Scale Factor - Side Length and Area of Similar Figures submitted by: Jeff LeMieux, August 2005 This narrative describes how I use my the Java tool, Side Length and Area of Similar Figures (and the companion tool: Side Length, Volume, and Surface Area of Similar Solids) cataloged in the Math Tools digital library, in the classroom. Course: Math 7 Topic: Scale Factor, similarity, ratio, proportion, exponents Resource type: Java Applet and Support Materials Resource location, Side Length and Area of Similar Figures: http://standards.nctm.org/document/eexamples/chap6/6.3/index.htm Math Forum catalogue entry: http://mathforum.org/mathtools/tool/13433/ Resource location, Side Length, Volume, and Surface Area of Similar Solids: http://standards.nctm.org/document/eexamples/chap6/6.3/part2.htm Math Forum catalogue entry: http://mathforum.org/mathtools/tool/13434/ Story:   One of my ongoing frustrations with middle level math is finding ways for students to grasp the concepts and relationships of perimeter, area and volume. Part of the problem is probably related to our systems of units, e.g., inches, square inches and cubic inches. Another part is the relative lack of real world experience with the interrelationship of these ideas and ideas of mathematical similarity. Scale Factor creates some its own difficulty when there is not sufficient emphasis placed on the fact that scale factor is a linear relationship. Making the connection between scale factor and perimeter is complicated by the side/perimeter realtionship. Apparently when things turn corners, problems arise. These two applets provide a good visual reference for these concepts. Their interactivity allows the student to take his/her time to make the changes and see what the actual results are. Where and how I used this: This applet is only used after the ideas of ratio and proportion have been introduced and after scale factor has been introduced as rating solely to linear measures. Students practice this aspect before discussion of the relationship of scale factor to area occurs. It is helpful to review exponents also as is a discussion of area formulas. Using manipulatives to create larger similar patterns is also a plus. Once students have a grounding in the ideas of mathematical similarity and the correspondence of similar figures, one can began to discuss the relationship of scale factor to area (scale factor x scale factor) and scale factor to volume (scale factor x scale factor x scale factor). These applets are then used as a demonstration in the class and links are placed on the lesson plan page for student review and problem checking. Send comments to Jeff LeMieux at tackweed@whidbey.net Jeff LeMieux August 2005 http://www2.whidbey.net/ohmsmath