Standard 6 : Circles (Archived)



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Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions, and prove theorems related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.

General Information

Number: MA.912.G.6
Title: Circles
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.G.6.1: Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons.
MA.912.G.6.2: Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.
MA.912.G.6.3: Prove theorems related to circles, including related angles, chords, tangents, and secants.
MA.912.G.6.4: Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).
MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.
MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.
MA.912.G.6.7: Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.912.G.6.In.a: Identify and describe the circumference, arc, diameter, and radius of circles using physical and visual models.
MA.912.G.6.In.b: Measure the diameter and radius of circles to solve real-world problems.
MA.912.G.6.In.c: Determine the relationship between a semi-circle and a circle.

Supported

Access Point Number Access Point Title
MA.912.G.6.Su.a: Identify the circumference, arc, and diameter of circles in real-world situations.
MA.912.G.6.Su.b: Compare the circumference and diameter of circles in real-world situations.
MA.912.G.6.Su.c: Identify examples of semi-circles in the environment.

Participatory

Access Point Number Access Point Title
MA.912.G.6.Pa.a: Identify objects, pictures, or signs with a circle in real-world situations.
MA.912.G.6.Pa.b: Match two or more objects with a circle based on a given feature, such as the distance around the outside (circumference) or inside (area) in real-world situations.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Image/Photograph

Name Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Lesson Plan

Name Description
Seeking Circle Segments:

Students will start this lesson with a "Pictionary" game to review circle vocabulary terms. They will then use computers and GeoGebra to discover the relationships between portions of segments that intersect in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and consensus on rules (formulas).

Professional Development

Name Description
Mathematical Modeling: Insights into Algebra, Teaching for Learning: This professional development resource provides a rich collection of information to help teachers engage students more effectively in mathematical modeling. It features videos of two complete lessons with commentary, background information on effective teaching, modeling, and lesson study, full lesson plans to teach both example lessons, examples of student work from the lessons, tips for effective teaching strategies, and list of helpful resources.
  • In Lesson 1 students use mathematical models (tables and equations) to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.
  • In Lesson 2 students mathematically model the growth of populations and use exponential functions to represent that growth.

Video/Audio/Animation

Name Description
Story of Pi: This video dynamically shows how Pi works, and how it is used.


Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Image/Photograph

Title Description
Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Video/Audio/Animation

Title Description
Story of Pi: This video dynamically shows how Pi works, and how it is used.