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’s work contains no evidence of the Pythagorean Theorem. The student calculates another quantity such as the radius of the table top or the area of the door.

Questions Eliciting Thinking What is this problem asking you to find? Can you draw and label a diagram for this problem? What type of figure do you see? Are there any right angles? Do you see any right triangles?
Does finding area answer the question about the length of the diagonal?
Do you know what the Pythagorean Theorem says? 
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 some 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. 
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 legs or the hypotenuse.
 Finds the square of the hypotenuse but neglects to take its square root.

Questions Eliciting Thinking What is the Pythagorean Theorem? Which variables represent the legs? Which variable represents the hypotenuse? Which sides are the legs of the right triangle in your diagram? Which side is the hypotenuse of the right triangle in your diagram?
Does it make sense that the length you found is 58 feet?
What did you actually solve for, c or ? 
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 a 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 some 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 or answers the question incorrectly. 
Examples of Student Work at this Level The student correctly uses the Pythagorean Theorem but:
 Squares 7 and gets 42. All other work is correct given the error.
 Finds the length of the diagonal of the doorway correctly but indicates that it is not long enough to accommodate the table.

Questions Eliciting Thinking You have a slight error in your work. Can you find it?
How does the length of the diagonal of the doorway compare to the length of the table? 
Instructional Implications Provide feedback to the student regarding any errors made and allow the student to revise his or her work. Encourage the student to carefully draw and label diagrams. Remind the student to show work neatly and completely to avoid careless errors.
If needed, assist the student in understanding how to determine if the table will fit through the doorway.
Remind the student to check for the reasonableness of the answer within the given context.
Consider implementing the MFAS task TV Size (GSRT.3.8) if not previously used. 
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 determines that the diagonal length of the doorway is approximately 7.6 feet and that the table will fit through the doorway.

Questions Eliciting Thinking How did you know to use the Pythagorean Theorem to solve this problem?
Can you restate the Pythagorean Theorem? To what kind of figure does it apply? 
Instructional Implications Challenge the student with more difficult mathematical and real world problems that require the use of the Pythagorean Theorem. For example, give the student the dimensions of a right rectangular prism, and ask the student to find the lengths of the segments that extend from a vertex of one face to each of the vertices of the opposite face.
Consider implementing the MFAS task TV Size (GSRT.3.8) if not previously used. 