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Geometry of Three-Dimensional Objects Activities for Middle School

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

Understanding the parts of three-dimensional shapes and how to calculate different measurements using them are important concepts in geometry. These activities will help your students explore the geometry of three-dimensional objects.

Everyday Objects

Three-dimensional shapes are all around us. Students eating an ice cream cone, playing basketball, or wrapping a gift are all using three-dimensional objects. Consider using these activities to help students explore the relationship between three-dimensional and two-dimensional shapes, identify parts of three-dimensional shapes, and calculate the volume and surface area of three-dimensional objects.

Exploring with Nets

Students will create three-dimensional shapes using paper nets of each shape.

Materials

  • Examples of three-dimensional shapes
  • Copies of nets for geometric shapes
  • Scissors
  • Tape/glue
  • Chart paper
  • Markers

Teacher Directions

  • Show students examples of three-dimensional shapes, such as a tissue box (rectangular prism) or a globe (sphere).
  • Tell students that they will be making three-dimensional shapes using nets, or flatten versions of three-dimensional shapes.
  • Divide the class into small groups, and provide each group with copies of nets, chart paper, markers, scissors, tape/glue. Consider using nets of the following shapes:
    • Rectangular prism
    • Cube
    • Cone
    • Square-based pyramid
    • Cylinder
    • Hexagonal prism
    • Dodecahedron
  • Each group will cut out their nets and assemble the three-dimensional shapes by folding them and taping/gluing the appropriate sides together.
  • Students will create a chart with their observations about the three-dimensional shapes. The chart should contain the following information:
    • Drawing of the net for each three-dimensional shape
    • Drawing of the assembled three-dimensional shape
    • List of the two-dimensional shapes, and quantity of each, that make up the three-dimensional shape
  • When students are finished, they will share their findings with the class.

Discussion Questions

  • How are the three-dimensional shapes you created the same and different?
  • How do the types of two-dimensional shapes found in the nets of three-dimensional shapes contribute to their structure?

Marshmallow Toothpick Shapes

Engage students in a hands-on activity to create three-dimensional shapes with toothpicks and marshmallows as they explore vertices, edges, and faces.

Materials

  • Three-dimensional objects (ex- dice)
  • Copies of chart of three-dimensional objects
  • Marshmallows
  • Toothpicks
  • Paper

Teacher Directions

  • Define 'vertex,' 'edge,' and 'face' for the class. Illustrate an example of a vertex, edge, and face on a three-dimensional object, such as a set of dice.
  • Divide the class into pairs, and provide each pair with a copy of a chart of three-dimensional objects, marshmallows, and toothpicks.
  • Have students recreate each three-dimensional shape using marshmallows and toothpicks. The marshmallows will represent the vertex where edges meet, and the toothpicks will represent edges.
  • Consider having students create common three-dimensional shapes, such as rectangular prisms, and more complex shapes like octahedrons.
  • Provide each pair with paper and have them create charts listing the number of vertices and edges and the number and shape of faces for each three-dimensional shape.
  • When finished, have students discuss their findings.

Discussion Questions

  • How are the number of vertices, edges, and faces related to each other in different three-dimensional shapes?
  • In what professions would people be concerned with understanding the vertices, edges, and faces of three-dimensional shapes.

Measure the Volume/Surface Area

Have students take measurements to figure out the surface area and/or volume of different three-dimensional objects.

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