K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

  • to measure the radius of a circle
  • to measure the central angle of a circle
  • to calculate the area of a sector
  • to calculate the length of an arc

Teacher planning

Time required for lesson

20 minutes

Materials/resources

  • Rulers
  • Protractors
  • Big cookies(at least 8 in. in diameter)
  • Plastic knives
  • Napkins

Pre-activities

Students will need to know how to find the area and circumference of a circle. They will need to know about central angles and their corresponding minor arcs.

Activities

  1. Divide the class into groups with varying numbers in each group. The number of groups should correspond to the number of cookies prepared.
  2. Students are to decide how to divide the cookie fairly among the members of their group. They are to write down the measure necessary for the central angle. They are to measure the radius of their cookie.
  3. Using this information, they should then discuss how knowing this information will help them to find the area of their slice. They also want to discuss how to find the length of the arc of their slice. Students are to calculate the following:
    • area of cookie
    • circumference of cookie
    • area of slice
    • length of arc on slice

Assessment

Students are to hand in one write-up per group of their findings. This should include all measurements taken as well as the number of members in their group.

Supplemental information

Comments

This is a fun way to end a lesson in which you have just discussed how to find the area and circumference of a circle. Whenever possible, I use this as a “Fun Friday” activity.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 7

        • Geometry
          • 7.G.4Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
          • 7.G.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
      • High School: Geometry

        • Circles
          • GEO.CIR.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Geometry

  • Goal 1: Number and Operations - The learner will perform operations with real numbers to solve problems.
    • Objective 1.02: Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grade 9–12 — Integrated Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will use properties of geometric figures to solve problems.
    • Objective 2.01: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grade 9–12 — Technical Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will measure and apply geometric concepts to solve problems.
    • Objective 2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.