Getting Started 
Misconception/Error The student is unable to write and solve equations to find unknown angle measures. 
Examples of Student Work at this Level The student:
 Cannot write or solve equations that represent the angle relationships.
 Is unable to write an equation for the first problem and is unable to solve for the variable in the second problem.

Questions Eliciting Thinking What do you know about supplementary angles?
What information is given in the diagram? What are you asked to find?
What do you think is meant by â€śwrite an equation?â€ť
If you represent the unknown angle measure with a variable, are you able to write an equation to model the relationship shown in the diagram (or described in the problem)?
What does it mean that the ratio of the angles is 2:3? 
Instructional Implications Define for the student that supplementary angles are two angles whose measures sum to 180Â°, and ask the student to identify the supplementary angles in the diagrams. Model how the angles in the diagram can be composed using addition (e.g., the measure of plus 117 equals 180Â°). Guide the student to determine the unknown angle in the problem and represent it with a variable. Assist the student in writing an equation to find the unknown angle measure. 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 117 + (180  117) =180. Instead, encourage the student to write an equation that reflects the angle relationship, for example, an equation such as 117 + xÂ =180. Explain to the student that this equation reflects the fact that the two angle measures sum to 180Â°.
Model for the student how to determine angle measures described by a ratio. Explain to the student that if the ratio of angle measures is 2:3 and the angle measures sum to 180, then 180 can be divided into five equal parts. Two of those parts combine to determine one of the angle measures and three of those parts combine to determine the other angle measure. Guide the student to represent the size of a part with a variable (e.g., x) and then write the equation as 2xÂ + 3xÂ = 180. Alternatively, the ratio can be interpreted as 2 is to 3 as m is to m which leads to the proportion = Â where x represents and 180 â€“ x represents .
Provide additional opportunities for the student to apply knowledge of supplementary angles to write and solve equations to determine unknown angle measures. 
Moving Forward 
Misconception/Error The student is unable to write or solve an equation when the angle relationship is described by a ratio. 
Examples of Student Work at this Level The student is able to write and solve an equation to determine the unknown measure in problem one. The student may or may not be able to write an equation but is unable to solve problem two. The student:
 Uses a guess and check strategy and is unable to write an equation representing the angle relationship.
 Writes an incorrect or incomplete equation for the second problem.
 Writes an appropriate equation for problem two but cannot solve it.

Questions Eliciting Thinking What does it mean that the ratio of the angles is 2:3? (If needed, prompt the student to explain in terms of parts.)
Can you explain how you solved for the angles that were in a ratio of 2:3 without an equation or a proportion?
Can you show me how you used the Distributive Property to rewrite 2(180 â€“ x)?
Can you explain what each part of your proportion represents? 
Instructional Implications Model for the student how to determine angle measures described by a ratio. Explain to the student that if the ratio of angle measures is 2:3 and the angle measures sum to 180, then 180 can be divided into five equal parts. Two of those parts combine to determine one of the angle measures and three of those parts combine to determine the other angle measure. Guide the student to represent the size of a part with a variable (e.g., x) and then write the equation as 2x + 3xÂ = 180. Alternatively, the ratio can be interpreted as 2 is to 3 as m is to m which leads to the proportion = Â where x represents and 180 â€“ x represents .
Provide additional opportunities for the student to apply knowledge of supplementary angles to write and solve equations to determine unknown angle measures. 
Almost There 
Misconception/Error The student makes a minor error or does not show written work appropriately. 
Examples of Student Work at this Level The student is able to write an appropriate equation to represent the supplementary relationship between and , but makes a mistake when solving. The student:
 Makes an error using the Distributive Property.
 Calculates m instead of m.
 Makes a minor computational error.
 Writes an equation that reflects a computational approach rather than the angle relationship for the first problem (e.g., x = 180 â€“ 117). All other work in the task is complete and correct.Â

Questions Eliciting Thinking Did you apply the Distributive Property correctly?
Can you reread the question? Did you find what the question asked for?
Can you check your work? Does your written work match your final answer? 
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 What Is Your Angle? (7.G.2.5), Solve for the Angle (7.G.2.5), or Find the Angle Measure (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:
 x + 117 = 180; x = 63 so the m = 63Â°.
 = ; 2x + 3x = 360 orÂ x = 72 so the m = 72Â°.

Questions Eliciting Thinking Can you use the ratio to write an expression for the measures of and ?
Can you think of any other way to solve the second problem?
Does the orientation of the angle have any effect on its measure? 
Instructional Implications 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 What is Your Angle? (7.G.2.5), Find the Angle Measure, or Solve for the Angle (7.G.2.5). 