MA.7.G.2.2Archived Standard

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Use formulas to find surface areas and volume of three-dimensional composite shapes.

Remarks

This extends the work of grade 5 to using general formulas to compute the solutions for a variety of shapes.

 

 

The figure being composed or decomposed may include circles or parts of circles.

 

 

Example: Given a 3-Dimensional "E" shaped figure with labeled side lengths, find the surface area of the figure.

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 7
Body of Knowledge: Geometry
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 2 - Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , GR item(s)

  • Clarification :
    Students will solve problems involving surface area or volume of three-dimensional composite figures.
  • Content Limits :
    Students will solve problems involving surface area or volume using the decomposition of three-dimensional figures. 

    Three-dimensional figures used in composite figures are limited to three and may include right-rectangular prisms, right triangular prisms, right-square pyramids, right circular cylinders, and cones. 

    Problems related to surface area will not include cones, but problems related to volume can include cones. 

    Items that include cones and cylinders used in the composition or decomposition may include only whole figures, half-figures, or quarter-figures. 

    Right-square pyramids used in the composition or decomposition must be whole pyramids only. 

    Items will not include truncated cones and pyramids. 

    Dimensions of composite figures used in calculations will be whole numbers.

  • Stimulus Attributes :
    Graphics should be used in all of these items, as appropriate.

    Items should be set in a real-world or mathematical context.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Rebecca used a right circular cylinder piece of ice to cut out a cone. The dimensions of the ice piece she used are shown below.

    Cylinder

    which is closest to the volume of the remaining ice after rebecca removes the largest cone possible from the right circular cylinder?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: A greenhouse has the shape of half a cylinder and a rectangular prism, as shown below.

    Greenhouse

    In order to air condition the building, the owner needs to know the volume of air space in the empty greenhouse. What is the volume, in cubic feet?
  • Difficulty: N/A
  • Type: GR: Gridded-Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plan

Cylinder Volume Lesson Plan:

Using volume in the real world

Type: Lesson Plan

Teaching Idea

Modeling: Making Matchsticks:

This lesson unit is intended to help you assess how well students are able to:

  • Interpret a situation and represent the variables mathematically.
  • Select appropriate mathematical methods.
  • Interpret and evaluate the data generated.
  • Communicate their reasoning clearly.
The context is estimating how many matchsticks (rectangular prisms) can be made from this tree (conic).

Type: Teaching Idea

Virtual Manipulative

Surface Area of Prisms:

This lesson is designed to develop students' knowledge of surface area and introduce them to calculating the surface area of a triangular prism. This lesson provides links to discussions and activities related to surface area as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.