Getting Started 
Misconception/Error The student does not demonstrate an understanding of the Pythagorean Theorem or the need to use it to solve the problem. 
Examples of Student Work at this Level The student’s work contains no evidence of the use of the Pythagorean Theorem. For example, the student:
 Estimates the width based on the given dimensions.
 Subtracts (or adds) the two known sides to determine the unknown side.
 Writes a proportion to determine the unknown side.
 Uses the area formula (area of triangle = bh).
Note: The student may or may not make calculation errors.

Questions Eliciting Thinking How did you determine your answer? Can you think of a way to find an exact answer rather than estimating?
Why would the diagonal equal the sum of the lengths of the other two sides?
Can you identify any right triangles in the diagram? What theorems do you know that involve the lengths of the sides of right triangles? 
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 states 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 realworld 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. 
Moving Forward 
Misconception/Error The student makes errors in applying the Pythagorean Theorem. 
Examples of Student Work at this Level The student recognizes the need to use the Pythagorean Theorem but makes significant errors in its application. For example, the student:
 Finds the square of a length but neglects to take its square root or reports the square as the actual length.
 Divides by two instead of taking a square root.
 Does not substitute the correct values for the lengths of the legs or the hypotenuse.

Questions Eliciting Thinking Do you think your answer is reasonable?
How did you decide which value to substitute for each variable? Which dimension would represent the hypotenuse (or legs)?
Can you tell me what you know about the Pythagorean Theorem? How did you apply it? 
Instructional Implications Review the properties of a right triangle, as needed. Be sure the student is able to identify the legs and hypotenuse of any right triangle.
Provide instruction, as needed, on evaluating squares and square roots. Emphasize the inverse relationship between squares and square roots. Use the square root symbol and be sure the student understands the distinction between evaluating square roots and dividing.
Give the student the opportunity to find missing lengths in right triangles in both realworld 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. 
Almost There 
Misconception/Error The student makes minor errors when applying the Pythagorean Theorem or does not completely justify each step. 
Examples of Student Work at this Level The student:
 Does not show all the steps needed to justify his or her answer.
 Writes an incorrect statement (e.g., = 45 instead of a = 45).
 Does not assign units to the measurement.

Questions Eliciting Thinking You did not show every step needed to justify your answer. Can you go back and fill in the missing steps?
How does ? If you take the square root of one side of an equation, shouldn’t you take the square root of the other side as well? 
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 label diagrams. Remind the student to show work neatly and completely to avoid careless errors.
Encourage the student to check for the reasonableness of answers in context and to label units of measure. 
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 applies the Pythagorean Theorem and provides work to show the TV is 45 inches wide, and therefore, will not fit in a 42 inch space. 
Questions Eliciting Thinking Can you apply the Pythagorean Theorem to any triangle? Explain.
Can you use the Pythagorean Theorem to determine lengths of two sides if you are only given the length of the hypotenuse? Explain. 
Instructional Implications Ask the student to determine the length of the diagonal of the largest television that can fit into the space that is 42 inches wide and 30 inches high.
Introduce the student to threedimensional figures such as rectangular prisms and square pyramids. Help the student identify right triangles within these figures and use the Pythagorean Theorem to find missing lengths. Consider using the MFAS task Three Dimensional Diagonal (8.G.2.7) and the MFAS task Pyramid Height (8.G.2.7). 