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Discovering the Area Formula for Circles

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Discovering the Area Formula for Circles

Grade Levels

6th Grade, 7th Grade, 8th Grade

Course, Subject

Geometry
Related Academic Standards
CC.2.3.8.A.1 CC.2.3.8.A.1
Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
CC.2.3.8.A.3 CC.2.3.8.A.3
Understand and apply the Pythagorean Theorem to solve problems.
M08.C-G.2.1.1 M08.C-G.2.1.1
Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
M08.C-G.2.1.2 M08.C-G.2.1.2
Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)
M08.C-G.2.1.3 M08.C-G.2.1.3
Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
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  • Big Ideas
    Measures can be estimated by using known referents.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical quantities and calculations can be estimated by using numbers that are close to the actual values, but easier to compute.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
  • Concepts
    Area and Volume
    Polygons and Polyhedra
    Representations
    Sampling as a method of estimation and prediction
  • Competencies
    Extend previous understandings of the characteristics of 2-d and 3-d shapes, including the measures of area and volumes, by exploring, solving, and interpreting real world problems.
    Extend previous understandings of the characteristics of 3d-shapes to develop an understanding of, and use formulas to determine surface areas and volumes.
    Use fundamental facts about distances and angles to describe and analyze figures and situations in 2- and 3-dimensional spaces and to solve problems including those with multiple steps.

Description

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.

Web-based Resource

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Discovering the Area Formula for Circles

Content Provider

Illuminations

 

Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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