Getting Started 
Misconception/Error The student does not demonstrate an understanding of sectors of circles. 
Examples of Student Work at this Level The student:
 States a formula that will not find the area of the sector.
 Describes a formula that can be used to find the area of another part of a circle such as a segment.
 Describes a formula that may be used to find the area of a sector of a circle but cannot clearly explain what the variables represent.

Questions Eliciting Thinking What is a sector?
How can you find the area of a circle?
How would you describe a sector of a circle in relationship to the circle? 
Instructional Implications Review terminology associated with circles (e.g., center, radius, diameter, arc, central angle, sector, and segment). Ensure that the student recognizes that a sector of a circle is a portion of the circle formed by two radii and the arc between them. Allow the student to explore the concept of the area of a sector using a site such as Open Math Reference (http://www.mathopenref.com/arcsectorarea.html). Guide the student to write a formula for finding the area of a sector as a fraction of the circle’s area. Assist the student in understanding that the measure of the central angle of the sector determines the fraction of the circle the sector represents.
Ask the student to find the areas of sectors and emphasize that the area of each sector is a fraction of the circle’s area. 
Making Progress 
Misconception/Error The student does not demonstrate an understanding of the formula for the area of a sector. 
Examples of Student Work at this Level The student states a correct formula that can be used to find the area of a sector but is unable to completely and correctly explain the formula using correct mathematical terminology.

Questions Eliciting Thinking How is a sector related to its circle?
Can you explain why your formula works to find the area of the sector?
What does the fraction tell you about the sector? 
Instructional Implications Guide the student to understand that the measure of the central angle of the sector determines the fraction of the circle the sector represents. Provide the student with a diagram of a sector of a circle and various degree measures, m, of its central angle and ask the student to determine the fraction of the circle each sector represents. Then show the student that when applying the sector area formula, , one is taking this same fraction of the circle’s area.
Relate the area of a sector formula to the arc length formula. Describe and explain the similarities in these formulas.
Consider implementing the MFAS tasks Sector Area (GC.2.5). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student describes a formula to find the area of a sector. For example, the student states:
 where is the area of the sector, r is the radius of the circle, and m is the degree measure of the central angle or arc associated with the sector.
 , where is the area of the sector, r is the radius of the circle, and m is the degree measure of the central angle or arc associated with the sector.
The student explains the formula in terms of finding a fraction (given by ) of the circle’s area or the proportionality of the central angle measure and the sector area.

Questions Eliciting Thinking How do you know that describes the fraction of the circle the sector represents?
How do you know the central angle measure is proportional to the sector area? 
Instructional Implications Ask the student to apply the formulas for finding sector area and arc length in both realworld and mathematical problems.
Consider implementing the MFAS tasks Sector Area (GC.2.5) and Arc Length (GC.2.5). 