Download Drawing Triangles SSS

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70699
Drawing Triangles SSS
Students are asked to draw a triangle with given side lengths, and explain 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_DrawingTrianglesSSS_Worksheet.docx
MFAS_DrawingTrianglesSSS_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 SSS worksheet.
2. The teacher asks follow-up questions, as needed.
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 with incorrect side lengths.
page 1 of 4 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 length of all three sides? Where is a good place to begin drawing?
How would using a ruler and compass 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
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 and compass to construct the triangle. Explain that a good way to begin is
by drawing a working line and “building” the triangle on it. Show the student how to set the radius of the compass to a needed length and how to mark this length on the
working line. Next, have the student set the compass to another given length and, with the compass point at one endpoint of the line, make a large sweeping arc. Then
have the student set the compass to the remaining length and, with the compass point at the other endpoint of the first side, make a sweeping arc that intersects the
previous arc. Show the student how the point of intersection of the arcs is the given distances from the endpoints of the first side. If needed, model how to properly label
the angles and sides of a triangle. Then have the student verify that the drawn triangle fits the given conditions.
Next, have the student use a ruler and draw two of the three sides of the triangle but forming an angle larger or smaller than the corresponding one in the original triangle.
Then challenge the student to fit the third side in the triangle. Guide the student to conclude that changing the angle measure will result in changing the length of the
opposite side. Therefore, if the length of the sides are not changed, neither are the measures of the opposite angles.
Provide the student with another set of measurements, and encourage the student to further experiment and confirm his or her conclusion. Model explaining that three
lengths determine a unique 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 is able to draw a triangle with sides of the given lengths but concludes that a different triangle can be constructed from the three lengths. For example, the
student concludes:
The triangles are not the same (e.g., congruent) because they are oriented differently.
The angles can have different measures when the sides are the same length.
Questions Eliciting Thinking
What will be different in the new triangle?
If you make an angle larger or smaller, will it affect the measure of the side opposite it?
Instructional Implications
Use tracing paper to demonstrate to the student that two triangles can be oriented differently but still be the same (e.g., congruent). If the student did not attempt to
construct a second triangle with the given lengths, ask the student to do so. Have the student confirm that the lengths of the sides correspond to the given lengths.
Finally, have the student use tracing paper to determine if the triangles are congruent.
Another option is to have the student use a ruler and draw two of the three sides of the triangle but forming an angle larger or smaller than the one in the original triangle.
Then challenge the student to position the third side to form the triangle. Guide the student to conclude that changing the angle measure will result in changing the length
of the opposite side. Therefore, if the lengths of the sides are not changed, neither are the measures of the opposite angles.
Provide the student with another set of SSS conditions, and encourage the student to further experiment and confirm his or her conclusion.
page 2 of 4 Almost There
Misconception/Error
The student does not adequately explain why the given conditions form a unique triangle.
Examples of Student Work at this Level
The student is able to draw a triangle with sides of the given lengths and says it is not possible to draw more than one triangle with these conditions, but does not provide
a clear explanation. The student explains:
You can only draw the triangle one way.
That’s not how triangles work. Questions Eliciting Thinking
What do you mean by “you can only draw the triangle one way?”
What is the relationship between the length of a side and the opposite angle measure?
Can you widen an angle and not affect the length of the opposite side?
What does congruent mean?
Instructional Implications
Help the student confirm his or her conclusion by constructing another triangle with the same three measurements. Have the student directly measure the angles and
compare the measurements to the angle measures of the original triangle. Guide the student in discussing the relationship among the sides and angles within a triangle.
Using a compass, model constructing a triangle with sides of the given lengths as described in the Getting Started Instructional Implications. Show the student that the arcs
drawn to locate the third vertex of the triangle have only one point of intersection (on the same side of the working line). Explain that this ensures that there is only one
way to draw the triangle. Model a concise explanation using mathematical terminology. For example, if the side on the working line is
, which is 9 cm in length, explain
that there is only one point that is both 4 cm from vertex A and 7 cm from vertex C. This means that there is only one possible location for vertex B. Therefore, a unique
triangle is determined.
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 sides of the given lengths and says it is not possible to draw more than one triangle with these conditions. The student explains
in terms of:
The uniqueness of the third vertex (see Instructional Implications for Almost There).
The relationship between the length of a side and the opposite angle measure.
page 3 of 4 Questions Eliciting Thinking
If sides AB and BC were switched, would the triangle be congruent to the original? Explain.
What does “congruent” mean? What does “proportional” mean?
Can you describe your strategy in drawing triangle ABC?
How important was accuracy and precision in completing this task?
Instructional Implications
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 AAA (7.G.1.2), if
not done previously.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Drawing Triangles SSS worksheet
Ruler
Compass
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
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