Ohio Resource Center
Content Supports
Circles and Their Areas
Discipline
Mathematics
6, 7, 8
Professional Commentary

Given that units of area are squares, how can we find the area of a circle or other curved region? Imagine a waffle-like grid inside a circle and a larger grid containing the circle. The area of the circle lies between the area of the inside grid and the area of the outside grid. Now imagine the grids becoming finer and finer. The inside area gets closer to the area of the circle, as does the outside area. Both areas approach the limit of (pi)r2, the area of the circle. The activity described is accessible to middle grades students, but the discussion accompanying the activity spans trigonometry and calculus, and thus is geared toward the teacher. This mathematically rich resource was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)

Ohio Mathematics Academic Content Standards (2001)
Measurement Standard
Benchmarks (5–7)
C.
Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.
3.
Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: a. estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; and b. measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.
Principles and Standards for School Mathematics
Measurement Standard
Apply appropriate techniques, tools, and formulas to determine measurements.
Expectations (6–8)
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;