Polygons Non-Shapes. Has an area that is completely enclosed Has no extraneous lines or curves as a part of the figure.

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1 Comparing Shapes Polygons Non-Shapes Concave Convex The student will be asked to give characteristics of shapes and their various subcategories. At least two comments about each category should be given. This could be completed as a class, individually, or in groups. Answer should be related to the characteristics of the items that fall into each category. These could include: type of lines, positioning of the lines, positioning of sides, among others. Shapes Polygons Has an area that is completely enclosed Has no extraneous lines or curves as a part of the figure. Only one area is enclosed. Shape that contains only straight line segments All segments intersect at both ends with another segment Segments intersect only at the ends Concave Convex Extended sides would have points inside the polygon Shape is dented An extension of the sides would not enter the polygon Shape is not dented anywhere Non-Shapes Extra lines do not appear as part of the figure. Does not contain an area that is fully enclosed

2 Classifying Using the pictures below, label each polygon by its number of sides (triangle, quadrilateral, pentagon, etc.) and then classify it as a convex polygon, a concave polygon Convex Polygon Concave Polygon Shape Outline each object then classify each appropriately. Figure 1: Figure 4: Figure 7: Figure 2: Figure 5: Figure 8: Figure 3: Figure 6: Figure 9:

3 The student would be asked to classify various figures that are found in everyday examples as convex polygons, concave polygons, or (non-polygon) shapes. Some examples used could be pictures of various types of houses, different types of sails for boats, and outlines of any household object. Convex Polygon Concave Polygon Shape Figure 1: Snow Shack Figure 3: Chain Link Fence Figure 8: Black and White Sail Figure 4: Utah Figure 5: Red Cross Figure 9: Mountain Range Figure 2: Ice Cream Cone Figure 6: Swimming Pool Figure 7: Blue and White Sail Figure 1: o Pentagon Figure 2: o Not a polygon Figure 3: o Hexagon Figure 4: o Pentagon Figure 5: o Dodecagon Figure 6: o Not a polygon Figure 7: o Not a polygon Figure 8: o Triangle Figure 9: o Octagon

4 Metaphors Area of shapes is a cup of water Area Shapes are filled by the appropriate amount of square units. The number of square units needed to fill a shape can be found using math Many different types of shapes exist Cup of water Cups are filled with the right amount of liquid The amount of water that fits in a cup can be found Many different cups and glasses can be found in stores Supplementary angles* are a pair of shoes Supplementary angles One angle without its supplement is still an angle Putting both angles together makes a more useful 180 o angle or straight line. Supplementary angles are more useful together. Two random angles are less useful Pair of shoes One shoe without its pair is still a shoe One shoe really needs its pair to be useful, although one shoe could still be used A pair of shoes are more fashionable together than 2 different shoes *This metaphor could also fit for complementary angles

5 Analogies Slope: Line:: Television: Channel Slope is to a line as a television is to its channel The slope of a line tells you what it will looks like and the form it will take. A different slope will change a line into a completely different object. Meanwhile, what you see on a television is fully dependent on its channel. A different channel will change a television s appearance completely. A line s appearance is depends on its slope and a television s appearance depends on its channel. Segments: Polygons:: Bricks: Houses Segments are to polygons as bricks are to houses Polygons are made entirely of segments and to change its shapes you will need more segments. Many houses are made of bricks and in order to add on to a house you will need more bricks. Polygons are built from segments and houses are built from bricks.

6 Reflection All of these ideas are useful for implementation in the classroom. I feel that in the math classroom, in this case geometry, that the analogies are the most useful. Students need something to relate the subject matter to. One of the problems in teaching math is that often we only tell the students what to do and expect them to memorize what to do in the future. This is in contrast to more meaningful learning where the students have developed an understanding of how the process works and can make applications to other subjects and other parts of their lives. The easiest to create, by far, are the analogies. Math is everywhere around us an applications of math can be made to all parts of life. Creating a classifying assignment was the most difficult. The easiest way to look at math is that it simply is rather than with any depth and that makes it difficult to find things that require classification. The issue with most secondary teaching is trying to make it meaningful to the students. Use of metaphors and analogies can make the biggest difference in this problem. The use of activities helps to stimulate the students rather than being forced to sit and listen to a teacher talk at them for an hour or more. The more involvement a teacher can get from a class the more meaningful that instruction will be. Teachers must also help to organize a student s thoughts and that is the role of graphic organizers for comparing and classifying. These forms allow students to easily see some of the similarities and differences that can help them differentiate things in an easily confused area. The use of all types of instruction is important in the classroom. This allows for variety to keep the class interesting. Also, it lets the teacher meet as many students learning styles as possible.