Download Bisecting a Segment and an Angle

Bisecting a Segment and an Angle
Resource ID#: 57266
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to construct the bisectors of a given segment and a given angle and to justify
one of the steps in each construction.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, constructions, angles, segments
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_BisectingASegmentAndAngle_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: MAFS.912.G-CO.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. Students should be exposed to a variety of
construction tools and methods throughout the geometry course.
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 Bisecting a Segment and an
Angle 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 draws the bisectors rather than constructing them.
The student makes some construction marks on his or her paper that are incomplete or unrelated to the construct
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
a ruler and a straightedge.
Guide the student through the steps of constructing bisectors of segments and angles. Prompt the student to justi
student to write out the steps of each construction and keep them for future reference.
Give the student additional opportunities to construct bisectors.
Moving Forward
Misconception/Error
The student attempts the construction, but makes a significant error.
Examples of Student Work at this Level
The student:


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Did not use the same compass radius for the arcs drawn from each endpoint.
Drew arcs that did not intersect and therefore did not have two points through which to draw the segmen
Did not draw the initial arc equidistant from the vertex of the angle, but instead used the last visible poin

Only drew the initial arc.
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Only drew a pair of arcs above (or below) the given segment.
Questions Eliciting Thinking
What is a segment bisector?
What is the midpoint of a segment?
What is an angle bisector?
Instructional Implications
Explain to the student the need to precisely locate points in constructions and in order to construct lines, rays, an
inadvertently change the radius setting.
Demonstrate these constructions using an interactive website such as Math Open Reference: Angle bisectors (ht
(http://www.mathopenref.com/constbisectline.html) . Provide the student with a variety of angles and segments
Making Progress
Misconception/Error
The student is not able to justify the step for one or both of the constructions.
Examples of Student Work at this Level
The student writes a statement such as:


The compass width needs to be slightly longer than half the length so you can get the segment bisector in
The initial arcs help you know where to draw the next set of arcs needed to construct the angle bisector.
Questions Eliciting Thinking
Can you explain what you meant in your answers to questions 2 and 4?
Instructional Implications
Have the student draw the initial arcs above and below the given segment to construct the segment bisector, first
equal to half of the length of the given segment. Encourage the student to determine and explain from this activi
Have the student use points on each side of the angle that are not the same distance from the vertex. Encourage t
Have the students identify the corresponding parts of the two congruent triangles that are formed by the angle bi
determine the significance in drawing the initial arc for the angle bisector construction and to prove that the angl
Almost There
Misconception/Error
The student correctly completes and justifies the construction but does not label the construction or leaves unnec
Examples of Student Work at this Level
The student correctly completes each construction but does not label the bisectors as indicated in the instructions
The student labels a second point on the bisector as point A.
Questions Eliciting Thinking
Why is it important to label the construction?
Where would you label the midpoint of the segment in Question 1?
How would you label the ray bisecting
?
Instructional Implications
Ask the student to label the constructed bisectors as indicated in the instructions and to remove any unnecessary
Provide the student with completed constructions for segment bisectors and angle bisectors. Have the students la
the angle bisector.
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. The student writes:


the compass radius needs to be slightly longer than half the length of the segment when drawing the arcs
it is necessary to draw the initial arc in order to locate points on each side of the angle that are equidistan
Questions Eliciting Thinking
If you connected the four points you located in your segment bisector construction, what kind of a figure would
Why was it important in this construction to locate points on each side of the angle that are equidistant from the
Does a bisector of a segment have to be perpendicular to the segment?
Instructional Implications
Review the definition of the angle bisector including the theorem that states that a point lies on the angle bisecto
the angle that is used to construct the angle bisector is actually on the angle bisector.
Introduce the student to points of concurrency. Have the student use the perpendicular bisectors construction to
intersection of the medians. Have the student construct angle bisectors for all three angles of a triangle. Ask the
the angle bisectors could ever intersect in the exterior of a triangle.
ACCOMMODATIONS & RECOMMENDATIONS
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Special Materials Needed:
o
Bisecting A Segment and Angle 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
License: CPALMS License - no distribution - non commercial
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.