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

Learning about length, perimeter, area, and volume of similar objects using interactive figures: Side length and area of similar figures

http://standards.nctm.org/document/eexamples/chap6/6.3/

A lesson plan for Grades 4–8 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
4–8
Subjects
mathematics (measurement)
Provider
National Council of Teachers of Mathematics

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Creative Commons License

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This two-part example illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length and Area of Similar Figures, the user can manipulate the side lengths of one of two similar rectangles and the scale factor to learn about how the side lengths, perimeters, and areas of the two rectangles are related. In the second part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes.

E-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 4

  • Goal 2: Measurement - The learner will understand and use perimeter and area.
    • Objective 2.01: Develop strategies to determine the area of rectangles and the perimeter of plane figures.
    • Objective 2.02: Solve problems involving perimeter of plane figures and areas of rectangles.

Grade 5

  • Goal 2: Measurement - The learner will recognize and use standard units of metric and customary measurement.
    • Objective 2.01: Estimate the measure of an object in one system given the measure of that object in another system.
  • Goal 3: Geometry - The learner will understand and use properties and relationships of plane figures.
    • Objective 3.01: Identify, define, describe, and accurately represent triangles, quadrilaterals, and other polygons.
    • Objective 3.02: Make and test conjectures about polygons involving:
      • Sum of the measures of interior angles.
      • Lengths of sides and diagonals.
      • Parallelism and perpendicularity of sides and diagonals.
    • Objective 3.03: Classify plane figures according to types of symmetry (line, rotational).
    • Objective 3.04: Solve problems involving the properties of triangles, quadrilaterals, and other polygons.
      • Sum of the measures of interior angles.
      • Lengths of sides and diagonals.
      • Parallelism and perpendicularity of sides and diagonals.

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.
  • Goal 3: Geometry -The learner will understand and use properties and relationships of geometric figures in the coordinate plane.
    • Objective 3.03: Transform figures in the coordinate plane and describe the transformation.
    • Objective 3.04: Solve problems involving geometric figures in the coordinate plane.

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.
    • Objective 3.01: Represent problem situations with geometric models.
    • Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.
    • Objective 3.03: Identify, predict, and describe dilations in the coordinate plane.