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circles, squares, rectangles, and trian gles in different environments, regard less of orientation, and explain reason ing.

each other with the folds to keep them precise. This would help the students with less dexterity. A co operative group could be used when there are stu dents who are unable to fold the entire wreath on their own. Duties can be divided among the group. For example, one or two students could fold the parallelograms described in the first section below. Another one or two students could put the parallel ograms together to form the octagon wreath. Stu dent duties could be determined by whether they are at Level 0 or Level 1 of the van Hiele model. The assignment of duties should also take into con sideration the dexterity of the students, or their ability to make precise folds. The directions for folding the octagon wreath are: Start with eight sheets of origami paper. You can use a variety of colors. With one sheet, do the fol lowing steps: 1. Fold the square top to bottom (horizontally). 2. With the fold toward you, bring the lower right - hand corner of the rectangle up to the top, open side of the rectangle so that your fold goes through the upper right - hand corner of the rectangle. 3. Fold the paper both directions in Step 2 (a double fold). 4. Open the paper back up to the original square. Folding the Octagon Wreath or Pinwheel

3.12

The student will:

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define polygon;

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• identify and name polygons with 10 or fewer sides; and

As students progress, more about the characteris tics of shapes can be found in the Mathematics Standards of Learning (2016). For example:

2.12

The student will

•

• draw a line of symmetry in a figure; and • identify and create figures with at least one line of symmetry.

5. 12

The student will

•

• classify and measure right, acute, ob tuse, and straight angles.

5. 13

The student will

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• classify triangles as right, acute, or ob tuse and equilateral, scalene, or isosce les; The study of shapes in a concrete form aids student understanding of shapes and their properties as well as helping them develop spatial reasoning. Howse and Howse (2014 – 2015) agree that, “ As students see, touch, and manipulate shapes, they begin to develop spatial reasoning skills ” (p. 305). Folding the Octagon Wreath and manipulating the octagon formed provides a concrete way to study a variety of shapes. Pierre M. van Hiele (1999) says, “... engage your students in play, activities, and games that offer an apprenticeship in geometric thinking. Children whose geometric thinking you nurture carefully will be better able to successfully study the kind of mathematics that Euclid creat ed ” (p. 316). The following origami activity, Fold ing an Octagon Wreath, is one way to allow stu dents to engage in play and activities to learn geo metric shapes. Students can fold the octagon wreath individually, with partners, or in coopera tive groups. Allowing the students to work collabo ratively would enable the students to talk about the folds and learn from each other. They could help

5. Fold the other two corners of the square over to the middle (it will be the place all of your other folds intersect).

Virginia Mathematics Teacher vol. 47, no. 1

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