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 rather construct a line parallel to n through point M.
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 constructing a line parallel to a given line through a given point. 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 experience with a variety of methods making explicit the definition, theorem, or postulate that justifies each method. Consider using http://www.mathopenref.com/constparallel.html (congruent corresponding angles method) and http://www.mathopenref.com/constparallelrhomb (rhombus method).
Give the student additional opportunities to construct parallel lines using a method of choice. 
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 congruent corresponding angles but does not know how to ensure that the angle with vertex M is congruent to the corresponding angle on line n.
The student attempts to construct congruent corresponding angles but uses the wrong compass radius.

Questions Eliciting Thinking Can you explain how you constructed the parallel line?
How did you ensure that it contained point M?
How did you ensure that it was parallel to n? 
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.
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 experience with a variety of methods making explicit the definition, theorem, or postulate that justifies each method. Consider using http://www.mathopenref.com/constparallel.html (congruent corresponding angles method) and http://www.mathopenref.com/constparallelrhomb (rhombus method).
Give the student additional opportunities to construct parallel lines using a method of choice. 
Making Progress 
Misconception/Error The student correctly completes the construction but is unable to provide a justification. 
Examples of Student Work at this Level The student constructs congruent corresponding angles but is unable to justify this approach with the relevant theorem (i.e., When two lines are intersected by a transversal so that corresponding angles are congruent, then the lines are parallel).
The student uses an approach that includes constructing a rhombus but is unable to justify this approach with the relevant theorem (i.e., Opposites sides of a rhombus are parallel).
The student uses an approach that includes constructing a parallelogram but is unable to justify this approach with the relevant definition (i.e., Opposites sides of a parallelogram are parallel).
The student uses an approach that includes constructing perpendicular lines but is unable to justify this approach with a relevant theorem (e.g., When two lines are intersected by a transversal so that sameside interior angles are supplementary, then the lines are parallel). 
Questions Eliciting Thinking What do you know about angle relationships and parallel lines? Do you see a special angle pair in your construction?
Do you see a quadrilateral with parallel sides in your construction? 
Instructional Implications Show the student a variety of ways to construct parallel lines. Challenge the student to find a geometric figure (e.g., a rhombus, parallelogram, or rectangle) or a familiar geometric diagram (e.g., two parallel lines intersected by a transversal) in each construction method. Then ask the student to describe the definition, postulate, or theorem that justifies each construction. 
Almost There 
Misconception/Error The student correctly completes and justifies the construction but does not label the construction or leaves unnecessary marks on the paper. 
Examples of Student Work at this Level The student correctly constructs a line parallel to line n and justifies the construction but does not label it as line p.
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 parallel 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 parallel line as line p and to remove any unnecessary marks or marks made in error from his or her paper.
Challenge the student to find another way to construct a line parallel to n through point M. 
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 the construction correctly and is able to justify the method. 
Questions Eliciting Thinking Is there any other method you could have used to construct parallel lines? 
Instructional Implications Challenge the student to review previous definitions, postulates, and theorems to find as many methods as possible to construct parallel lines. 