Getting Started 
Misconception/Error The student sketches or draws rather than constructs. 
Examples of Student Work at this Level The student uses a straightedge to draw a lines that appear perpendicular
The student makes some construction marks on his or her paper unrelated to the construction.

Questions Eliciting Thinking What is the difference between drawing and constructing?
When doing a geometric construction, what tools are typically used?
What is the difference between a straightedge and a ruler?
What is it that you are supposed to construct? 
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.
Guide the student through the steps of each construction. Prompt the student to justify each step. Have the student label each perpendicular line as indicated in the instructions. 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.
Give the student additional opportunities to construct perpendicular lines as part of other constructions such as the construction of a square or rectangle.
The following website contains interactive demonstrations of each perpendicular line construction:

Moving Forward 
Misconception/Error The student attempts the construction but makes a significant error. 
Examples of Student Work at this Level The student attempts to construct the perpendicular bisector of line n using the arrowheads as endpoints.
The student does not maintain the same radius setting on the compass when making arcs on line n from point M.
When making the final two arcs on the second construction, the student does not have the compass open enough and the arcs do not intersect.

Questions Eliciting Thinking Can lines be bisected?
What must be true of the radius settings on your compass in order to ensure that the line is perpendicular?
How did you determine the radius setting on your compass? 
Instructional Implications 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.
Review how to construct congruent angles and perpendicular bisectors and then guide the student through the parts of his or her construction that contained errors. Have the student remove any unnecessary marks or marks made in error. Ask the student to write out the steps of the construction and keep them for future reference.
Give the student additional opportunities to construct perpendicular lines as part of other constructions such as the construction of a square or rectangle. 
Almost There 
Misconception/Error The student correctly completes the constructions but does not label the constructions or leaves unnecessary marks on the paper. 
Examples of Student Work at this Level The student correctly completes each construction but does not label the perpendiculars as indicated in the instructions.
The student correctly constructs, labels, and justifies the construction but leaves several construction marks on his or her paper that are not needed for the construction. 
Questions Eliciting Thinking Where, specifically, is the perpendicular line you constructed? How were you to label this line?
What are these arcs for? Did you use them in your construction? 
Instructional Implications Ask the student to label the constructed perpendicular lines as indicated in the instructions and to remove any unnecessary marks or marks made in error from his or her paper.
For the first construction, ask the student to use the compass marks to draw congruent segments from point M to line n. For the second construction, ask the student to use the compass marks to draw congruent segments from the intersecting arcs to line n. Challenge the student to label and describe the resulting triangles along with all congruent angles and congruent segments in the constructions. 
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 completes and labels both constructions correctly.

Questions Eliciting Thinking Explain how you know that your lines are perpendicular.
What other geometric figure could you have constructed this way? 
Instructional Implications Challenge the student to construct angles of specified measures such as 22.5°, 45°, 90°, and 135°. 