Discovering the area formula for circles
http://illuminations.nctm.org/LessonDetail.aspx?ID=L574
A lesson plan for Grades 6–7 Mathematics
About this resource
- Appropriate grades
- 6–7
- Subjects
- mathematics (measurement)
- Provider
- National Council of Teachers of Mathematics
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Using a circle that has been divided into congruent sectors, students will discover the area formula by using their knowledge of parallelograms. Students will then calculate the area of various flat circular objects that they have brought to school. Finally, students will investigate various strategies for estimating the area of circles. Illuminations provides activity sheets and detailed instructions for completing the lesson.
Students will:
- Measure the radius and diameter of various circular objects using appropriate units of measurement.
- Discover the formula for the area of a circle.
- Estimate the area of circles using alternative methods.
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 2.02: Solve problems involving perimeter/circumference and area of plane figures.
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.
