# MA.912.GR.6.4

Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.

### Clarifications

Clarification 1: Instruction focuses on the conceptual understanding that for a given angle measure the length of the intercepted arc is proportional to the radius, and for a given radius the length of the intercepted arc is proportional is the angle measure.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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 benchmark.

## Formative Assessments

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

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

Sector Area:

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

Type: Formative Assessment

## Lesson Plans

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

## 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

## MFAS Formative Assessments

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.

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.

Sector Area:

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

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

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