Reflection: Flexibility Properties of Parallelograms and Special Parallelograms - Section 4: Practice: Determining Parallelograms


Most of my students became deeply engaged in the Determining Parallelograms task. I think an important characteristic of the task made a big difference. In this case, the directions for the task were simple.

At first, some students were not completely engaged. However, their peers' critiques of their reasoning recruited more and more students into a higher level of engagement. The task, which seemed deceptively simple at first, was rich with potential pitfalls, a quality that helped to establish an environment of intrigue. 

Very quickly, students were engaged in rich mathematical discussions. The simplicity of the instructions gave them freedom to explore the features of quadrilaterals openly. This enabled students to establish their own perspective, ultimately producing the opportunity for respectful disagreement. Students began to recognize the importance of listening to a peer's entire explanation, trying to make sense of where he/she was coming from. The task lent itself to active consideration of counterexamples and lots of sketching, as students shared their own reasoning.     

  Flexibility: Pose a Simple Question to Free Students to Justify Their Conclusions
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Properties of Parallelograms and Special Parallelograms

Unit 8: Discovering and Proving Polygon Properties
Lesson 6 of 9

Objective: Students will be able to apply angle relationships and properties of isosceles triangles and trapezoids in a proof.

Big Idea: In the Logical Road Map, students will make sense of multiple pathways to writing a proof.

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Math, Geometry, polygons (Determining Measurements), properties of polygons, reasoning and proof, parallelogram
  90 minutes
prop of parallel li
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