Type:

Other

Description:

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally are not packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

Subjects:

  • Mathematics > General
  • Education > General

Education Levels:

  • Grade 1
  • Grade 2
  • Grade 3
  • Grade 4
  • Grade 5
  • Grade 6
  • Grade 7
  • Grade 8
  • Grade 9
  • Grade 10
  • Grade 11
  • Grade 12

Keywords:

Cube,Surface Area,NSDL,oai:nsdl.org:2200/20120614151519756T,Middle School,Grade 6,NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-016,Volume,Rectangular Prism,Vocational/Professional Development Education,Mathematics,Education,Grade 7

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution Non-Commercial Share Alike

Collections:

None
Update Standards?

CCSS.Math.Content.6.G.A.2: Common Core State Standards for Mathematics

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.

CCSS.Math.Content.6.G.A.4: Common Core State Standards for Mathematics

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.

CCSS.Math.Content.7.G.A.1: Common Core State Standards for Mathematics

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

CCSS.Math.Content.7.G.B.6: Common Core State Standards for Mathematics

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.
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