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

Go with green rectangles

http://illuminations.nctm.org/LessonDetail.aspx?ID=L260

A lesson plan for grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics


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This is the second in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity using perimeter and area of various rectangular shapes. Students manipulate 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters of similar rectangles, and the relationship between scale factor and ratio of areas of similar rectangles. Illuminations provides an activity sheet, grid paper, and an applet for completing the lesson. As students experiment with similar rectangles and different scale factors relative to side lengths, they have the opportunity to observe and interpret the changes in the perimeter and area. Using questions provided in the lesson plan, the teacher leads students in a discussion of their process.

Students will:

  • Compare the perimeter and area ratios of similar rectangles with various scale factors.
  • Discover and articulate the relationship between scale factor perimeter and area through the use of tables and graphs.
  • Recognize the area relationship of similar rectangles and the square of 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:

  • Creating and critiquing inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
  • Examining the congruence, similarity, and line or rotational symmetry of objects using transformations.
  • Using geometric models to represent and explain numerical and algebraic relationships.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • 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 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.