NCGA GeoMath Lesson Plan Name of Lesson Finding the Circumcenter Time for Instruction 20-25 minutes Essential Question(s) If given three locations on a map, determine the point equidistant from those three locations? Common Core Standard(s) Make geometric constructions Common Core Mathematics CCSS.Math.Content.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. National Geography Objective(s) th 8 grade 1 3. Geospatial technologies—Internet-based mapping applications, GIS, GPS, geovisualization, and remote sensing—can be used to construct geographic representations using geospatial data Prerequisite skills/knowledge Construct a perpendicular bisector with a compass and straightedge as well as using mathematical software. Insert a background image into the mathematical software called Geogebra. Anticipatory Activity/Bellringer/Warmup Place a large map in the front of the room with three cities marked. As students enter the classroom, ask them to place a small post-it note or sticker of the location that they foresee as equidistant from the three cities. Choose three cities that form an obtuse triangle when connected for the most diverse predictions. Vocabulary Mathematical Terms Geography Terms Collinear Noncollinear Perpendicular Bisector Equidistant Circumcenter Instructional Strategies/Sequence Using Geogebra, place points to represent three cities and then complete the process to locate the circumcenter. Drag the points to create multiple types of triangles: acute, right, obtuse, and observe the location of the circumcenter. Independent Practice Change the location of the cities and observe the corresponding change of the circumcenter. Instructional Resources Geogebra Formative Assessment Students should locate another map and construct the circumcenter. Include the circle to illustrate that the circumcenter is equidistant from the three cities. Export the screen image to the program’ Differentiation Complete the same procedure with a compass and straight edge Enrichment Write conditional statements (if/then statements) to model the location of the circumcenter for cities that form acute, right and obtuse triangles. For example, if three cities form an obtuse triangle, then the circumcenter is located outside of the triangle. If the three cities form and acute triangle, then the circumcenter is inside the triangle. If the three cities form a right triangle, then the circumcenter is the midpoint of the hypotenuse of the right triangle. If the three cities form an obtuse triangle, then the circumcenter is locate outside of the triangle.