Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 121285
Angles of a Parallelogram
Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measures of all four angles
describing any theorems used.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Keywords: MFAS, parallelogram, opposite angles, consecutive angles
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AnglesOfAParallelogram_Worksheet.pdf
MFAS_AnglesOfAParallelogram_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 problem on the Angles of a Parallelogram worksheet.
2. If necessary, remind the student to find the measures of all four angles of the parallelogram.
3. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not recognize
and
as a pair of opposite angles or understand its implications.
Examples of Student Work at this Level
The student:
Sketches parallelogram ABDC (rather than parallelogram ABCD) and concludes that
and
are consecutive. The student may or may not be able to continue.
page 1 of 4 Correctly sketches parallelogram ABCD but writes an equation in which the expressions for the measures of
and
are summed and set equal to 180.
Questions Eliciting Thinking
When sketching parallelogram ABCD, is the order of the vertices important?
What kind of angle pair are
and
? What do you know about this kind of angle pair?
Instructional Implications
Review conventions in naming parallelograms and guide the student to sketch parallelogram ABCD correctly. Ask the student to revise his or her solution. If the student
does not recognize the need to rewrite the equation, then review theorems related to the angles of a parallelogram (i.e., opposite angles of a parallelogram are congruent,
consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°). Guide the student in applying the appropriate
theorem to write an equation. Ask the student to solve the equation and find the measures of all four angles. Ask the student to describe any additional theorems used.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
Moving Forward
Misconception/Error
The student errs in solving the equation or finding an angle measure.
Examples of Student Work at this Level
The student writes the equation 6x + 5 = 9x – 16. However, the student:
Solves the equation incorrectly.
Solves the equation correctly but makes an error in determining the measure of an angle.
The student also may not be explicit in describing any theorems used.
Questions Eliciting Thinking
Can you explain how you solved your equation?
Can you explain how you used the solution of your equation to find the angle measures?
What theorem did you apply when you wrote your equation? Shouldn’t the measures you found for What theorem can you apply to find the measures of
and
and
be the same?
?
Instructional Implications
Provide feedback on any errors made and allow the student to revise his or her work. Review theorems related to the angles of a parallelogram (i.e., opposite angles of a
parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a quadrilateral is 360°). Guide the
student to apply and cite these theorems when finding the measures of the angles of a parallelogram.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
Consider implementing MFAS task Finding Angle C (G-CO.3.11).
Almost There
Misconception/Error
The student is unable to correctly or completely describe the theorems used.
Examples of Student Work at this Level
The student writes the equation 6x + 5 = 9x – 16 and determines that x = 7,
=
= 47°, and =
= 133°. However, the student:
Describes only one or neither theorem.
page 2 of 4 Describes theorems incorrectly or incompletely.
Describes a theorem that was not used in addition to describing the correct theorems.
Describes a theorem using incorrect terminology.
Questions Eliciting Thinking
How did you know how to write your equation? What theorem did you apply when you wrote your equation?
What theorem did you apply to find the measures of
and
?
Did you use all of the theorems you described?
What kind of angle pair are
and
?
and
?
Instructional Implications
Review theorems related to the angles of a parallelogram (i.e., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are
supplementary, and the sum of the interior angles of a quadrilateral is 360°). Ask the student to describe the theorems used to both write the equation and to find the
measures of the angles. Explain that it is not necessary to describe other theorems related to parallelograms that were not explicitly used. Correct any misuse of
terminology.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
Consider implementing MFAS task Finding Angle C (G-CO.3.11).
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 writes the equation 6x + 5 = 9x – 16 and determines that x = 7,
=
= 47°, and =
= 133°. The student describes appropriate
theorems (e.g., opposite angles of a parallelogram are congruent, consecutive pairs of angles of a parallelogram are supplementary, and the sum of the interior angles of a
quadrilateral is 360°) to support his or her work.
Questions Eliciting Thinking
When did you apply each of the theorems that you described?
Was it necessary to calculate the measures of both
Suppose you calculated different measures for
and
and
?
. What would you have done next?
Instructional Implications
Provide the student with similar problems in which solutions of equations are noninteger rational numbers.
page 3 of 4 Provide the student with problems in which expressions for three angle measures are given using two variables so that the student must write and solve a system of
equations.
Provide additional opportunities to apply theorems related to the angles, sides, and diagonals of a parallelogram to find missing lengths and angle measures.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Angles of a Parallelogram worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.3.11:
Description
Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include:
opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
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