Volume
5th Grade


Arizona  K12 Academic Standards:
5.MD.C.3a
Common Core State Standards:
Math.5.MD.3a or 5.MD.C.3.A
Kentucky Academic Standards (KAS):
5.MD.3.a
Mississippi College and CareerReadiness Standards:
5.MD.3a

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. 
Tennessee Academic Standards:
5.MD.C.3.a

Understand that 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. 
Alabama Course of Study Standards:
18.a
Arizona  K12 Academic Standards:
5.MD.C.3b
Common Core State Standards:
Math.5.MD.3b or 5.MD.C.3.B
Kentucky Academic Standards (KAS):
5.MD.3.b
Mississippi College and CareerReadiness Standards:
5.MD.3b

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. 
New York State Next Generation Learning Standards:
5.MD.3.b

Recognize that 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. 
Tennessee Academic Standards:
5.MD.C.3.b

Understand that 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. 
Common Core State Standards:
Math.5.MD.4 or 5.MD.C.4

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 
North Carolina  Standard Course of Study:
5.MD.4

Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic
feet, and improvised units. 
Tennessee Academic Standards:
5.MD.C.4

Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. 
Alabama Course of Study Standards:
19.a

Use the associative property of multiplication to find the volume of a right rectangular prism and relate
it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the
three edge lengths or by multiplying the height by the area of the base. 
Arkansas Academic Standards:
5.MD.C.5.A

 Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base (B)
 Represent threefold wholenumber products as volumes (e.g., to represent the associative property of multiplication)

Arizona  K12 Academic Standards:
5.MD.C.5a

Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes (e.g., to represent the associative property of multiplication). 
Common Core State Standards:
Math.5.MD.5a or 5.MD.C.5.A
Kentucky Academic Standards (KAS):
5.MD.5.a
Mississippi College and CareerReadiness Standards:
5.MD.5a

Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. 
Georgia Standards of Excellence (GSE):
5.GSR.8.3

Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems. 
North Carolina  Standard Course of Study:
5.MD.5.a

Find the volume of a rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths. 
New York State Next Generation Learning Standards:
5.MD.5.a

Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. 
Ohio's Learning Standards:
5.MD.5.a

Find the volume of a right rectangular prism with whole number
side lengths by packing it with unit cubes, and show that the
volume is the same as would be found by multiplying the edge
lengths, equivalently by multiplying the height by the area of the
base. Represent threefold whole number products as volumes,
e.g., to represent the Associative Property of Multiplication. 
Tennessee Academic Standards:
5.MD.C.5.a

Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent wholenumber products of three factors as volumes (e.g., to represent the associative property of multiplication). 
Alabama Course of Study Standards:
19.b

Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right
rectangular prisms with wholenumber edge lengths in the context of solving realworld and
mathematical problems. 
Arkansas Academic Standards:
5.MD.C.5.B

Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems 
Arizona  K12 Academic Standards:
5.MD.C.5b

Understand and use the formulas V = l × w × h and V = B × h, where in this case B is the area of the base (B = l × w), for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths to solve
mathematical problems and problems in realworld contexts. 
Common Core State Standards:
Math.5.MD.5b or 5.MD.C.5.B
Kentucky Academic Standards (KAS):
5.MD.5.b
Mississippi College and CareerReadiness Standards:
5.MD.5b

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. 
Georgia Standards of Excellence (GSE):
5.GSR.8.4

Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems. 
Massachusetts Curriculum Frameworks:
5.MD.C.5.b

Apply the formulas V = l × w × h and V = B × h (where B stands for the area of the base) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems. 
North Carolina  Standard Course of Study:
5.MD.5.b

Build understanding of the volume formula for rectangular prisms with wholenumber edge lengths in the context of solving problems. 
Tennessee Academic Standards:
5.MD.C.5.b

Know and apply the formulas V = l × w × h and V = B × h (where B represents the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving realworld and mathematical problems. 
Alabama Course of Study Standards:
19.c

Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the
volumes of the two parts, applying this technique to solve realworld problems. 
Arkansas Academic Standards:
5.MD.C.5.C

 Recognize volume as additive
 Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems
Example: John was finding the volume of this figure. He decided to break it apart into two separate rectangular prisms. John found the volume of the solid below using this expression: (4 × 4 × 1) + (2 × 4 × 2). Decompose the figure into two rectangular prisms and shade them in different colors to show one way John might have thought about it. Phillis also broke this solid into two rectangular prisms, but she did it differently than John. She found the volume of the solid below using this expression: (2 × 4 × 3) + (2 × 4 × 1). Decompose the figure into two rectangular prisms and shade them in different colors to show one way Phillis might have thought about it.

Arizona  K12 Academic Standards:
5.MD.C.5c

Understand volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms, applying this technique to solve mathematical problems and problems in realworld contexts. 
Common Core State Standards:
Math.5.MD.5c or 5.MD.C.5.C
Kentucky Academic Standards (KAS):
5.MD.5.c
Mississippi College and CareerReadiness Standards:
5.MD.5c

Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems. 
North Carolina  Standard Course of Study:
5.MD.5.c

Find volume of solid figures with onedigit dimensions composed of two nonoverlapping rectangular prisms. 
Tennessee Academic Standards:
5.MD.C.5.c

Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve realworld problems. 
Pennsylvania Core Standards:
CC.2.4.5.A.5

Apply concepts of volume to solve problems and relate volume to multiplication and to addition. 
Pennsylvania Core Standards:
M05.DM.3.1.1

Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving realworld and mathematical problems. 
Pennsylvania Core Standards:
M05.DM.3.1.2

Find volumes of solid figures composed of two nonoverlapping right rectangular prisms. 
Georgia Standards of Excellence (GSE):
5.GSR.8.3

Investigate volume of right
rectangular prisms by packing
them with unit cubes without gaps
or overlaps. Then, determine the
total volume to solve problems. 
Georgia Standards of Excellence (GSE):
5.GSR.8.4

Discover and explain how the
volume of a right rectangular
prism can be found by multiplying
the area of the base times the
height to solve authentic,
mathematical problems. 
