative Light Bulb. Image includes gray lightbulb on purple background.
In this video, (approx. 4:15 min) Sal uses a rectangular prism with edge lengths of 1/4 ft. He explains the two ways to solve for volume and students can see and hear each step of the process.

“Volume with Fractional Cubes” by Khan Academy

Decorative Light Bulb. Image includes gray lightbulb on purple background.
In this video, (approx. 9:00 min) Jeff models two examples (one with fractional side lengths) of finding volume of rectangular prisms. He explains both formulas that can be used and the benefits of each. There is also an example of finding the height when given the length, width, and volume.

“Volume a Rectangular Prisms” by Math Anywhere

Decorative Light Bulb. Image includes gray lightbulb on purple background.
In this video (approx. 4:15 min), Sal uses a model to show how the formula for finding the volume of a rectangular prism is derived from the area of the base (l x w) multiplied by the height. He shows each step of the process.

“Volume of Rectangular Prisms with Fractional dimensions” by Khan Academy

Hook/Performance Tasks
Hook/Performance Tasks
Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: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.

Banana Bread

Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: This task is third in a series of increasing in complexity. Here, the student is given the volume and is asked to find the height. They must know that 1 liter = 1000 cubic centimeters.
Computing Volume Progression 3
Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics:The purpose of this task is to see the relationship between the side-lengths of a cube and its volume. This is first in a series of tasks that gradually build in complexity.

Computing Volume Progression 1

Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: This is the last in a series of four tasks that gradually build in complexity. This problem is based on Archimedes’ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.
Computing Volume Progression 4
Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: This is a second task in a series that gradually increase in complexity. The tasks build naturally from accessible and concrete to a more abstract understanding of volume. Here, the lines that delineate individual unit cubes have been removed.
Computing Volume Progression 2
Achievement Level Descriptors Logo. Includes a dark gray document symbol on a yellow background.
Illustrative Mathematics: The purpose of this task is to introduce students to fractional units for volume. Teachers can extend the formula for non-whole number side lengths, practice fraction multiplication, and highlight volume can be numerically smaller number than side lengths.

Volumes with Fractional Edge Lengths

Problem Based Lessons
Problem Based Lessons
Test Design Summary Logo
This 3-Act Task supports students in modeling the mathematics, SMP 4, leading them to determine many boxes of girl scout cookies will fit into a car trunk?

“Girl Scout Cookies” by Dan Meyer

Test Design Summary Logo
We're currently looking for great content to go here.

Change Me To Real Text

Test Design Summary Logo
We're currently looking for great content to go here.

Change Me To Real Text