1 Investigating Special Right Triangles and Area of a Regular Polygon Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–8 Professional Commentary: This 3-lesson unit engages students in investigating special right triangle properties for both 30°– 60°– 90° and 45°– 45°– 90° triangles. Students develop the general formula for the area of any regular polygon using Geometer’s Sketchpad® and apply special right triangle properties to find the area of equilateral triangles, squares, and hexagons.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–8 Professional Commentary: In this self-guided investigation, students use Geometer’s Sketchpad ® to construct a right triangle and discover a geometric proof of the Pythagorean Theorem. Students test the geometric proof with acute and obtuse triangles.... 3 Concurrent Events: An Exploration of the Points of Concurrency in a Triangle Using Geometer's Sketchpad Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: This lesson enhances student knowledge of how to use Geometer's Sketchpad™ to explore geometric concepts that take much longer to do using hand-held tools, specifically in this case, the points of concurrency in a triangle. The unit begins with a key-by-key introduction to Sketchpad, followed by the construction of line segments, triangles, circles, perpendicular bisectors of... Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: In this lesson students learn the definition of median and investigate the centroid as the center of gravity. It is assumed that students can name and classify triangles by sides and angles and know basic terms, such as vertices and midpoint.... 5 Perplexing Parallelograms Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: A surprising result occurs when two line segments are drawn through a point on the diagonal of a parallelogram and parallel to the sides. From multiple instances of this construction, students can arrive at various conjectures.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–12 Professional Commentary: This lesson focuses on a problem: Given a line segment AB in a plane, find all points C in the plane such that triangle ABC is (a) right, (b) acute, (c) obtuse, (d) isosceles, (e) scalene, or (f) equilateral. An applet, activity sheet, discussion questions, a lesson extension, suggestions for assessment, and prompts for teacher reflection are... 7 Pythagoras Wasn't Just a Square! Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–8 Professional Commentary: While most students are familiar with the Pythagorean Theorem (a2+ b2 = c2), many do not realize why or how it works. With knowledge of similar figures, students can verify that the areas of any similar figures drawn on the sides of right triangles satisfy the Pythagorean relationship. This lesson is designed to use Geometer’s Sketchpad, and step-by-step instructions... Resource Type: Content Supports Discipline: Mathematics Grades: Grades 6–12 Professional Commentary: This site provides step-by-step instructions for constructing pinwheels using rotations, translations, and reflections of triangles and other plane figures on Geometer's Sketchpad. A printable worksheet and three discussion questions are included.... |