Getting Started 
Misconception/Error The student does not have an effective strategy for solving the problem. 
Examples of Student Work at this Level The student may write some relevant formula on his or her paper, possibly with other irrelevant or unnecessary work. But, the student is unable to describe a strategy for determining whether the triangle is scalene, isosceles, or equilateral. For example, the student:
 Does not indicate a need to determine the lengths of the sides of the triangle.
 Writes the distance formula, but does not use it.
 Writes the Pythagorean Theorem, but does not use it.
 Attempts to use the slope formula or the midpoint formula.

Questions Eliciting Thinking What do the terms scalene, isosceles, and equilateral mean?
What do you need to know about the triangle in order to determine if it is scalene, isosceles, or equilateral?
What formula will help you determine the length of the triangle’s sides? 
Instructional Implications Guide the student to develop an overall strategy for solving the problem presented in this task, that is, determine the lengths of the sides of the triangle and make a decision about the triangle type based on the lengths of the sides. Model implementing the strategy, as well as showing and labeling written work in a logical, complete, and correct manner. Be sure the student understands the definitions of the terms scalene, isosceles, and equilateral.
Provide instruction on how to use the distance formula to determine the side lengths of geometric figures in the coordinate plane. Give the student additional opportunities to use this formula in a variety of problem contexts. 
Moving Forward 
Misconception/Error The student’s work shows evidence of an effective strategy for solving the problem but the implementation is incomplete or contains significant errors. 
Examples of Student Work at this Level The student:
 Attempts to use the distance formula, but makes significant errors.
 Correctly applies the distance formula or the Pythagorean Theorem to find the lengths of only two sides of the triangle.

Questions Eliciting Thinking Can you write out the distance formula? How did you substitute values into the distance formula?
Your work correctly shows that the triangle is isosceles, but how do you know if it is equilateral or not? 
Instructional Implications Review the distance formula and assist the student in correctly applying it to find the length of one of the sides. Directly address any errors the student initially made when using the formula. Ask the student to find the lengths of the remaining two sides and provide feedback.
If needed, discuss with the student the need to find the length of the third side of the triangle to determine if the triangle can also be described as equilateral. Present the student with the lengths of two of the three sides of a triangle and ask the student to determine the remaining length (if possible) so that the triangle is each of scalene, isosceles, and equilateral (but be sure the student provides a length that can actually determine a triangle).
If needed, review the definitions of the terms scalene, isosceles, and equilateral. Guide the student to choose the appropriate term to describe the triangle. 
Almost There 
Misconception/Error The student makes a minor error in implementing some aspect of an effective strategy for solving the problem. 
Examples of Student Work at this Level The student:
 Makes a computation error when using the distance formula to find the length of one of the sides.
 Correctly determines the lengths of the sides of the triangle but confuses the terms scalene and isosceles.

Questions Eliciting Thinking You made a mistake in one of your calculations. Can you find and correct it?
What do the terms scalene and isosceles mean? 
Instructional Implications Provide feedback to the student concerning any errors made and allow the student to revise his or her work. Provide additional problems that require the use of the midpoint, distance, or slope formulas. Pair the student with another Almost There student in order to compare work and resolve differences. 
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 correctly calculates the lengths of the sides: , , and . The student concludes that since exactly two sides are congruent, the triangle is best described as isosceles.

Questions Eliciting Thinking How would you determine if triangle PQR is a right triangle?
How could you locate the endpoints of a midsegment of triangle PQR? 
Instructional Implications Challenge the student to prove geometric theorems using coordinate geometry. Consider implementing MFAS tasks Diagonals of a Rectangle (GGPE.2.4). 