Getting Started 
Misconception/Error The student is unable to apply an appropriate strategy. 
Examples of Student Work at this Level The student:
 Attempts a guessandtest strategy.
 Sketches a diagram that includes a point that is equidistant from A, B, and C but does not identify it as such and offers no justification.
 Calculates the distance between points A and C but does not locate a point equidistant from A, B, and C.
 Shows the path of two sprinters converging on a common point but does not identify this point or relate it to the distance traveled by the third sprinter.
 Assigns coordinates to A, B, and C, and guesses a location of the center of the finish circle but is unable to justify or verify the location.

Questions Eliciting Thinking Can you explain your strategy to me? How does your strategy assist you in identifying the center of the finish circle?
Can you explain to me why you chose the distance formula? How does the distance formula assist you with identifying the center of the finish circle?
The finish circle is equidistant from each of the three sprinters. What approximate location on the grid would be the same distance from each starting point? 
Instructional Implications Guide the student to use his or her intuition to locate a point that is equidistant from A, B, and C. Then ask the student to use a compass to check the location. Explain that the point that is equidistant from A, B, and C can be precisely located using a variety of strategies. Review the points of concurrency related to triangles and explain that the circumcenter is equidistant from the vertices of a triangle. Ask the student to draw and then construct the perpendicular bisectors of its sides in order to locate the circumcenter. Ask the student to construct the circumscribed circle and explain why its center is equidistant from the vertices of the triangle.
Prompt the student to also describe the circumcenter with respect to (the midpoint of the hypotenuse of right triangle ABC) and the diagonals of rectangle where point is the image of point B after a reflection across (the point where the diagonals of the rectangle intersect).
Consider implementing other MFAS tasks aligned to (GMG.1.3). 
Making Progress 
Misconception/Error The student correctly locates a point equidistant from points A, B, and C but is unable to justify its location. 
Examples of Student Work at this Level The student clearly identifies the midpoint of as a point that is equidistant from A, B, and C but is unable to provide adequate justification.

Questions Eliciting Thinking How do you know the midpoint of is equidistant from A, B, and C?
Can you mathematically justify why the midpoint of is equidistant from A, B, and C? 
Instructional Implications Review with the student a strategy for justifying the midpoint of as a point that is equidistant from A, B, and C. Then ask the student to write up a justification, providing the details. Expose the student to effective strategies used by others.
Review the points of concurrency related to triangles and explain that the circumcenter is equidistant from the vertices of a triangle. Ask the student to draw and then construct the perpendicular bisectors of its sides in order to locate the circumcenter. Ask the student to construct the circumscribed circle and explain why its center is equidistant from the vertices of the triangle.
Consider implementing other MFAS tasks aligned to (GMG.1.3). 
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 identifies the center of the finish circle using an appropriate strategy or method and justifies that process mathematically.
The student identifies the center of the finish circle using one of the following methods:
 By locating the point of concurrency (intersection) of the perpendicular bisectors of the sides of the triangle.
 By locating the midpoint of and justifying this point as equidistant from A, B, and C using properties of inscribed angles of circles.
 By locating the intersection of the diagonals of a composed rectangle and using properties of the diagonals of a rectangle to justify that this point is equidistant from points A, B, and C.
 By locating the midpoint of (point D) and showing that ADÂ = CD = BD. By calculating their lengths.

Questions Eliciting Thinking Do you know another way to find the center of the finish circle?
How many different ways can you think of to geometrically describe the center of the finish circle? 
Instructional Implications Correct any misuses of notation. Then challenge the student to explore other strategies that mathematically justify why the center of the finish circle is the midpoint of the hypotenuse of right triangle ABC (other than the method the student originally used). If necessary, provide some hints (e.g., finding a point of concurrency, using an inscribed angle, or using properties of diagonals of rectangles).
Consider implementing other MFAS tasks aligned to (GMG.1.3). 