Getting Started 
Misconception/Error The student does not understand that concept of area of a sector. 
Examples of Student Work at this Level The student:
 Indicates that he or she does not understand how to complete the problem.
 Attempts to find the sector area but does not use the correct formula.

Questions Eliciting Thinking What are you being asked to find? Can you show me on the diagram the region whose area you are trying to find?
What is the name of the sector whose area you are trying to find?
How is the sector area related to the total area of the circle? How do you find the area of a circle?
What fraction of the circle’s area are you looking for? How do you determine that fraction?
What is the arc measure? How is the arc measure related to the area of the sector?
Do you know the formula for the sector area? What formula did you use? 
Instructional Implications Review the definitions of sector and arc measure and the formula for finding the area of a circle. If necessary, review the relationship between the diameter and the radius of a circle. Then explain sector area in terms of the area of the circle. Describe the area of a sector as a fraction of the circle’s area. Explain that the fraction is determined by the degree measure of the arc that bounds the sector. Guide the student to write a general formula for finding the area of a sector. Initially, use as an example a sector bounded by a 180º arc or semicircle, and show the student that the area of a semicircle is equal to one half the area of the circle. Then use a sector bounded by a 90º arc, and ask the student to identify the fraction of the circle’s area that this sector represents. Show the student that the ratio of the degree measure of the arc that bounds the sector to the degree measure of the circle, 360, is the fraction of the circle’s area that the sector represents. Model finding the area of a sector given the measure of the arc that bounds it and the radius and/or diameter.
Give the student more opportunities to find the areas of sectors, giving assistance as needed. Ask the student to identify the measure of the arc that bounds the sector and the radius in each problem and to highlight the sector whose area he or she is asked to find. Require that the student write the formula for the area of a sector for each problem and show all work carefully and completely.
Use an interactive resource such as Math Open Reference Sector Area (http://www.mathopenref.com/arcsectorarea.html) to let the student explore the relationship between the central angle and the area of the sector. 
Moving Forward 
Misconception/Error The student makes an error in using the sector area formula. 
Examples of Student Work at this Level The student writes the correct formula to find the area of a sector but
 Uses the diameter instead of the radius of the circle.
 Does not square the radius.

Questions Eliciting Thinking What do the variables in your formula represent?
In problem two, are you given the radius or diameter? How do you convert the diameter to the radius?
How would you find the area of the entire circle?
What fraction of the circle’s total area are you trying to find? How do you determine that fraction? 
Instructional Implications Review the meaning of the variables in the formula and guide the student to find the appropriate values from the diagram. If needed, also review the relationship between the diameter and radius of a circle.
Review the relationship between the area of the circle and the area of the sector. Be sure the student understands that the area of a sector is a fraction of a circle’s area and that fraction depends on the degree measure of the arc that bounds the sector.
If needed, explain the difference between writing an answer in exact form (i.e., in terms of ) and in approximate form, by using an approximation for . Explain why it is not possible to write an exact answer as a rational number. Provide the student with additional opportunities to find the areas of sectors. 
Almost There 
Misconception/Error The student makes a minor computational or rounding error. 
Examples of Student Work at this Level The student identifies the correct formula and substitutes the appropriate values for the radius and arc measure but:
 Does not give the answer in the form requested.
 Rounds factors before multiplying producing an answer with more error than is necessary.
 Does not label the answer with the correct unit.

Questions Eliciting Thinking There is a small error in your work. Can you find it? How were you asked to give your answer?
Explain to me how you got your answer. Did you round during the problem or only at the end of the problem. How could that make a difference?
Did you label your answer with a unit of measure? What is the correct unit of measure? 
Instructional Implications Review with the student that rounding several factors before multiplying introduces a greater degree of error than is necessary. Remind the student that and guide the student to multiply 18,081 by a suitable approximation of p and then divide this product by 360 in one step on the calculator. Then round the final answer as directed.
If needed, explain the difference between writing an answer in exact form (i.e., in terms of ) and in approximate form, by using an approximation for . Explain why it is not possible to write an exact answer as a rational number. Provide the student with additional opportunities to find the areas of sectors. 
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 writes that:
The area of sector MCN = or .
The area of sector YCZ =.

Questions Eliciting Thinking How is finding the area of a sector like finding arc length?
If you had a circle with only the arc length and radius given, could you find the area of the sector bounded by that arc length? Explain how. 
Instructional Implications Introduce the student to the concept of a segment of a circle. Challenge the student to find the area of a segment of a circle.
Consider using MFAS task Deriving the Sector Area Formula (GC.5), if not previously used. 