Download Drawing Triangles SSA

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70698
Drawing Triangles SSA
Students are asked to draw a triangle given the lengths of two of its sides and the measure of a nonincluded angle and to decide if these conditions
determine a unique triangle.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, triangle, angles, sides
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DrawingTrianglesSSA_Worksheet.docx
MFAS_DrawingTrianglesSSA_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Drawing Triangles SSA worksheet.
2. The teacher asks follow-up questions, as needed.
Note: The teacher should explain the meaning of included angle and nonincluded angle if these terms are unfamiliar to the student.
TASK RUBRIC
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 does not fit the given conditions.
page 1 of 4 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 30°?
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 hands-on 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
. Using endpoint C as a vertex, ask the student to construct the 30° angle (the nonincluded angle). Extend the length of the ray drawn to
create the 30° angle (which will contain side student to observe that this arc intersects
). 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
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.
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 triangle 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 side
of the triangle without affecting the size of the
?
When you increase or decrease the measure of an angle, does it affect the length of all the sides of the triangle?
page 2 of 4 If you draw a second triangle using the same conditions and its shape changes, do the given conditions determine a 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
. Using endpoint C as a vertex, ask the student to construct the 30° angle (the nonincluded angle). Extend the length of the ray drawn to
create the 30° angle (which will contain side student to observe that this arc intersects
). 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
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 “because the third side can
be a different length.”
The student constructs another triangle with the given conditions that is different from 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.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Drawing Triangles SSA worksheet
Ruler
Compass (optional)
Protractor
Technology such as Geogebra (optional)
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
page 3 of 4 Related Standards
Name
MAFS.7.G.1.2:
Description
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on
constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle,
more than one triangle, or no triangle.
page 4 of 4