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

Covering the Plane with Rep-Tiles

http://illuminations.nctm.org/LessonDetail.aspx?ID=L251

A lesson plan for grades 5–7 Mathematics

Provider: National Council of Teachers of Mathematics


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In this lesson from Illuminations, students discover and explore a special kind of tiling of the plane. Rep-tiles are geometric figures such that n copies can fit together to form a larger, similar figure. Students experiment with various shapes and values of n. Spatial sense is encouraged by the need to visualize and perform transformations with the shapes involved.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 5

  • Goal 3: Geometry - The learner will understand and use properties and relationships of plane figures.
    • 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 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.