Geometry can be an exercise arena for strengthening those logic muscles that middle school students need to flex. When we work with a geometric figure—a circle, for instance—and apply the ancient tools of compass and straightedge, geometry can become a rich ground for developing design. And a circle has size, so a unit on this topic necessarily brings in the mathematics of its measurement. Circles, then, is a geometric topic that can provide mental challenge, opportunity for artistic development, and connections to both the history of measurement and its everyday applications. For this unit we have selected online activities that will enable your students to look at circles from these various viewpoints. The activities range from measurement to theorems about the circle to art and symmetry. Many will engage students in solving problems or in creating designs. Others will allow them to investigate the thinking behind the area and circumference formulas, either through virtual simulations or hands-on projects. We hope these activities will add to your repertoire of ways to present the "many-sided" topic of circles.
This lesson will introduce students to angles using a resource of Shodor Education Foundation, Inc. Permission has been granted for the use of the materials as part of the workshop "Interactivate Your Bored Math Students."
This lesson will assist students to see angle relationships and the relationship of parallel lines and transversals. This exercise is good for visual and tactile learners since it is of a concrete nature. Students of all academic levels can enjoy this.
An interactive applet and associated web page that show the concept of adjacent angles (two angles that share a common leg). The applet shows three line segments with a common endpoint. The user can move the center one and see that the angles on both sides (the adjacent angles) of it are affected. Applet can be enlarged to full screen size for use with a classroom projector. After use in the classroom, students can access it again from any web browser at home or in the library with no login required. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
An interactive applet and associated web page that demonstrate the concept of complementary angles (angles that add to 90 degrees). The applet shows two angles. You can drag the endpoints of each angle and the other angle changes so that they always add to 90 degrees. They are drawn in such a way that it is visually obvious that together they form a right angle, although they are separate on the page. The angle measure readouts can be turned off for class discussions. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
An interactive applet and associated web page that demonstrate supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
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