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Pi Day - Calculating the Area of a Circle


  • Project TitlePi Day - Calculating the Area of a Circle
  • ThemeGeometry; Estimation
  • Submitted ByJennifer Leonard
  • OrganizationThe Skills Library
  • Brief DescriptionA brief afterschool program activity for Pi Day.
  • Materials / ResourcesAt least 64 square tiles
    Paper and scissors to make circles
    Snack foods (pies)

Units / Activities

  • Introduce PIMath lovers typically celebrate "Pi Day" on March 14th -- the date, 3.14 resembles the first digits of PI. In our Science Wednesday program we served pies for snack and talked about the question "what if we didn‘t know the formula for calculating the area of a circle. Could we figure it out?"
  • Use tiles to estimate the area of a circleExplain that you can use square tiles to estimate the area of geometric shapes. However, estimating the area of a circle is challenging because, of course, square tiles will not fit exactly inside a circle. We know from textbooks that the area of a circle is pi r squared. But what if we didn‘t know that formula?

    Draw and cut out a circle with a radius equal to 4 tiles.

    Using the illustrations as a guide, try different combinations of tiles to estimate the area of the circle. Start with a set of four squares that are four tiles by four tiles (64 tiles total). Notice that this square is much bigger than the circle. Also notice that the formula for this larger square would be 4 * r squared.

    Try arranging 32 tiles (2 * r squared) or 48 tiles (3 * r squared).

    The correct number seems to be more than 3, but definitely less than 4. We are on the path to discovering the value of PI and the formula PI r squared.

  •  /project646_6739/PiDayTiles_1.png
  • Wrap-up discussionIn a mixed age group, older students will be familiar with the formulas while younger students will focus on simply using tiles to estimate the size of a circle, and will appreciate the idea that mathematicians worked and experimented to develop the formula and that the key number in the formula, PI, cannot be expressed as an exact fraction or integer.
  •  /project646_6739/PiDayTiles_2.png

Frameworks / Skills

  • Mathematics
    Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • Mathematics
    Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Tags = geometry | Science-Wednesdays | Subject = Mathematics | Grade Level = Elem, MS | Time Period = | Program/Funding = |
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