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FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
 The teacher asks the student to complete the problems on the Triangles and Midpoints worksheet.
 The teacher asks followup questions, as needed.
Note: In the rubric, the following definitions and theorem are referenced by name:
Definition of a midsegment of a triangle – A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle.
Definition of a parallelogram – A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
Triangle Midsegment Theorem – A midsegment of a triangle is parallel to the third side of a triangle and half the length of the third side of the triangle.
TASK RUBRIC
Getting Started 
Misconception/Error The student provides an incorrect justification. 
Examples of Student Work at this Level The student says that quadrilateral ADEF is a parallelogram because it has four sides or four equal sides.

Questions Eliciting Thinking What is the definition of a parallelogram?
What do you know about a segment, such as , whose endpoints are midpoints of the sides of a triangle?
What does the Triangle Midsegment Theorem say? 
Instructional Implications Review the definition of a parallelogram, the definition of a midsegment of a triangle, and the Triangle Midsegment Theorem. Use the Triangle Midsegment Theorem to explain why quadrilateral ADEF is a parallelogram and why the perimeter of is half that of .
Provide additional opportunities for the student to apply the Triangle Midsegment Theorem to find missing lengths in diagrams involving triangles and their midsegments. 
Making Progress 
Misconception/Error The student does not cite the Triangle Midsegment Theorem in the explanation given. 
Examples of Student Work at this Level The student understands that quadrilateral ADEF is a parallelogram because both pairs of opposite sides are parallel and that the perimeter of is 18.5. However, the student does not clearly cite the Triangle Midsegment Theorem to justify these conclusions.

Questions Eliciting Thinking How do you know that the sides of the quadrilateral are parallel?
How do you know that the perimeter of is half the perimeter of ? 
Instructional Implications Model using the Triangle Midsegment Theorem to explain why quadrilateral ADEF is a parallelogram and why the perimeter of is half that of . Challenge the student to identify congruent angles and congruent triangles in diagrams involving triangles and their midsegments and to justify each identification. 
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 uses the Triangle Midsegment Theorem to explain why quadrilateral ADEF is a parallelogram and to determine that the perimeter of is 18.5. For example, the student applies the definition of a midsegment of a triangle to identify , , and as midsegments of . The student says that is parallel to and is parallel to by the Triangle Midsegment Theorem. Consequently, by definition, quadrilateral ADEF is a parallelogram. Also, since , , and are midsegments of , each has a length that is half the length of the side to which it is parallel. Therefore, the perimeter of is half the perimeter of or (37) = 18.5. 
Questions Eliciting Thinking What do you suppose is the relationship among the four triangles within formed by the midsegments?
What is the area of in terms of the area of ? 
Instructional Implications Ask the student to provide the algebraic details to show that the perimeter of is half the perimeter of .
Ask the student to prove that is congruent to . 
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
 Triangles and Midpoints worksheet
SOURCE AND ACCESS INFORMATION
Contributed by:
MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.