Getting Started 
Misconception/Error The student is unable to draw a triangle with the given conditions. 
Examples of Student Work at this Level The student draws:
 A triangle that doesÂ not fit the given conditions.
 A figure that is not a triangle.

Questions Eliciting Thinking How are the parts of a triangle described?
What does the term nonincluded angle mean?
What strategy did you use to draw this triangle? How did you ensure that the sides measured the given lengths and a nonincluded angle measured 30Â°? 
Instructional Implications Define a triangle as a polygon with three sides. Make clear that an open figure with three sides is not a triangle (since it is not a polygon). Describe the parts of a triangle and how to name them (e.g., the vertices, sides, and angles). Be sure the student understands how to measure angles.
Provide the student with a manipulative such as or software such as Geogebra (www.geogebra.org) to assist in building triangles with given conditions. The student may be more adept in drawing triangles with given conditions after working with a handson manipulative or software.
Guide the student to draw a triangle with the given conditions. Assist the student in using a ruler, protractor, and compass to construct the triangle. Explain that a good way to begin is by drawing a working line on which the triangle can be constructed. Next, have the student mark the endpoints of a 5 cm line segment on the working line. Label the line segment .Â Using endpoint C as a vertex, ask the student to construct theÂ 30Â° angle (the nonincluded angle). Extend the length of the ray drawn to create the 30Â° angle (which will contain side ). Next, assist the student in using a compass to draw an arc centered at point B and with a radius of 3 cm. Guide the student to observe that this arc intersects Â in two different points, each of which can serve as the third vertex of the triangle. Consequently, two possible triangles can be drawn that fit the given conditions. Use this exercise as an opportunity to conclude that two sides and a nonincluded angle do not determine a unique triangle.
Allow the student to further experiment to confirm these conclusions. If needed, model how to properly label the angles and sides of the triangle. 
Moving Forward 
Misconception/Error The student is unable to correctly determine if the given conditions form a unique triangle. 
Examples of Student Work at this Level The student:
 Correctly draws a triangle with the given conditions. However, the student determines that no other triangle can be formed using the given measures.Â
 Attempts to draw a different triangle with the given conditions but is unable to complete the drawing. Therefore, the student concludes that it is not possible to draw a different triangleÂ that fits the given conditions.
 Draws two different triangles neither of which fit the given conditions and concludes that it is possible.

Questions Eliciting Thinking Can you extend sideÂ Â of the triangle without affecting the size of theÂ ?
When you increase or decrease the measure of an angle, does it affect the length of all the sides of the triangle?Â
If you draw a second triangle using the same conditions and its shape changes, do the given conditions determine aÂ unique triangle? 
Instructional Implications Guide the student to draw a triangle with the given conditions. Assist the student in using a ruler, protractor, and compass to construct the triangle. Explain that a good way to begin is by drawing a working line on which the triangle can be constructed. Next, have the student mark the endpoints of a 5 cm line segment on the working line. Label the line segment .Â Using endpoint C as a vertex, ask the student to construct theÂ 30Â° angle (the nonincluded angle). Extend the length of the ray drawn to create the 30Â° angle (which will contain side ). Next, assist the student in using a compass to draw an arc centered at point B and with a radius of 3 cm. Guide the student to observe that this arc intersects Â in two different points, each of which can serve as the third vertex of the triangle. Consequently, two possible triangles can be drawn that fit the given conditions. Use this exercise as an opportunity to conclude that two sides and a nonincluded angle do not determine a unique triangle.
Allow the student to further experiment to confirm these conclusions. 
Almost There 
Misconception/Error The student does not adequately explain why the given conditions do not determine a unique triangle. 
Examples of Student Work at this Level The student correctly draws a triangle with the given conditions and concludes that a different triangle can be formed with the given conditions â€śbecause the third side can be a different length.â€ť
The student constructs another triangle with the given conditions that is different fromÂ triangle ABC, but does not explain how it is possible. 
Questions Eliciting Thinking How are the angles and sides of a triangle related? What is the relationship between the length of a side and the opposite angle measure?
What happens to the length of a side if the angle opposite from it increases or decreases in measure? 
Instructional Implications Explain to the student that two sides and a nonincluded angle do not determine a unique triangle. Provide opportunities for the student to observe that the length of the side opposite the included angle can be extended, thus altering the measure of the included angle, but not affecting the lengths of the two given sides and the nonincluded angle. Discuss with the student the relationship among the sides and angles within a triangle. Model a concise explanation using mathematical terminology. 
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 recognizes that it is possible to draw more than one triangle when given the measures of two sides and a nonincluded angle. The student explains that the length of the side opposite the included angle can be extended, thus altering the measure of the included angle, but not affecting the lengths of the two given sides and the nonincluded angle. 
Questions Eliciting Thinking What are some sets of conditions that will form a unique triangle?
Can you think of another set of conditions that will not form a unique triangle? 
Instructional Implications Consider pairing the student with a Moving Forward partner to share strategies for drawing triangles.
Consider implementing the MFAS tasks Drawing Triangles SAS, Drawing Triangles ASA, Drawing Triangles SSS, Drawing Triangles AAS, Drawing Triangles AAA, or Sides of Triangles (7.G.1.2), if not done previously. 