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Mathematics

 Grade 8: Geometry and Spatial Sense Planning: Term # Tracking: Ach. Level Overall Expectations 1 2 3 4 • demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world; • develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles; • represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world. Specific Expectations Geometric Properties – sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software) (Sample problem: Which quadrilaterals have diagonals that bisect each other perpendicularly?); – construct a circle, given its centre and radius, or its centre and a point on the circle, or three points on the circle; – 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 variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes (Sample problem: Construct three similar rectangles, using grid paper or a geoboard, and compare the perimeters and areas of the rectangles.); – 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; – 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); – 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) (Sample problem: Use Polydrons and/or paper nets to construct the five Platonic solids [i.e., tetrahedron, cube, octahedron, dodecahedron, icosahedron], and compare the sum of the numbers of faces and vertices to the number of edges for each solid.). Location and Movement – graph the image of a point, or set of points, 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 movements that are translations, reflections, and rotations. Student Name:

Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.