Getting Started 
Misconception/Error The student does not use proportional reasoning to solve the problem. 
Examples of Student Work at this Level The student:
 Does not attempt to use a proportion or a scale factor for question number one.
 Subtracts the difference between 112 and 100 from 140 to find the distance from the park entrance to the rides.

Questions Eliciting Thinking What kind of triangles are these? What do you know about the angles and sides of similar triangles?
How are the lengths 112 and 140 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 write and solve an appropriate proportion to find the distance from the park entrance to the rides.
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.
 Calculates the scale factor incorrectly (e.g., as instead of as ).
 Correctly sets up and solves a proportion but then subtracts the lengths of the sides.

Questions Eliciting Thinking Can you explain how you set up your proportion?
Can you explain how you solved your proportion?
How did you find the scale factor? 
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 Basketball Goal (GSRT.2.5) 
Almost There 
Misconception/Error The student provides correct responses but with insufficient reasoning or imprecise language. 
Examples of Student Work at this Level The student correctly writes and solves proportions but does not justify why it is appropriate to write proportions. 
Questions Eliciting Thinking How did you know to write a proportion to find the unknown distance? What justifies using proportions to solve this problem?
Could you have reasoned that the distance from the restrooms to the rides is 140 yards without having to actually write and solve a proportion? 
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.
Consider implementing MFAS tasks Basketball Goal (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’s response includes these three components:
 A statement that a proportion (or scale factor) can be used to find the missing distances because the triangles are similar.
 For question one, a proportion relating corresponding parts (or scale factor) showing how to calculate the distance. For example, the student writes the proportion and correctly solves it, or the student uses the scale factor to calculate the distance: =1.25 so, 1.25(100) = 125, and concludes the distance from the park entrance to the rides is 125 yards.
 For question two, the conclusion that the distance from the rides to the restrooms is 140 yards which is justified by observing that since one triangle is isosceles, the other triangle must also be isosceles because of the proportionality of sides. Next, 140 yards is added to 112 yards (the given distance from the restrooms to the refreshments) which yields a total distance of 252 yards from the rides to the refreshment area at the fair.

Questions Eliciting Thinking How can you prove the two triangles in the diagram are similar?
Could you have reasoned that the distance from the restrooms to the rides is 140 yards without having to actually write and solve a proportion? 
Instructional Implications Challenge the student to solve problems involving similar triangles that are overlapping or require multiple steps.
Consider implementing MFAS tasks Basketball Goal (GSRT.2.5), Similar Triangles 1(GSRT.2.5), Prove Rhombus Diagonals Bisect Angles (GSRT.2.5), and Similar Triangles 2 (GSRT.2.5). 