See figure 8 for a way to prove that these segments bisect each other. Fourth, the familiar midline-theorem's corollary, which states that four congruent triangles are formed when the midlines are drawn, can help students catch a glimpse of the fascinating topic of fractals using Sierpinski triangles. If midlines are drawn to create new triangles, then midlines of those triangles are drawn, and this process is repeated, students are invited to use their imaginations to see where creating problems and conjectures might lead them. Although the manipulative for these activities can be any rigid representation of a line segment, Pixy Stix segments do offer several advantages. Second, the reward is immediate, especially if a new straw is supplied at each station.
Students can literally break straws at the midpoint that was agreed on and enjoy the contents.
Third, marks can be made on the paper straw when the midpoint has been determined. Fourth, the activity is fun and the experience and the discoveries are likely to be remembered. Thus, whether your students are encountering a new term by building on previous knowledge and experiences, extending a familiar concept by creating their own conjectures and problems, or discovering new ways to organize and remember theorems, perhaps a little bit of pixie magic can provide a lift. The coordinates of M are 3. Answers will vary.