Standard 6: Use properties and theorems related to circles.

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General Information
Number: MA.912.GR.6
Title: Use properties and theorems related to circles.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.GR.6.AP.1
Identify and describe the relationship involving the length of a secant, tangent, segment or chord in a given circle.
MA.912.GR.6.AP.2
Identify the relationship involving the measures of arcs and related angles, limited to central, inscribed and intersections
MA.912.GR.6.AP.3
Identify and describe the relationship involving triangles and quadrilaterals inscribed in a circle.
MA.912.GR.6.AP.4
Identify and describe the relationship involving the arc length and area of a sector in a given circle.

Related Resources

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

Formative Assessments

Central and Inscribed Angles:

Students are asked to describe the relationship between a central angle and an inscribed angle that intercept the same arc.

Type: Formative Assessment

Tangent Line and Radius:

Students are asked to draw a circle, a tangent to the circle, and a radius to the point of tangency. Students are then asked to describe the relationship between the radius and the tangent line.

Type: Formative Assessment

Softball Complex:

Students are asked to solve a design problem in which a softball complex is to be located on a given tract of land subject to a set of specifications.

Type: Formative Assessment

Inscribed Quadrilaterals:

Students are asked to prove that opposite angles of a quadrilateral, inscribed in a circle, are supplementary.

Type: Formative Assessment

Deriving the Sector Area Formula:

Students are asked to write a formula to find the area of a sector of a circle and then explain and justify that formula.

Type: Formative Assessment

Arc Length and Radians:

Students are asked to explain why the length of an arc intercepted by an angle is proportional to the radius and then explain how that proportionality leads to a definition of the radian measure of an angle.

Type: Formative Assessment

The Sprinters’ Race:

Students are given a grid with three points (vertices of a right triangle) representing the starting locations of three sprinters in a race and are asked to determine the center of the finish circle, which is equidistant from each sprinter.

Type: Formative Assessment

Inscribed Angle on Diameter:

Students are asked to find the measures of two inscribed angles of a circle.

Type: Formative Assessment

Similar Circles:

Students are given two circles with different radii and are asked to prove that the circles are similar.

Type: Formative Assessment

Circles with Angles:

Students are given a diagram with inscribed, central, and circumscribed angles and are asked to identify each type of angle, determine angle measures, and describe relationships among them.

Type: Formative Assessment

All Circles Are Similar:

Students are given two circles with different radius lengths and are asked to prove that the circles are similar.

Type: Formative Assessment

Sector Area:

Students are asked to find the areas of sectors in two different circles.

Type: Formative Assessment

Arc Length:

Students are asked to find the lengths of arcs in two different circles.

Type: Formative Assessment

Lesson Plans

Seeking Circle Angles:

Students will start this lesson with a win-lose-draw game to review circle vocabulary words. They will then use examples on a discovery sheet to discover the relationships between arcs and the angles whose vertex is located on a circle, in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and questions answered on white boards.

Type: Lesson Plan

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).

Type: Lesson Plan

The Grass is Always Greener:

The lesson introduces area of sectors of circles then uses the areas of circles and sectors to approximate area of 2-D figures. The lesson culminates in using the area of circles and sectors of circles as spray patterns in the design of a sprinkler system between a house and the perimeter of the yard (2-D figure).

Type: Lesson Plan

Rotation Debate: Radians vs Degrees:

In this lesson, students will convert from degrees to radians and radians to degrees and calculate arc length using both degrees and radians. Students will come to consensus as to why radians are the preferred measure of an angle. This lesson normally takes two 50 minute class periods to teach.

  • Day 1: Bell Ringer-Day 1, Lesson Notes, Activity 1
  • Day 2: Day 1 Review and Wrap-up, Bell Ringer-Day 2, Activity 2

Type: Lesson Plan

Perspectives Video: Professional/Enthusiast

All Circles Are Similar- Especially Circular Pizza!:

What better way to demonstrate that all circles are similar then to use pizzas! Gaines Street Pies explains how all pizza pies are similar through transformations.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Text Resource

Why Tau Trumps Pi:

This informational text resource is intended to support reading in the content area. The author tries to convince the reader that two pi, or tau, occurs more often in mathematics than pi by itself. The author provides several examples and indicates the history behind society's choice of pi rather than tau.

Type: Text Resource

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