Getting Started 
Misconception/Error The student does not demonstrate an understanding of the Pythagorean Theorem or the need to use it to solve this problem. 
Examples of Student Work at this Level The student may sketch an altitude of the triangle in the diagram and find the length of the altitude as 11 feet (3524). However, the student’s work contains no evidence of the use of the Pythagorean Theorem. The student finds another quantity such as the area of the triangle.

Questions Eliciting Thinking What kind of triangle is shown on the house? How can you use the given lengths to find the height of that triangle?
Could you find a way to create a right triangle in this diagram? What would the dimensions of that right triangle be?
What are you asked to find? What can you use to find the length of a side of a right triangle? 
Instructional Implications Provide the student with basic instruction on the Pythagorean Theorem. Be sure to review the parts of a right triangle (e.g., vertices, right angle, acute angles, hypotenuse, and legs). When initially introducing the Pythagorean Theorem, emphasize that it only applies to right triangles. Be very explicit about what the theorem says describing it verbally and with mathematical symbols. Caution the student to be careful not to confuse the legs and hypotenuse when applying the theorem. Give the student the opportunity to find missing lengths in right triangles in both real world and mathematical problems. Include problems in which the length of the hypotenuse is unknown, the length of a leg is unknown, unknown lengths are integers, unknown lengths are rational or irrational numbers, and diagrams must be sketched and labeled. Guide the student to show work completely and in an organized manner.
If needed, review finding and approximating square roots.
Encourage the student to explore the Pythagorean theorem using an interactive online site such as http://www.mathopenref.com/pythagorastheorem.html. 
Moving Forward 
Misconception/Error The student makes errors in applying the Pythagorean Theorem. 
Examples of Student Work at this Level The student does not substitute the correct values for the lengths of the legs of the right triangle.

Questions Eliciting Thinking On what triangle were you using the Pythagorean theorem?
What are the lengths of the legs? Where is the hypotenuse? 
Instructional Implications Review the Pythagorean Theorem. Be sure the student is correctly able to identify the right angle, the legs, and the hypotenuse of the right triangle in the diagram. If the student has difficulty distinguishing the legs from the hypotenuse of a right triangle embedded in a diagram, encourage the student to redraw the right triangle separately and label its parts. Give the student the opportunity to find missing lengths in right triangles in both real world and mathematical problems. Include problems in which the length of the hypotenuse is unknown, the length of a leg is unknown, unknown lengths are integers, unknown lengths are rational or irrational numbers, and diagrams must be sketched and labeled. Guide the student to show work completely and in an organized manner.
Remind the student to check for the reasonableness of the answer. 
Almost There 
Misconception/Error The student makes a minor computational error. 
Examples of Student Work at this Level The student:
 Finds the length of the hypotenuse of the triangle but fails to double it to find how many feet of lights are needed.
 Finds the length of lights needed but does not round correctly or according to the directions of the problem.

Questions Eliciting Thinking There is a small error in your work. Can you find it?
Can you show me on the diagram the length you found?
Where will the lights be placed on the house?
If Mr. Peabody only buys 16 feet of lights, will the lights stretch across the roof as shown when the house is 24 feet wide? 
Instructional Implications Provide feedback to the student regarding any errors made and allow the student to revise his or her work. Remind the student to review any question asked in the problem to be sure that it has been answered.
Remind the student to check for the reasonableness of the answer within the given context. 
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:
 Sketches an altitude of the triangle in the diagram and finds the length of the altitude as 11 feet (35  24).
 Recognizes that the base of the triangle will be bisected since the triangle is isosceles and the altitude is also a median.
 Labels the base of the right triangle as 12 feet and uses the Pythagorean Theorem to find the hypotenuse of the right triangle that is formed: , and finds 16.2788 feet.
 Doubles the result and rounds to the nearest foot to find the length of lights needed, 33 feet.

Questions Eliciting Thinking Is the triangle in the original diagram a right triangle? How could you find out?
Do you have enough information to find the angle in which the roof lines meet? 
Instructional Implications Challenge the student with more difficult mathematical and real world problems that require the use of the Pythagorean Theorem. For example, ask the student to find the slant height and length of a lateral edge of a square pyramid given its height and the length of a base edge.
Consider implementing MFAS tasks Will It Fit (GSRT.3.8) and TV Size (GSRT.3.8). 