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http://illuminations.nctm.org/LessonDetail.aspx?ID=L261

A lesson plan for grades 7–8 Mathematics

Provider: National Council of Teachers of Mathematics


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This is the third in a sequence of four lessons designed for students to understand scale factor and volume of various rectangular prisms. In this lesson, the student can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships between edge lengths and volumes. Illuminations provides an activity sheet and a link to the applet for completing this lesson. After engaging students in a discussion about their knowledge of volume, the teacher demonstrates how to use the program. Then, students explore the program, recording volumes, ratios, and scale factors for rectangular prisms.

Students will:

  • Explain the three-dimensionality of volume.
  • Apply the volume formula for rectangular prisms.
  • Understand that the relationship between the volume of two similar rectangular prisms and the scale factor is cubic.
  • Use the applet to explain the relationship between the volume of two similar rectangular prisms and the scale factor.
  • Create pattern units of squares, predict how patterns with different numbers of squares will appear when repeated in a grid, and check their predictions.
  • Analyze how repeating patterns are generated.

NCTM Standards and Expectations covered in this lesson include:

  • Precisely describing, classifying, and understanding relationships among types of two- and three-dimensional objects using their defining properties.
  • Using geometric models to represent and explain numerical and algebraic relationships.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 7

  • Goal 2: Measurement - The learner will understand and use measurement involving two- and three-dimensional figures.
    • Objective 2.02: Solve problems involving volume and surface area of cylinders, prisms, and composite shapes.
  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Using three-dimensional figures:
      • Identify, describe, and draw from various views (top, side, front, corner).
      • Build from various views.
      • Describe cross-sectional views.
    • Objective 3.02: Identify, define, and describe similar and congruent polygons with respect to angle measures, length of sides, and proportionality of sides.
    • Objective 3.03: Use scaling and proportional reasoning to solve problems related to similar and congruent polygons.

Grade 8

  • Goal 2: Measurement - The learner will understand and use measurement concepts.
    • Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.
  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.