Getting Started 
Misconception/Error The student sketches or draws rather than constructs. 
Examples of Student Work at this Level Using the compass and straightedge, the student attempts to draw the inscribed circle rather than construct it.

Questions Eliciting Thinking What does it mean to construct? How is it different that drawing?
When doing a geometric construction, what tools are typically used?
What is an inscribed circle of a triangle? What are some of its properties? 
Instructional Implications Explain to the student the difference between drawing and constructing. Show the student the tools traditionally used in geometric constructions and explain the purpose of each. Be sure the student understands the difference between a ruler and a straightedge.
If necessary, review the definition of a circle inscribed in a triangle and its relationship to the bisectors of the angles of a triangle. Review important vocabulary such as: angle bisector, point of concurrency, incenter, tangent, perpendicular bisector, and inscribed circle.
If necessary, review constructing angle bisectors. Then guide the student through the steps of constructing the incenter of a triangle. Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them for future reference.
Model finding the incenter of the triangle by using other construction techniques such as paper folding. Instruct the student to draw a large triangle on unlined paper using a ruler or straightedge. Be sure the sides of the triangle are darkened so they can be seen through the paper when folding. Have the student label the vertices of the triangle A, B and C. Then guide the student to make a fold at vertex A so that and align with each other. Suggest to the student that he or she hold the paper up to the light to ensure the sides are aligned and the fold is directly through the vertex. Ask the student to crease the paper completely forming the bisector of < A. Have the student construct the bisector of < B and the bisector of < C to locate the incenter of the triangle. Guide the student to construct the perpendicular from the incenter to one side of the triangle and use it to find the radius of the inscribed circle. Then have the student use a compass to complete the construction of the inscribed circle.
Demonstrate constructions using an interactive website such as Open Math Reference. Begin with the simpler constructions such as copying a segment or angle and then transition to the more complex constructions. (http://www.mathopenref.com/tocs/constructionstoc.html)
To assess an understanding of basic constructions, consider implementing MFAS tasks Constructing a Congruent Segment (GCO.3.12), Constructing a Congruent Angle (GCO.3.12), and Bisecting a Segment and Angle (GCO.3.12). 
Moving Forward 
Misconception/Error The student is unable to correctly construct an angle bisector. 
Examples of Student Work at this Level The student attempts the construction of the angle bisectors but does not complete all necessary steps to ensure that the bisectors are constructed. In addition, the student may not be able to correctly answer the questions asked in the task.

Questions Eliciting Thinking Can you explain what you constructed?
How did you construct the angle bisectors?
Why was it necessary to construct the angle bisectors? 
Instructional Implications Guide the student through the parts of his or her construction that contained errors or are incomplete. Have the student remove any unnecessary marks or marks made in error. Ask the student to write out the steps of the construction including important vocabulary such as angle bisector, point of concurrency, incenter, tangent, perpendicular bisector, and inscribed circle, and keep them for future reference. Be sure the student understands how to correctly answer the questions asked in the task.
Demonstrate the construction of the inscribed circle of a triangle by using interactive websites such as Math Is Fun (http://www.mathsisfun.com/geometry/constructtriangleinscribe.html) or Math Open Reference (http://www.mathopenref.com/constincircle.html).
Provide additional opportunities to construct inscribed circles of a variety of triangle types. Guide the student to draw a generalization about the location of the incenter with regard to the triangle.
To assess an understanding of basic constructions, consider implementing MFAS tasks Constructing a Congruent Segment (GCO.3.12), Constructing a Congruent Angle (GCO.3.12), and Bisecting a Segment and Angle (GCO.3.12). 
Almost There 
Misconception/Error The student’s construction is not precise. 
Examples of Student Work at this Level The student correctly constructs angle bisectors to locate the incenter, but he or she does not construct a perpendicular on which to measure the radius of the circle.
The student correctly constructs angle bisectors to locate the incenter and attempts to find the radius by constructing a perpendicular segment from the incenter to a side of the triangle, but the student’s markings are slightly off and the construction is not precise.

Questions Eliciting Thinking Do all of your angle bisectors appear to divide the angle into two equal parts?
How did you find the radius of the inscribed circle? Why does it matter how you find the radius?
Why do you think your circle is not tangent to all three sides of the triangle?
How do you think drawing the point of concurrency as a large dot would affect your construction? 
Instructional Implications If necessary, explain to the student the need to precisely locate points in constructions. Help the student find a way to hold the compass so as not to inadvertently change the radius setting.
Explain the need to construct the perpendicular from the incenter to a side of the triangle in order to precisely identify the radius of the circle.
Provide the student more opportunities to construct inscribed circles of a variety of triangle types using several different tools and methods. Use real world contexts when possible (such as placing a park or public facility on a map so that it is equidistant from three access roads that intersect in three distinct points) to demonstrate the need to understand and apply geometric constructions.
Consider implementing MFAS Task Circumscribed Circle Construction (GC.1.3). 
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 constructs the angle bisectors of each of the angles of the triangle and marks the point of concurrency or the incenter. The student then constructs a perpendicular segment from the point of concurrency to the side of the triangle to find the length of the radius of the inscribed circle. Using the compass to measure the radius, the student constructs the inscribed circle. In response to the questions asked in the task, the student states that he or she constructed the angle bisectors to locate the center of the inscribed circle and identifies this point as the incenter.

Questions Eliciting Thinking Was it really necessary to construct all three angle bisectors? Could you have located the incenter by constructing only two of them?
Can you think of any realworld situations when this construction would be helpful? 
Instructional Implications Challenge the student to solve realworld problems using constructions, such as locating a house on a plot of land bounded by three roads that intersect in three distinct points so as to minimize traffic noise.
Challenge the student to prove that the incenter is equidistant from the sides of the triangle.
Provide the student the opportunity to complete constructions using dynamic geometry software such as Geogebra or Geometer’s Sketchpad.
Consider implementing MFAS Task Circumscribed Circle Construction (GC.1.3). 