1071 Pythagoras Wasn't Just a Square! Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–11 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 are provided. Activity sheets, solutions, and extensions are included.... 1072 Detective Slope -- An Investigation of the Slopes of Lines and Shapes Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 6–10 Professional Commentary: This learning unit is designed for students to investigate the definition of slope and the slopes of parallel and perpendicular lines. Students are introduced to special parallelograms by applying the concept of slope using Geometer’s Sketchpad®.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students use Geometer's Sketchpad® to explore relationships among the angles formed when parallel lines are cut by a transversal. The software is integral to the lesson, and step-by-step instructions are provided.... 1074 Tangents, Secants, and Chords . . .OH MY! Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students use Geometer's Sketchpad® to explore numerous relationships among measures of central and inscribed angles, arc lengths, and lengths of chords, tangents, and secants. The software is integral to the lesson, and step-by-step instructions are provided.... Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: Students use algebra or geometry software to discover that the height at which guy wires supporting two vertical poles cross does not depend on how far apart the poles are. This counterintuitive result can lead to conjecturing and testing hypotheses as to what factors determine the height at which the wires cross.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 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.... 1077 Regular Pentagons, "Star Polygons," and the Golden Ratio Resource Type: Instructional Resource -- Best Practice Discipline: Mathematics Ohio Standards Alignment: Grades 9–12 Professional Commentary: This learning unit helps students explore the golden ratio and golden rectangles and to find the golden ratio in regular pentagons and in the Fibonacci sequence. Students use Geometer's Sketchpad® to rotate, translate, and dilate various figures to solve problems.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–10 Professional Commentary: Students draw a triangle and the three medians of the triangle using Geometer's Sketchpad®. The students identify and measure the line segments between the vertices of the triangle and the centroid and between the centroid and the midpoints of the opposite sides using Sketchpad.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 10–12 Professional Commentary: This lesson is primarily a graphing activity in which students manipulate equations of a circle in order to translate the center from the origin to another point. They write the equation of a circle in parametric form, match equations of circles to given graphs, use the equation of a circle and appropriate windows to graph regular polygons, and then rotate the polygons.... Resource Type: Instructional Resource -- Promising Practice Discipline: Mathematics Ohio Standards Alignment: Grades 8–12 Professional Commentary: Students determine the dimensions of a can that has minimum surface area for a given volume. Reviewers liked the systematic approach described in the lesson and noted that this activity leads naturally into the minimum of a function.... |