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 with incorrect angle measures.
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The student draws a figure that is not a triangle (e.g., an open figure with three sides).

Questions Eliciting Thinking What are the features of a triangle?
What strategies would you use to draw a triangle given the measures of the angles? Where is a good place to begin drawing?
How would using a protractor help you draw a triangle with the given measurements? 
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 Â 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 given conditions. Assist the student in using a protractor to draw and measure angles. Explain that a good way to begin is by drawing a working line and â€śbuildingâ€ť the triangle on it. If needed, model how to properly label the angles and sides of a triangle.
Next, ask the student to draw a working line and measure a length that is double the length of one side of the triangle to serve as a side of a new triangle. Using the endpoints of the side as vertices, have the student draw angles using two of the given measures. Next, have the student extend the sides of these angles until they intersect in the third vertex of the triangle. Have the student measure the lengths of these sides and compare them to the lengths of the corresponding sides of the original triangle. Also, ask the student to measure the angle formed by these two sides and compare this measure to the third given angle measure. Use this exercise as an opportunity to conclude:
 Three angle measures do not determine a unique triangle.
 Two angle measures determine the measure of the third angle of the triangle.
 Two angle measures and their included side length will determine a unique triangle.
Relate these conclusions to the relevant aspects of the exercise. Allow the student to further experiment to confirm these conclusions.

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 is able to draw a triangle with angle measures 110Â°, 30Â°, and 40Â° but says it is not possible to draw more than one triangle with these conditions.
The student justifies this decision by explaining:
 If you tried to draw a different triangle with the same angles, youâ€™d get the same triangle but it would just be turned to a different side. Therefore, the sides would stay the same for every possible triangle you try to make with the same angles.
 There is only one way that you can make the angles the right measure.
 No matter how you arrange the angles, they will always be the same distance from each side.

Questions Eliciting Thinking How long are the sides of your triangle? Did they have to be these lengths?
What if you doubled the length of each side of the triangle? Would the angle measures change? How can you find out? 
Instructional Implications Ask the student to draw a working line and measure a length that is double the length of one side of the triangle to serve as a side of a new triangle. Using the endpoints of the side as vertices, have the student draw angles using two of the given measures. Next have the student extend the sides of these angles until they intersect in the third vertex of the triangle. Have the student measure the lengths of these sides and compare them to the lengths of the corresponding sides of the original triangle. Finally, ask the student to measure the angle formed by these two sides and compare this measure to the third given angle measure. Use this exercise as an opportunity to conclude:
 Three angle measures do not determine a unique triangle.
 Two angle measures determine the measure of the third angle of the triangle.
 Two angle measures and their included side length will determine a unique triangle.
Relate these conclusions to the relevant aspects of the exercise. 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 is able to draw a triangle with angle measures 110Â°, 30Â°, and 40Â° and says it is possible to draw more than one triangle with these conditions, but does not provide a clear explanation.
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The student explains:
 You can extend the sides and not change the angles.
 You can have the lengths different but the angles the same.
 You could have the same angle measures but different lengths of the sides. For example, if you shortened the sides you could still have the same angles.
 They would still have the same angle measures just different sides.Â

Questions Eliciting Thinking Can you change the side to any length or do they have to be proportional to the original lengths? How do you know?
Show me (draw) an example of another triangle with different lengths but the same three angle measures. What do you notice about the lengths of the sides compared to the original triangle?
What vocabulary words describe this situation?
Do you know what proportional means? 
Instructional Implications Explain to the student that three angle measures do not determine a unique triangle. Provide opportunities for the student to observe that if the sides are scaled proportionally, the resulting triangle will have the same angle measures as the original. Relate this result to making scale drawings. Explain that when making scale drawings, the lengths of sides change by a scale factor (e.g., proportionally) but the relationship between the sides (e.g., the angles between them) stays the same. Assist the student in developing mathematical vocabulary, such as scale factor and proportional, that can aid in providing a clear explanation. 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 is able to draw a triangle with angle measures 110Â°, 30Â°, and 40Â° and says it is possible to draw more than one triangle with these conditions. The student explains that if the sides are increased proportionally, or by the same factor, the angle measures will not be changed.

Questions Eliciting Thinking What do you mean by increase or decrease all the lengths? Are you referring to addition and subtraction or multiplication and division? 
Instructional Implications Address any issues with the use of notation or the placement of symbols in the drawing.
Pair 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 SSA, Drawing Triangles AAS, or Drawing Triangles SSS (7.G.1.2). 