LEARN NC

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

Square circles

http://illuminations.nctm.org/LessonDetail.aspx?ID=L697

A lesson plan for Grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
6–8
Subjects
mathematics (applied mathematics, measurement)
Provider
National Council of Teachers of Mathematics

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This lesson allows students to use a variety of units when measuring the side length and perimeter of squares and the diameter and circumference of circles. From these measurements, students will discover the constant ratio of 1:4 for all squares and the ratio of 1:3.14 for all circles. Illuminations provides helpful resources and detailed instructions for completing the lesson.

Students will:

  • Identify various units of measure based on their appropriateness for each shape and size.
  • Draw conclusions about the relationship of side/perimeter in squares and diameter/circumference in circles based on collected data.
  • Through physical representations, develop the idea of a constant that relates a circle’s diameter and circumference, namely pi.

NCTM Standards and Expectations:

  • Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
  • Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

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.
  • Goal 3: Geometry -The learner will understand and use properties and relationships of geometric figures in the coordinate plane.
    • Objective 3.02: Identify the radius, diameter, chord, center, and circumference of a circle; determine the relationships among them.

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 3.03: 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.