Perimeter, Area, Volume, & Surface Area
6th Grade


Alabama Course of Study Standards:
26

Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into
known shapes. Apply the techniques of composing and decomposing polygons to find area in the context of solving realworld
and mathematical problems.

Arkansas Academic Standards:
6.G.A.1

 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
 Apply these techniques in the context of solving realworld and mathematical problems
Note: Trapezoids will be defined to be a quadrilateral with at least one pair of opposite sides parallel, therefore all parallelograms are trapezoids.

Arizona  K12 Academic Standards:
6.G.A.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques to solve mathematical problems and problems in realworld context. 
Common Core State Standards:
Math.6.G.1 or 6.G.A.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
Georgia Standards of Excellence (GSE):
MGSE6.G.1

Find area of right triangles, other triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
North Carolina  Standard Course of Study:
6.G.1

Create geometric models to solve realworld and mathematical problems to: Find the area of triangles by composing into rectangles and decomposing into right triangles.
 Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.

New York State Next Generation Learning Standards:
6.G.1

Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving realworld and mathematical problems. Note: The inclusive definition of a trapezoid will be utilized, which defines a trapezoid as "A quadrilateral with at least one pair of parallel sides." (This definition includes parallelograms.) 
Tennessee Academic Standards:
6.G.A.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; know and apply these techniques in the context of solving realworld and mathematical problems. 
Alabama Course of Study Standards:
28

Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve
realworld and mathematical problems. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

Arkansas Academic Standards:
6.G.A.2

 Find the volume of a right rectangular prism including whole number and 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 including fractional edge lengths in the context of solving realworld and mathematical problems

Arizona  K12 Academic Standards:
6.G.A.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. Understand and use the formula V = B · h, where in this case, B is the area of the base (B = l × w) to find volumes of right rectangular prisms with fractional edge lengths in mathematical problems and problems in realworld context. 
Common Core State Standards:
Math.6.G.2 or 6.G.A.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 realworld and mathematical problems. 
Georgia Standards of Excellence (GSE):
MGSE6.G.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 (1/2 u), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = (length) x (width) x (height) and V= (area of base) x (height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 
North Carolina  Standard Course of Study:
6.G.2

Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving realworld and mathematical problems. 
New York State Next Generation Learning Standards:
6.G.2

Find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 
Tennessee Academic Standards:
6.G.A.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. Know and apply the formulas V = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 
Alabama Course of Study Standards:
25

Graph polygons in the coordinate plane given coordinates of the vertices to solve realworld and mathematical
problems.  Determine missing vertices of a rectangle with the same xcoordinate or the same ycoordinate when graphed in
the coordinate plane.
 Use coordinates to find the length of a side between points having the same xcoordinate or the same ycoordinate.
 Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which
consecutive vertices have the same xcoordinate or the same ycoordinate).

Arkansas Academic Standards:
6.G.A.3

Apply the following techniques in the context of solving realworld and mathematical problems: Draw polygons in the coordinate plane given coordinates for the vertices
 Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate

Arizona  K12 Academic Standards:
6.G.A.3

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques to solve mathematical problems and problems in a realworld context. 
Common Core State Standards:
Math.6.G.3 or 6.G.A.3
Georgia Standards of Excellence (GSE):
MGSE6.G.3

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. 
North Carolina  Standard Course of Study:
6.G.3

Use the coordinate plane to solve realworld and mathematical problems by: Drawing polygons in the coordinate plane given coordinates for the vertices.
 Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

New York State Next Generation Learning Standards:
6.G.3

Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. 
Tennessee Academic Standards:
6.G.A.3

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Know and apply these techniques in the context of solving realworld and mathematical problems. 
Alabama Course of Study Standards:
27

Determine the surface area of threedimensional figures by representing them with nets composed of rectangles and
triangles to solve realworld and mathematical problems. 
Arkansas Academic Standards:
6.G.A.4

Apply the following techniques in the context of solving realworld and mathematical problems: Represent threedimensional figures using nets made up of rectangles and triangles
 Use the nets to find the surface area of these figures

Arizona  K12 Academic Standards:
6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques to solve mathematical problems and problems in realworld context. 
Common Core State Standards:
Math.6.G.4 or 6.G.A.4
Georgia Standards of Excellence (GSE):
MGSE6.G.4
Tennessee Academic Standards:
6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. 
North Carolina  Standard Course of Study:
6.G.4

Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. 
New York State Next Generation Learning Standards:
6.G.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. Note: Threedimensional figures include only right rectangular prisms, right rectangular pyramids, and right triangular prisms. When finding surface areas, all necessary measurements will be given. 
Pennsylvania Core Standards:
CC.2.3.6.A.1

Apply appropriate tools to solve realworld and mathematical problems involving area, surface area, and volume 
Pennsylvania Core Standards:
M06.CG.1.1.1

Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). 
Pennsylvania Core Standards:
M06.CG.1.1.2

Determine the area of irregular or compound polygons. 
Pennsylvania Core Standards:
M06.CG.1.1.3

Determine the volume of right rectangular prisms with fractional edge lengths. 
Pennsylvania Core Standards:
M06.CG.1.1.4

Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). 
Pennsylvania Core Standards:
M06.CG.1.1.5

Represent threedimensional figures using nets made of rectangles and triangles. 
Pennsylvania Core Standards:
M06.CG.1.1.6

Determine the surface area of triangular and rectangular prisms (including cubes). 
Florida  Benchmarks for Excellent Student Thinking:
MA.6.GR.1.3

Solve mathematical and realworld problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle 
Florida  Benchmarks for Excellent Student Thinking:
MA.6.GR.2.1

Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangle. 
Florida  Benchmarks for Excellent Student Thinking:
MA.6.GR.2.2

Solve mathematical and realworld problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles. 
Florida  Benchmarks for Excellent Student Thinking:
MA.6.GR.2.3

Solve mathematical and realworld problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula. 
Florida  Benchmarks for Excellent Student Thinking:
MA.6.GR.2.4

Given a mathematical or realworld context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net. 
