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Teacher Technology Companion for Grade 8 Geometry Overall Expectations: (Ontario Mathematics Curriculum, rev. 2005) ► 8m40: demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world; ► 8m41: develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles; ► 8m42: represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world. “GSP” refers to The Geometer’s Sketchpad®, licensed for publicly-funded schools in Ontario and for students in these schools to take home to install on their home machines; information may be found at: http://www.hpedsb.on.ca/sg/quinte/gsp.htm Links: ► All “GSP Connection” files can be found at: http://www.hpedsb.on.ca/sg/quinte/grade_8.htm ► “Internet Connection” sites are linked from either: o (A) http://www.hpedsb.on.ca/sg/quinte/geometry.htm or o (B) http://www.hpedsb.on.ca/sg/quinte/interactive_math.htm#is Additional Help: William Lundy, SETS-Mathematics, Hastings and Prince Edward DSB, 613-966-1170 ext 3326; [email protected] # Specific Expectation Geometric Properties sort and classify quadrilaterals by geometric 8m43 properties, including those based on diagonals, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software) 8m44 GSP Connection “Quadrilaterals and Diagonals” (2 activities) Internet Connection Remarks If extensive review of quadrilaterals is needed, refer to the “Grade 4” GSP page (modify URL above to “…grade_4” vice “…grade_8”): use “The Story of Quadrilaterals” (2 parts) construct a circle, given its centre and Use GSP help menu, radius, or its centre and a point on the circle, index, and search for or three points on the circle; “Circles”: “Circle by center + point”, “Circle by center + radius” Teacher Technology Companion for Grade 8 Page 1 of 3 investigate and describe applications of geometric properties (e.g., properties of triangles, quadrilaterals, and circles) in the real world. Geometric Relationships determine, through investigation using a 8m46 variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, protractor) and strategies (e.g., paper folding), the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle; 8m45 8m47 “Proportions with Area” 8m48 solve angle-relationship problems involving triangles (e.g., finding interior angles or complementary angles), intersecting lines (e.g., finding supplementary angles or opposite angles), and parallel lines and transversals (e.g., finding alternate angles or corresponding angles); Teacher Technology Companion for Grade 8 “Dog Pens” “Quadrilateral Puzzle” “Angle Properties of Parallel Lines and Transversals” “Angle Relationships” “Exploring Angles Formed by Parallel Lines and a Transversal” “Investigating the Triangle Sum Conjecture” “Parallel Lines and Triangles” “Plane Geometry” See remarks to right Use GSP files for 8m47 to develop concepts and big ideas before penciland-paper activities for this expectation Page 2 of 3 8m49 8m50 determine the Pythagorean relationship, through investigation using a variety of tools (e.g., dynamic geometry software; paper and scissors; geoboard) and strategies; solve problems involving right triangles geometrically, using the Pythagorean relationship; determine, through investigation using concrete materials, the relationship between the numbers of faces, edges, and vertices of a polyhedron (i.e., number of faces + number of vertices = number of edges + 2) Location and Movement graph the image of a point, or set of points, 8m52 on the Cartesian coordinate plane after applying a transformation to the original point(s) (i.e., translation; reflection in the x-axis, the y-axis, or the angle bisector of the axes that passes through the first and third quadrants; rotation of 90°, 180°, or 270° about the origin); identify, through investigation, real-world 8m53 movements that are translations, reflections, and rotations. 8m51 Teacher Technology Companion for Grade 8 “The Pythagorean Relationship” (A) “Pythagorean Theorem” (A) “How High? Making and Using an Inclinometer to Measure the Heights of Very Tall Objects” (A) “Paper Models of Polyhedra” Internet activity uses Pythagorean principles but not the theorem directly. (B) “Transmographer” “Plotting on the Cartesian Plane” – use for review of grade 7 topic “Pythagorean Triples” “The 30º-60º-Right Triangle” n/a “Plotting on the Cartesian Plane” (A) “Pantograph” Page 3 of 3