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

Blue squares and beyond

http://illuminations.nctm.org/LessonDetail.aspx?ID=L259

A lesson plan for grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics


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This is the first in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity. This lesson invites students to manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world.Illuminations provides an activity sheet, a link to a helpful applet, and detailed instructions for completing the lesson.

Students will:

  • Apply the concept of similarity.
  • Construct and interpret figures by using scale factor.
  • Apply the scale factor of two rectangles to the ratio of area.
  • 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:

  • Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
  • Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

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 3.02: 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 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • 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.