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Midpoints of Sides of a Quadrilateral Resource ID#: 59184 Primary Type: Formative Assessment This document was generated on CPALMS - www.cpalms.org Students are asked to prove that the quadrilateral formed by connecting the midpoints of the sides of a given quadrilateral is a parallelogram. Subject(s): Mathematics Grade Level(s): 9, 10, 11, 12 Intended Audience: Educators Freely Available: Yes Keywords: MFAS, quadrilateral, coordinates, special quadrilateral, midpoints, parallelogram Instructional Component Type(s): Formative Assessment Resource Collection: MFAS Formative Assessments ATTACHMENTS MFAS_MidpointsOfSidesOfaQuadrilateral_Worksheet.docx 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 problem on the Midpoints of Sides of a Quadrilateral worksheet. 2. The teacher asks follow-up questions, as needed. TASK RUBRIC Getting Started Misconception/Error The student does not have an effective strategy for completing the proof. Examples of Student Work at this Level The student calculates (correctly or incorrectly) the coordinates of the midpoints of the sides (E, F, G and H) Questions Eliciting Thinking What are you asked to show in this problem? How can you show a quadrilateral is a parallelogram? Instructional Implications Review the conditions that are necessary and sufficient for a quadrilateral to be a parallelogram, i.e., opposite slope formula to show that segments are parallel, the distance formula to show that segments are congruent, a Guide the student to develop an overall strategy for solving the problem presented in this task, i.e., (1) find th and provide feedback. Give the student additional opportunities to use the slope, distance, and midpoint formulas in a variety of prob Two segments having the same slope. Two segments having opposite reciprocal slopes. Two segments having the same length. The two diagonals of a quadrilateral having the same midpoint. If needed, provide feedback on the appropriate use of notation. Moving Forward Misconception/Error The student does not explicitly draw an appropriate conclusion to complete the proof. Examples of Student Work at this Level The student correctly calculates the coordinates of the midpoints of the sides (E, F, G and H) and provides wo Questions Eliciting Thinking Can you explain how you showed the figure is a parallelogram? What is your conclusion? Is the quadrilateral a parallelogram? Instructional Implications Discuss with the student how to write a clear and complete proof. Show the student a model coordinate geom explicitly stated, and no extraneous work is left on the paper). If needed, provide feedback on the appropriate use of notation. Almost There Misconception/Error The student does not use mathematical terminology or notation correctly. Examples of Student Work at this Level The student correctly calculates the coordinates of the midpoints of the sides (E, F, G and H) ,shows appropri Uses notation incorrectly, e.g., refers to as EH. Uses the term congruent to describe slopes that are equal. Questions Eliciting Thinking What is the difference between and EH? What does congruent mean? Can slopes be congruent? Instructional Implications Provide direct feedback to the student regarding his or her use of notation. Review the use of notation with re notation has been used incorrectly and to rewrite the statements so that they are written correctly. Consider implementing MFAS tasks Describe the Quadrilateral (G-GPE.2.4), Diagonals of a Rectangle (G-G 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 correctly calculates the coordinates of the midpoints of the sides (E, F, G and H) ,shows appropri Questions Eliciting Thinking Do you think joining the midpoints of any quadrilateral will create a figure that is a parallelogram? How coul What if the quadrilateral is concave? Will the figure formed by connecting the midpoints of the sides be a par Instructional Implications Challenge the student to prove geometric theorems using coordinate geometry. Consider implementing MFAS Consider implementing other MFAS quadrilateral tasks Diagonals of a Rectangle (G-GPE.2.4) and Describe ACCOMMODATIONS & RECOMMENDATIONS Special Materials Needed: o Midpoints of Sides of a Quadrilateral worksheet 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 License: CPALMS License - no distribution - non commercial Related Standards Name MAFS.912.G-GPE.2.4: Description Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Remarks/Examples: Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.