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 is unable to write equations that reflect angle relationships. The student may also demonstrate little or no understanding of complementary or supplementary angle relationships. The student:
 Uses a numerical approach to find the measure of , rather than writing and solving an equation.
 Makes an attempt to write an equation but it does not reflect complementary or supplementary angle relationships.

Questions Eliciting Thinking What are complementary angles? What are supplementary angles?
What are you asked to find? What information is given in the diagram?
What do you think is meant by â€śwrite an equationâ€ť?
Can you show me on the diagram the unknown angle measure you need to find? What do you know about these angles? 
Instructional Implications Review the definitions of complementary, supplementary, adjacent angles, and straight 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. 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.
Provide additional opportunities for the student to apply knowledge of complementary and supplementary angles to write and solve equations to determine unknown angle measures. 
Moving Forward 
Misconception/Error The student does not understand one of the terms supplementary or complementary. 
Examples of Student Work at this Level The student is able to correctly write and solve an equation for only one of the problems. The student:
 Writes and solves an equation to determine the measure of , but gives the same answer when asked for the complement of .
 Writes and solves an equation to determine the complement of , but writes an equation in two variables to determine the measure of .
 Writes and solves an equation to calculate the complement of , but writes the equation 90 = x â€“ 53 to find the measure of .

Questions Eliciting Thinking What do you know about complementary angles (supplementary angles)? What is the difference between complementary and supplementary angles?
Which angle measures 53Â°? Is that what the question asks you to find?
Are both questions asking about the same unknown angle? How are the problems different?
Why did you use two variables? If you represent the unknown angle with a variable, can you write an equation with one variable to determine the unknown angle measure? 
Instructional Implications Review with the student that complementary angles are two angles whose measures sum to 90Â° and supplementary angles are two angles whose measures sum to 180Â°. If needed, assist the student in writing an equation to model the angle relationship. Provide additional opportunities for the student to apply knowledge of complementary and supplementary angles to write and solve equations to determine unknown angle measures.
Consider implementing the MFAS tasks What Is Your Angle? (7.G.2.5), Straight Angles (7.G.2.5), or Find the Angle Measure (7.G.2.5). 
Almost There 
Misconception/Error The student does not show written work appropriately. 
Examples of Student Work at this Level The student:
 Records subtraction in the wrong order.
 Writes equations that reflect a computational approach rather than the angle relationships.

Questions Eliciting Thinking Can you check your work? Does your written work match your final answer?
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 What Is Your Angle? (7.G.2.5), Straight Angles (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 and solves equations of the form x + p = q and determines the unknown measures are 127Â° and 37Â°.
 x + 53 = 180; x = 127 so that theÂ mÂ = 127.
 x + 53 = 90; x = 37 so that the measure of the complement ofÂ Â is 37.

Questions Eliciting Thinking Can you explain how you knew to write your equation this way?
What do you know about vertical angles? Adjacent angles? 
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 (7.G.2.5), or Straight Angles (7.G.2.5). 