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

The ratio of circumference to diameter

http://illuminations.nctm.org/LessonDetail.aspx?ID=L573

A lesson plan for grades 6–7 Mathematics

Provider: National Council of Teachers of Mathematics


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Students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula. Illuminations provides a link to a circle ratios applet, an activity sheet and detailed instructions for completing the lesson.

Students will:

  • Measure the circumference and diameter of various circular objects.
  • Calculate the ratio of circumference to diameter.
  • Discover the formula for the circumference of a circle.

NCTM Standards and Expectations:

  • Understand both metric and customary systems of measurement.
  • Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
  • 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.