Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70723
What Is Your Angle?
Students are asked use knowledge of angle relationships to write and solve an equation to determine an unknown angle measure.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, supplementary, complementary, adjacent, vertical, angle, equation
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WhatIsYourAngle_Worksheet.docx
MFAS_WhatIsYourAngle_Worksheet.pdf
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 problems on the What Is Your Angle? worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the relationships among angle measures in the diagram.
Examples of Student Work at this Level
The student does not understand the relationship between the measures of vertical angles or angles that form a linear pair. For example, the student:
Subtracts 63 from 90 to find the measure of
, an angle vertical to the 63° angle. page 1 of 4 Subtracts twice the measure of an angle from 180 in order to find the measure of another angle with which it forms a linear pair.
Questions Eliciting Thinking
What kind of angles are
and
What kind of angles are
and
?
?
What do you know about vertical angles?
What do you know about linear pairs of angles?
Instructional Implications
Review the definitions of vertical angles, adjacent angles, straight angles, supplementary angles, and linear pairs of angles. Use diagrams to show examples of each. Then ask
the student to identify special angle pairs in diagrams. Model for the student how to write and solve equations to find unknown angle measures based on knowledge of
angle relationships. Guide the student to represent the unknown angle in the problem with a variable. If necessary, review how to solve equations of the form x + p = q
where x, p, and q are rational numbers. Provide additional opportunities for the student to write and solve equations of the form x + p = q, px = q, and px + q = r.
Caution the student against writing an equation such as 180 - 63 = 117. Instead, encourage the student to write an equation that models the angle relationship (e.g., 117
+ x = 180). Explain to the student that this equation reflects the fact that the two angle measures sum to 180.
Assist the student in identifying, describing, and justifying the measures of vertical angles. Model explaining that the measure of
vertical angles and
is 63° since and
are
= 63°. Provide additional examples for the student to explore and guide the student to recognize the relative positions of vertical angles and
conclude they have equal measures.
Moving Forward
Misconception/Error
The student does not understand the relationships among angle measures in the diagram.
Examples of Student Work at this Level
The student does not understand the relationship between the measures of vertical angles or angles that form a linear pair. For example, the student:
Subtracts 63 from 90 to find the measure of
, an angle vertical to the 63° angle.
Subtracts twice the measure of an angle from 180 in order to find the measure of another angle with which it forms a linear pair.
Questions Eliciting Thinking
What kind of angle pair are
and
?
What kind of angle pair are
and
?
What do you know about vertical angles?
What do you know about linear pairs of angles?
Instructional Implications
Ask the student to verbalize the relationship between
and
. Assist the student in using appropriate terminology (e.g., straight angle, linear pair of angles, and
supplementary) Guide the student to write an equation that models the relationship between
and
. Then ask the student to solve the equation. Provide
additional opportunities for the student to apply knowledge of angle relationships to write and solve equations to determine unknown angle measures.
Almost There
Misconception/Error
The student makes an error in terminology, notation, or showing work.
Examples of Student Work at this Level
The student:
page 2 of 4 Refers to vertical angles incorrectly, for example, as angles that are across, opposite, diagonal, or adjacent.
Uses notation incorrectly when naming angles or referring to their measures.
Makes a computational error.
Writes an equation showing a computational approach rather than the angle relationship (e.g., 180 – 117 = x).
Questions Eliciting Thinking
Do you know the term that describes the relationship between
and
?
How should you write the name of an angle? How can you refer to its measure?
Can you check your work? Are your calculations all correct?
Can you write an equation that shows the relationship between the two angles?
Instructional Implications
Provide specific feedback concerning any errors made and allow the student to revise his or her work. Provide additional opportunities for the student to apply knowledge of
angle relationships to write and solve equations to determine unknown angle measures.
Consider implementing the MFAS tasks Find the Angle Measure (7.G.2.5), Straight Angles (7.G.2.5), or Solve for the Angle (7.G.2.5).
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:
= 63° since and
are vertical angles and the measure of
x + 63 = 180; x = 117, so the measure of
has the same measure as
is
or
is
.
= 117°.
since these angles are vertical.
Questions Eliciting Thinking
Was it necessary to write and solve an equation to find the measure of
? Why or why not?
Are there any other angles in the diagram that have the same measure? How do you know?
Instructional Implications
Challenge the student to identify other angles in the diagram with equal measures. Ask the student what condition(s), if any, must be assumed. Tell the student ABCD is a
parallelogram and ask if all interior and exterior angles can be determined given only
= 63°.
Provide problems of higher complexity asking the student to use knowledge of vertical, adjacent, complementary, and/or supplementary angle relationships in order to write
and solve equations to determine unknown angle measures.
Consider implementing the MFAS tasks Find the Angle Measure (7.G.2.5), Solve for the Angle (7.G.2.5), or Straight Angles (7.G.2.5).
ACCOMMODATIONS & RECOMMENDATIONS
page 3 of 4 Special Materials Needed:
What Is Your 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
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.G.2.5:
Description
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and
solve simple equations for an unknown angle in a figure.
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