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Response : In parallelogram C, angles 1 and 3 are acute and angles 2 and 4 are obtuse.

contents of this book available at: https:// origami.me/diagrams/.

Misconceptions when identifying the shapes might be due to the orientation. Turning the paper can help students see the triangles and the parallelo grams. Misconceptions could appear when identi fying the types of angles. A protractor could be used to measure them and determine which are acute, obtuse, and right. 2. How many lines of symmetry does the com pleted octagon wreath have if you ignore the colors? (step 5 in “ Pictures of Putting the Paral lelograms Together ”) The most common misconception here may be counting a line of symmetry twice. This can be clarified by having students place their com pleted octagon wreath on a sheet of paper and drawing the lines of symmetry. Another possi ble misconception is the belief that lines of symmetry are either through the midpoints of the sides only or through the vertices of the oc tagon only. Once again, drawing the lines of symmetry can help clarify this. 3. When the wreath is finished, move the different sections and identify the shapes formed in the center. (See “ Pictures of Shapes Formed in the Center of the Octagon Wreath ”). Throughout this activity, formative assessment is used. At each step, the teacher can observe and/or have the students record their responses to the questions. Upon completion of the activity, shapes or pictures of shapes could be given to students for identification. They could draw lines of symmetry on the shapes. Students could be asked to write a summary of the shape, attributes, and symmetries they learned about while folding the octagon wreath. Students could also be asked to draw the shapes they identified in the activity. Teachers may choose to incorporate more origami into the study of geometry with their students. There are many books and videos online to aid with directions. One book with an abundance of information is, “ Everyone Can Learn Origami ” by Peter Saydak. There is a web site with some of the Response : Eight Possible Response(s) shown : Hexagon, Square, Rectangle

References

Howse, T. D., & Howse, M. E. (2015). Linking the van Hiele theory to instruction. Teaching Children Mathematics , 21 , 305– 313. Octagon Star. (n.d.). Retrieved from http:// sierra.nmsu.edu/morandi/CourseMaterials/ OctagonStar.html. Origami Directions. (2017). Retrieved from https:// origami.me/diagrams/. PPO. (2015, May 27). Octagon Star Video Direc tions [Video]. Youtube . https:// www.youtube.com/watch? v=n01fsCDWAUc. Saydak, P. (2017). Everyone can learn origami. Origami.me. van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics , 5 , 310– 316. VDOE. (2016, January). Standards of learning & testing. VDOE. https:// www.doe.virginia.gov/testing/index.shtml.

Dr. Deborah A. Crocker Appalachian State University Boone, NC crockerda@appstate.edu

Dr. Betty B. Long Appalachian State University Boone, NC longbb@appstate.edu

Virginia Mathematics Teacher vol. 47, no. 1

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