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K–12 teaching and learning · from the UNC School of Education

Scaling away

http://illuminations.nctm.org/LessonDetail.aspx?ID=L584

A lesson plan for grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics


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Students will measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. Students will then compare the surface area and volume of the original object and the enlarged model. Illuminations provides activity sheets, overheads, links to helpful applets, and detailed instructions for completing the lesson.

Students will:

  • Measure the dimensions of a rectangular prism or cylinder, and determine the dimensions of an enlarged model using a scale factor of 3, 4, 5, 6, 7, or 8.
  • Compute surface area and volume and determine the ratio of surface areas and volumes between the object and the model.
  • Learn that if the dimensions of an object are multiplied by a scale factor n, then the surface area is multiplied by n2 and the volume is multiplied by n3.

NCTM Standards and Expectations:

  • Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
  • Solve problems involving scale factors, using ratio and proportion.
  • Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 2: Measurement - The learner will select and use appropriate tools to measure two- and three-dimensional figures.
    • Objective 2.01: Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.
    • Objective 2.02: Solve problems involving perimeter/circumference and area of plane figures.

Grade 7

  • Goal 2: Measurement - The learner will understand and use measurement involving two- and three-dimensional figures.
    • Objective 2.01: Draw objects to scale and use scale drawings to solve problems.
    • Objective 2.02: Solve problems involving volume and surface area of cylinders, prisms, and composite shapes.

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.