Building a Box

This lesson presents the students with a real-world situation to help develop their spatial visualization skills using nets of a cube. The students are to design all the different nets possible that can be folded into a cube. This lesson presents the students with a real-world situation to help develop their spatial visualization skills using nets of a cube. The students are to design all the different nets possible that can be folded into a cube.

 

Standards & Objectives

Academic standards
CCSS.Math.Content.3.G.A.1
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that...
CCSS.Math.Content.4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a...
CCSS.Math.Content.5.G.B.3
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all...
CCSS.Math.Content.5.G.B.4
Classify two-dimensional figures in a hierarchy based on properties.
CCSS.Math.Content.5.MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
CCSS.Math.Content.5.MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
CCSS.Math.Content.5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
CCSS.Math.Content.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...
CCSS.Math.Content.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....
CCSS.Math.Content.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,...
CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
GLE 0306.4.1
Describe, compare, and analyze properties of polygons.
GLE 0306.4.3
Understand and use attributes of 2- and 3-dimensional figures to solve problems.
GLE 0506.4.2
Describe polyhedral solids and analyze their properties, including volume and surface area.
GLE 0606.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
GLE 0606.4.3
Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
GLE 0606.4.4
Develop and use formulas for surface area and volume of 3-dimensional figures.
SPI 0306.4.1
Recognize polygons and be able to identify examples based on geometric definitions.
SPI 0406.4.1
Classify lines and line segments as parallel, perpendicular, or intersecting.
SPI 0406.4.4
Identify acute, obtuse, and right angles in 2-dimensional shapes.
SPI 0406.4.5
Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes.
SPI 0506.4.3
Identify a three-dimensional object from two-dimensional representations of that object and vice versa.
SPI 0506.4.4
Solve problems involving surface area and volume of rectangular prisms and polyhedral solids.
SPI 0606.4.5
Determine the surface area and volume of prisms, pyramids and cylinders.
SPI 0606.4.6
Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
TSS.Math.3.G.A.1
Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Recognize rhombuses,...
TSS.Math.4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified...
TSS.Math.5.G.B.3
Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also...
TSS.Math.5.MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
TSS.Math.5.MD.C.4
Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units.
TSS.Math.5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms.
TSS.Math.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...
TSS.Math.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...
TSS.Math.7.G.B.5
Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles,...
TSS.Math.8.G.C.7
Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Learning objectives: 

Students will:

  • Create, compare and describe different two-dimensional nets that can be folded into a three-dimensional cube.
  • Examine the properties of the nets and resulting cubes, including surface area.
  • Use rotations and flips to compare various nets.

Lesson Variations

Blooms taxonomy level: 
Applying
Extension suggestions: 
  • Have students determine the net for a typical cereal box. Draw a sketch, and then cut it out and fold it. See if they can design nets for other boxes they have seen. Also, you might have them use the Patch Tool to create nets for other three‎ dimensional objects using triangles, hexagons, and rhombi.
  • Give students the following challenge problem:
  • The ACME box company wants to make these jewelry boxes as efficiently as possible. They can save money by fitting as many nets as possible on one piece of cardboard. If the company use a piece of cardboard that measures 20 cm × 20 cm, how many nets (of any type) can you arrange to fit on one piece of cardboard? You may use any of the working net designs you created and you may arrange them in any way on your piece of cardboard.
  • As an alternative, allow students to use the drawing area of the Patch Tool to represent the cardboard, and see how many different nets they can fit into this region.
  • Draw a net on a single sheet of 8½" × 11" piece of paper that will result in the largest cube possible. Which net will you use? What is its volume?
     

Helpful Hints

Materials:

  • Computers with Internet connection
  • Building a Box Activity Sheet 
  • Square Polydron or Geofix pieces, or centimeter grid paper to cut and fold

References

Contributors: