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 63Â° angle.
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 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.
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Questions Eliciting Thinking What kind of angles are Â and ?
What kind of angles are Â 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  63Â = 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 Â is 63Â° since Â andÂ are vertical angles and = 63Â°. 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 63Â° 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.
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Questions Eliciting Thinking What kind of angle pair are Â and ?
What kind of angle pair are Â 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 Â 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 Â 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:
 Refers to vertical angles incorrectly, for example, as angles that are across, opposite, diagonal, or adjacent.
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 Uses notation incorrectly when naming angles or referring to their measures.
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 Makes a computational error.
 Writes an equation showing a computational approach rather than the angle relationship (e.g., 180 â€“ 117 = x).
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Questions Eliciting Thinking Do you know the term that describes the relationship between Â 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:

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 identifyÂ 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 = 63Â°.
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). 