Surface Area of a Rectangular Prism

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Lessons

Standards in this Lesson

Common Core Math Standards

6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
HSA.CED.A: Create equations that describe numbers or relationships.

CSTA Standards

2-AP-11: Create clearly named variables that represent different data types and perform operations on their values.
2-AP-17: Systematically test and refine programs using a range of test cases
2-AP-19: Document programs in order to make them easier to follow, test, and debug.

Alabama Standards

AL.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
AL.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
AL.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
AL.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
AL.HSA.CED.A: Create equations that describe numbers or relationships.

Arkansas Standards

AR.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
AR.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
AR.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
AR.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
AR.HSA.CED.A: Create equations that describe numbers or relationships.

California Standards

CA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
CA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
CA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
CA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
CA.HSA.CED.A: Create equations that describe numbers or relationships.

Colorado Standards

CO.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
CO.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
CO.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
CO.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
CO.HSA.CED.A: Create equations that describe numbers or relationships.

Connecticut Standards

CT.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
CT.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
CT.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
CT.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
CT.HSA.CED.A: Create equations that describe numbers or relationships.

Delaware Standards

DE.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
DE.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
DE.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
DE.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
DE.HSA.CED.A: Create equations that describe numbers or relationships.

Delaware Standards

GA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
GA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
GA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
GA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
GA.HSA.CED.A: Create equations that describe numbers or relationships.

Hawaii Standards

HI.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
HI.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
HI.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
HI.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
HI.HSA.CED.A: Create equations that describe numbers or relationships.

Idaho Standards

ID.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
ID.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
ID.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
ID.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
ID.HSA.CED.A: Create equations that describe numbers or relationships.

Illinois Standards

IL.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
IL.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
IL.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
IL.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
IL.HSA.CED.A: Create equations that describe numbers or relationships.

Iowa Standards

IA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
IA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
IA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
IA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
IA.HSA.CED.A: Create equations that describe numbers or relationships.

Kansas Standards

KS.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
KS.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
KS.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
KS.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
KS.HSA.CED.A: Create equations that describe numbers or relationships.

Kentucky Standards

KY.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
KY.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
KY.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
KY.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
KY.HSA.CED.A: Create equations that describe numbers or relationships.

Louisiana Standards

LA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
LA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
LA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
LA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
LA.HSA.CED.A: Create equations that describe numbers or relationships.

Maine Standards

ME.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
ME.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
ME.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
ME.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
ME.HSA.CED.A: Create equations that describe numbers or relationships.

Michigan Standards

MI.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MI.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MI.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MI.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MI.HSA.CED.A: Create equations that describe numbers or relationships.

Maryland Standards

MD.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MD.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MD.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MD.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MD.HSA.CED.A: Create equations that describe numbers or relationships.

Massachusetts Standards

MA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MA.HSA.CED.A: Create equations that describe numbers or relationships.

Mississippi Standards

MS.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MS.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MS.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MS.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MS.HSA.CED.A: Create equations that describe numbers or relationships.

Missouri Standards

MO.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MO.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MO.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MO.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MO.HSA.CED.A: Create equations that describe numbers or relationships.

Montana Standards

MT.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MT.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
MT.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
MT.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
MT.HSA.CED.A: Create equations that describe numbers or relationships.

New Hampshire Standards

NH.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NH.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NH.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NH.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NH.HSA.CED.A: Create equations that describe numbers or relationships.

Nevada Standards

NV.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NV.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NV.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NV.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NV.HSA.CED.A: Create equations that describe numbers or relationships.

New Jersey Standards

NJ.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NJ.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NJ.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NJ.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NJ.HSA.CED.A: Create equations that describe numbers or relationships.

New Mexico Standards

NM.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NM.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NM.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NM.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NM.HSA.CED.A: Create equations that describe numbers or relationships.

North Carolina Standards

NC.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NC.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NC.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NC.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NC.HSA.CED.A: Create equations that describe numbers or relationships.

North Dakota Standards

ND.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
ND.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
ND.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
ND.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
ND.HSA.CED.A: Create equations that describe numbers or relationships.

