Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56752
Definition of Line Segment
Students are asked to draw, label, and give a precise definition of a line segment.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, line segment, definition
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DefinitionOfALineSegment_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the Definition of Line Segment worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student draws an incomplete or incorrect figure and is unable to precisely define the term line segment.
Examples of Student Work at this Level
The student draws a line or ray, rather than a line segment, with two named points (usually A and B) and is unable to indicate which portion of the drawing includes the line
segment. The student does not provide a precise definition of a line segment.
page 1 of 4 Questions Eliciting Thinking
Does your line segment have a beginning and an end?
In your figure, which is the line and which is the line segment?
Are points A and B on your line segment? Are there other points on your line segment?
Instructional Implications
Review the concept of a point and then provide direct instruction on the differences among lines, rays, and line segments. Guide the student to draw and label examples of
each.
Draw a line with three named points A, B, C on the line. Then ask the student to identify and name as many line segments as possible using the three named points.
Discuss with the student the qualities of a definition that make it precise and complete. Then offer the student a precise definition of a line segment such as, “Line segment
AB consists of the points A and B and all of the points between A and B on line AB.” Discuss with the student the features of this definition that make it precise. Introduce
the student to the concept of a counterexample. Challenge the student to find a counterexample (i.e., a figure that consists of the points A and B, and all of the points
between A and B on line AB) that is not a line segment. Indicate that a quality of a good definition is that it eliminates all counterexamples.
Moving Forward
Misconception/Error
The student correctly draws and labels the line segment but is unable to provide a precise mathematical definition.
Examples of Student Work at this Level
The student correctly draws and labels a line segment. When defining a line segment, the student:
Describes it as a line with a certain quality such as a line with two points or two endpoints.
Writes a definition that is incomplete or imprecise.
Provides a circular definition such as “a line segment is a segment of a line.”
Questions Eliciting Thinking
How does a line segment differ from a line?
What points are included on a line segment? How can you describe these points?
Could someone who did not know what a line segment is draw one based on your definition?
Instructional Implications
Discuss with the student the qualities of a definition that make it precise and complete. Then offer the student a precise definition of a line segment such as, “Line segment
AB consists of the points A and B and all of the points between A and B on line AB.” Discuss with the student the features of this definition that make it precise. Explain the
distinction between a line and a line segment and why it is incorrect to define a line segment as a line with a certain quality. Be sure the student understands that lines and
line segments are related but that a line segment, by definition, is not a line.
Introduce the student to the concept of a counterexample. Challenge the student to find a counterexample (i.e., a figure that consists of the points A and B and all of the
points between A and B on line AB) that is not a line segment. Indicate that a quality of a good definition is that it eliminates all counterexamples.
Almost There
Misconception/Error
The student’s definition is incomplete or imprecise.
page 2 of 4 Examples of Student Work at this Level
The student correctly draws and labels a line segment. The student provides the foundation of a good definition (“a line segment is part of a line”) but is unable to precisely
describe how the part is characterized.
Questions Eliciting Thinking
Is a ray part of a line? How does a line segment differ from a ray? Is a line segment part of a ray?
Do line segments have length?
Can there be more than one line segment on a given line?
Instructional Implications
Discuss with the student the qualities of a definition that make it precise and complete. Have the student work with other Almost There students to identify features of
their definitions that are imprecise or incomplete. Afterward, ask the Almost There student to revise his or her definition. Then present a precise definition of a line segment
such as, “Line segment AB consists of the points A and B and all of the points between A and B on line AB.” Have the student compare his or her revised definition to this
one and identify features of this definition that make it precise.
Introduce the student to the concept of a counter example. Challenge the student to find a counterexample for the definition that he or she wrote. For example, if the
student defined a line segment as “part of a line” then a ray would serve as a counterexample. In this case, explain that the ray satisfies the conditions of the definition but
is not a line segment. Consequently, this definition of a line segment is not complete.
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 correctly draws and labels the line segment. The student defines the line segment as “two points on a line and all the points between these points on the
line” or “part of a line that consists of two distinct points and all of the points between them.”
Questions Eliciting Thinking
Since you have defined a line segment in terms of points and a line, do you need to define point and line? What about the term between? Do you think this needs to be
defined?
What if you name a line segment
instead of
What happens if you draw two line segments,
? Does that name the same line segment or a different one?
and
that have a common endpoint, B. Under what circumstances will AC < AB + BC?
Instructional Implications
Introduce the student to the use of notation in defining line segments. For example, offer the student the following definition, "
well as all points between A and B on
consists of points A and B on
as
." Ask the student to consider the number of points on a line and the number of points on a line segment.
Introduce the student to biconditional statements and the role they play in definitions. Have the student rewrite geometric definitions as explicit biconditional statements
(i.e., in the form “if p then q and if q then p” or “p if and only if q”).
Introduce the student to the concept of a counterexample. Challenge the student to find counterexamples, if they exist, for statements such as:
All right angles measure 90°.
All rectangles are squares.
All triangles are scalene.
For any triangle, the sum of the measures of its angles is 180°.
All isosceles triangles are equilateral.
If
= 16, then x = 4.
page 3 of 4 ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Definition of Line Segment 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
Related Standards
Name
MAFS.912.G-CO.1.1:
Description
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined
notions of point, line, distance along a line, and distance around a circular arc.
page 4 of 4