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 circumscribed circle rather than construct it.

Questions Eliciting Thinking What does it mean to construct? How is it different than drawing?
When doing a geometric construction, what tools are typically used?
What is a circumscribed 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 circumscribed circle of a triangle and its relationship to the perpendicular bisectors of the sides of a triangle. Review important vocabulary such as: perpendicular bisector, point of concurrency, circumcenter, and circumscribed circle.
Model finding the circumcenter 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 fold the paper so that vertex A meets vertex B, making sure aligns with itself when holding it up to the light. Ask the student to crease the paper completely forming the perpendicular bisector of . Have the student construct the perpendicular bisectors of the remaining two sides to locate the circumcenter of the triangle. Then guide the student to use a compass to measure the distance from one of the vertices to the circumcenter and use this radius to construct the circumscribed 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 perpendicular bisectors of the sides of the triangle. 
Examples of Student Work at this Level The student constructs the altitudes of the triangle and then draws a circle over the triangle.
The student’s work shows some correct marks for constructing the perpendicular bisectors but the perpendicular bisectors are not completed.

Questions Eliciting Thinking Can you explain what you constructed?
How did you construct the perpendicular bisectors?
Why was it necessary to construct the perpendicular 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 perpendicular bisector, point of concurrency, circumcenter, and circumscribed circle, and keep them for future reference. Be sure the student understands how to correctly answer the questions asked in the task.
Provide additional opportunities to construct circumscribed circles of a variety of triangle types. Guide the student to draw generalizations about the location of the circumcenter with regard to the triangle depending on the triangle type.
For intermediate level practice on constructions, consider implementing MFAS tasks Constructions for Parallel Lines (GCO.3.12) and Constructions for Perpendicular Lines (GCO.3.12). 
Almost There 
Misconception/Error The student’s construction is not precise. 
Examples of Student Work at this Level The student constructs all three perpendicular bisectors and finds their point of concurrency (circumcenter), however the point of concurrency is too large and the radius of the circle is not precise. The circle only goes through one of the three vertices of the triangle.

Questions Eliciting Thinking Do all of your perpendicular bisectors appear to be perpendicular to and bisecting the sides of the triangle?
How do you think drawing the point of concurrency as a large dot would affect your construction?
Why do you think your circle does not intersect all three vertices of the triangle? 
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.
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 towns represented by noncollinear points on the map) to demonstrate the need to understand and apply geometric constructions.
Consider implementing MFAS Task Inscribed 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 perpendicular bisectors of each of the three sides of the triangle and finds their point of concurrency (circumcenter). The student uses the compass to measure the distance from the circumcenter to one of the three vertices of the triangle and constructs the circumscribed circle. In response to the questions asked in the task, the student states that he or she constructed the perpendicular bisectors of the sides of the triangle to locate the center of the circumscribed circle and identifies this point as the circumcenter.

Questions Eliciting Thinking Was it really necessary to construct all three perpendicular bisectors? Could you have located the circumcenter by constructing only two of them?
Can you think of any realworld situations when this construction would be helpful? 
Instructional Implications Challenge the students to solve realworld problems using constructions, such as placing a park or public facility on a map so that it is equidistant from three towns represented by noncollinear points on the map.
Challenge the student to prove that the circumcenter is equidistant from the vertices 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 Inscribed Circle Construction (GC.1.3). 