New York Standards

NY.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
NY.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
NY.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
NY.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
NY.HSA.CED.A: Create equations that describe numbers or relationships.

Oklahoma Standards

OK.7.AP.A.01: Select and modify an existing algorithm in natural language or pseudocode to solve complex problems.
OK.7.GM.1.1: Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rational-valued edge lengths can be found by wrapping the figure with samesized square units without gaps or overlap. Use appropriate measurements such as cm^2
OK.G.3D.1.1: Solve real-world and mathematical problems using the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composites of these figures. Use nets, measuring devices, or formulas as appropriate.
OK.L1.AP.A.01: Create a prototype that uses algorithms (e.g., searching, sorting, finding shortest distance) to provide a possible solution for a real-world problem.
OK.PA.GM.2: Calculate surface area and volume of three-dimensional figures.
OK.PA.GM.2.1: Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units of measure, such as square centimeters.
OK.PA.GM.2.2: Calculate the surface area of a cylinder, in terms of pi and using approximations for pi, using decomposition or nets. Use appropriate units of measure, such as square centimeters.

Ohio Standards

OH.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
OH.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
OH.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
OH.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
OH.HSA.CED.A: Create equations that describe numbers or relationships.

Oregon Standards

OR.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
OR.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
OR.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
OR.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
OR.HSA.CED.A: Create equations that describe numbers or relationships.

Pennsylvania Standards

PA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
PA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
PA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
PA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
PA.HSA.CED.A: Create equations that describe numbers or relationships.

Rhode Island Standards

RI.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
RI.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
RI.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
RI.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
RI.HSA.CED.A: Create equations that describe numbers or relationships.

South Dakota Standards

SD.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
SD.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
SD.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
SD.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
SD.HSA.CED.A: Create equations that describe numbers or relationships.

Tennessee Standards

TN.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
TN.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
TN.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
TN.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
TN.HSA.CED.A: Create equations that describe numbers or relationships.

Utah Standards

UT.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
UT.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
UT.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
UT.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
UT.HSA.CED.A: Create equations that describe numbers or relationships.

Vermont Standards

VT.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
VT.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
VT.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
VT.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
VT.HSA.CED.A: Create equations that describe numbers or relationships.

Washington Standards

WA.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
WA.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
WA.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
WA.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
WA.HSA.CED.A: Create equations that describe numbers or relationships.

West Virginia Standards

WV.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
WV.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
WV.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
WV.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
WV.HSA.CED.A: Create equations that describe numbers or relationships.

Wisconsin Standards

WI.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
WI.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
WI.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
WI.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
WI.HSA.CED.A: Create equations that describe numbers or relationships.

Wyoming Standards

WY.6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
WY.6.G.A: Solve real-world and mathematical problems involving area, surface area, and volume.
WY.6.G.A.4: Represent three-dimensional 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 real-world and mathematical problems.
WY.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
WY.HSA.CED.A: Create equations that describe numbers or relationships.

Textbook Alignment

IM Algebra 1

IM.Alg1.2.3: Writing Equations to Model Relationships (Part 2)
IM.Alg1.2.2: Writing Equations to Model Relationships (Part 1)

IM 7 Math™

IM.7.7.14: Surface Area of Right Prisms

IM 6 Math™

IM.6.1.15: More Nets, More Surface Area
IM.6.1.14: Nets and Surface Area
IM.6.1.13: Polyhedra
IM.6.1.12: What is Surface Area?

Connected Math

CMP.7.7: Filling and Wrapping: Three Dimensional Measurement
CMP.6.4: Covering and Surrounding: Two Dimensional Measurement

Practices in this Lesson

Math

MP.4: Model with mathematics

(Also available in Pyret)

Students define the shapes used to build a rectangular prism, print them, cut them out, and build the rectangular prism. Then they use their model to calculate the surface area.

Lesson Goals

Students will be able to:

Demonstrate understanding of surface area and use that understanding to calculate surface area of rectangular prisms

Student-facing Goals

I can explain what surface area is.
I can use my understanding of surface area to calculate the surface area of any rectangular prism.

