Download Constructions for Parallel Lines

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 57411
Constructions for Parallel Lines
Students are asked to construct a line parallel to a given line through a given point.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, construction, compass, straightedge, parallel lines
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ConstructionsForParallelLines_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: MAFS.912.G­CO.4.12 requires students to “make formal geometric constructions with a variety of tools and methods.” This task and rubric assume the use of a
compass and straightedge but can be adapted for use with any tool. Throughout the geometry course, students should be exposed to a variety of construction tools and
methods.
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Constructions for Parallel Lines worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
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.
page 1 of 4 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).
page 2 of 4 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 same-side 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.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Compass and straightedge,
Translucent paper,
Reflective devices, or
Dynamic geometry software
Constructions for Parallel Lines Worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
page 3 of 4 Related Standards
Name
MAFS.912.G-CO.4.12:
Description
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment;
bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point not on the line.
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric
phenomenon and can lead to conjectures and proofs.
page 4 of 4