Getting Started 
Misconception/Error The student does not use proportional reasoning to solve the problem. 
Examples of Student Work at this Level The student:
 Subtracts to find the difference in the lengths of the shadows then adds this value to the gym teacher's height to find the height of the goal.
 Draws a diagram involving triangles but is unable to use proportional reasoning to solve the problem.

Questions Eliciting Thinking What kind of triangles did you draw? How are these triangles related?
What are similar triangles? Could these triangles be similar?
How are the lengths of the sides of similar triangles related? 
Instructional Implications Review the definition of similarity and its consequences (i.e., corresponding angles of similar triangles are congruent and corresponding sides are proportional). Guide the student to recognize that this problem involves similar triangles by drawing an appropriate diagram and verifying that the triangles are similar. If needed, review ways to prove two triangles are similar (AA, SAS, SSS) and what must be established in order to conclude two triangles are similar using each method. Remind the student that once two triangles are proven similar, all corresponding angles are congruent and all corresponding sides are proportional. Guide the student to write and solve an appropriate proportion. Then ask the student to consider the question asked in the problem and to provide an answer.
Provide additional opportunities to solve problems involving similar triangles and guide the student to write and solve proportions to find missing lengths. 
Moving Forward 
Misconception/Error The student uses proportional reasoning but makes an error in writing or solving the proportion. 
Examples of Student Work at this Level The student:
 Makes an error in writing the proportion.
 Makes an error in solving the proportion.
 Does not solve the proportion but assumes the height of the goal is 10 feet.

Questions Eliciting Thinking What would a diagram representing this problem look like? Can you draw one with all of the lengths and the unknown labeled?
Can you explain how you set up your proportion?
Can you explain how you solved your proportion?
What does your solution indicate about the height of the goal? 
Instructional Implications Provide feedback to the student concerning any errors in writing or solving the proportion. Allow the student to revise his or her work.
If needed, provide more practice with solving proportions and give the student additional opportunities to solve problems involving similar triangles.
Consider implementing MFAS task County Fair (GSRT.2.5). 
Almost There 
Misconception/Error The student provides a correct response but with insufficient reasoning or imprecise language. 
Examples of Student Work at this Level The student:
 Draws a diagram and finds a height of 9.6 feet but shows no supporting work.
 Writes a proportion but does not show work to support his or her conclusion.
 Writes the proportion as and correctly solves for x but cannot explain or interpret what the solution means for the problem.

Questions Eliciting Thinking How did you find the height of the goal? How do you know the goal is not regulation?
How can you support your conclusion?
What question are you trying to answer? What does your answer mean in that context? 
Instructional Implications Explain to the student that all responses to mathematical problems should be adequately written and justified. Model showing an appropriate amount of work to communicate to the reader what was done to solve the problem. Encourage the student to omit any unnecessary work. Remind the student to always review the question posed in the problem to be sure that it was answered.
If necessary, assist the student with interpreting the solution of his or her equation. Explain that there is often more than one correct approach to solving mathematical problems. Encourage the student to use an approach that makes sense to him or her.
Provide additional opportunities to solve problems involving similar triangles and guide the student to show work completely and concisely.
Consider implementing MFAS tasks County Fair (GSRT.2.5), Similar Triangles 1(GSRT.2.5), Prove Rhombus Diagonals Bisect Angles (GSRT.2.5), and Similar Triangles 2 (GSRT.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 draws a diagram involving two right triangles which the student recognizes as similar. The student writes a proportion to find:
 The height of the goal given its shadow length, and determines the height to be 9.6 feet which is less than the regulation height of 10 feet.
 The length of the goal’s shadow if its height is 10 feet: and determines the shadow length to be 8 feet which is longer than the actual shadow indicating that the goal is lower than the regulation height.

Questions Eliciting Thinking How do you know these two triangles are similar? Why were you able to set up a proportion to find this length?
What does the variable in your proportion represent?
Is there another way you could have solved this problem? 
Instructional Implications Challenge the student to solve problems involving similar triangles that are overlapping or require multiple steps.
Consider implementing MFAS tasks County Fair (GSRT.2.5), Similar Triangles 1(GSRT.2.5), Prove Rhombus Diagonals Bisect Angles (GSRT.2.5), and Similar Triangles 2 (GSRT.2.5). 