Materials

Lesson Slides
Surface Area of a Rectangular Prism Starter File
Surface Area of a Rectangular Prism - Explore
Classroom visual: Language Table

Preparation

This lesson requires a printer, scissors and tape.
Decide whether students will be printing in black & white or in color.
If you’re printing in black & white, colored pencils may be useful for some students.

Key Points For The Facilitator

This lesson focuses on developing students' understanding of Surface Area of prisms, such that they can build their own formulas. Instructors are encouraged not to reference any pre-defined formulas during the exploration.

Glossary

dimension: a measurement of something in a particular direction, especially height, length, or width. The dimensions of a computer screen, for example, are given as width x height.
face: the flat surfaces on the outside of a solid figure
rectangular prism: a solid figure which has 6 faces, all of which are rectangular
surface area: the sum of the areas of all of the faces of a solid figure (polyhedron) or the total area that the surface of the object occupies

🔗Surface Area

Overview

Students build on their experience with writing code to define shapes. They will define shapes for all of the faces of a rectangular prism, print them, cut them out, and build the rectangular prism. Then they will use their model to calculate the surface area and write code to do the same.

Launch

Turn to Surface Area of a Rectangular Prism - Explore. Complete the first two questions.

Invite students to share out to gauge their prior knowledge of surface area.

Now, open the Surface Area of a Rectangular Prism Starter File in a new tab, save a copy, and click "Run".
Type prism into the Interactions Area to see an image of a rectangular prism. What do you notice about the prism?

Be sure that students notice that the faces and dimensions (length, width, and height) are labeled. Invite them to observe how many faces there are, as well as how many differently sized faces there are. Students who clearly see that there are three sizes of faces, with two faces in each size, will be able to move more confidently through the remainder of the activity.

Faces are the flat surfaces on the outside of a solid figure. Edges are the line segments where the faces meet in each of the three dimensions. The surface area of a prism is calculated by adding the areas of its faces.

Go to PART 1 and look at the definitions for front and back. Type front into the Interactions Area. What do you get?
- A black-outlined rectangle that has a width of 180 and a height of 50.
The faces front and back have been defined to draw a rectangle whose dimensions are width and height. You will need to write definitions for each of the other faces of the prism.
Click "Run" and test each of the faces in the Interactions Area to make sure that they match the prism you started with.

Facilitation Note The sample definitions were written to make images of outlined rectangles with a black and white printer in mind. If you have access to a color printer in your classroom, you may want students to change the code of front and back to better match what they see in the image of prism and code the remaining faces with solid rectangles to match the image they are looking at. If you do not have access to a color printer, but think that colors would support your students, you can have them color the rectangles on the printout before cutting and assembling the prism.

If you do not have a classroom printer, consider splitting this lesson over two days - the Launch segment on Day 1, and the Investigate and Synthesize segments on Day 2. At the end of Day 1, direct students to share their images with you. Print the images and distribute them before beginning the Investigate segment on Day 2.

Go to PART 2 in the code. Type (print-imgs faces) into the Interactions Area. How many rectangles do you see?
- Two.
The code in PART 2 says (define faces (list front back)) , which defines faces to be a list of values. This list will include all of the faces of the prism, but right now it only includes front and back. Add the names of each of the remaining faces to the list. Ensure that students' lists include all six faces of the rectangular prism.

When you’ve finished, click "Run" and again type (print-imgs faces). What do you Notice? What do you Wonder?
Do you have enough shapes to cover all of the faces of the prism?
Read the comments in PART 3 of the file to learn how to print the faces to build your prism.

Investigate

Have students cut out and tape together the images they defined to form a 3-dimensional paper model of a rectangular prism. Students will then use their models to calculate the surface area.

Supporting students with learning variations

Labeling the shapes with face names and/or area before taping them together may help some students.
Printing two copies of the file (one to cut and one to write on) might best support other students.

Once you’ve built your prism, use it to help you calculate the surface area of the figure.
Then, go to PART 4 in the Surface Area of a Rectangular Prism Starter File and define surface-area using length, width, and height.

Synthesize

Have students share the code they wrote to define surface-area. Did students all write the code the same way?

For further debriefing, discuss the following:

How did building the prism help you to understand surface area?
How did writing the code for surface area help you to understand surface area?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.