Introduction
Symmetry has always seemed an afterthought, when teaching geometry in the elementary grades. We have always stressed an importance on learning about the different kinds of polygons, without giving a complete understanding of how symmetry plays into defining the polygons themselves. In fact, I would venture to bet that most elementary school teachers do not fully understand, themselves, how symmetry is inherent to different kinds of quadrilaterals. When I realized that these two elements were connected, I thought that this would be a perfect opportunity for me to bridge this gap in understanding with my students.
This unit has been created with fifth grade curriculum in mind, but I think would be appropriate for third through sixth grade. Students will need to have an understanding of properties of quadrilaterals in order to get the most out of this unit, but some of the activities may be appropriate for students that are still learning about geometry at a more basic level. In my fifth grade class, we work with geometry for eight weeks. For the majority of the time, we investigate polygons and their properties. We spend a great deal of time exploring the properties of quadrilaterals and triangles. The students look at how the diagonals of a polygon, along with its sides and angles, define the kind of polygon it is. Another big focus of the unit is for them to make and test conjectures about triangles, quadrilaterals, and other polygons.
I teach at an elementary school in North Carolina. In my instruction, I follow the local pacing guide that is supplied to our school by the school district. The curriculum is based on the North Carolina Standard Course of Study for fifth grade. Most students come from homes with parents that have college degrees, and in some cases are professors at the local college. For the most part, the students are very high achieving and work hard every day. I also teach students with special needs, so I try to provide lessons that allow students to work with physical representations of the concepts, as well as use lots of examples of what we are working on. I also have to be careful to balance that with work that is challenging enough to stimulate the advanced students in my class. Through this unit, I hope to provide both of those kinds of learning opportunities to my students.
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