Monday, January 25, 2016

Questioning about Quadrilaterals

After the winter storm break I began my geometry lesson posing the following questions:
"What are similarities and/or differences between a trapezoid and a parallelogram?"  "What are similarities and/or difference between a kite and a parallelogram?"  To answer the first question I drew a Venn diagram on the board and asked students to share responses.  After waiting for a couple of minutes with no responses I then drew a picture of each inside the diagram without markings.  One student responded, "The sides are equal".  I then asked, "Which sides"?  He responded , "The ones across from each other".  I paraphrased using the correct terms, "So, you mean opposite sides are congruent in a parallelogram".  I added the markings to the picture and wrote the stated property in the parallelogram circle of the Venn diagram. Another student responded, "they both have four sides".  I added this property to the overlapping circle.  I then posed the question, "Does a kite have congruent sides?"  The class responded, "Yes" !  I then asked,  "What is the relationship between these congruent sides?".  A different student responded, "They are next to each other".  I responded, "Yes, they are adjacent to one another".  I then added the markings that showed congruence.  After a pause with no student responses I then asked, "Does a kite have parallel sides?" Several students responded, "No". We continued with this sequence of questioning and answering until as a class we had a least three properties within each portion of the Venn Diagram.  Every time we named a property I added the correct markings to the figure where appropriate. After working individually on several problems from the text I brought the class back together to address the second question.  This time instead of a Venn Diagram I used a three column chart to note properties of kite and parallelogram.

I noticed in both discussions students knew the properties but needed help using the correct vocabulary terms to express what they knew. Students would get confused about the symbol for parallel and congruence. Also, visually students may see a figure but when the orientation of the figure changes, such as with a rotated trapezoid, they appeared confused.  Another misconception for students was being able to properly distinguish between a kite, parallelogram, and a rhombus.  I plan to create a diagram comparing all three quadrilaterals towards the end of this week.  Class discussions encourage participation of all learners and each person has an opportunity to share what they know about the topic; these discourse patterns solidify proper use of vocabulary as well as gives me the opportunity to address misconceptions with immediate feedback.

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